%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW362+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n026.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 12:26:02 EDT 2023

% Result   : Theorem 69.25s 66.90s
% Output   : Proof 69.25s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SWW362+1 : TPTP v8.1.2. Released v5.2.0.
% 0.11/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n026.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 22:29:05 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 69.25/66.90  
% 69.25/66.90  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 69.25/66.90  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 69.25/66.90  %-----------------------------------------------------
% 69.25/66.90  ncf(matrix, plain, [(52791 ^ _2084906) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))], !, (52763 ^ _779203) ^ [_1837874, _1837876] : [-(hBOOL(_1837874)), -(hBOOL(hAPP(hAPP(c_fimplies, _1837874), _1837876)))], (21791 ^ _779203) ^ [_1162849, _1162851] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1162849)), c_Int_OBit1(_1162851)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1162849), c_Int_Osucc(_1162851))))], (17984 ^ _779203) ^ [] : [-(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))))], (47797 ^ _779203) ^ [_1742509, _1742511] : [-(c_List_Olist__all(_1742509, _1742511, c_List_Olist_ONil(_1742509)))], (43249 ^ _779203) ^ [_1642144, _1642146, _1642148] : [_1642144 = c_List_Olist_ONil(_1642146), -(c_List_Obutlast(_1642146, hAPP(hAPP(c_List_Oappend(_1642146), _1642148), _1642144)) = c_List_Obutlast(_1642146, _1642148))], (40243 ^ _779203) ^ [_1565289, _1565291, _1565293, _1565295, _1565297] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565289, _1565289)), hAPP(hAPP(c_Product__Type_OPair(_1565289, _1565289), _1565291), _1565293)), c_Transitive__Closure_Otrancl(_1565289, _1565295))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565289, _1565289)), hAPP(hAPP(c_Product__Type_OPair(_1565289, _1565289), _1565293), _1565297)), _1565295)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565289, _1565289)), hAPP(hAPP(c_Product__Type_OPair(_1565289, _1565289), _1565291), _1565297)), c_Transitive__Closure_Otrancl(_1565289, _1565295))))], (10389 ^ _779203) ^ [_958144, _958146, _958148, _958150] : [class_Rings_Ocomm__semiring__1(_958144), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958144), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958144), _958146), _958148)), _958150) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958144), _958146), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958144), _958148), _958150)))], (13438 ^ _779203) ^ [_1012101, _1012103] : [class_Groups_Oab__semigroup__mult(_1012101), hBOOL(hAPP(c_Finite__Set_Ofinite(_1012101), _1012103)), -(_1012103 = c_Orderings_Obot__class_Obot(tc_fun(_1012101, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1012101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1012101), 13451 ^ [_1012101, _1012103]), 13452 ^ [_1012101, _1012103])), hAPP(hAPP(c_Set_Oinsert(_1012101), 13451 ^ [_1012101, _1012103]), hAPP(hAPP(c_Set_Oinsert(_1012101), 13452 ^ [_1012101, _1012103]), c_Orderings_Obot__class_Obot(tc_fun(_1012101, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1012101), hAPP(c_Finite__Set_Ofold1(_1012101, c_Groups_Otimes__class_Otimes(_1012101)), _1012103)), _1012103)))], (52393 ^ _779203) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (1900 ^ _779203) ^ [_805913, _805915] : [-(class_Power_Opower(_805913)), _805915 = _805913, class_Power_Opower(_805915)], (48406 ^ _779203) ^ [_1755324, _1755326] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755324), _1755326))), -(c_Lazy__Sequence_Osmall__lazy_H(_1755324, _1755326) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1755326), c_Lazy__Sequence_Osmall__lazy_H(_1755324, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1755326), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (712 ^ _779203) ^ [_789897, _789899, _789901, _789903, _789905, _789907] : [-(c_List_Oall__interval__int(_789905, _789901, _789897)), c_List_Oall__interval__int(_789907, _789903, _789899), _789907 = _789905, _789903 = _789901, _789899 = _789897], (49350 ^ _779203) ^ [_1776943, _1776945, _1776947, _1776949] : [c_Relation_Osym(_1776943, _1776945), -(c_Relation_Osym(_1776947, hAPP(hAPP(c_Relation_Oinv__image(_1776943, _1776947), _1776945), _1776949)))], (22137 ^ _779203) ^ [_1170013, _1170015, _1170017] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1170013), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1170015, _1170017)), _1170017) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1170013), _1170015), _1170017))], (41541 ^ _779203) ^ [_1600649, _1600651, _1600653, _1600655, _1600657, _1600659] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600649), tc_List_Olist(_1600649))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600649), tc_List_Olist(_1600649)), hAPP(hAPP(c_List_Olist_OCons(_1600649), _1600651), _1600653)), hAPP(hAPP(c_List_Olist_OCons(_1600649), _1600655), _1600657))), c_List_Olistrel1(_1600649, _1600659)))), 41542 ^ _779203 : [(41549 ^ _779203) ^ [] : [_1600651 = _1600655, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600649), tc_List_Olist(_1600649))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600649), tc_List_Olist(_1600649)), _1600653), _1600657)), c_List_Olistrel1(_1600649, _1600659)))], (41543 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1600649, _1600649)), hAPP(hAPP(c_Product__Type_OPair(_1600649, _1600649), _1600651), _1600655)), _1600659)), _1600653 = _1600657]]], (29382 ^ _779203) ^ [_1300242, _1300244, _1300246, _1300248] : [hBOOL(hAPP(hAPP(c_member(_1300242), _1300244), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300242, tc_HOL_Obool)), _1300246), _1300248))), 29385 ^ _779203 : [(29388 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1300242), _1300244), _1300248)))], (29386 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1300242), _1300244), _1300246)))]]], (1170 ^ _779203) ^ [_796788, _796790] : [-(class_Rings_Oring__1__no__zero__divisors(_796788)), _796790 = _796788, class_Rings_Oring__1__no__zero__divisors(_796790)], (32805 ^ _779203) ^ [_1379782, _1379784, _1379786, _1379788] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1379782, tc_fun(_1379784, tc_HOL_Obool))), _1379786), _1379788))], (41951 ^ _779203) ^ [_1612136, _1612138, _1612140, _1612142] : [-(hAPP(hAPP(c_List_Otake(_1612136), _1612138), hAPP(hAPP(c_List_Otake(_1612136), _1612140), _1612142)) = hAPP(hAPP(c_List_Otake(_1612136), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1612138), _1612140)), _1612142))], (33421 ^ _779203) ^ [_1390708, _1390710] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1390708, _1390710), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1390708), _1390710)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1390708, _1390710)))))], (22880 ^ _779203) ^ [_1182267] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182267))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1182267)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48078 ^ _779203) ^ [_1748381, _1748383, _1748385, _1748387] : [-(c_Predicate_Oconversep(_1748381, _1748383, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1748381, tc_fun(_1748383, tc_HOL_Obool))), _1748385), _1748387)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1748383, tc_fun(_1748381, tc_HOL_Obool))), c_Predicate_Oconversep(_1748381, _1748383, _1748385)), c_Predicate_Oconversep(_1748381, _1748383, _1748387)))], (4942 ^ _779203) ^ [_854500, _854502, _854504, _854506, _854508, _854510, _854512, _854514] : [-(c_Product__Type_Ocurry(_854514, _854510, _854506, _854502) = c_Product__Type_Ocurry(_854512, _854508, _854504, _854500)), _854514 = _854512, _854510 = _854508, _854506 = _854504, _854502 = _854500], (25550 ^ _779203) ^ [_1229339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1229339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1229339))))], (22147 ^ _779203) ^ [_1170242, _1170244] : [class_Divides_Osemiring__div(_1170242), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1170242), _1170244), c_Groups_Ozero__class_Ozero(_1170242)) = c_Groups_Ozero__class_Ozero(_1170242))], (24560 ^ _779203) ^ [_1211788, _1211790, _1211792] : [class_Rings_Olinordered__idom(_1211788), 24563 ^ _779203 : [(24572 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1211788), hAPP(hAPP(c_Power_Opower__class_Opower(_1211788), _1211790), 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(_1211788), _1211792), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1211788)), _1211790 = c_Groups_Ozero__class_Ozero(_1211788), _1211792 = c_Groups_Ozero__class_Ozero(_1211788)], (24564 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1211788), hAPP(hAPP(c_Power_Opower__class_Opower(_1211788), _1211790), 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(_1211788), _1211792), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1211788), 24567 ^ _779203 : [(24570 ^ _779203) ^ [] : [-(_1211792 = c_Groups_Ozero__class_Ozero(_1211788))], (24568 ^ _779203) ^ [] : [-(_1211790 = c_Groups_Ozero__class_Ozero(_1211788))]]]]], (16634 ^ _779203) ^ [_1071735, _1071737, _1071739] : [class_Orderings_Olinorder(_1071735), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071735), _1071737)), -(_1071737 = c_Orderings_Obot__class_Obot(tc_fun(_1071735, tc_HOL_Obool))), 16645 ^ _779203 : [(16655 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071735), hAPP(c_Finite__Set_Ofold1(_1071735, c_Orderings_Oord__class_Omin(_1071735)), _1071737)), _1071739))), 16656 ^ _779203 : [(16657 ^ _779203) ^ [_1072124] : [hBOOL(hAPP(hAPP(c_member(_1071735), _1072124), _1071737)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071735), _1072124), _1071739))]]], (16646 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071735), hAPP(c_Finite__Set_Ofold1(_1071735, c_Orderings_Oord__class_Omin(_1071735)), _1071737)), _1071739)), 16650 ^ _779203 : [(16653 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1071735), 16649 ^ [_1071735, _1071737, _1071739]), _1071739)))], (16651 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071735), 16649 ^ [_1071735, _1071737, _1071739]), _1071737)))]]]]], (39373 ^ _779203) ^ [_1544904, _1544906, _1544908, _1544910, _1544912, _1544914] : [hBOOL(hAPP(hAPP(c_member(_1544904), _1544906), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1544908, _1544910, tc_fun(_1544904, tc_HOL_Obool)), _1544912), _1544914))), 39378 ^ _779203 : [(39381 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1544904), _1544906), hAPP(hAPP(_1544912, 39376 ^ [_1544904, _1544906, _1544908, _1544910, _1544912, _1544914]), 39377 ^ [_1544904, _1544906, _1544908, _1544910, _1544912, _1544914]))))], (39379 ^ _779203) ^ [] : [-(_1544914 = hAPP(hAPP(c_Product__Type_OPair(_1544908, _1544910), 39376 ^ [_1544904, _1544906, _1544908, _1544910, _1544912, _1544914]), 39377 ^ [_1544904, _1544906, _1544908, _1544910, _1544912, _1544914]))]]], (48509 ^ _779203) ^ [_1757601, _1757603, _1757605] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757601), _1757605), _1757603)), -(hBOOL(hAPP(hAPP(c_member(_1757601), _1757603), hAPP(c_List_Oset(_1757601), _1757605))))], (47919 ^ _779203) ^ [_1744731, _1744733, _1744735] : [47921 ^ _779203 : [(47924 ^ _779203) ^ [] : [hBOOL(hAPP(_1744733, 47920 ^ [_1744731, _1744733, _1744735]))], (47922 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744731), 47920 ^ [_1744731, _1744733, _1744735]), hAPP(c_List_Oset(_1744731), _1744735))))]], -(c_List_Olist__all(_1744731, _1744733, _1744735))], (30871 ^ _779203) ^ [_1331552, _1331554] : [class_Lattices_Olattice(_1331552), -(c_Big__Operators_Olattice__class_OInf__fin(_1331552, hAPP(hAPP(c_Set_Oinsert(_1331552), _1331554), c_Orderings_Obot__class_Obot(tc_fun(_1331552, tc_HOL_Obool)))) = _1331554)], (21271 ^ _779203) ^ [_1154217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1154217)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1154217))))], (34470 ^ _779203) ^ [_1414749, _1414751, _1414753, _1414755] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1414749, tc_HOL_Obool), tc_fun(_1414751, tc_HOL_Obool)), _1414753), hAPP(hAPP(c_COMBC(tc_fun(_1414749, tc_HOL_Obool), tc_fun(_1414749, tc_fun(_1414751, tc_HOL_Obool)), tc_fun(_1414751, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414749, tc_fun(_1414751, tc_HOL_Obool))), _1414755)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414749, tc_fun(_1414751, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1414749, tc_HOL_Obool), _1414753)), _1414755))], (35316 ^ _779203) ^ [] : [-(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)))))], (22329 ^ _779203) ^ [_1173242] : [hBOOL(hAPP(_1173242, 22330 ^ [_1173242])), 22333 ^ _779203 : [(22334 ^ _779203) ^ [_1173336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173336)), -(hBOOL(hAPP(_1173242, hAPP(c_Int_Onat, _1173336))))]]], (51867 ^ _779203) ^ [_1826549, _1826551, _1826553, _1826555] : [-(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), _1826549, _1826551)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826553, _1826555)))), 51868 ^ _779203 : [(51871 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826553), _1826549)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826551), _1826555))], (51869 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826549), _1826551)))]]], (34577 ^ _779203) ^ [_1417881, _1417883, _1417885, _1417887, _1417889] : [hBOOL(hAPP(hAPP(c_member(_1417881), _1417883), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1417885, tc_fun(_1417881, tc_HOL_Obool)), _1417887), _1417889))), 34580 ^ _779203 : [(34581 ^ _779203) ^ [_1418005] : [hBOOL(hAPP(hAPP(c_member(_1417885), _1418005), _1417887)), -(hBOOL(hAPP(hAPP(c_member(_1417881), _1417883), hAPP(_1417889, _1418005))))]]], (46718 ^ _779203) ^ [_1718647, _1718649, _1718651] : [-(hAPP(c_List_Orev(_1718647), hAPP(hAPP(c_List_Odrop(_1718647), _1718649), _1718651)) = hAPP(hAPP(c_List_Otake(_1718647), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718647)), _1718651)), _1718649)), hAPP(c_List_Orev(_1718647), _1718651)))], (7333 ^ _779203) ^ [_900545, _900547, _900549] : [class_Orderings_Oorder(_900545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900545), _900547), _900549)), _900547 = _900549], (21739 ^ _779203) ^ [_1161880, _1161882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1161880)), c_Int_OBit0(_1161882))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161880), _1161882)))], (21943 ^ _779203) ^ [_1166005, _1166007] : [-(_1166005 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1166007), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1166005), _1166007))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1166005, _1166007)))], (52287 ^ _779203) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (17882 ^ _779203) ^ [_1094411, _1094413, _1094415, _1094417, _1094419] : [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), _1094411), _1094413)), _1094415)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1094411), _1094417)), _1094419))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1094415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094415), _1094411)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094419), _1094411)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094413), _1094417)))], (12128 ^ _779203) ^ [_988796, _988798, _988800] : [class_Groups_Ocomm__monoid__add(_988796), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_988798, _988796), _988800), c_Orderings_Obot__class_Obot(tc_fun(_988798, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_988796))], (35413 ^ _779203) ^ [_1440880, _1440882, _1440884, _1440886, _1440888, _1440890] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1440886, _1440886)), hAPP(hAPP(c_Product__Type_OPair(_1440886, _1440886), hAPP(_1440890, _1440882)), hAPP(_1440890, _1440884))), _1440888)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1440880, _1440880)), hAPP(hAPP(c_Product__Type_OPair(_1440880, _1440880), _1440882), _1440884)), hAPP(hAPP(c_Relation_Oinv__image(_1440886, _1440880), _1440888), _1440890))))], (43369 ^ _779203) ^ [_1645109, _1645111, _1645113, _1645115, _1645117, _1645119, _1645121, _1645123] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1645109, _1645109)), hAPP(hAPP(c_Product__Type_OPair(_1645109, _1645109), _1645111), _1645113)), _1645115)), _1645117 = hAPP(hAPP(c_List_Oappend(_1645109), _1645119), hAPP(hAPP(c_List_Olist_OCons(_1645109), _1645111), _1645121)), _1645123 = hAPP(hAPP(c_List_Oappend(_1645109), _1645119), hAPP(hAPP(c_List_Olist_OCons(_1645109), _1645113), _1645121)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645109), tc_List_Olist(_1645109))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645109), tc_List_Olist(_1645109)), _1645117), _1645123)), c_List_Olistrel1(_1645109, _1645115))))], (3468 ^ _779203) ^ [_830969, _830971, _830973, _830975, _830977, _830979] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_830979, _830975, _830971) = c_SetInterval_Oord__class_OgreaterThanLessThan(_830977, _830973, _830969)), _830979 = _830977, _830975 = _830973, _830971 = _830969], (14345 ^ _779203) ^ [_1028730, _1028732, _1028734, _1028736, _1028738] : [class_Fields_Olinordered__field(_1028730), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028730), c_Groups_Ozero__class_Ozero(_1028730)), _1028732)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028730), _1028732), _1028734)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028730), c_Groups_Ozero__class_Ozero(_1028730)), _1028736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028730), _1028736), _1028738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028730), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1028730), _1028732), _1028738)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1028730), _1028734), _1028736))))], (3030 ^ _779203) ^ [_824182, _824184, _824186, _824188] : [-(c_List_Olistset(_824188, _824184) = c_List_Olistset(_824186, _824182)), _824188 = _824186, _824184 = _824182], (6005 ^ _779203) ^ [_874514, _874516, _874518, _874520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874514, tc_HOL_Obool)), _874516), _874518)), hBOOL(hAPP(hAPP(c_member(_874514), _874520), _874516)), -(hBOOL(hAPP(hAPP(c_member(_874514), _874520), _874518)))], (11744 ^ _779203) ^ [_981812, _981814] : [class_Rings_Olinordered__ring(_981812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981812), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981812), _981814), _981814)), c_Groups_Ozero__class_Ozero(_981812)))], (35347 ^ _779203) ^ [_1438469, _1438471, _1438473, _1438475] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1438469, tc_HOL_Obool), tc_fun(_1438469, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1438469, tc_HOL_Obool), tc_fun(_1438469, tc_HOL_Obool)), _1438473), _1438475)), c_Wellfounded_Omax__ext(_1438469, _1438471))), -(c_Wellfounded_Omax__extp(_1438469, hAPP(hAPP(c_COMBC(_1438469, tc_fun(tc_prod(_1438469, _1438469), tc_HOL_Obool), tc_fun(_1438469, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1438469, tc_fun(tc_fun(tc_prod(_1438469, _1438469), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1438469, _1438469), tc_HOL_Obool), tc_fun(_1438469, tc_HOL_Obool)), _1438469), c_COMBC(_1438469, tc_fun(tc_prod(_1438469, _1438469), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1438469, tc_prod(_1438469, _1438469)), tc_fun(_1438469, tc_fun(tc_fun(tc_prod(_1438469, _1438469), tc_HOL_Obool), tc_HOL_Obool)), _1438469), hAPP(c_COMBB(tc_prod(_1438469, _1438469), tc_fun(tc_fun(tc_prod(_1438469, _1438469), tc_HOL_Obool), tc_HOL_Obool), _1438469), c_member(tc_prod(_1438469, _1438469)))), c_Product__Type_OPair(_1438469, _1438469)))), _1438471), _1438473, _1438475))], (46580 ^ _779203) ^ [_1715746, _1715748] : [_1715748 = c_List_Olist_ONil(_1715746), -(hAPP(c_List_Orev(_1715746), _1715748) = c_List_Olist_ONil(_1715746))], (13537 ^ _779203) ^ [_1014198, _1014200, _1014202, _1014204, _1014206] : [class_Fields_Ofield(_1014198), hBOOL(hAPP(c_Finite__Set_Ofinite(_1014200), _1014202)), -(hAPP(_1014204, _1014206) = c_Groups_Ozero__class_Ozero(_1014198)), 13548 ^ _779203 : [(13555 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1014200), _1014206), _1014202))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1014200, _1014198), _1014204), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014200, tc_HOL_Obool)), _1014202), hAPP(hAPP(c_Set_Oinsert(_1014200), _1014206), c_Orderings_Obot__class_Obot(tc_fun(_1014200, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1014200, _1014198), _1014204), _1014202))], (13549 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1014200), _1014206), _1014202)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1014200, _1014198), _1014204), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1014200, tc_HOL_Obool)), _1014202), hAPP(hAPP(c_Set_Oinsert(_1014200), _1014206), c_Orderings_Obot__class_Obot(tc_fun(_1014200, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014198), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1014200, _1014198), _1014204), _1014202)), hAPP(_1014204, _1014206)))]]], (23822 ^ _779203) ^ [_1198470, _1198472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1198470)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1198472)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1198472), _1198470)), _1198472)))], (37539 ^ _779203) ^ [_1490306, _1490308, _1490310, _1490312, _1490314, _1490316] : [class_Groups_Ocomm__monoid__mult(_1490306), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490308, _1490306), hAPP(hAPP(c_COMBC(_1490308, tc_fun(_1490310, tc_HOL_Obool), _1490306), hAPP(hAPP(c_COMBB(tc_fun(_1490310, _1490306), tc_fun(tc_fun(_1490310, tc_HOL_Obool), _1490306), _1490308), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1490310, _1490306)), _1490312)), _1490314)), _1490316) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1490308, _1490310), _1490306), hAPP(c_Product__Type_Oprod_Oprod__case(_1490308, _1490310, _1490306), _1490312)), hAPP(hAPP(c_Product__Type_OSigma(_1490308, _1490310), _1490316), hAPP(c_COMBK(tc_fun(_1490310, tc_HOL_Obool), _1490308), _1490314))))], (41939 ^ _779203) ^ [_1611923, _1611925, _1611927, _1611929] : [hBOOL(hAPP(hAPP(c_member(_1611923), _1611925), hAPP(c_List_Oset(_1611923), hAPP(hAPP(c_List_Olist_OCons(_1611923), _1611927), _1611929)))), -(_1611925 = _1611927), -(hBOOL(hAPP(hAPP(c_member(_1611923), _1611925), hAPP(c_List_Oset(_1611923), _1611929))))], (5608 ^ _779203) ^ [_864909, _864911] : [_864911 = _864909, -(c_Orderings_Obot__class_Obot(_864911) = c_Orderings_Obot__class_Obot(_864909))], (18337 ^ _779203) ^ [_1102729, _1102731] : [class_Rings_Olinordered__semidom(_1102729), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102729), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1102729), _1102731)), c_Groups_Ozero__class_Ozero(_1102729)))], (52267 ^ _779203) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (42167 ^ _779203) ^ [_1619003, _1619005, _1619007, _1619009, _1619011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619003), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619005)), _1619007))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619003), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1619009)), _1619011))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1619005, _1619009)), hAPP(hAPP(c_List_Ozip(_1619005, _1619009), _1619007), _1619011)), _1619003) = hAPP(hAPP(c_Product__Type_OPair(_1619005, _1619009), hAPP(hAPP(c_List_Onth(_1619005), _1619007), _1619003)), hAPP(hAPP(c_List_Onth(_1619009), _1619011), _1619003)))], (23816 ^ _779203) ^ [_1198365, _1198367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1198365)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198365), _1198367)), _1198365) = _1198367)], (11942 ^ _779203) ^ [_985426, _985428, _985430] : [class_Rings_Olinordered__ring__strict(_985426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985426), _985428), c_Groups_Ozero__class_Ozero(_985426))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985426), _985430), c_Groups_Ozero__class_Ozero(_985426))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985426), c_Groups_Ozero__class_Ozero(_985426)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985426), _985428), _985430))))], (52457 ^ _779203) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (31709 ^ _779203) ^ [_1348637, _1348639, _1348641, _1348643] : [class_Groups_Ocomm__monoid__add(_1348637), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348637), _1348639), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1348641), hAPP(c_Nat_OSuc, _1348643))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1348637), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1348637, tc_Nat_Onat), _1348639), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1348641, _1348643)))], (35968 ^ _779203) ^ [_1454580, _1454582] : [c_Equiv__Relations_Oequivp(_1454580, hAPP(hAPP(c_COMBC(_1454580, tc_fun(tc_prod(_1454580, _1454580), tc_HOL_Obool), tc_fun(_1454580, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454580, tc_fun(tc_fun(tc_prod(_1454580, _1454580), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454580, _1454580), tc_HOL_Obool), tc_fun(_1454580, tc_HOL_Obool)), _1454580), c_COMBC(_1454580, tc_fun(tc_prod(_1454580, _1454580), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454580, tc_prod(_1454580, _1454580)), tc_fun(_1454580, tc_fun(tc_fun(tc_prod(_1454580, _1454580), tc_HOL_Obool), tc_HOL_Obool)), _1454580), hAPP(c_COMBB(tc_prod(_1454580, _1454580), tc_fun(tc_fun(tc_prod(_1454580, _1454580), tc_HOL_Obool), tc_HOL_Obool), _1454580), c_member(tc_prod(_1454580, _1454580)))), c_Product__Type_OPair(_1454580, _1454580)))), _1454582)), -(c_Equiv__Relations_Oequiv(_1454580, c_Orderings_Otop__class_Otop(tc_fun(_1454580, tc_HOL_Obool)), _1454582))], (45468 ^ _779203) ^ [_1691728, _1691730] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691728)), c_List_Oremdups(_1691728, c_List_Oconcat(_1691728, _1691730))) = hAPP(c_Finite__Set_Ocard(_1691728), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1691728), tc_fun(_1691728, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1691728)), _1691730)), c_List_Oset(_1691728))))], (24876 ^ _779203) ^ [_1217657, _1217659, _1217661] : [class_Rings_Oring__1__no__zero__divisors(_1217657), -(_1217659 = c_Groups_Ozero__class_Ozero(_1217657)), hAPP(hAPP(c_Power_Opower__class_Opower(_1217657), _1217659), _1217661) = c_Groups_Ozero__class_Ozero(_1217657)], (20540 ^ _779203) ^ [_1141435, _1141437] : [class_Groups_Oordered__ab__group__add__abs(_1141435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141435), _1141437), c_Groups_Ozero__class_Ozero(_1141435))), -(hAPP(c_Groups_Oabs__class_Oabs(_1141435), _1141437) = hAPP(c_Groups_Ouminus__class_Ouminus(_1141435), _1141437))], (5920 ^ _779203) ^ [_873037, _873039] : [-(hBOOL(hAPP(hAPP(c_member(_873037), 5921 ^ [_873037, _873039]), _873039))), -(_873039 = c_Orderings_Obot__class_Obot(tc_fun(_873037, tc_HOL_Obool)))], (25474 ^ _779203) ^ [_1228264, _1228266] : [c_Nat__Transfer_Ois__nat(_1228264), c_Nat__Transfer_Ois__nat(_1228266), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1228264), _1228266)))], (8839 ^ _779203) ^ [_928514, _928516, _928518, _928520] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_928514), 8842 ^ _779203 : [(8849 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928514), _928518), _928520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928514), _928516), _928518)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928514), _928516), _928520))))], (8843 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928514), _928516), _928518)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928514), _928516), _928520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928514), _928518), _928520)))]]], (19518 ^ _779203) ^ [_1123286, _1123288, _1123290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1123286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1123288), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1123290), 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), _1123290), _1123288))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1123286)))))], (34516 ^ _779203) ^ [_1416443, _1416445, _1416447, _1416449] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416443, tc_fun(_1416445, tc_HOL_Obool)), _1416447), _1416449) = c_Orderings_Otop__class_Otop(tc_fun(_1416445, tc_HOL_Obool)), 34519 ^ _779203 : [(34520 ^ _779203) ^ [_1416559] : [hBOOL(hAPP(hAPP(c_member(_1416443), _1416559), _1416447)), -(hAPP(_1416449, _1416559) = c_Orderings_Otop__class_Otop(tc_fun(_1416445, tc_HOL_Obool)))]]], (23671 ^ _779203) ^ [_1195718, _1195720, _1195722] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195718), _1195720)), _1195722) = 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), _1195718), _1195722)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1195720), _1195722))), 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, _1195718, _1195722)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1195720, _1195722))), _1195722)))], (23018 ^ _779203) ^ [_1184467, _1184469, _1184471] : [class_Divides_Osemiring__div(_1184467), -(_1184469 = c_Groups_Ozero__class_Ozero(_1184467)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1184467), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184467), _1184471), _1184469)), _1184469) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184467), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1184467), _1184471), _1184469)), c_Groups_Oone__class_Oone(_1184467)))], (52611 ^ _779203) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (35059 ^ _779203) ^ [_1431185, _1431187, _1431189, _1431191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1431185), _1431187)), -(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), _1431185), _1431189)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1431187), _1431191))), c_FunDef_Opair__less)))], (47728 ^ _779203) ^ [_1740805, _1740807, _1740809, _1740811] : [47729 ^ _779203 : [(47732 ^ _779203) ^ [] : [c_List_Olist__ex(_1740805, _1740807, _1740811)], (47730 ^ _779203) ^ [] : [hBOOL(hAPP(_1740807, _1740809))]], -(c_List_Olist__ex(_1740805, _1740807, hAPP(hAPP(c_List_Olist_OCons(_1740805), _1740809), _1740811)))], (40434 ^ _779203) ^ [_1570786, _1570788] : [-(hAPP(c_Relation_ORange(_1570786, _1570786), c_Transitive__Closure_Ortrancl(_1570786, _1570788)) = c_Orderings_Otop__class_Otop(tc_fun(_1570786, tc_HOL_Obool)))], (42005 ^ _779203) ^ [_1613401, _1613403, _1613405] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1613401)), _1613403), c_List_Olists(_1613401, _1613405))), 42008 ^ _779203 : [(42009 ^ _779203) ^ [_1613509] : [hBOOL(hAPP(hAPP(c_member(_1613401), _1613509), hAPP(c_List_Oset(_1613401), _1613403))), -(hBOOL(hAPP(hAPP(c_member(_1613401), _1613509), _1613405)))]]], (49824 ^ _779203) ^ [_1786903] : [-(_1786903 = hAPP(c_Code__Numeral_Oof__nat, 49822 ^ [_1786903]))], (51889 ^ _779203) ^ [_1826972, _1826974, _1826976, _1826978, _1826980] : [class_Rings_Ocomm__semiring__1(_1826972), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826972), _1826974), _1826976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1826978), _1826980)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826972), hAPP(hAPP(c_Power_Opower__class_Opower(_1826972), _1826974), _1826978)), hAPP(hAPP(c_Power_Opower__class_Opower(_1826972), _1826976), _1826980))))], (28134 ^ _779203) ^ [_1276297] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1276297) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1276297))], (1780 ^ _779203) ^ [_804413, _804415] : [-(class_Rings_Ozero__neq__one(_804413)), _804415 = _804413, class_Rings_Ozero__neq__one(_804415)], (31573 ^ _779203) ^ [_1345629, _1345631, _1345633, _1345635] : [class_Lattices_Osemilattice__sup(_1345629), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345629), _1345631)), 31583 ^ _779203 : [(31586 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345629), 31582 ^ [_1345629, _1345631, _1345633, _1345635]), _1345633))], (31584 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1345629), 31582 ^ [_1345629, _1345631, _1345633, _1345635]), _1345631)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345629), hAPP(hAPP(c_Finite__Set_Ofold(_1345629, _1345629, c_Lattices_Osemilattice__sup__class_Osup(_1345629)), _1345635), _1345631)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1345629), _1345633), _1345635))))], (17522 ^ _779203) ^ [_1088104] : [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)), _1088104)), _1088104) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (12845 ^ _779203) ^ [_1001245, _1001247, _1001249] : [class_Rings_Olinordered__ring(_1001245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001245), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001245), _1001247), _1001247)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001245), _1001249), _1001249))), c_Groups_Ozero__class_Ozero(_1001245)))], (29708 ^ _779203) ^ [_1306664, _1306666, _1306668, _1306670] : [-(hBOOL(hAPP(hAPP(c_member(_1306664), _1306666), _1306668))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306664, tc_HOL_Obool)), _1306668), hAPP(hAPP(c_Set_Oinsert(_1306664), _1306666), _1306670)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306664, tc_HOL_Obool)), _1306668), _1306670))], (18933 ^ _779203) ^ [_1112787, _1112789] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1112787) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1112789), -(_1112787 = _1112789)], (29092 ^ _779203) ^ [_1294123, _1294125, _1294127, _1294129] : [hBOOL(hAPP(_1294123, _1294125)), hBOOL(hAPP(_1294127, _1294125)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1294129, tc_HOL_Obool)), _1294123), _1294127), _1294125)))], (49194 ^ _779203) ^ [_1773727, _1773729] : [c_Relation_Oantisym(_1773727, _1773729), 49197 ^ _779203 : [(49198 ^ _779203) ^ [_1773839, _1773841] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773727, _1773727)), hAPP(hAPP(c_Product__Type_OPair(_1773727, _1773727), _1773841), _1773839)), _1773729)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773727, _1773727)), hAPP(hAPP(c_Product__Type_OPair(_1773727, _1773727), _1773839), _1773841)), _1773729)), -(_1773841 = _1773839)]]], (4742 ^ _779203) ^ [_851330, _851332, _851334, _851336] : [-(c_Complete__Lattice_OInf__class_OInf(_851336, _851332) = c_Complete__Lattice_OInf__class_OInf(_851334, _851330)), _851336 = _851334, _851332 = _851330], (34871 ^ _779203) ^ [_1426289, _1426291] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426289, tc_fun(_1426289, tc_HOL_Obool)), _1426291), hAPP(hAPP(c_COMBC(_1426289, tc_fun(_1426289, tc_HOL_Obool), tc_fun(_1426289, tc_HOL_Obool)), c_Set_Oinsert(_1426289)), c_Orderings_Obot__class_Obot(tc_fun(_1426289, tc_HOL_Obool)))) = _1426291)], (34443 ^ _779203) ^ [_1413773, _1413775, _1413777, _1413779, _1413781] : [34445 ^ _779203 : [(34448 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413773, tc_HOL_Obool)), hAPP(_1413779, 34444 ^ [_1413773, _1413775, _1413777, _1413779, _1413781])), _1413781))], (34446 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1413775), 34444 ^ [_1413773, _1413775, _1413777, _1413779, _1413781]), _1413777)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413773, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413775, tc_fun(_1413773, tc_HOL_Obool)), _1413777), _1413779)), _1413781)))], (44089 ^ _779203) ^ [_1661648, _1661650, _1661652, _1661654, _1661656] : [class_Orderings_Olinorder(_1661648), -(hBOOL(hAPP(hAPP(c_member(_1661648), hAPP(_1661650, _1661652)), hAPP(c_Set_Oimage(_1661654, _1661648, _1661650), hAPP(c_List_Oset(_1661654), _1661656))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661654, _1661648, _1661650, _1661652, _1661656) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661654, _1661648, _1661650), _1661652), _1661656))], (1082 ^ _779203) ^ [_795490, _795492, _795494, _795496, _795498, _795500, _795502, _795504, _795506, _795508] : [-(c_Finite__Set_Ofolding__image(_795506, _795502, _795498, _795494, _795490)), c_Finite__Set_Ofolding__image(_795508, _795504, _795500, _795496, _795492), _795508 = _795506, _795504 = _795502, _795500 = _795498, _795496 = _795494, _795492 = _795490], (43636 ^ _779203) ^ [_1652069, _1652071, _1652073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1652069), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652071)), _1652073))), -(hAPP(hAPP(c_List_Olist_OCons(_1652071), hAPP(hAPP(c_List_Onth(_1652071), _1652073), _1652069)), hAPP(hAPP(c_List_Odrop(_1652071), hAPP(c_Nat_OSuc, _1652069)), _1652073)) = hAPP(hAPP(c_List_Odrop(_1652071), _1652069), _1652073))], (6939 ^ _779203) ^ [_892728, _892730, _892732, _892734, _892736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892728, tc_HOL_Obool)), _892730), _892732)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892728, tc_HOL_Obool)), _892734), _892736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892728, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892728, tc_HOL_Obool)), _892730), _892736)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892728, tc_HOL_Obool)), _892732), _892734))))], (40717 ^ _779203) ^ [_1577537, _1577539, _1577541, _1577543, _1577545] : [-(hAPP(c_Relation_Oconverse(_1577537, _1577539), hAPP(hAPP(c_Relation_Orel__comp(_1577537, _1577541, _1577539), _1577543), _1577545)) = hAPP(hAPP(c_Relation_Orel__comp(_1577539, _1577541, _1577537), hAPP(c_Relation_Oconverse(_1577541, _1577539), _1577545)), hAPP(c_Relation_Oconverse(_1577537, _1577541), _1577543)))], (11750 ^ _779203) ^ [_981922, _981924, _981926, _981928] : [class_Rings_Olinordered__ring__strict(_981922), 11753 ^ _779203 : [(11768 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981922), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981922), _981924), _981926)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981922), _981928), _981926)))), 11769 ^ _779203 : [(11776 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981922), _981926), c_Groups_Ozero__class_Ozero(_981922))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981922), _981928), _981924))], (11770 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981922), c_Groups_Ozero__class_Ozero(_981922)), _981926)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981922), _981924), _981928))]]], (11754 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981922), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981922), _981924), _981926)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_981922), _981928), _981926))), 11759 ^ _779203 : [(11762 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981922), _981924), _981928)))], (11760 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981922), c_Groups_Ozero__class_Ozero(_981922)), _981926)))]], 11763 ^ _779203 : [(11766 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981922), _981928), _981924)))], (11764 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981922), _981926), c_Groups_Ozero__class_Ozero(_981922))))]]]]], (38768 ^ _779203) ^ [_1529941, _1529943, _1529945] : [hAPP(c_Relation_ODomain(_1529941, _1529943), _1529945) = c_Orderings_Obot__class_Obot(tc_fun(_1529941, tc_HOL_Obool)), -(_1529945 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529941, _1529943), tc_HOL_Obool)))], (26486 ^ _779203) ^ [_1245029, _1245031] : [hAPP(_1245029, 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), _1245029), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1245031)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1245029), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1245031)))], (2058 ^ _779203) ^ [_808888, _808890] : [_808890 = _808888, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_808890) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_808888))], (22858 ^ _779203) ^ [_1181886, _1181888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1181888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1181886), _1181888)), _1181886)))], (24970 ^ _779203) ^ [_1219345, _1219347, _1219349] : [class_Rings_Olinordered__idom(_1219345), -(hAPP(c_Groups_Oabs__class_Oabs(_1219345), hAPP(hAPP(c_Power_Opower__class_Opower(_1219345), _1219347), _1219349)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1219345), hAPP(c_Groups_Oabs__class_Oabs(_1219345), _1219347)), _1219349))], (31233 ^ _779203) ^ [_1338410, _1338412, _1338414, _1338416] : [class_Groups_Ocomm__monoid__mult(_1338410), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338412), _1338414)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338412, _1338410), _1338416), _1338414) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1338410, _1338412, c_Groups_Otimes__class_Otimes(_1338410)), _1338416), c_Groups_Oone__class_Oone(_1338410)), _1338414))], (41006 ^ _779203) ^ [_1584756, _1584758, _1584760] : [-(hAPP(hAPP(c_Nat_Ocompow(_1584756, _1584756), hAPP(c_Nat_OSuc, _1584758)), _1584760) = hAPP(c_Fun_Ocomp(_1584756, _1584756, _1584756, _1584760), hAPP(hAPP(c_Nat_Ocompow(_1584756, _1584756), _1584758), _1584760)))], (21351 ^ _779203) ^ [_1155366, _1155368] : [class_Int_Onumber__ring(_1155366), class_Rings_Olinordered__idom(_1155366), 21358 ^ _779203 : [(21365 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1155368), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155366), hAPP(c_Int_Onumber__class_Onumber__of(_1155366), _1155368)), c_Groups_Oone__class_Oone(_1155366))))], (21359 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155366), hAPP(c_Int_Onumber__class_Onumber__of(_1155366), _1155368)), c_Groups_Oone__class_Oone(_1155366))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1155368), c_Int_OBit1(c_Int_OPls))))]]], (8348 ^ _779203) ^ [_918529, _918531, _918533, _918535] : [-(hBOOL(hAPP(hAPP(c_member(_918529), _918531), _918533))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918529, tc_Nat_Onat), _918535), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918529, tc_HOL_Obool)), _918533), hAPP(hAPP(c_Set_Oinsert(_918529), _918531), c_Orderings_Obot__class_Obot(tc_fun(_918529, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918529, tc_Nat_Onat), _918535), _918533))], (32287 ^ _779203) ^ [_1363262, _1363264, _1363266, _1363268] : [class_Groups_Ocomm__monoid__add(_1363262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1363264), _1363266)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363262), _1363268), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1363264, _1363266)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363262), hAPP(_1363268, _1363264)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363262), _1363268), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1363264, _1363266))))], (33927 ^ _779203) ^ [_1400859, _1400861, _1400863, _1400865, _1400867, _1400869] : [hBOOL(hAPP(_1400859, _1400861)), hBOOL(hAPP(_1400863, _1400865)), 33934 ^ _779203 : [(33937 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1400863, hAPP(c_Product__Type_Osnd(_1400867, _1400869), hAPP(hAPP(c_Product__Type_OPair(_1400867, _1400869), _1400861), _1400865)))))], (33935 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1400859, hAPP(c_Product__Type_Ofst(_1400867, _1400869), hAPP(hAPP(c_Product__Type_OPair(_1400867, _1400869), _1400861), _1400865)))))]]], (43125 ^ _779203) ^ [_1639707, _1639709, _1639711, _1639713, _1639715, _1639717] : [hAPP(hAPP(c_List_Oappend(_1639707), _1639709), _1639711) = _1639713, _1639715 = hAPP(hAPP(c_List_Oappend(_1639707), _1639711), _1639717), -(hAPP(hAPP(c_List_Oappend(_1639707), _1639709), _1639715) = hAPP(hAPP(c_List_Oappend(_1639707), _1639713), _1639717))], (34466 ^ _779203) ^ [_1414569, _1414571, _1414573, _1414575] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414569, tc_fun(_1414571, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1414569, tc_HOL_Obool), _1414573)), _1414575) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1414569, tc_HOL_Obool), tc_fun(_1414571, tc_HOL_Obool)), _1414573), hAPP(hAPP(c_COMBC(tc_fun(_1414569, tc_HOL_Obool), tc_fun(_1414569, tc_fun(_1414571, tc_HOL_Obool)), tc_fun(_1414571, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414569, tc_fun(_1414571, tc_HOL_Obool))), _1414575)))], (41053 ^ _779203) ^ [_1585981, _1585983, _1585985] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585981, _1585981)), _1585983), c_Transitive__Closure_Otrancl(_1585981, _1585985))), 41057 ^ _779203 : [(41060 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585981, _1585981)), _1585983), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1585981, _1585981), tc_HOL_Obool), 41056 ^ [_1585981, _1585983, _1585985]), _1585985))))], (41058 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41056 ^ [_1585981, _1585983, _1585985])))]]], (37305 ^ _779203) ^ [_1484137, _1484139, _1484141, _1484143] : [-(hAPP(c_Set_Ovimage(_1484137, _1484139, _1484141), _1484143) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1484139, tc_fun(_1484137, tc_HOL_Obool)), _1484143), hAPP(hAPP(c_COMBB(tc_fun(_1484139, tc_HOL_Obool), tc_fun(_1484137, tc_HOL_Obool), _1484139), c_Set_Ovimage(_1484137, _1484139, _1484141)), hAPP(hAPP(c_COMBC(_1484139, tc_fun(_1484139, tc_HOL_Obool), tc_fun(_1484139, tc_HOL_Obool)), c_Set_Oinsert(_1484139)), c_Orderings_Obot__class_Obot(tc_fun(_1484139, tc_HOL_Obool))))))], (47185 ^ _779203) ^ [_1728532, _1728534, _1728536] : [hBOOL(hAPP(c_List_Odistinct(_1728532), _1728534)), -(hBOOL(hAPP(c_List_Odistinct(_1728532), c_List_Oinsert(_1728532, _1728536, _1728534))))], (27178 ^ _779203) ^ [_1257661, _1257663, _1257665] : [class_Orderings_Oord(_1257661), 27181 ^ _779203 : [(27188 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257661), _1257665), _1257663)), -(hBOOL(hAPP(hAPP(c_member(_1257661), _1257663), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257661), _1257665))))], (27182 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1257661), _1257663), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257661), _1257665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1257661), _1257665), _1257663)))]]], (17600 ^ _779203) ^ [_1089448, _1089450] : [class_Orderings_Olinorder(_1089448), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089448), _1089450)), -(c_Big__Operators_Olattice_OSup__fin(_1089448, c_Orderings_Oord__class_Omax(_1089448), _1089450) = hAPP(c_Finite__Set_Ofold1(_1089448, c_Orderings_Oord__class_Omax(_1089448)), _1089450))], (18445 ^ _779203) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20474 ^ _779203) ^ [_1140347, _1140349] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1140347)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1140349), 20477 ^ _779203 : [(20480 ^ _779203) ^ [] : [-(_1140349 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20478 ^ _779203) ^ [] : [-(_1140347 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (51389 ^ _779203) ^ [_1818183, _1818185] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818183), _1818185)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818185), _1818183))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818185), _1818183)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818183), _1818185)))], (19764 ^ _779203) ^ [_1127745, _1127747, _1127749] : [class_Int_Onumber__ring(_1127745), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127745), hAPP(c_Groups_Ouminus__class_Ouminus(_1127745), hAPP(c_Int_Onumber__class_Onumber__of(_1127745), _1127747))), _1127749) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1127745), hAPP(c_Int_Onumber__class_Onumber__of(_1127745), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1127747))), _1127749))], (35051 ^ _779203) ^ [_1430827, _1430829, _1430831, _1430833, _1430835] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1430827, tc_fun(_1430829, tc_HOL_Obool)), _1430831), hAPP(hAPP(c_COMBS(_1430827, tc_fun(_1430829, tc_HOL_Obool), tc_fun(_1430829, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1430829, tc_HOL_Obool), tc_fun(tc_fun(_1430829, tc_HOL_Obool), tc_fun(_1430829, tc_HOL_Obool)), _1430827), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430829, tc_HOL_Obool))), _1430833)), _1430835)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1430829, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1430829, tc_HOL_Obool), hAPP(c_Set_Oimage(_1430827, tc_fun(_1430829, tc_HOL_Obool), _1430833), _1430831))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1430829, tc_HOL_Obool), hAPP(c_Set_Oimage(_1430827, tc_fun(_1430829, tc_HOL_Obool), _1430835), _1430831))))], (34276 ^ _779203) ^ [_1408672, _1408674, _1408676, _1408678, _1408680, _1408682, _1408684, _1408686] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408672, tc_fun(_1408674, tc_fun(_1408676, tc_HOL_Obool))), _1408678), _1408680), _1408682), _1408684)), hBOOL(hAPP(hAPP(c_member(_1408672), _1408686), _1408678)), -(hBOOL(hAPP(hAPP(hAPP(_1408680, _1408686), _1408682), _1408684)))], (5624 ^ _779203) ^ [_865143, _865145, _865147, _865149] : [-(hAPP(_865149, _865145) = hAPP(_865147, _865143)), _865149 = _865147, _865145 = _865143], (40412 ^ _779203) ^ [_1570205, _1570207, _1570209, _1570211, _1570213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570205, _1570205)), hAPP(hAPP(c_Product__Type_OPair(_1570205, _1570205), _1570207), _1570209)), c_Transitive__Closure_Ortrancl(_1570205, _1570211))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570205, _1570205)), hAPP(hAPP(c_Product__Type_OPair(_1570205, _1570205), _1570209), _1570213)), _1570211)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570205, _1570205)), hAPP(hAPP(c_Product__Type_OPair(_1570205, _1570205), _1570207), _1570213)), c_Transitive__Closure_Ortrancl(_1570205, _1570211))))], (28664 ^ _779203) ^ [_1286246, _1286248, _1286250] : [class_Orderings_Oorder(_1286246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286246), _1286248), _1286250)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1286246, _1286250, _1286248) = c_Orderings_Obot__class_Obot(tc_fun(_1286246, tc_HOL_Obool)))], (23561 ^ _779203) ^ [_1193916, _1193918, _1193920] : [-(hBOOL(hAPP(_1193916, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1193918, _1193920)))), 23564 ^ _779203 : [(23567 ^ _779203) ^ [] : [hBOOL(hAPP(_1193916, _1193918))], (23565 ^ _779203) ^ [] : [-(_1193920 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 23570 ^ _779203 : [(23571 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193920)))], (23577 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23573 ^ [_1193916, _1193918, _1193920]), _1193920)))], (23581 ^ _779203) ^ [] : [hBOOL(hAPP(_1193916, 23573 ^ [_1193916, _1193918, _1193920]))], (23579 ^ _779203) ^ [] : [-(_1193918 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193920), 23572 ^ [_1193916, _1193918, _1193920])), 23573 ^ [_1193916, _1193918, _1193920]))], (23575 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23573 ^ [_1193916, _1193918, _1193920])))]], 23582 ^ _779203 : [(23583 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193920), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23589 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23585 ^ [_1193916, _1193918, _1193920]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23593 ^ _779203) ^ [] : [hBOOL(hAPP(_1193916, 23585 ^ [_1193916, _1193918, _1193920]))], (23591 ^ _779203) ^ [] : [-(_1193918 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193920), 23584 ^ [_1193916, _1193918, _1193920])), 23585 ^ [_1193916, _1193918, _1193920]))], (23587 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193920), 23585 ^ [_1193916, _1193918, _1193920])))]]], (49703 ^ _779203) ^ [_1783847, _1783849, _1783851, _1783853, _1783855, _1783857] : [hAPP(c_Set_Oimage(_1783847, _1783849, _1783851), _1783853) = _1783855, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1783849, tc_HOL_Obool)), _1783857), _1783855)), -(hAPP(c_Set_Oimage(_1783847, _1783849, _1783851), hAPP(c_Set_Oimage(_1783849, _1783847, c_Hilbert__Choice_Oinv__into(_1783847, _1783849, _1783853, _1783851)), _1783857)) = _1783857)], (45262 ^ _779203) ^ [_1687479, _1687481, _1687483] : [-(c_Enum_Osublists(_1687479, hAPP(hAPP(c_List_Olist_OCons(_1687479), _1687481), _1687483)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1687479)), tc_List_Olist(tc_List_Olist(_1687479))), c_Enum_Osublists(_1687479, _1687483)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1687479)), tc_List_Olist(tc_List_Olist(_1687479)), tc_List_Olist(tc_List_Olist(_1687479))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1687479)), tc_fun(tc_List_Olist(tc_List_Olist(_1687479)), tc_List_Olist(tc_List_Olist(_1687479))), tc_List_Olist(tc_List_Olist(_1687479))), c_List_Oappend(tc_List_Olist(_1687479))), hAPP(c_List_Omap(tc_List_Olist(_1687479), tc_List_Olist(_1687479)), hAPP(c_List_Olist_OCons(_1687479), _1687481)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1687479))))))], (1130 ^ _779203) ^ [_796288, _796290] : [-(class_Lattices_Obounded__lattice(_796288)), _796290 = _796288, class_Lattices_Obounded__lattice(_796290)], (13801 ^ _779203) ^ [_1018996, _1018998, _1019000, _1019002] : [class_Fields_Olinordered__field(_1018996), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018996), c_Groups_Ozero__class_Ozero(_1018996)), _1018998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018996), _1019000), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018996), _1019002), _1018998))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018996), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1018996), _1019000), _1018998)), _1019002)))], (18118 ^ _779203) ^ [_1098853, _1098855] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098853), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098853)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098855)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19892 ^ _779203) ^ [_1129929, _1129931] : [class_Groups_Ogroup__add(_1129929), 19895 ^ _779203 : [(19902 ^ _779203) ^ [] : [_1129931 = c_Groups_Ozero__class_Ozero(_1129929), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1129929), _1129931) = c_Groups_Ozero__class_Ozero(_1129929))], (19896 ^ _779203) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1129929), _1129931) = c_Groups_Ozero__class_Ozero(_1129929), -(_1129931 = c_Groups_Ozero__class_Ozero(_1129929))]]], (10359 ^ _779203) ^ [_957523, _957525, _957527] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957523), _957525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957527), _957525))))], (41826 ^ _779203) ^ [_1608965, _1608967, _1608969] : [-(hAPP(hAPP(c_List_Onth(_1608965), hAPP(hAPP(c_List_Olist_OCons(_1608965), _1608967), _1608969)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1608967)], (2254 ^ _779203) ^ [_812094, _812096, _812098, _812100, _812102, _812104, _812106, _812108] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_812108, _812104, _812100, _812096) = c_Nat_Osemiring__1__class_Oof__nat__aux(_812106, _812102, _812098, _812094)), _812108 = _812106, _812104 = _812102, _812100 = _812098, _812096 = _812094], (3050 ^ _779203) ^ [_824480, _824482, _824484, _824486, _824488, _824490, _824492, _824494] : [-(c_Nat_Onat_Onat__case(_824494, _824490, _824486, _824482) = c_Nat_Onat_Onat__case(_824492, _824488, _824484, _824480)), _824494 = _824492, _824490 = _824488, _824486 = _824484, _824482 = _824480], (35487 ^ _779203) ^ [_1442755, _1442757, _1442759, _1442761, _1442763] : [-(hBOOL(hAPP(hAPP(c_member(_1442755), _1442757), hAPP(c_Relation_OImage(_1442759, _1442755, _1442761), _1442763)))), 35488 ^ _779203 : [(35489 ^ _779203) ^ [_1442841] : [hBOOL(hAPP(hAPP(c_member(_1442759), _1442841), _1442763)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1442759, _1442755)), hAPP(hAPP(c_Product__Type_OPair(_1442759, _1442755), _1442841), _1442757)), _1442761))]]], (35497 ^ _779203) ^ [_1443021, _1443023, _1443025, _1443027, _1443029, _1443031] : [hBOOL(hAPP(hAPP(c_member(_1443021), _1443023), _1443025)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1443021, _1443027)), hAPP(hAPP(c_Product__Type_OPair(_1443021, _1443027), _1443023), _1443029)), _1443031)), -(hBOOL(hAPP(hAPP(c_member(_1443027), _1443029), hAPP(c_Relation_OImage(_1443021, _1443027, _1443031), _1443025))))], (1420 ^ _779203) ^ [_799913, _799915] : [-(class_Lattices_Obounded__lattice__bot(_799913)), _799915 = _799913, class_Lattices_Obounded__lattice__bot(_799915)], (32549 ^ _779203) ^ [_1369906, _1369908, _1369910] : [-(c_Nat_Onat_Onat__case(_1369906, _1369908, _1369910, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1369908)], (22405 ^ _779203) ^ [_1174468] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174468) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1174468)))], (39993 ^ _779203) ^ [_1559209, _1559211, _1559213] : [-(hBOOL(hAPP(hAPP(c_member(_1559209), _1559211), c_Wellfounded_Oacc(_1559209, _1559213)))), 39997 ^ _779203 : [(40000 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1559209), 39996 ^ [_1559209, _1559211, _1559213]), c_Wellfounded_Oacc(_1559209, _1559213)))], (39998 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559209, _1559209)), hAPP(hAPP(c_Product__Type_OPair(_1559209, _1559209), 39996 ^ [_1559209, _1559211, _1559213]), _1559211)), _1559213)))]]], (38522 ^ _779203) ^ [_1524958, _1524960, _1524962, _1524964] : [hBOOL(hAPP(c_Predicate_ORangeP(_1524958, _1524960, _1524962), _1524964)), -(hBOOL(hAPP(hAPP(_1524962, 38525 ^ [_1524958, _1524960, _1524962, _1524964]), _1524964)))], (30030 ^ _779203) ^ [_1313941, _1313943, _1313945] : [class_Lattices_Osemilattice__inf(_1313941), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313941), _1313943)), hBOOL(hAPP(hAPP(c_member(_1313941), _1313945), _1313943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313941), hAPP(c_Finite__Set_Ofold1(_1313941, c_Lattices_Osemilattice__inf__class_Oinf(_1313941)), _1313943)), _1313945)))], (12438 ^ _779203) ^ [_993718, _993720, _993722, _993724] : [_993718 = c_Finite__Set_Ofold1(_993720, _993722), -(hAPP(_993718, hAPP(hAPP(c_Set_Oinsert(_993720), _993724), c_Orderings_Obot__class_Obot(tc_fun(_993720, tc_HOL_Obool)))) = _993724)], (48004 ^ _779203) ^ [_1746510, _1746512, _1746514, _1746516, _1746518] : [_1746510 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1746512, _1746514, _1746516, _1746518), _1746510) = c_Lazy__Sequence_Ohit__bound(_1746514))], (45065 ^ _779203) ^ [_1683313, _1683315, _1683317, _1683319, _1683321, _1683323] : [c_List_Olist__all2(_1683313, _1683315, _1683317, _1683319, _1683321), -(c_List_Olist__all2(_1683313, _1683315, _1683317, hAPP(hAPP(c_List_Odrop(_1683313), _1683323), _1683319), hAPP(hAPP(c_List_Odrop(_1683315), _1683323), _1683321)))], (43975 ^ _779203) ^ [_1659174, _1659176, _1659178] : [class_Orderings_Olinorder(_1659174), hBOOL(hAPP(c_Finite__Set_Ofinite(_1659174), _1659176)), -(c_List_Olinorder__class_Osorted__list__of__set(_1659174, hAPP(hAPP(c_Set_Oinsert(_1659174), _1659178), _1659176)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659174, _1659174, c_COMBI(_1659174)), _1659178), c_List_Olinorder__class_Osorted__list__of__set(_1659174, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659174, tc_HOL_Obool)), _1659176), hAPP(hAPP(c_Set_Oinsert(_1659174), _1659178), c_Orderings_Obot__class_Obot(tc_fun(_1659174, tc_HOL_Obool)))))))], (21207 ^ _779203) ^ [_1153166] : [-(c_Int_OBit1(_1153166) = 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)), _1153166)), _1153166))], (37811 ^ _779203) ^ [_1498239, _1498241, _1498243, _1498245] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1498239), _1498241)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1498239, _1498239), tc_HOL_Obool)), _1498243), hAPP(hAPP(c_Product__Type_OSigma(_1498239, _1498239), _1498241), hAPP(c_COMBK(tc_fun(_1498239, tc_HOL_Obool), _1498239), _1498241)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1498239, tc_HOL_Obool)), _1498245), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1498239), _1498241), _1498243))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1498239), _1498245)))], (41893 ^ _779203) ^ [_1610838, _1610840] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1610838), hAPP(c_List_Oset(_1610838), _1610840))))], (30684 ^ _779203) ^ [_1327481, _1327483, _1327485] : [class_Complete__Lattice_Ocomplete__lattice(_1327481), hBOOL(hAPP(hAPP(c_member(_1327481), _1327483), _1327485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327481), _1327483), c_Complete__Lattice_OSup__class_OSup(_1327481, _1327485))))], (52503 ^ _779203) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (17674 ^ _779203) ^ [_1090715, _1090717, _1090719] : [class_Orderings_Olinorder(_1090715), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090715), _1090717)), hBOOL(hAPP(hAPP(c_member(_1090715), _1090719), _1090717)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090715), _1090719), c_Big__Operators_Olattice_OInf__fin(_1090715, c_Orderings_Oord__class_Omin(_1090715), _1090717)) = _1090719)], (44978 ^ _779203) ^ [_1681030, _1681032, _1681034, _1681036] : [hBOOL(hAPP(c_List_Olistsp(_1681030, _1681032), hAPP(hAPP(c_List_Oappend(_1681030), _1681034), _1681036))), 44981 ^ _779203 : [(44984 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1681030, _1681032), _1681036)))], (44982 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1681030, _1681032), _1681034)))]]], (42224 ^ _779203) ^ [_1620214] : [c_List_Onat__list(_1620214), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1620214)))], (18294 ^ _779203) ^ [_1101907, _1101909] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101907)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101909))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1101907), _1101909)))], (29232 ^ _779203) ^ [_1297175, _1297177, _1297179] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297175, tc_HOL_Obool)), _1297177), _1297179) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297175, tc_HOL_Obool)), _1297179), _1297177))], (38810 ^ _779203) ^ [_1530833, _1530835, _1530837, _1530839, _1530841] : [c_Relation_Orefl__on(_1530833, _1530835, _1530837), c_Relation_Orefl__on(_1530833, _1530839, _1530841), -(c_Relation_Orefl__on(_1530833, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1530833, tc_HOL_Obool)), _1530835), _1530839), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1530833, _1530833), tc_HOL_Obool)), _1530837), _1530841)))], (21905 ^ _779203) ^ [_1164994, _1164996, _1164998] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1164994), _1164996)), _1164998) = 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), _1164994), _1164998)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1164996), _1164998))), 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, _1164994, _1164998)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1164996, _1164998))), _1164998)))], (18359 ^ _779203) ^ [_1103099, _1103101] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1103099)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1103101)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103099), _1103101)))], (10797 ^ _779203) ^ [_965933, _965935] : [class_Groups_Ocomm__monoid__add(_965933), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965933), c_Groups_Ozero__class_Ozero(_965933)), _965935) = _965935)], (22123 ^ _779203) ^ [_1169742] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1169742, _1169742) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22047 ^ _779203) ^ [_1168151, _1168153, _1168155, _1168157] : [class_Divides_Osemiring__div(_1168151), -(c_Divides_Odiv__class_Omod(_1168151, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168151), _1168153), _1168155), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168151), _1168157), _1168155)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168151), c_Divides_Odiv__class_Omod(_1168151, _1168153, _1168157)), _1168155))], (40739 ^ _779203) ^ [_1578022, _1578024, _1578026, _1578028] : [-(hAPP(c_Relation_Oconverse(_1578022, _1578024), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1578022, _1578024), tc_HOL_Obool)), _1578026), _1578028)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1578024, _1578022), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1578022, _1578024), _1578026)), hAPP(c_Relation_Oconverse(_1578022, _1578024), _1578028)))], (22712 ^ _779203) ^ [_1179462, _1179464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179464), 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), _1179462), _1179464)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52181 ^ _779203) ^ [_1831743, _1831745] : [class_Orderings_Oorder(_1831743), -(class_Orderings_Oorder(tc_fun(_1831745, _1831743)))], (25624 ^ _779203) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (34554 ^ _779203) ^ [_1417382, _1417384, _1417386, _1417388] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1417382), _1417384)), 34557 ^ _779203 : [(34558 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1417386), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417382, tc_fun(_1417386, tc_HOL_Obool)), _1417384), _1417388))), 34561 ^ _779203 : [(34562 ^ _779203) ^ [_1417566] : [hBOOL(hAPP(hAPP(c_member(_1417382), _1417566), _1417384)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1417386), hAPP(_1417388, _1417566))))]]], (34568 ^ _779203) ^ [] : [34570 ^ _779203 : [(34573 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1417386), hAPP(_1417388, 34569 ^ [_1417382, _1417384, _1417386, _1417388])))], (34571 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417382), 34569 ^ [_1417382, _1417384, _1417386, _1417388]), _1417384)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1417386), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1417382, tc_fun(_1417386, tc_HOL_Obool)), _1417384), _1417388))))]]], (26962 ^ _779203) ^ [_1254070, _1254072, _1254074] : [class_Orderings_Olinorder(_1254070), 26965 ^ _779203 : [(26972 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254070), _1254072), _1254074)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1254070, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1254070), _1254072)), hAPP(c_SetInterval_Oord__class_OlessThan(_1254070), _1254074))))], (26966 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1254070, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1254070), _1254072)), hAPP(c_SetInterval_Oord__class_OlessThan(_1254070), _1254074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254070), _1254072), _1254074)))]]], (23705 ^ _779203) ^ [_1196513, _1196515, _1196517] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1196513, _1196515)), _1196517) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196513), _1196517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196515), _1196517)))], (4392 ^ _779203) ^ [_845869, _845871] : [_845871 = _845869, -(c_Lazy__Sequence_Oyieldn(_845871) = c_Lazy__Sequence_Oyieldn(_845869))], (10377 ^ _779203) ^ [_957824, _957826, _957828, _957830, _957832] : [class_Rings_Ocomm__semiring__1(_957824), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957824), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957824), _957826), _957828)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957824), _957830), _957832)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957824), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957824), _957826), _957830)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_957824), _957828), _957832)))], (52317 ^ _779203) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (28984 ^ _779203) ^ [_1291922, _1291924, _1291926] : [class_Lattices_Olattice(_1291922), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291922), _1291924)), -(c_Big__Operators_Olattice__class_OSup__fin(_1291922, hAPP(hAPP(c_Set_Oinsert(_1291922), _1291926), _1291924)) = hAPP(hAPP(c_Finite__Set_Ofold(_1291922, _1291922, c_Lattices_Osemilattice__sup__class_Osup(_1291922)), _1291926), _1291924))], (27016 ^ _779203) ^ [_1254989] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1254989)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1254989)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1254989)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (50895 ^ _779203) ^ [_1809993, _1809995] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809993), _1809995))), -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809993, _1809995) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (44380 ^ _779203) ^ [_1667578, _1667580, _1667582, _1667584] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667578)), hAPP(hAPP(c_List_Omap(_1667580, _1667578), _1667582), _1667584)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667580)), _1667584))], (9345 ^ _779203) ^ [_938520, _938522, _938524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938520), _938522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938520), _938524)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938522), _938524))))], (31693 ^ _779203) ^ [_1348237, _1348239, _1348241, _1348243] : [class_Groups_Oordered__ab__group__add__abs(_1348237), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348237), hAPP(c_Groups_Oabs__class_Oabs(_1348237), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348239, _1348237), _1348241), _1348243))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348239, _1348237), hAPP(hAPP(c_COMBB(_1348237, _1348237, _1348239), c_Groups_Oabs__class_Oabs(_1348237)), _1348241)), _1348243))))], (49945 ^ _779203) ^ [_1789386, _1789388, _1789390, _1789392, _1789394, _1789396, _1789398, _1789400] : [c_Fun_Obij__betw(_1789386, _1789388, _1789390, _1789392, _1789394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1789386, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1789396, _1789386, _1789398), _1789400)), _1789392)), 49952 ^ _779203 : [(49959 ^ _779203) ^ [] : [c_Fun_Obij__betw(_1789396, _1789388, hAPP(c_Fun_Ocomp(_1789386, _1789388, _1789396, _1789390), _1789398), _1789400, _1789394), -(c_Fun_Obij__betw(_1789396, _1789386, _1789398, _1789400, _1789392))], (49953 ^ _779203) ^ [] : [c_Fun_Obij__betw(_1789396, _1789386, _1789398, _1789400, _1789392), -(c_Fun_Obij__betw(_1789396, _1789388, hAPP(c_Fun_Ocomp(_1789386, _1789388, _1789396, _1789390), _1789398), _1789400, _1789394))]]], (23405 ^ _779203) ^ [_1191134, _1191136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191134)), 23408 ^ _779203 : [(23415 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191134), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1191134)), _1191136)))], (23409 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1191134)), _1191136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191134), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1191136))))]]], (24382 ^ _779203) ^ [_1208805, _1208807] : [-(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), _1208805)), _1208807))))], (46254 ^ _779203) ^ [_1709164, _1709166, _1709168, _1709170, _1709172] : [class_Orderings_Olinorder(_1709164), c_List_Olinorder__class_Osorted(_1709164, hAPP(hAPP(c_List_Omap(_1709166, _1709164), _1709168), _1709170)), -(c_List_Olinorder__class_Osorted(_1709164, hAPP(hAPP(c_List_Omap(_1709166, _1709164), _1709168), c_List_Oremove1(_1709166, _1709172, _1709170))))], (42321 ^ _779203) ^ [_1622407, _1622409, _1622411, _1622413, _1622415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622407), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622409)), _1622411))), 42324 ^ _779203 : [(42331 ^ _779203) ^ [] : [-(_1622407 = _1622413), -(hAPP(hAPP(c_List_Onth(_1622409), hAPP(hAPP(c_List_Olist__update(_1622409, _1622411), _1622407), _1622415)), _1622413) = hAPP(hAPP(c_List_Onth(_1622409), _1622411), _1622413))], (42325 ^ _779203) ^ [] : [_1622407 = _1622413, -(hAPP(hAPP(c_List_Onth(_1622409), hAPP(hAPP(c_List_Olist__update(_1622409, _1622411), _1622407), _1622415)), _1622413) = _1622415)]]], (10803 ^ _779203) ^ [_966028, _966030] : [class_Groups_Omonoid__add(_966028), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966028), c_Groups_Ozero__class_Ozero(_966028)), _966030) = _966030)], (4350 ^ _779203) ^ [_845182, _845184, _845186, _845188] : [-(c_Lazy__Sequence_Osmall__lazy_H(_845188, _845184) = c_Lazy__Sequence_Osmall__lazy_H(_845186, _845182)), _845188 = _845186, _845184 = _845182], (52477 ^ _779203) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (48022 ^ _779203) ^ [_1746802, _1746804, _1746806, _1746808, _1746810] : [-(_1746802 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1746804, _1746806, _1746808, _1746810), _1746802) = hAPP(c_Lazy__Sequence_Obind(_1746804, _1746806, hAPP(_1746808, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1746802), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1746804, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1746806)), _1746810), _1746802)))], (19818 ^ _779203) ^ [_1128739, _1128741, _1128743] : [class_Lattices_Oboolean__algebra(_1128739), 19821 ^ _779203 : [(19828 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128739), _1128743), _1128741)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128739), hAPP(c_Groups_Ouminus__class_Ouminus(_1128739), _1128741)), hAPP(c_Groups_Ouminus__class_Ouminus(_1128739), _1128743))))], (19822 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128739), hAPP(c_Groups_Ouminus__class_Ouminus(_1128739), _1128741)), hAPP(c_Groups_Ouminus__class_Ouminus(_1128739), _1128743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128739), _1128743), _1128741)))]]], (17294 ^ _779203) ^ [_1084277, _1084279] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084277), _1084279))), -(_1084277 = _1084279), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084279), _1084277)))], (28041 ^ _779203) ^ [_1274305, _1274307] : [28043 ^ _779203 : [(28046 ^ _779203) ^ [] : [hBOOL(hAPP(_1274307, 28042 ^ [_1274305, _1274307]))], (28044 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 28042 ^ [_1274305, _1274307]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1274305))))]], 28047 ^ _779203 : [(28048 ^ _779203) ^ [_1274458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1274458), _1274305)), -(hBOOL(hAPP(_1274307, _1274458)))]]], (50923 ^ _779203) ^ [_1810372, _1810374] : [50924 ^ _779203 : [(50927 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810374), _1810372))], (50925 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810372), _1810374)))]], -(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)))), _1810372, _1810374))], (18331 ^ _779203) ^ [_1102626, _1102628] : [class_Rings_Olinordered__semidom(_1102626), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102626), c_Groups_Ozero__class_Ozero(_1102626)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1102626), _1102628))))], (48963 ^ _779203) ^ [_1768201, _1768203, _1768205, _1768207] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1768201, tc_fun(_1768203, tc_HOL_Obool)), _1768205), _1768207) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1768203, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1768203, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768201, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1768203, tc_HOL_Obool)), c_HOL_OEx(_1768201)), hAPP(hAPP(c_COMBB(tc_fun(_1768201, tc_HOL_Obool), tc_fun(_1768201, tc_HOL_Obool), tc_fun(_1768203, tc_HOL_Obool)), hAPP(c_COMBS(_1768201, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1768201), c_fconj), hAPP(hAPP(c_COMBC(_1768201, tc_fun(_1768201, tc_HOL_Obool), tc_HOL_Obool), c_member(_1768201)), _1768205)))), hAPP(hAPP(c_COMBC(tc_fun(_1768203, tc_HOL_Obool), tc_fun(_1768201, tc_fun(_1768203, tc_HOL_Obool)), tc_fun(_1768201, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768203, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1768201, tc_fun(_1768203, tc_HOL_Obool)), tc_fun(_1768201, tc_HOL_Obool)), tc_fun(_1768203, tc_HOL_Obool)), c_COMBB(tc_fun(_1768203, tc_HOL_Obool), tc_HOL_Obool, _1768201)), c_fequal)), _1768207))))))], (45272 ^ _779203) ^ [_1687895, _1687897] : [-(c_Enum_Oenum__the(_1687895, _1687897) = c_HOL_OThe(_1687895, _1687897))], (31177 ^ _779203) ^ [_1337397, _1337399, _1337401, _1337403, _1337405, _1337407, _1337409] : [c_Big__Operators_Ocomm__monoid__big(_1337397, _1337399, _1337401, _1337403, _1337405), 31180 ^ _779203 : [(31187 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337399), _1337407))), -(hAPP(hAPP(_1337405, _1337409), _1337407) = _1337403)], (31181 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1337399), _1337407)), -(hAPP(hAPP(_1337405, _1337409), _1337407) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1337397, _1337399, _1337401), _1337409), _1337403), _1337407))]]], (12234 ^ _779203) ^ [_990393, _990395] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990393), _990395) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 12239 ^ _779203 : [(12242 ^ _779203) ^ [] : [-(_990395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12240 ^ _779203) ^ [] : [-(_990393 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 12243 ^ _779203 : [(12246 ^ _779203) ^ [] : [-(_990395 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12244 ^ _779203) ^ [] : [-(_990393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (48495 ^ _779203) ^ [_1757305, _1757307, _1757309, _1757311] : [48496 ^ _779203 : [(48499 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757305), _1757309), _1757311))], (48497 ^ _779203) ^ [] : [_1757307 = _1757311]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1757305), hAPP(hAPP(c_List_Olist_OCons(_1757305), _1757307), _1757309)), _1757311)))], (15482 ^ _779203) ^ [_1050664, _1050666, _1050668, _1050670] : [class_Orderings_Olinorder(_1050664), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050664), _1050666), _1050668)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050664), _1050670), _1050668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050664), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1050664), _1050666), _1050670)), _1050668)))], (17826 ^ _779203) ^ [_1093481, _1093483, _1093485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1093481)), _1093481 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093483), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1093481), _1093485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1093483)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1093485), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (17312 ^ _779203) ^ [_1084472, _1084474] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084472), _1084474))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084472), _1084474)), -(_1084472 = _1084474)], (20066 ^ _779203) ^ [_1133033, _1133035, _1133037] : [class_Groups_Oab__group__add(_1133033), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1133033), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1133033), _1133035), _1133037)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1133033), _1133037), _1133035))], (40923 ^ _779203) ^ [_1582724, _1582726, _1582728, _1582730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1582724, _1582726), tc_HOL_Obool)), _1582728), _1582730)), c_Relation_Osingle__valued(_1582724, _1582726, _1582730), -(c_Relation_Osingle__valued(_1582724, _1582726, _1582728))], (18800 ^ _779203) ^ [_1110548] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110548), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110548)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1110548)))], (22428 ^ _779203) ^ [_1174853, _1174855] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1174853), _1174855) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1174853, _1174855) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (47696 ^ _779203) ^ [_1740272, _1740274, _1740276] : [-(c_List_Olist__ex(_1740272, _1740274, _1740276)), 47697 ^ _779203 : [(47698 ^ _779203) ^ [_1740329] : [hBOOL(hAPP(hAPP(c_member(_1740272), _1740329), hAPP(c_List_Oset(_1740272), _1740276))), hBOOL(hAPP(_1740274, _1740329))]]], (52787 ^ _779203) ^ [] : [-(v_G = hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))], (40119 ^ _779203) ^ [_1562397, _1562399] : [c_Wellfounded_Owf(_1562397, _1562399), 40122 ^ _779203 : [(40123 ^ _779203) ^ [_1562529] : [40124 ^ _779203 : [(40125 ^ _779203) ^ [_1562634] : [hBOOL(hAPP(hAPP(c_member(_1562397), _1562634), _1562529))]], 40127 ^ _779203 : [(40130 ^ _779203) ^ [_1562756] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562397, _1562397)), hAPP(hAPP(c_Product__Type_OPair(_1562397, _1562397), _1562756), 40126 ^ [_1562397, _1562399, _1562529])), _1562399)), hBOOL(hAPP(hAPP(c_member(_1562397), _1562756), _1562529))], (40128 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562397), 40126 ^ [_1562397, _1562399, _1562529]), _1562529)))]]]]], (26510 ^ _779203) ^ [_1245551, _1245553, _1245555, _1245557] : [class_Groups_Ocomm__monoid__add(_1245551), 26513 ^ _779203 : [(26520 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1245553)), _1245555))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245551), _1245557), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1245555, hAPP(c_Nat_OSuc, _1245553))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245551), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245551), _1245557), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1245555, _1245553))), hAPP(_1245557, hAPP(c_Nat_OSuc, _1245553))))], (26514 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1245553)), _1245555)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245551), _1245557), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1245555, hAPP(c_Nat_OSuc, _1245553))) = c_Groups_Ozero__class_Ozero(_1245551))]]], (42455 ^ _779203) ^ [_1625406, _1625408] : [hBOOL(hAPP(c_List_Odistinct(_1625406), _1625408)), -(hAPP(c_Finite__Set_Ocard(_1625406), hAPP(c_List_Oset(_1625406), _1625408)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625406)), _1625408))], (48456 ^ _779203) ^ [_1756477] : [-(c_Lazy__Sequence_Oyieldn(_1756477) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1756477), _1756477, c_Lazy__Sequence_Oyield(_1756477)))], (22171 ^ _779203) ^ [_1170640, _1170642, _1170644] : [class_Divides_Osemiring__div(_1170640), -(c_Divides_Odiv__class_Omod(_1170640, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170640), _1170642), _1170644), _1170642) = c_Groups_Ozero__class_Ozero(_1170640))], (27728 ^ _779203) ^ [_1267845, _1267847, _1267849, _1267851, _1267853] : [class_Lattices_Olattice(_1267845), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267847, _1267845)), _1267849), _1267851), _1267853) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267845), hAPP(_1267849, _1267853)), hAPP(_1267851, _1267853)))], (29598 ^ _779203) ^ [_1304305, _1304307, _1304309] : [class_Lattices_Olattice(_1304305), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304305), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1304305), _1304307), _1304309)), _1304307)))], (38388 ^ _779203) ^ [_1519629, _1519631, _1519633, _1519635] : [hAPP(hAPP(c_Relation_Orel__comp(_1519629, _1519629, _1519629), _1519631), _1519633) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519629, _1519629), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1519629, _1519629, _1519629), _1519635), _1519633) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519629, _1519629), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1519629, _1519629, _1519629), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1519629, _1519629), tc_HOL_Obool)), _1519631), _1519635)), _1519633) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519629, _1519629), tc_HOL_Obool)))], (34326 ^ _779203) ^ [_1410345, _1410347, _1410349, _1410351, _1410353] : [-(_1410345 = c_Orderings_Obot__class_Obot(tc_fun(_1410347, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410347, tc_fun(_1410349, tc_HOL_Obool)), _1410345), hAPP(hAPP(c_COMBB(tc_fun(_1410349, tc_HOL_Obool), tc_fun(_1410349, tc_HOL_Obool), _1410347), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410349, tc_HOL_Obool)), _1410351)), _1410353)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410349, tc_HOL_Obool)), _1410351), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410347, tc_fun(_1410349, tc_HOL_Obool)), _1410345), _1410353)))], (39798 ^ _779203) ^ [_1554764, _1554766, _1554768, _1554770] : [c_Finite__Set_Ofolding(_1554764, _1554766, _1554768, _1554770), -(hAPP(_1554770, c_Orderings_Obot__class_Obot(tc_fun(_1554764, tc_HOL_Obool))) = c_Fun_Oid(_1554766))], (52645 ^ _779203) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (37351 ^ _779203) ^ [_1485665, _1485667] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1485665)), -(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)), _1485665))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1485667))))) = 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)), _1485665))), 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, _1485667))))))], (5286 ^ _779203) ^ [_860006, _860008, _860010, _860012, _860014, _860016, _860018, _860020, _860022, _860024] : [-(c_SetInterval_Oord_OatLeastLessThan(_860024, _860020, _860016, _860012, _860008) = c_SetInterval_Oord_OatLeastLessThan(_860022, _860018, _860014, _860010, _860006)), _860024 = _860022, _860020 = _860018, _860016 = _860014, _860012 = _860010, _860008 = _860006], (23747 ^ _779203) ^ [_1197187, _1197189] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197187, _1197189) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1197187 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1197189), 23750 ^ [_1197187, _1197189]))], (21733 ^ _779203) ^ [_1161720, _1161722] : [class_Int_Onumber__ring(_1161720), -(hAPP(c_Int_Onumber__class_Onumber__of(_1161720), c_Int_OBit0(_1161722)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161720), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1161720), c_Groups_Ozero__class_Ozero(_1161720)), hAPP(c_Int_Onumber__class_Onumber__of(_1161720), _1161722))), hAPP(c_Int_Onumber__class_Onumber__of(_1161720), _1161722)))], (45014 ^ _779203) ^ [_1681801, _1681803, _1681805, _1681807, _1681809] : [-(c_Enum_Oproduct(_1681801, _1681803, hAPP(hAPP(c_List_Olist_OCons(_1681801), _1681805), _1681807), _1681809) = hAPP(hAPP(c_List_Oappend(tc_prod(_1681801, _1681803)), hAPP(hAPP(c_List_Omap(_1681803, tc_prod(_1681801, _1681803)), hAPP(c_Product__Type_OPair(_1681801, _1681803), _1681805)), _1681809)), c_Enum_Oproduct(_1681801, _1681803, _1681807, _1681809)))], (39285 ^ _779203) ^ [_1542105, _1542107, _1542109, _1542111] : [-(hAPP(c_Set_OCollect(_1542105), hAPP(hAPP(c_COMBB(tc_fun(_1542107, tc_HOL_Obool), tc_HOL_Obool, _1542105), c_HOL_OAll(_1542107)), hAPP(hAPP(c_COMBB(tc_fun(_1542107, tc_HOL_Obool), tc_fun(_1542107, tc_HOL_Obool), _1542105), hAPP(c_COMBS(_1542107, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542107), c_fimplies), hAPP(hAPP(c_COMBC(_1542107, tc_fun(_1542107, tc_HOL_Obool), tc_HOL_Obool), c_member(_1542107)), _1542109)))), _1542111))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1542107, tc_fun(_1542105, tc_HOL_Obool)), _1542109), hAPP(hAPP(c_COMBB(tc_fun(_1542105, tc_HOL_Obool), tc_fun(_1542105, tc_HOL_Obool), _1542107), c_Set_OCollect(_1542105)), hAPP(c_COMBC(_1542105, _1542107, tc_HOL_Obool), _1542111))))], (10643 ^ _779203) ^ [_963418, _963420, _963422] : [class_Orderings_Olinorder(_963418), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963418, tc_HOL_Obool)), _963420), _963422)), -(_963420 = c_Orderings_Obot__class_Obot(tc_fun(_963418, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_963418), _963422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963418), c_Big__Operators_Olinorder__class_OMin(_963418, _963422)), c_Big__Operators_Olinorder__class_OMin(_963418, _963420))))], (44540 ^ _779203) ^ [_1671419, _1671421, _1671423, _1671425] : [c_Fun_Oinj__on(_1671419, _1671421, _1671423, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1671419, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1671419), tc_fun(_1671419, tc_HOL_Obool), c_List_Oset(_1671419)), _1671425))), -(c_Fun_Oinj__on(tc_List_Olist(_1671419), tc_List_Olist(_1671421), hAPP(c_List_Omap(_1671419, _1671421), _1671423), _1671425))], (52159 ^ _779203) ^ [_1831456, _1831458] : [class_Orderings_Opreorder(_1831456), -(class_Orderings_Opreorder(tc_fun(_1831458, _1831456)))], (43588 ^ _779203) ^ [_1650767, _1650769, _1650771, _1650773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650767), _1650769)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650771)), _1650773))), -(hAPP(hAPP(c_List_Onth(_1650771), hAPP(hAPP(c_List_Odrop(_1650771), _1650767), _1650773)), _1650769) = hAPP(hAPP(c_List_Onth(_1650771), _1650773), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1650767), _1650769)))], (52707 ^ _779203) ^ [_1837182] : [hBOOL(hAPP(c_fNot, _1837182)), hBOOL(_1837182)], (5406 ^ _779203) ^ [_861920, _861922] : [_861922 = _861920, -(c_Divides_Odiv__class_Odiv(_861922) = c_Divides_Odiv__class_Odiv(_861920))], (36832 ^ _779203) ^ [_1473304, _1473306, _1473308, _1473310] : [c_Fun_Oinj__on(_1473304, _1473306, _1473308, c_Orderings_Otop__class_Otop(tc_fun(_1473304, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1473304, _1473306, c_Orderings_Otop__class_Otop(tc_fun(_1473304, tc_HOL_Obool)), _1473308), hAPP(_1473308, _1473310)) = _1473310)], (46935 ^ _779203) ^ [_1723232, _1723234, _1723236] : [hBOOL(hAPP(c_List_Odistinct(_1723232), _1723234)), hBOOL(hAPP(hAPP(c_member(_1723232), _1723236), hAPP(c_List_Oset(_1723232), _1723234))), -(c_List_OtakeWhile(_1723232, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723232), c_fNot), hAPP(hAPP(c_COMBC(_1723232, _1723232, tc_HOL_Obool), c_fequal), _1723236)), hAPP(c_List_Orev(_1723232), _1723234)) = hAPP(c_List_Orev(_1723232), hAPP(c_List_Otl(_1723232), c_List_OdropWhile(_1723232, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723232), c_fNot), hAPP(hAPP(c_COMBC(_1723232, _1723232, tc_HOL_Obool), c_fequal), _1723236)), _1723234))))], (28322 ^ _779203) ^ [_1280040, _1280042] : [class_Orderings_Olinorder(_1280040), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1280040, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1280040), _1280042)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1280040), _1280042))], (49572 ^ _779203) ^ [_1780913, _1780915, _1780917] : [c_Fun_Oinj__on(_1780913, _1780915, _1780917, c_Orderings_Otop__class_Otop(tc_fun(_1780913, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780915, _1780913, _1780913, c_Hilbert__Choice_Oinv__into(_1780913, _1780915, c_Orderings_Otop__class_Otop(tc_fun(_1780913, tc_HOL_Obool)), _1780917)), _1780917) = c_Fun_Oid(_1780913))], (18379 ^ _779203) ^ [_1103434, _1103436, _1103438] : [class_Rings_Olinordered__semidom(_1103434), 18382 ^ _779203 : [(18389 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103436), _1103438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103434), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103434), _1103436)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103434), _1103438))))], (18383 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103434), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103434), _1103436)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103434), _1103438))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103436), _1103438)))]]], (21009 ^ _779203) ^ [_1149668] : [_1149668 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1149668) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35521 ^ _779203) ^ [_1443709] : [-(c_Wellfounded_Omeasure(_1443709) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1443709), c_Wellfounded_Oless__than))], (21991 ^ _779203) ^ [_1166899, _1166901, _1166903, _1166905] : [class_Divides_Osemiring__div(_1166899), -(c_Divides_Odiv__class_Omod(_1166899, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166899), _1166901), _1166903), _1166905) = c_Divides_Odiv__class_Omod(_1166899, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166899), c_Divides_Odiv__class_Omod(_1166899, _1166901, _1166905)), c_Divides_Odiv__class_Omod(_1166899, _1166903, _1166905)), _1166905))], (4040 ^ _779203) ^ [_840309, _840311, _840313, _840315] : [-(c_Lazy__Sequence_Ohb__single(_840315, _840311) = c_Lazy__Sequence_Ohb__single(_840313, _840309)), _840315 = _840313, _840311 = _840309], (19204 ^ _779203) ^ [_1117577] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1117577)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1117577))], (3040 ^ _779203) ^ [_824331, _824333, _824335, _824337] : [-(c_List_Olistrel1(_824337, _824333) = c_List_Olistrel1(_824335, _824331)), _824337 = _824335, _824333 = _824331], (38226 ^ _779203) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (4248 ^ _779203) ^ [_843467, _843469, _843471, _843473, _843475, _843477, _843479, _843481, _843483, _843485] : [-(c_Predicate_Opred__comp(_843485, _843481, _843477, _843473, _843469) = c_Predicate_Opred__comp(_843483, _843479, _843475, _843471, _843467)), _843485 = _843483, _843481 = _843479, _843477 = _843475, _843473 = _843471, _843469 = _843467], (41743 ^ _779203) ^ [_1606694, _1606696, _1606698, _1606700] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606694)), hAPP(hAPP(c_List_Olist_OCons(_1606694), _1606696), _1606698)), c_List_Olists(_1606694, _1606700)))), hBOOL(hAPP(hAPP(c_member(_1606694), _1606696), _1606700)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606694)), _1606698), c_List_Olists(_1606694, _1606700)))], (44564 ^ _779203) ^ [_1671977, _1671979, _1671981, _1671983] : [class_Groups_Ocomm__monoid__add(_1671977), hBOOL(hAPP(c_List_Odistinct(_1671979), _1671981)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1671977), hAPP(hAPP(c_List_Omap(_1671979, _1671977), _1671983), _1671981)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1671979, _1671977), _1671983), hAPP(c_List_Oset(_1671979), _1671981)))], (25512 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (26852 ^ _779203) ^ [_1252248, _1252250, _1252252] : [class_Orderings_Olinorder(_1252248), 26855 ^ _779203 : [(26862 ^ _779203) ^ [] : [_1252250 = _1252252, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1252248), _1252250) = hAPP(c_SetInterval_Oord__class_OlessThan(_1252248), _1252252))], (26856 ^ _779203) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1252248), _1252250) = hAPP(c_SetInterval_Oord__class_OlessThan(_1252248), _1252252), -(_1252250 = _1252252)]]], (25096 ^ _779203) ^ [_1221500, _1221502, _1221504] : [class_Power_Opower(_1221500), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1221500), _1221502), hAPP(c_Nat_OSuc, _1221504)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221500), _1221502), hAPP(hAPP(c_Power_Opower__class_Opower(_1221500), _1221502), _1221504)))], (46847 ^ _779203) ^ [_1721467, _1721469, _1721471, _1721473, _1721475] : [-(hAPP(hAPP(c_List_Ozip(_1721467, _1721469), _1721471), c_List_OtakeWhile(_1721469, _1721473, _1721475)) = c_List_OtakeWhile(tc_prod(_1721467, _1721469), hAPP(c_Fun_Ocomp(_1721469, tc_HOL_Obool, tc_prod(_1721467, _1721469), _1721473), c_Product__Type_Osnd(_1721467, _1721469)), hAPP(hAPP(c_List_Ozip(_1721467, _1721469), _1721471), _1721475)))], (52601 ^ _779203) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (29934 ^ _779203) ^ [_1311927, _1311929, _1311931] : [class_Orderings_Oorder(_1311927), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311927, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1311927, _1311929), _1311931)), hAPP(c_SetInterval_Oord__class_OatLeast(_1311927), _1311931)) = c_Orderings_Obot__class_Obot(tc_fun(_1311927, tc_HOL_Obool)))], (52469 ^ _779203) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (23287 ^ _779203) ^ [_1188882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1188882)), -(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, _1188882))))], (38451 ^ _779203) ^ [_1521300, _1521302, _1521304, _1521306] : [38452 ^ _779203 : [(38453 ^ _779203) ^ [_1521375] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1521304, _1521300)), hAPP(hAPP(c_Product__Type_OPair(_1521304, _1521300), _1521375), _1521302)), _1521306))]], -(hBOOL(hAPP(hAPP(c_member(_1521300), _1521302), hAPP(c_Relation_ORange(_1521304, _1521300), _1521306))))], (5677 ^ _779203) ^ [_868793, _868795, _868797, _868799, _868801, _868803] : [_868793 = hAPP(_868795, _868797), hBOOL(hAPP(hAPP(c_member(_868799), _868797), _868801)), -(hBOOL(hAPP(hAPP(c_member(_868803), _868793), hAPP(c_Set_Oimage(_868799, _868803, _868795), _868801))))], (46714 ^ _779203) ^ [_1718546, _1718548] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1718546), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1718546))), c_List_Otranspose(_1718546, _1718548)))))], (32315 ^ _779203) ^ [_1364030, _1364032] : [hAPP(c_Nat_OSuc, _1364030) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1364032), -(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(_1364032))), 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)), _1364030))))))], (9602 ^ _779203) ^ [_943268, _943270] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943268), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943268), _943270)))))], (7807 ^ _779203) ^ [_907627, _907629, _907631] : [class_Orderings_Oorder(_907627), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907627), _907629), _907631)), -(_907631 = _907629), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907627), _907629), _907631)))], (43921 ^ _779203) ^ [_1657937, _1657939, _1657941] : [class_Lattices_Olattice(_1657937), -(c_Big__Operators_Olattice__class_OSup__fin(_1657937, hAPP(c_List_Oset(_1657937), hAPP(hAPP(c_List_Olist_OCons(_1657937), _1657939), _1657941))) = hAPP(c_List_Ofoldl(_1657937, _1657937, c_Lattices_Osemilattice__sup__class_Osup(_1657937), _1657939), _1657941))], (35425 ^ _779203) ^ [_1441219, _1441221] : [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)), _1441219), _1441221)), 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)), _1441219), 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)), _1441221), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (43957 ^ _779203) ^ [_1658723, _1658725, _1658727, _1658729] : [class_Complete__Lattice_Ocomplete__lattice(_1658723), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1658725, _1658723), hAPP(c_List_Oset(_1658725), _1658727)), _1658729) = hAPP(c_List_Ofoldl(_1658723, _1658725, hAPP(c_COMBC(_1658725, _1658723, _1658723), hAPP(hAPP(c_COMBB(_1658723, tc_fun(_1658723, _1658723), _1658725), c_Lattices_Osemilattice__sup__class_Osup(_1658723)), _1658729)), c_Orderings_Obot__class_Obot(_1658723)), _1658727))], (36894 ^ _779203) ^ [_1474460, _1474462, _1474464, _1474466, _1474468, _1474470] : [c_Typedef_Otype__definition(_1474460, _1474462, _1474464, _1474466, _1474468), -(hAPP(_1474466, hAPP(_1474464, _1474470)) = _1474470)], (32327 ^ _779203) ^ [_1364288] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1364288))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1364288)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19296 ^ _779203) ^ [_1119143, _1119145, _1119147] : [class_Groups_Oordered__ab__group__add__abs(_1119143), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119143), hAPP(c_Groups_Oabs__class_Oabs(_1119143), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1119143), hAPP(c_Groups_Oabs__class_Oabs(_1119143), _1119145)), hAPP(c_Groups_Oabs__class_Oabs(_1119143), _1119147)))), hAPP(c_Groups_Oabs__class_Oabs(_1119143), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1119143), _1119145), _1119147)))))], (3488 ^ _779203) ^ [_831275, _831277, _831279, _831281, _831283, _831285, _831287, _831289] : [-(c_List_Olinorder__class_Osort__key(_831289, _831285, _831281, _831277) = c_List_Olinorder__class_Osort__key(_831287, _831283, _831279, _831275)), _831289 = _831287, _831285 = _831283, _831281 = _831279, _831277 = _831275], (40438 ^ _779203) ^ [_1570864, _1570866] : [-(c_Relation_Orefl__on(_1570864, c_Orderings_Otop__class_Otop(tc_fun(_1570864, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1570864, _1570866)))], (34941 ^ _779203) ^ [_1428100, _1428102, _1428104] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428100, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1428100, tc_HOL_Obool), _1428102)), _1428104) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1428100, tc_HOL_Obool), tc_fun(_1428100, tc_HOL_Obool)), _1428102), hAPP(hAPP(c_COMBC(tc_fun(_1428100, tc_HOL_Obool), tc_fun(_1428100, tc_HOL_Obool), tc_fun(_1428100, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428100, tc_HOL_Obool))), _1428104)))], (1970 ^ _779203) ^ [_807582, _807584] : [_807584 = _807582, -(v_mgt(_807584) = v_mgt(_807582))], (9411 ^ _779203) ^ [_939629, _939631, _939633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939629), _939631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939631), _939633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939629), _939633)))], (8689 ^ _779203) ^ [_925631, _925633, _925635, _925637] : [class_Groups_Ocancel__semigroup__add(_925631), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925631), _925633), _925635) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925631), _925637), _925635), -(_925633 = _925637)], (30519 ^ _779203) ^ [_1323988, _1323990, _1323992] : [class_Orderings_Olinorder(_1323988), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323988), _1323990)), -(_1323990 = c_Orderings_Obot__class_Obot(tc_fun(_1323988, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323988), _1323992)), -(_1323992 = c_Orderings_Obot__class_Obot(tc_fun(_1323988, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323988, tc_HOL_Obool)), _1323990), _1323992) = c_Orderings_Obot__class_Obot(tc_fun(_1323988, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1323988, c_Orderings_Oord__class_Omax(_1323988), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1323988, tc_HOL_Obool)), _1323990), _1323992)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1323988), c_Big__Operators_Olattice_OSup__fin(_1323988, c_Orderings_Oord__class_Omax(_1323988), _1323990)), c_Big__Operators_Olattice_OSup__fin(_1323988, c_Orderings_Oord__class_Omax(_1323988), _1323992)))], (52589 ^ _779203) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (17530 ^ _779203) ^ [_1088256, _1088258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1088256), _1088258)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1088256), _1088258)))], (47509 ^ _779203) ^ [_1736576, _1736578, _1736580, _1736582, _1736584] : [-(hAPP(hAPP(c_List_Olist_OCons(_1736576), _1736578), _1736580) = hAPP(c_List_Ofilter(_1736576, _1736582), _1736584)), 47510 ^ _779203 : [(47511 ^ _779203) ^ [_1736704, _1736706] : [_1736584 = hAPP(hAPP(c_List_Oappend(_1736576), _1736706), hAPP(hAPP(c_List_Olist_OCons(_1736576), _1736578), _1736704)), 47517 ^ _779203 : [(47520 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1736582, 47516 ^ [_1736576, _1736578, _1736580, _1736582, _1736584, _1736704, _1736706])))], (47518 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1736576), 47516 ^ [_1736576, _1736578, _1736580, _1736582, _1736584, _1736704, _1736706]), hAPP(c_List_Oset(_1736576), _1736706))))]], hBOOL(hAPP(_1736582, _1736578)), _1736580 = hAPP(c_List_Ofilter(_1736576, _1736582), _1736704)]]], (42277 ^ _779203) ^ [_1621306, _1621308, _1621310, _1621312] : [-(_1621306 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621308)), _1621310)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1621308, hAPP(hAPP(c_List_Olist__update(_1621308, _1621310), _1621306), _1621312)) = hAPP(hAPP(c_List_Olist__update(_1621308, c_List_Obutlast(_1621308, _1621310)), _1621306), _1621312))], (35535 ^ _779203) ^ [_1444071, _1444073] : [-(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), _1444071), _1444073)), 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), _1444073), _1444071)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (36534 ^ _779203) ^ [_1466597, _1466599, _1466601, _1466603, _1466605] : [c_Fun_Oinj__on(_1466597, _1466599, _1466601, c_Orderings_Otop__class_Otop(tc_fun(_1466597, tc_HOL_Obool))), 36537 ^ _779203 : [(36544 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466597, tc_HOL_Obool)), _1466603), _1466605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466599, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466597, _1466599, _1466601), _1466603)), hAPP(c_Set_Oimage(_1466597, _1466599, _1466601), _1466605))))], (36538 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466599, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466597, _1466599, _1466601), _1466603)), hAPP(c_Set_Oimage(_1466597, _1466599, _1466601), _1466605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466597, tc_HOL_Obool)), _1466603), _1466605)))]]], (37525 ^ _779203) ^ [_1489871, _1489873, _1489875, _1489877] : [37526 ^ _779203 : [(37529 ^ _779203) ^ [] : [_1489877 = c_Orderings_Obot__class_Obot(tc_fun(_1489873, tc_HOL_Obool))], (37527 ^ _779203) ^ [] : [_1489875 = c_Orderings_Obot__class_Obot(tc_fun(_1489871, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1489871, _1489873), _1489875), hAPP(c_COMBK(tc_fun(_1489873, tc_HOL_Obool), _1489871), _1489877)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489871, _1489873), tc_HOL_Obool)))], (41051 ^ _779203) ^ [_1585927, _1585929] : [-(hAPP(hAPP(c_Nat_Ocompow(_1585927, _1585927), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1585929) = c_Fun_Oid(_1585927))], (27024 ^ _779203) ^ [_1255159, _1255161] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1255159), _1255161))))], (37939 ^ _779203) ^ [_1502827, _1502829, _1502831, _1502833, _1502835, _1502837] : [class_Groups_Ocomm__monoid__add(_1502827), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502829), _1502831)), 37949 ^ _779203 : [(37952 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1502833), hAPP(_1502835, 37948 ^ [_1502827, _1502829, _1502831, _1502833, _1502835, _1502837])))], (37950 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502829), 37948 ^ [_1502827, _1502829, _1502831, _1502833, _1502835, _1502837]), _1502831)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1502829, _1502827), hAPP(hAPP(c_COMBS(_1502829, tc_fun(_1502833, tc_HOL_Obool), _1502827), hAPP(hAPP(c_COMBB(tc_fun(_1502833, _1502827), tc_fun(tc_fun(_1502833, tc_HOL_Obool), _1502827), _1502829), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1502833, _1502827)), _1502837)), _1502835)), _1502831) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1502829, _1502833), _1502827), hAPP(c_Product__Type_Oprod_Oprod__case(_1502829, _1502833, _1502827), _1502837)), hAPP(hAPP(c_Product__Type_OSigma(_1502829, _1502833), _1502831), _1502835)))], (43536 ^ _779203) ^ [_1649599, _1649601, _1649603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649599)), _1649601)), _1649603)), -(hAPP(hAPP(c_List_Odrop(_1649599), _1649603), _1649601) = c_List_Olist_ONil(_1649599))], (45689 ^ _779203) ^ [_1697299, _1697301, _1697303, _1697305, _1697307] : [-(hAPP(c_List_Ofilter(_1697299, _1697301), hAPP(hAPP(c_List_Omap(_1697303, _1697299), _1697305), _1697307)) = hAPP(hAPP(c_List_Omap(_1697303, _1697299), _1697305), hAPP(c_List_Ofilter(_1697303, hAPP(c_Fun_Ocomp(_1697299, tc_HOL_Obool, _1697303, _1697301), _1697305)), _1697307)))], (5761 ^ _779203) ^ [_870326, _870328, _870330, _870332] : [_870326 = _870328, hBOOL(hAPP(hAPP(c_member(_870330), _870328), _870332)), -(hBOOL(hAPP(hAPP(c_member(_870330), _870326), _870332)))], (42071 ^ _779203) ^ [_1615385, _1615387, _1615389, _1615391] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1615385), tc_List_Olist(_1615385))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1615385), tc_List_Olist(_1615385)), _1615387), _1615389)), c_List_Olistrel(_1615385, _1615391))), 42074 ^ _779203 : [(42077 ^ _779203) ^ [_1615721] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1615385, _1615385)), _1615721), hAPP(c_List_Oset(tc_prod(_1615385, _1615385)), hAPP(hAPP(c_List_Ozip(_1615385, _1615385), _1615387), _1615389)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1615385, _1615385, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1615385, tc_fun(tc_prod(_1615385, _1615385), tc_HOL_Obool), tc_fun(_1615385, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615385, tc_fun(tc_fun(tc_prod(_1615385, _1615385), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1615385, _1615385), tc_HOL_Obool), tc_fun(_1615385, tc_HOL_Obool)), _1615385), c_COMBC(_1615385, tc_fun(tc_prod(_1615385, _1615385), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1615385, tc_prod(_1615385, _1615385)), tc_fun(_1615385, tc_fun(tc_fun(tc_prod(_1615385, _1615385), tc_HOL_Obool), tc_HOL_Obool)), _1615385), hAPP(c_COMBB(tc_prod(_1615385, _1615385), tc_fun(tc_fun(tc_prod(_1615385, _1615385), tc_HOL_Obool), tc_HOL_Obool), _1615385), c_member(tc_prod(_1615385, _1615385)))), c_Product__Type_OPair(_1615385, _1615385)))), _1615391)), _1615721)))], (42075 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615385)), _1615387) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1615385)), _1615389))]]], (12426 ^ _779203) ^ [_993500, _993502, _993504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993500), _993502)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993504), _993500)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993504), _993502))))], (9661 ^ _779203) ^ [_944273, _944275, _944277] : [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, _944273)), _944275)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _944273)), _944277))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944275), _944277)))], (37507 ^ _779203) ^ [_1489372, _1489374, _1489376, _1489378] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1489372, _1489374)), hAPP(hAPP(c_Product__Type_OSigma(_1489372, _1489374), _1489376), hAPP(c_COMBK(tc_fun(_1489374, tc_HOL_Obool), _1489372), _1489378))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1489372), _1489376)), hAPP(c_Finite__Set_Ocard(_1489374), _1489378)))], (16042 ^ _779203) ^ [_1060786, _1060788, _1060790, _1060792] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060786), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060786), _1060788), _1060790)), hAPP(c_Int_Onumber__class_Onumber__of(_1060786), _1060792)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060786), _1060788), hAPP(c_Int_Onumber__class_Onumber__of(_1060786), _1060792))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060786), _1060790), hAPP(c_Int_Onumber__class_Onumber__of(_1060786), _1060792)))), class_Int_Onumber(_1060786), class_Rings_Osemiring(_1060786)], (38384 ^ _779203) ^ [_1519393, _1519395, _1519397, _1519399, _1519401, _1519403, _1519405] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1519393, _1519395, _1519397), _1519399), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519401, tc_fun(tc_prod(_1519395, _1519397), tc_HOL_Obool)), _1519403), _1519405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519401, tc_fun(tc_prod(_1519393, _1519397), tc_HOL_Obool)), _1519403), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1519395, _1519397), tc_HOL_Obool), tc_fun(tc_prod(_1519393, _1519397), tc_HOL_Obool), _1519401), hAPP(c_Relation_Orel__comp(_1519393, _1519395, _1519397), _1519399)), _1519405)))], (35183 ^ _779203) ^ [_1434394, _1434396, _1434398, _1434400, _1434402, _1434404, _1434406] : [35185 ^ _779203 : [(35188 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1434402, 35184 ^ [_1434394, _1434396, _1434398, _1434400, _1434402, _1434404, _1434406]), _1434404), _1434406))], (35186 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1434394), 35184 ^ [_1434394, _1434396, _1434398, _1434400, _1434402, _1434404, _1434406]), _1434400)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1434394, tc_fun(_1434396, tc_fun(_1434398, tc_HOL_Obool))), _1434400), _1434402), _1434404), _1434406)))], (2960 ^ _779203) ^ [_823029, _823031, _823033, _823035, _823037, _823039, _823041, _823043, _823045, _823047, _823049, _823051] : [-(c_Product__Type_Omap__pair(_823051, _823047, _823043, _823039, _823035, _823031) = c_Product__Type_Omap__pair(_823049, _823045, _823041, _823037, _823033, _823029)), _823051 = _823049, _823047 = _823045, _823043 = _823041, _823039 = _823037, _823035 = _823033, _823031 = _823029], (25844 ^ _779203) ^ [_1233830, _1233832] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1233830, _1233832))))], (39383 ^ _779203) ^ [_1545173, _1545175, _1545177, _1545179, _1545181, _1545183] : [39386 ^ _779203 : [(39389 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1545179), _1545181), hAPP(hAPP(_1545183, 39384 ^ [_1545173, _1545175, _1545177, _1545179, _1545181, _1545183]), 39385 ^ [_1545173, _1545175, _1545177, _1545179, _1545181, _1545183])))], (39387 ^ _779203) ^ [] : [-(_1545173 = hAPP(hAPP(c_Product__Type_OPair(_1545175, _1545177), 39384 ^ [_1545173, _1545175, _1545177, _1545179, _1545181, _1545183]), 39385 ^ [_1545173, _1545175, _1545177, _1545179, _1545181, _1545183]))]], -(hBOOL(hAPP(hAPP(c_member(_1545179), _1545181), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1545175, _1545177, tc_fun(_1545179, tc_HOL_Obool)), _1545183), _1545173))))], (25108 ^ _779203) ^ [_1221728, _1221730] : [class_Power_Opower(_1221728), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1221728), _1221730), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1221728))], (39548 ^ _779203) ^ [_1548903, _1548905, _1548907] : [hBOOL(hAPP(_1548903, _1548905)), -(hBOOL(hAPP(_1548903, c_Hilbert__Choice_OEps(_1548907, _1548903))))], (34795 ^ _779203) ^ [_1424338, _1424340, _1424342] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424338, tc_fun(_1424340, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1424338, tc_HOL_Obool))), _1424342) = c_Orderings_Otop__class_Otop(tc_fun(_1424340, tc_HOL_Obool)))], (26170 ^ _779203) ^ [_1239511, _1239513, _1239515] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1239511, tc_HOL_Obool)), _1239513), hAPP(c_Set_OPow(_1239511), _1239515))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239511, tc_HOL_Obool)), _1239513), _1239515)))], (2530 ^ _779203) ^ [_816400, _816402, _816404, _816406] : [-(c_Divides_Odivmod__nat__rel(_816406, _816402) = c_Divides_Odivmod__nat__rel(_816404, _816400)), _816406 = _816404, _816402 = _816400], (18435 ^ _779203) ^ [_1104374, _1104376, _1104378] : [class_Rings_Osemiring__1(_1104374), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104374), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1104376), _1104378)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1104374), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104374), _1104376)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104374), _1104378)))], (45570 ^ _779203) ^ [_1693848, _1693850] : [class_Orderings_Olinorder(_1693848), -(c_List_Olinorder__class_Osort__key(_1693848, _1693848, c_COMBI(_1693848), _1693850) = hAPP(c_List_Ofoldl(tc_List_Olist(_1693848), _1693848, hAPP(c_COMBC(_1693848, tc_List_Olist(_1693848), tc_List_Olist(_1693848)), c_List_Olinorder__class_Oinsort__key(_1693848, _1693848, c_COMBI(_1693848))), c_List_Olist_ONil(_1693848)), _1693850))], (24544 ^ _779203) ^ [_1211564, _1211566] : [class_Rings_Olinordered__idom(_1211564), 24547 ^ _779203 : [(24554 ^ _779203) ^ [] : [-(_1211566 = c_Groups_Ozero__class_Ozero(_1211564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211564), c_Groups_Ozero__class_Ozero(_1211564)), hAPP(hAPP(c_Power_Opower__class_Opower(_1211564), _1211566), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (24548 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211564), c_Groups_Ozero__class_Ozero(_1211564)), hAPP(hAPP(c_Power_Opower__class_Opower(_1211564), _1211566), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1211566 = c_Groups_Ozero__class_Ozero(_1211564)]]], (5845 ^ _779203) ^ [_871669, _871671, _871673, _871675] : [-(hAPP(hAPP(c_Set_Oinsert(_871669), _871671), hAPP(hAPP(c_Set_Oinsert(_871669), _871673), _871675)) = hAPP(hAPP(c_Set_Oinsert(_871669), _871673), hAPP(hAPP(c_Set_Oinsert(_871669), _871671), _871675)))], (29012 ^ _779203) ^ [_1292344, _1292346, _1292348] : [class_Lattices_Olattice(_1292344), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292344), _1292346)), 29019 ^ _779203 : [(29026 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1292344, tc_HOL_Obool)), _1292346), hAPP(hAPP(c_Set_Oinsert(_1292344), _1292348), c_Orderings_Obot__class_Obot(tc_fun(_1292344, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1292344, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1292344, hAPP(hAPP(c_Set_Oinsert(_1292344), _1292348), _1292346)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292344), _1292348), c_Big__Operators_Olattice__class_OSup__fin(_1292344, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1292344, tc_HOL_Obool)), _1292346), hAPP(hAPP(c_Set_Oinsert(_1292344), _1292348), c_Orderings_Obot__class_Obot(tc_fun(_1292344, tc_HOL_Obool)))))))], (29020 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1292344, tc_HOL_Obool)), _1292346), hAPP(hAPP(c_Set_Oinsert(_1292344), _1292348), c_Orderings_Obot__class_Obot(tc_fun(_1292344, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1292344, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1292344, hAPP(hAPP(c_Set_Oinsert(_1292344), _1292348), _1292346)) = _1292348)]]], (19668 ^ _779203) ^ [_1126210, _1126212] : [-(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, _1126210)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1126212))))], (38782 ^ _779203) ^ [_1530217, _1530219, _1530221, _1530223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530217, _1530219), tc_HOL_Obool)), _1530221), _1530223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1530217, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1530217, _1530219), _1530221)), hAPP(c_Relation_ODomain(_1530217, _1530219), _1530223))))], (2716 ^ _779203) ^ [_819285, _819287, _819289, _819291, _819293, _819295, _819297, _819299] : [-(c_Product__Type_Oapfst(_819299, _819295, _819291, _819287) = c_Product__Type_Oapfst(_819297, _819293, _819289, _819285)), _819299 = _819297, _819295 = _819293, _819291 = _819289, _819287 = _819285], (6905 ^ _779203) ^ [_892057, _892059, _892061, _892063] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_892057, _892059, _892061), _892063), c_Orderings_Obot__class_Obot(tc_fun(_892057, tc_HOL_Obool))) = _892063)], (34067 ^ _779203) ^ [_1403843, _1403845, _1403847, _1403849, _1403851, _1403853, _1403855] : [hBOOL(hAPP(_1403843, _1403845)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1403847, _1403847)), hAPP(hAPP(c_Product__Type_OPair(_1403847, _1403847), _1403849), _1403851)), hAPP(_1403853, _1403845))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1403855, _1403847), tc_prod(_1403855, _1403847))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1403855, _1403847), tc_prod(_1403855, _1403847)), hAPP(hAPP(c_Product__Type_OPair(_1403855, _1403847), _1403845), _1403849)), hAPP(hAPP(c_Product__Type_OPair(_1403855, _1403847), _1403845), _1403851))), c_Recdef_Osame__fst(_1403855, _1403847, _1403843, _1403853))))], (42245 ^ _779203) ^ [_1620616, _1620618, _1620620] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1620616), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1620618))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1620618), _1620616), _1620620)) = 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), _1620618)), _1620620)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1620618), _1620616)))], (48010 ^ _779203) ^ [_1746607, _1746609, _1746611, _1746613, _1746615] : [-(_1746607 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1746609, _1746611, _1746613, _1746615), _1746607) = c_Lazy__Sequence_Ohb__bind(_1746609, _1746611, hAPP(_1746613, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1746607), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1746609, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1746611))), _1746615), _1746607)))], (28328 ^ _779203) ^ [_1280151, _1280153, _1280155, _1280157, _1280159] : [c_Finite__Set_Ofolding__one__idem(_1280151, _1280153, _1280155), hBOOL(hAPP(c_Finite__Set_Ofinite(_1280151), _1280157)), -(_1280157 = c_Orderings_Obot__class_Obot(tc_fun(_1280151, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1280151), _1280159)), -(_1280159 = c_Orderings_Obot__class_Obot(tc_fun(_1280151, tc_HOL_Obool))), -(hAPP(_1280155, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1280151, tc_HOL_Obool)), _1280157), _1280159)) = hAPP(hAPP(_1280153, hAPP(_1280155, _1280157)), hAPP(_1280155, _1280159)))], (42906 ^ _779203) ^ [_1634446, _1634448, _1634450, _1634452, _1634454] : [-(hAPP(hAPP(c_List_Ozip(_1634446, _1634448), hAPP(hAPP(c_List_Olist_OCons(_1634446), _1634450), _1634452)), _1634454) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1634446, _1634448)), _1634448, c_List_Olist_ONil(tc_prod(_1634446, _1634448)), hAPP(hAPP(c_COMBC(_1634448, tc_fun(tc_List_Olist(_1634448), tc_List_Olist(tc_prod(_1634446, _1634448))), tc_fun(tc_List_Olist(_1634448), tc_List_Olist(tc_prod(_1634446, _1634448)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1634446, _1634448)), tc_List_Olist(tc_prod(_1634446, _1634448))), tc_fun(tc_fun(tc_List_Olist(_1634448), tc_List_Olist(tc_prod(_1634446, _1634448))), tc_fun(tc_List_Olist(_1634448), tc_List_Olist(tc_prod(_1634446, _1634448)))), _1634448), c_COMBB(tc_List_Olist(tc_prod(_1634446, _1634448)), tc_List_Olist(tc_prod(_1634446, _1634448)), tc_List_Olist(_1634448))), hAPP(hAPP(c_COMBB(tc_prod(_1634446, _1634448), tc_fun(tc_List_Olist(tc_prod(_1634446, _1634448)), tc_List_Olist(tc_prod(_1634446, _1634448))), _1634448), c_List_Olist_OCons(tc_prod(_1634446, _1634448))), hAPP(c_Product__Type_OPair(_1634446, _1634448), _1634450)))), hAPP(c_List_Ozip(_1634446, _1634448), _1634452))), _1634454))], (23741 ^ _779203) ^ [_1197073, _1197075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1197073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197075, _1197073)), _1197073)))], (44135 ^ _779203) ^ [_1662443, _1662445, _1662447, _1662449, _1662451] : [class_Orderings_Olinorder(_1662443), hBOOL(hAPP(hAPP(c_member(_1662443), hAPP(_1662445, _1662447)), hAPP(c_Set_Oimage(_1662449, _1662443, _1662445), hAPP(c_List_Oset(_1662449), _1662451)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1662449, _1662443, _1662445, _1662447, _1662451) = _1662451)], (17428 ^ _779203) ^ [_1086536, _1086538] : [17429 ^ _779203 : [(17432 ^ _779203) ^ [] : [_1086536 = _1086538], (17430 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086536), _1086538))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086536), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086538), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (45260 ^ _779203) ^ [_1687435] : [-(c_Enum_Osublists(_1687435, c_List_Olist_ONil(_1687435)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687435)), c_List_Olist_ONil(_1687435)), c_List_Olist_ONil(tc_List_Olist(_1687435))))], (43247 ^ _779203) ^ [_1642097, _1642099] : [-(hAPP(hAPP(c_List_Oappend(_1642097), c_List_Olist_ONil(_1642097)), _1642099) = _1642099)], (6058 ^ _779203) ^ [_875636, _875638, _875640, _875642, _875644] : [hAPP(hAPP(c_Set_Oinsert(_875636), _875638), hAPP(hAPP(c_Set_Oinsert(_875636), _875640), c_Orderings_Obot__class_Obot(tc_fun(_875636, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_875636), _875642), hAPP(hAPP(c_Set_Oinsert(_875636), _875644), c_Orderings_Obot__class_Obot(tc_fun(_875636, tc_HOL_Obool)))), 6063 ^ _779203 : [(6066 ^ _779203) ^ [] : [-(_875640 = _875644)], (6064 ^ _779203) ^ [] : [-(_875638 = _875642)]], 6067 ^ _779203 : [(6070 ^ _779203) ^ [] : [-(_875640 = _875642)], (6068 ^ _779203) ^ [] : [-(_875638 = _875644)]]], (44682 ^ _779203) ^ [_1674423, _1674425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1674423)), hAPP(c_Code__Numeral_Oof__nat, _1674425))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1674423), _1674425)))], (18524 ^ _779203) ^ [_1105921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1105921), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105921) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44777 ^ _779203) ^ [_1676579] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1676579)) = _1676579)], (4086 ^ _779203) ^ [_841060, _841062] : [_841062 = _841060, -(c_New__Random__Sequence_Opos__single(_841062) = c_New__Random__Sequence_Opos__single(_841060))], (4560 ^ _779203) ^ [_848493, _848495] : [_848495 = _848493, -(c_DSequence_Ounion(_848495) = c_DSequence_Ounion(_848493))], (35545 ^ _779203) ^ [_1444350] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1444350) = 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, _1444350)), 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))))))))], (45893 ^ _779203) ^ [_1702786, _1702788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702786), _1702788)), -(c_List_Oupt(_1702786, _1702788) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702786), c_List_Oupt(hAPP(c_Nat_OSuc, _1702786), _1702788)))], (12058 ^ _779203) ^ [_987592, _987594, _987596] : [class_Rings_Olinordered__ring__strict(_987592), 12061 ^ _779203 : [(12070 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987592), _987594), _987594)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987592), _987596), _987596)) = c_Groups_Ozero__class_Ozero(_987592)), _987594 = c_Groups_Ozero__class_Ozero(_987592), _987596 = c_Groups_Ozero__class_Ozero(_987592)], (12062 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987592), _987594), _987594)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987592), _987596), _987596)) = c_Groups_Ozero__class_Ozero(_987592), 12065 ^ _779203 : [(12068 ^ _779203) ^ [] : [-(_987596 = c_Groups_Ozero__class_Ozero(_987592))], (12066 ^ _779203) ^ [] : [-(_987594 = c_Groups_Ozero__class_Ozero(_987592))]]]]], (51317 ^ _779203) ^ [_1817031, _1817033] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817031), _1817033)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817033), _1817031)), -(_1817031 = _1817033)], (36990 ^ _779203) ^ [_1476743, _1476745, _1476747, _1476749] : [-(c_Wellfounded_Omax__extp(_1476743, _1476745, _1476747, _1476749)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476743), _1476747)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1476743), _1476749)), -(_1476749 = c_Orderings_Obot__class_Obot(tc_fun(_1476743, tc_HOL_Obool))), 37004 ^ _779203 : [(37007 ^ _779203) ^ [_1477088] : [hBOOL(hAPP(hAPP(c_member(_1476743), _1477088), _1476749)), hBOOL(hAPP(hAPP(_1476745, 37003 ^ [_1476743, _1476745, _1476747, _1476749]), _1477088))], (37005 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476743), 37003 ^ [_1476743, _1476745, _1476747, _1476749]), _1476747)))]]], (49638 ^ _779203) ^ [_1782357, _1782359, _1782361, _1782363, _1782365, _1782367] : [c_Fun_Oinj__on(_1782357, _1782359, _1782361, _1782363), hBOOL(hAPP(hAPP(c_member(_1782357), _1782365), _1782363)), hAPP(_1782361, _1782365) = _1782367, -(hAPP(c_Hilbert__Choice_Oinv__into(_1782357, _1782359, _1782363, _1782361), _1782367) = _1782365)], (3814 ^ _779203) ^ [_836404, _836406, _836408, _836410, _836412, _836414, _836416, _836418, _836420, _836422, _836424, _836426, _836428, _836430] : [-(c_New__Random__Sequence_Oneg__decr__bind(_836430, _836426, _836422, _836418, _836414, _836410, _836406) = c_New__Random__Sequence_Oneg__decr__bind(_836428, _836424, _836420, _836416, _836412, _836408, _836404)), _836430 = _836428, _836426 = _836424, _836422 = _836420, _836418 = _836416, _836414 = _836412, _836410 = _836408, _836406 = _836404], (26482 ^ _779203) ^ [_1244956, _1244958] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1244956, _1244958))))], (28438 ^ _779203) ^ [_1282194, _1282196, _1282198] : [class_Orderings_Olinorder(_1282194), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282194), _1282196)), -(_1282196 = c_Orderings_Obot__class_Obot(tc_fun(_1282194, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282194), _1282198)), -(_1282198 = c_Orderings_Obot__class_Obot(tc_fun(_1282194, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1282194, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282194, tc_HOL_Obool)), _1282196), _1282198)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282194), c_Big__Operators_Olinorder__class_OMax(_1282194, _1282196)), c_Big__Operators_Olinorder__class_OMax(_1282194, _1282198)))], (41417 ^ _779203) ^ [_1596754, _1596756, _1596758, _1596760, _1596762, _1596764] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596754), tc_List_Olist(_1596754))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596754), tc_List_Olist(_1596754)), hAPP(hAPP(c_List_Olist_OCons(_1596754), _1596756), _1596758)), hAPP(hAPP(c_List_Olist_OCons(_1596754), _1596760), _1596762))), c_List_Olexord(_1596754, _1596764))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1596754, _1596754)), hAPP(hAPP(c_Product__Type_OPair(_1596754, _1596754), _1596756), _1596760)), _1596764))), 41424 ^ _779203 : [(41427 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1596754), tc_List_Olist(_1596754))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1596754), tc_List_Olist(_1596754)), _1596758), _1596762)), c_List_Olexord(_1596754, _1596764))))], (41425 ^ _779203) ^ [] : [-(_1596756 = _1596760)]]], (21865 ^ _779203) ^ [_1164235, _1164237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1164235), 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)))), _1164237))), 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)))), _1164235)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1164237), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1164235))], (45620 ^ _779203) ^ [_1695570, _1695572, _1695574, _1695576] : [-(c_List_Otranspose(_1695570, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695570)), hAPP(hAPP(c_List_Olist_OCons(_1695570), _1695572), _1695574)), _1695576)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695570)), hAPP(hAPP(c_List_Olist_OCons(_1695570), _1695572), c_List_Oconcat(_1695570, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695570), tc_List_Olist(_1695570)), c_List_Olist_Olist__case(tc_List_Olist(_1695570), _1695570, c_List_Olist_ONil(_1695570), hAPP(hAPP(c_COMBB(tc_List_Olist(_1695570), tc_fun(tc_List_Olist(_1695570), tc_List_Olist(_1695570)), _1695570), c_COMBK(tc_List_Olist(_1695570), tc_List_Olist(_1695570))), hAPP(hAPP(c_COMBC(_1695570, tc_List_Olist(_1695570), tc_List_Olist(_1695570)), c_List_Olist_OCons(_1695570)), c_List_Olist_ONil(_1695570))))), _1695576)))), c_List_Otranspose(_1695570, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1695570)), _1695574), c_List_Oconcat(tc_List_Olist(_1695570), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695570), tc_List_Olist(tc_List_Olist(_1695570))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1695570)), _1695570, c_List_Olist_ONil(tc_List_Olist(_1695570)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1695570), tc_List_Olist(tc_List_Olist(_1695570))), _1695570), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695570), tc_List_Olist(tc_List_Olist(_1695570)), tc_List_Olist(tc_List_Olist(_1695570))), c_List_Olist_OCons(tc_List_Olist(_1695570))), c_List_Olist_ONil(tc_List_Olist(_1695570)))))), _1695576))))))], (37717 ^ _779203) ^ [_1495301, _1495303, _1495305, _1495307, _1495309, _1495311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1495301, _1495303), tc_HOL_Obool)), _1495305), hAPP(hAPP(c_Product__Type_OSigma(_1495301, _1495303), _1495307), hAPP(c_COMBK(tc_fun(_1495303, tc_HOL_Obool), _1495301), _1495309)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495303, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1495301, _1495303, _1495305), _1495311)), _1495309)))], (38947 ^ _779203) ^ [_1533992, _1533994, _1533996, _1533998] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533992, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1533992, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1533992, _1533994), _1533996)), hAPP(c_Relation_ODomain(_1533992, _1533994), _1533998))), hAPP(c_Relation_ODomain(_1533992, _1533994), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1533992, _1533994), tc_HOL_Obool)), _1533996), _1533998)))))], (25664 ^ _779203) ^ [_1231054] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1231054), hAPP(c_Int_Onumber__class_Onumber__of(_1231054), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1231054)), class_Int_Onumber__ring(_1231054), class_Rings_Olinordered__idom(_1231054)], (29110 ^ _779203) ^ [_1294439, _1294441, _1294443, _1294445] : [hBOOL(hAPP(hAPP(c_member(_1294439), _1294441), _1294443)), hBOOL(hAPP(hAPP(c_member(_1294439), _1294441), _1294445)), -(hBOOL(hAPP(hAPP(c_member(_1294439), _1294441), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1294439, tc_HOL_Obool)), _1294443), _1294445))))], (28762 ^ _779203) ^ [_1287841, _1287843, _1287845, _1287847] : [hBOOL(hAPP(_1287841, _1287843)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287845, tc_HOL_Obool)), _1287841), _1287847), _1287843)))], (2592 ^ _779203) ^ [_817377, _817379] : [_817379 = _817377, -(c_Wellfounded_Omeasure(_817379) = c_Wellfounded_Omeasure(_817377))], (930 ^ _779203) ^ [_793130, _793132, _793134, _793136, _793138, _793140] : [-(c_Relation_Orefl__on(_793138, _793134, _793130)), c_Relation_Orefl__on(_793140, _793136, _793132), _793140 = _793138, _793136 = _793134, _793132 = _793130], (18959 ^ _779203) ^ [_1113205] : [-(c_Int_Opred(_1113205) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1113205), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (41213 ^ _779203) ^ [_1590555, _1590557] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590555, _1590555)), _1590557), c_Relation_OId(_1590555))), -(_1590557 = hAPP(hAPP(c_Product__Type_OPair(_1590555, _1590555), 41216 ^ [_1590555, _1590557]), 41216 ^ [_1590555, _1590557]))], (34605 ^ _779203) ^ [_1418604, _1418606, _1418608, _1418610, _1418612] : [-(hBOOL(hAPP(hAPP(c_member(_1418604), _1418606), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418608, tc_fun(_1418604, tc_HOL_Obool)), _1418610), _1418612)))), 34606 ^ _779203 : [(34607 ^ _779203) ^ [_1418686] : [hBOOL(hAPP(hAPP(c_member(_1418608), _1418686), _1418610)), hBOOL(hAPP(hAPP(c_member(_1418604), _1418606), hAPP(_1418612, _1418686)))]]], (13169 ^ _779203) ^ [_1006909, _1006911, _1006913, _1006915, _1006917] : [class_Groups_Ocomm__monoid__mult(_1006909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006911), _1006913)), -(hBOOL(hAPP(hAPP(c_member(_1006911), _1006915), _1006913))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1006911, _1006909), _1006917), hAPP(hAPP(c_Set_Oinsert(_1006911), _1006915), _1006913)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1006909), hAPP(_1006917, _1006915)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1006911, _1006909), _1006917), _1006913)))], (32920 ^ _779203) ^ [_1382275, _1382277, _1382279, _1382281, _1382283, _1382285] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1382275, _1382277, _1382279), _1382281), hAPP(hAPP(c_Product__Type_OPair(_1382275, _1382277), _1382283), _1382285)) = hAPP(hAPP(_1382281, _1382283), _1382285))], (17402 ^ _779203) ^ [_1086103, _1086105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086103), _1086105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086103), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1086105)))], (8210 ^ _779203) ^ [_915546, _915548, _915550, _915552] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_915546, _915548, _915550, _915552, c_Orderings_Obot__class_Obot(tc_fun(_915546, tc_HOL_Obool))), _915552)))], (18496 ^ _779203) ^ [_1105417, _1105419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1105417), _1105419)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105419)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1105417)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1105419), _1105417)))], (5478 ^ _779203) ^ [_862970, _862972] : [_862972 = _862970, -(tc_List_Olist(_862972) = tc_List_Olist(_862970))], (29270 ^ _779203) ^ [_1297939, _1297941, _1297943] : [class_Lattices_Osemilattice__inf(_1297939), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297939), _1297941), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297939), _1297941), _1297943)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297939), _1297941), _1297943))], (34462 ^ _779203) ^ [_1414428, _1414430] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1414428, tc_HOL_Obool), _1414430) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1414428, tc_HOL_Obool), tc_fun(_1414428, tc_HOL_Obool)), _1414430), c_COMBI(tc_fun(_1414428, tc_HOL_Obool))))], (48816 ^ _779203) ^ [_1765049] : [-(c_Relation_Otrans(_1765049, c_Relation_OId(_1765049)))], (33193 ^ _779203) ^ [_1387126, _1387128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1387126), _1387128)), -(c_Divides_Odivmod__nat(_1387126, _1387128) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1387126))], (8669 ^ _779203) ^ [_925297, _925299, _925301, _925303] : [class_Groups_Ocancel__semigroup__add(_925297), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925297), _925299), _925301) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925297), _925299), _925303), -(_925301 = _925303)], (51337 ^ _779203) ^ [_1817329, _1817331, _1817333] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817329), _1817331)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817331), _1817333)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817329), _1817333)))], (30601 ^ _779203) ^ [_1325700, _1325702, _1325704] : [30603 ^ _779203 : [(30606 ^ _779203) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325700, tc_HOL_Obool)), 30602 ^ [_1325700, _1325702, _1325704]), _1325704) = c_Orderings_Obot__class_Obot(tc_fun(_1325700, tc_HOL_Obool))], (30604 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1325700, tc_HOL_Obool)), 30602 ^ [_1325700, _1325702, _1325704]), _1325702)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325700, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1325700, tc_HOL_Obool), _1325702)), _1325704) = c_Orderings_Obot__class_Obot(tc_fun(_1325700, tc_HOL_Obool)))], (11784 ^ _779203) ^ [_982528, _982530, _982532, _982534] : [class_Rings_Olinordered__ring__strict(_982528), 11787 ^ _779203 : [(11802 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982528), _982530), _982532)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982528), _982530), _982534)))), 11803 ^ _779203 : [(11810 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982528), _982530), c_Groups_Ozero__class_Ozero(_982528))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982528), _982534), _982532))], (11804 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982528), c_Groups_Ozero__class_Ozero(_982528)), _982530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982528), _982532), _982534))]]], (11788 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982528), _982530), _982532)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_982528), _982530), _982534))), 11793 ^ _779203 : [(11796 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982528), _982532), _982534)))], (11794 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982528), c_Groups_Ozero__class_Ozero(_982528)), _982530)))]], 11797 ^ _779203 : [(11800 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982528), _982534), _982532)))], (11798 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_982528), _982530), c_Groups_Ozero__class_Ozero(_982528))))]]]]], (22003 ^ _779203) ^ [_1167177, _1167179, _1167181, _1167183] : [class_Divides_Osemiring__div(_1167177), -(c_Divides_Odiv__class_Omod(_1167177, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167177), c_Divides_Odiv__class_Omod(_1167177, _1167179, _1167181)), _1167183), _1167181) = c_Divides_Odiv__class_Omod(_1167177, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167177), _1167179), _1167183), _1167181))], (11147 ^ _779203) ^ [_971080, _971082, _971084] : [class_Groups_Ocomm__monoid__mult(_971080), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_971082, _971080), _971084), c_Orderings_Obot__class_Obot(tc_fun(_971082, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_971080))], (15996 ^ _779203) ^ [_1059955, _1059957] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1059955)), hAPP(c_Nat_OSuc, _1059957)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1059955), _1059957)))], (35131 ^ _779203) ^ [_1432978, _1432980, _1432982, _1432984, _1432986, _1432988] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432978, tc_fun(_1432980, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432982, tc_fun(_1432978, tc_HOL_Obool)), _1432984), _1432986)), _1432988) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432982, tc_fun(_1432980, tc_HOL_Obool)), _1432984), hAPP(hAPP(c_COMBC(_1432982, tc_fun(_1432978, tc_fun(_1432980, tc_HOL_Obool)), tc_fun(_1432980, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432978, tc_HOL_Obool), tc_fun(tc_fun(_1432978, tc_fun(_1432980, tc_HOL_Obool)), tc_fun(_1432980, tc_HOL_Obool)), _1432982), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432978, tc_fun(_1432980, tc_HOL_Obool))), _1432986)), _1432988)))], (3068 ^ _779203) ^ [_824781, _824783, _824785, _824787] : [-(c_Nat_Ocompow(_824787, _824783) = c_Nat_Ocompow(_824785, _824781)), _824787 = _824785, _824783 = _824781], (49863 ^ _779203) ^ [_1787635, _1787637, _1787639, _1787641, _1787643] : [hBOOL(hAPP(_1787635, hAPP(hAPP(c_Product__Type_OPair(_1787637, _1787639), _1787641), _1787643))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1787637, _1787639, tc_HOL_Obool, _1787635), _1787641), _1787643)))], (29874 ^ _779203) ^ [_1310553, _1310555, _1310557] : [class_Orderings_Oorder(_1310553), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310553, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1310553), _1310555)), c_SetInterval_Oord__class_OatLeastAtMost(_1310553, _1310555, _1310557)) = c_Orderings_Obot__class_Obot(tc_fun(_1310553, tc_HOL_Obool)))], (5176 ^ _779203) ^ [_858171, _858173, _858175, _858177] : [-(c_Lazy__Sequence_Oflat(_858177, _858173) = c_Lazy__Sequence_Oflat(_858175, _858171)), _858177 = _858175, _858173 = _858171], (46865 ^ _779203) ^ [_1721886, _1721888, _1721890, _1721892] : [-(hBOOL(hAPP(_1721886, _1721888))), -(c_List_OtakeWhile(_1721890, _1721886, hAPP(hAPP(c_List_Olist_OCons(_1721890), _1721888), _1721892)) = c_List_Olist_ONil(_1721890))], (27350 ^ _779203) ^ [_1260901, _1260903, _1260905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260901, tc_HOL_Obool)), _1260903), _1260905)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260901, tc_HOL_Obool)), _1260905), _1260903) = _1260905)], (25070 ^ _779203) ^ [_1221030, _1221032, _1221034, _1221036] : [class_Rings_Olinordered__semidom(_1221030), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1221030), c_Groups_Oone__class_Oone(_1221030)), _1221032)), 25077 ^ _779203 : [(25084 ^ _779203) ^ [] : [_1221034 = _1221036, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1221030), _1221032), _1221034) = hAPP(hAPP(c_Power_Opower__class_Opower(_1221030), _1221032), _1221036))], (25078 ^ _779203) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1221030), _1221032), _1221034) = hAPP(hAPP(c_Power_Opower__class_Opower(_1221030), _1221032), _1221036), -(_1221034 = _1221036)]]], (40356 ^ _779203) ^ [_1568807, _1568809, _1568811, _1568813] : [40357 ^ _779203 : [(40360 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568807, _1568807)), _1568809), c_Transitive__Closure_Ortrancl(_1568807, _1568813)))], (40358 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1568807, _1568807)), _1568809), c_Transitive__Closure_Ortrancl(_1568807, _1568811)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568807, _1568807)), _1568809), c_Transitive__Closure_Ortrancl(_1568807, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568807, _1568807), tc_HOL_Obool)), _1568811), _1568813)))))], (26030 ^ _779203) ^ [_1236966] : [class_Int_Onumber__ring(_1236966), -(hAPP(c_Int_Oring__1__class_Oof__int(_1236966), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1236966), c_Int_OMin))], (48176 ^ _779203) ^ [_1750938, _1750940, _1750942] : [-(_1750938 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1750940, c_List_Oreplicate(_1750940, _1750938, _1750942)) = _1750942)], (42285 ^ _779203) ^ [_1621437, _1621439, _1621441, _1621443, _1621445, _1621447, _1621449] : [-(hAPP(hAPP(c_List_Ozip(_1621437, _1621439), hAPP(hAPP(c_List_Olist__update(_1621437, _1621441), _1621443), _1621445)), hAPP(hAPP(c_List_Olist__update(_1621439, _1621447), _1621443), _1621449)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1621437, _1621439), hAPP(hAPP(c_List_Ozip(_1621437, _1621439), _1621441), _1621447)), _1621443), hAPP(hAPP(c_Product__Type_OPair(_1621437, _1621439), _1621445), _1621449)))], (30700 ^ _779203) ^ [_1327739, _1327741] : [class_Complete__Lattice_Ocomplete__lattice(_1327739), -(c_Complete__Lattice_OSup__class_OSup(_1327739, hAPP(hAPP(c_Set_Oinsert(_1327739), _1327741), c_Orderings_Obot__class_Obot(tc_fun(_1327739, tc_HOL_Obool)))) = _1327741)], (39654 ^ _779203) ^ [_1551362, _1551364, _1551366, _1551368, _1551370, _1551372, _1551374] : [class_Groups_Oab__semigroup__mult(_1551362), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551364), _1551366)), c_Fun_Oinj__on(_1551364, _1551368, _1551370, _1551366), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1551362, _1551368, c_Groups_Otimes__class_Otimes(_1551362)), _1551372), _1551374), hAPP(c_Set_Oimage(_1551364, _1551368, _1551370), _1551366)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1551362, _1551364, c_Groups_Otimes__class_Otimes(_1551362)), hAPP(c_Fun_Ocomp(_1551368, _1551362, _1551364, _1551372), _1551370)), _1551374), _1551366))], (52583 ^ _779203) ^ [_1835838, _1835840] : [-(class_Nat_Osize(tc_prod(_1835838, _1835840)))], (35768 ^ _779203) ^ [_1449863, _1449865, _1449867, _1449869, _1449871, _1449873, _1449875] : [c_Equiv__Relations_Oequiv(_1449863, _1449865, _1449867), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449863, tc_HOL_Obool)), _1449869), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449863), _1449865), _1449867))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449863, tc_HOL_Obool)), _1449871), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449863), _1449865), _1449867))), hBOOL(hAPP(hAPP(c_member(_1449863), _1449873), _1449869)), hBOOL(hAPP(hAPP(c_member(_1449863), _1449875), _1449871)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1449863, _1449863)), hAPP(hAPP(c_Product__Type_OPair(_1449863, _1449863), _1449873), _1449875)), _1449867)), -(_1449869 = _1449871)], (52491 ^ _779203) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (39268 ^ _779203) ^ [_1541790, _1541792, _1541794] : [39270 ^ _779203 : [(39273 ^ _779203) ^ [] : [hBOOL(hAPP(_1541792, 39269 ^ [_1541790, _1541792, _1541794]))], (39271 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1541790), 39269 ^ [_1541790, _1541792, _1541794]), _1541794)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1541790, _1541792), _1541794)))], (18453 ^ _779203) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (52227 ^ _779203) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (50150 ^ _779203) ^ [_1793290, _1793292, _1793294, _1793296, _1793298, _1793300, _1793302] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1793290, tc_HOL_Obool)), _1793292), _1793294) = c_Orderings_Obot__class_Obot(tc_fun(_1793290, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1793296, tc_HOL_Obool)), _1793298), _1793300) = c_Orderings_Obot__class_Obot(tc_fun(_1793296, tc_HOL_Obool)), c_Fun_Obij__betw(_1793290, _1793296, _1793302, _1793292, _1793298), c_Fun_Obij__betw(_1793290, _1793296, _1793302, _1793294, _1793300), -(c_Fun_Obij__betw(_1793290, _1793296, _1793302, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793290, tc_HOL_Obool)), _1793292), _1793294), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793296, tc_HOL_Obool)), _1793298), _1793300)))], (46130 ^ _779203) ^ [_1707199, _1707201, _1707203] : [class_Orderings_Olinorder(_1707199), 46133 ^ _779203 : [(46140 ^ _779203) ^ [] : [c_List_Olinorder__class_Osorted(_1707199, _1707203), -(c_List_Olinorder__class_Osorted(_1707199, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1707199, _1707199, c_COMBI(_1707199)), _1707201), _1707203)))], (46134 ^ _779203) ^ [] : [c_List_Olinorder__class_Osorted(_1707199, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1707199, _1707199, c_COMBI(_1707199)), _1707201), _1707203)), -(c_List_Olinorder__class_Osorted(_1707199, _1707203))]]], (45362 ^ _779203) ^ [_1689784, _1689786] : [hBOOL(hAPP(c_List_Odistinct(_1689784), _1689786)), -(c_List_Oremdups(_1689784, _1689786) = _1689786)], (32607 ^ _779203) ^ [_1371225, _1371227] : [class_Rings_Oring__1(_1371225), 32610 ^ _779203 : [(32617 ^ _779203) ^ [] : [-(_1371227 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32620 ^ _779203 : [(32627 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371227), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1371225), _1371227) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1371225), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1371225, _1371225)), tc_fun(tc_Int_Oint, _1371225)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1371225, _1371225), _1371225), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1371225, _1371225)), tc_fun(tc_Int_Oint, _1371225)), tc_Int_Oint), c_COMBB(tc_fun(_1371225, _1371225), _1371225, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1371225, tc_fun(tc_fun(_1371225, _1371225), _1371225), tc_Int_Oint), c_HOL_OLet(_1371225, _1371225)), c_Int_Oring__1__class_Oof__int(_1371225)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1371225, _1371225), tc_fun(_1371225, _1371225)), hAPP(hAPP(c_COMBB(tc_fun(_1371225, tc_fun(_1371225, _1371225)), tc_fun(tc_fun(_1371225, _1371225), tc_fun(_1371225, _1371225)), tc_Int_Oint), c_COMBS(_1371225, _1371225, _1371225)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1371225, _1371225), tc_fun(_1371225, tc_fun(_1371225, _1371225))), hAPP(hAPP(c_COMBB(tc_fun(_1371225, tc_fun(_1371225, _1371225)), tc_fun(tc_fun(_1371225, _1371225), tc_fun(_1371225, tc_fun(_1371225, _1371225))), tc_Int_Oint), c_COMBB(_1371225, tc_fun(_1371225, _1371225), _1371225)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1371225, tc_fun(_1371225, _1371225)), tc_Int_Oint), c_If(_1371225)), 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(_1371225, _1371225, _1371225), c_Groups_Oplus__class_Oplus(_1371225)), c_COMBI(_1371225))))), hAPP(hAPP(c_COMBC(_1371225, _1371225, _1371225), hAPP(hAPP(c_COMBB(_1371225, tc_fun(_1371225, _1371225), _1371225), c_Groups_Oplus__class_Oplus(_1371225)), hAPP(hAPP(c_COMBS(_1371225, _1371225, _1371225), c_Groups_Oplus__class_Oplus(_1371225)), c_COMBI(_1371225)))), c_Groups_Oone__class_Oone(_1371225))))), c_Divides_Odivmod__int(_1371227, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (32621 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371227), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1371225), _1371227) = hAPP(c_Groups_Ouminus__class_Ouminus(_1371225), hAPP(c_Int_Oring__1__class_Oof__int(_1371225), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1371227))))]]], (32611 ^ _779203) ^ [] : [_1371227 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1371225), _1371227) = c_Groups_Ozero__class_Ozero(_1371225))]]], (5466 ^ _779203) ^ [_862800, _862802] : [_862802 = _862800, -(c_Rings_Odvd__class_Odvd(_862802) = c_Rings_Odvd__class_Odvd(_862800))], (24285 ^ _779203) ^ [_1207211, _1207213] : [class_Rings_Ocomm__semiring__1(_1207211), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1207211), _1207213), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1207211))], (4436 ^ _779203) ^ [_846515, _846517, _846519, _846521] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846521, _846517) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_846519, _846515)), _846521 = _846519, _846517 = _846515], (38535 ^ _779203) ^ [_1525221, _1525223, _1525225, _1525227, _1525229, _1525231, _1525233] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1525221, _1525223, _1525225, _1525227, _1525229), _1525231), _1525233)), 38539 ^ _779203 : [(38542 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1525229, 38538 ^ [_1525221, _1525223, _1525225, _1525227, _1525229, _1525231, _1525233]), _1525233)))], (38540 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1525227, _1525231), 38538 ^ [_1525221, _1525223, _1525225, _1525227, _1525229, _1525231, _1525233])))]]], (2608 ^ _779203) ^ [_817611, _817613, _817615, _817617, _817619, _817621] : [-(c_Wellfounded_Omlex__prod(_817621, _817617, _817613) = c_Wellfounded_Omlex__prod(_817619, _817615, _817611)), _817621 = _817619, _817617 = _817615, _817613 = _817611], (42832 ^ _779203) ^ [_1632852] : [-(c_List_Olists(_1632852, c_Orderings_Obot__class_Obot(tc_fun(_1632852, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1632852)), c_List_Olist_ONil(_1632852)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1632852), tc_HOL_Obool))))], (37599 ^ _779203) ^ [_1492136, _1492138, _1492140] : [-(hBOOL(hAPP(_1492136, _1492138))), -(hAPP(c_Set_OCollect(_1492140), hAPP(hAPP(c_COMBS(_1492140, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1492140), c_fconj), hAPP(hAPP(c_COMBC(_1492140, _1492140, tc_HOL_Obool), c_fequal), _1492138))), _1492136)) = c_Orderings_Obot__class_Obot(tc_fun(_1492140, tc_HOL_Obool)))], (2172 ^ _779203) ^ [_810717, _810719, _810721, _810723, _810725, _810727, _810729, _810731, _810733, _810735] : [-(c_Nitpick_Opair__box_Opair__box__rec(_810735, _810731, _810727, _810723, _810719) = c_Nitpick_Opair__box_Opair__box__rec(_810733, _810729, _810725, _810721, _810717)), _810735 = _810733, _810731 = _810729, _810727 = _810725, _810723 = _810721, _810719 = _810717], (24538 ^ _779203) ^ [_1211454, _1211456] : [class_Rings_Olinordered__idom(_1211454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1211454), hAPP(hAPP(c_Power_Opower__class_Opower(_1211454), _1211456), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1211454)))], (32487 ^ _779203) ^ [_1368152, _1368154] : [-(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), _1368152)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1368154), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1368152))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7241 ^ _779203) ^ [_899512, _899514, _899516] : [class_Orderings_Olinorder(_899512), 7244 ^ _779203 : [(7245 ^ _779203) ^ [] : [-(_899514 = _899516), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899512), _899514), _899516))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899512), _899516), _899514)))], (7255 ^ _779203) ^ [] : [7256 ^ _779203 : [(7259 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899512), _899516), _899514))], (7257 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899512), _899514), _899516))]], _899514 = _899516]]], (45730 ^ _779203) ^ [_1698124, _1698126, _1698128, _1698130] : [-(hBOOL(hAPP(_1698124, _1698126))), -(hAPP(c_List_OremoveAll(_1698128, _1698126), hAPP(c_List_Ofilter(_1698128, _1698124), _1698130)) = hAPP(c_List_Ofilter(_1698128, _1698124), _1698130))], (28316 ^ _779203) ^ [_1279929, _1279931] : [class_Orderings_Olinorder(_1279929), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1279929, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1279929), _1279931)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1279929), _1279931))], (28384 ^ _779203) ^ [_1281233, _1281235, _1281237, _1281239] : [class_Groups_Ocomm__monoid__add(_1281233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1281235), _1281237)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1281233), _1281239), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1281235), _1281237)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1281233), hAPP(_1281239, _1281235)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1281233), _1281239), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1281235)), _1281237))))], (32581 ^ _779203) ^ [_1370499, _1370501] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1370499), hAPP(c_Nat_OSuc, _1370501)) = 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), _1370499), _1370501)))], (24458 ^ _779203) ^ [_1210004, _1210006] : [class_Rings_Ocomm__semiring__1(_1210004), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210004), _1210006), _1210006) = hAPP(hAPP(c_Power_Opower__class_Opower(_1210004), _1210006), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (6455 ^ _779203) ^ [_883378, _883380, _883382] : [class_Orderings_Oorder(_883378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883378), _883380), _883382)), 6462 ^ _779203 : [(6469 ^ _779203) ^ [] : [_883382 = _883380, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883378), _883382), _883380)))], (6463 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883378), _883382), _883380)), -(_883382 = _883380)]]], (41260 ^ _779203) ^ [_1591859, _1591861, _1591863] : [-(c_Product__Type_Ointernal__split(_1591859, _1591861, _1591863) = c_Product__Type_Oprod_Oprod__case(_1591859, _1591861, _1591863))], (28132 ^ _779203) ^ [_1276251, _1276253] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1276251), _1276253) = 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)), _1276251)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1276253))))], (41587 ^ _779203) ^ [_1602020, _1602022, _1602024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602020, _1602020), tc_HOL_Obool)), _1602022), _1602024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1602020), tc_List_Olist(_1602020)), tc_HOL_Obool)), c_List_Olistrel(_1602020, _1602022)), c_List_Olistrel(_1602020, _1602024))))], (19494 ^ _779203) ^ [_1122945] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122945))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1122945)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (40099 ^ _779203) ^ [_1561919, _1561921, _1561923, _1561925] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1561919, _1561921, _1561923, tc_prod(_1561921, _1561923)), _1561925), c_Product__Type_OPair(_1561921, _1561923)) = _1561925)], (41327 ^ _779203) ^ [_1593269, _1593271, _1593273, _1593275, _1593277] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1593269), tc_List_Olist(_1593269))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1593269), tc_List_Olist(_1593269)), _1593271), _1593273)), hAPP(c_List_Olexn(_1593269, _1593275), _1593277))), 41330 ^ _779203 : [(41333 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593269)), _1593273) = _1593277)], (41331 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593269)), _1593271) = _1593277)]]], (9123 ^ _779203) ^ [_934502, _934504, _934506, _934508, _934510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _934502), _934504)), 9126 ^ _779203 : [(9133 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _934508), 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), _934504), _934502)), _934506)), _934510))), -(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), _934502), _934506)), _934508)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _934504), _934506)), _934510))))], (9127 ^ _779203) ^ [] : [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), _934502), _934506)), _934508)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _934504), _934506)), _934510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _934508), 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), _934504), _934502)), _934506)), _934510))))]]], (35600 ^ _779203) ^ [_1445813, _1445815, _1445817] : [-(hAPP(c_Relation_OField(_1445813), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1445813, _1445813), tc_HOL_Obool)), _1445815), _1445817)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445813, tc_HOL_Obool)), hAPP(c_Relation_OField(_1445813), _1445815)), hAPP(c_Relation_OField(_1445813), _1445817)))], (35053 ^ _779203) ^ [_1430956, _1430958, _1430960, _1430962, _1430964] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1430956, tc_fun(_1430958, tc_HOL_Obool)), _1430960), hAPP(hAPP(c_COMBS(_1430956, tc_fun(_1430958, tc_HOL_Obool), tc_fun(_1430958, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1430958, tc_HOL_Obool), tc_fun(tc_fun(_1430958, tc_HOL_Obool), tc_fun(_1430958, tc_HOL_Obool)), _1430956), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430958, tc_HOL_Obool))), _1430962)), _1430964)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1430958, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1430958, tc_HOL_Obool), hAPP(c_Set_Oimage(_1430956, tc_fun(_1430958, tc_HOL_Obool), _1430962), _1430960))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1430958, tc_HOL_Obool), hAPP(c_Set_Oimage(_1430956, tc_fun(_1430958, tc_HOL_Obool), _1430964), _1430960))))], (44327 ^ _779203) ^ [_1666345, _1666347, _1666349, _1666351] : [c_List_Olist_ONil(_1666345) = hAPP(hAPP(c_List_Omap(_1666347, _1666345), _1666349), _1666351), -(_1666351 = c_List_Olist_ONil(_1666347))], (34456 ^ _779203) ^ [_1414190, _1414192, _1414194, _1414196, _1414198, _1414200] : [-(hAPP(c_Set_Oimage(_1414190, _1414192, _1414194), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414196, tc_fun(_1414190, tc_HOL_Obool)), _1414198), _1414200)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414196, tc_fun(_1414192, tc_HOL_Obool)), _1414198), hAPP(hAPP(c_COMBB(tc_fun(_1414190, tc_HOL_Obool), tc_fun(_1414192, tc_HOL_Obool), _1414196), c_Set_Oimage(_1414190, _1414192, _1414194)), _1414200)))], (18792 ^ _779203) ^ [] : [-(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))))], (40933 ^ _779203) ^ [_1582891, _1582893, _1582895] : [c_Wellfounded_Owf(_1582891, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582891, _1582891), tc_HOL_Obool), _1582893), _1582895)), -(c_Wellfounded_Owf(_1582891, _1582895))], (37094 ^ _779203) ^ [_1479103, _1479105, _1479107] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1479103), _1479105), _1479107) = c_Nitpick_OAbs__Frac(_1479103, c_Nitpick_Onorm__frac(_1479105, _1479107)))], (48286 ^ _779203) ^ [_1752939, _1752941, _1752943] : [c_List_Olist_ONil(_1752939) = c_List_Oreplicate(_1752939, _1752941, _1752943), -(_1752941 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50500 ^ _779203) ^ [_1802519] : [-(c_Lazy__Sequence_Oflat(_1802519, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1802519))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1802519))], (42776 ^ _779203) ^ [_1631674, _1631676] : [-(c_List_Osublist(_1631674, _1631676, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1631674))], (40312 ^ _779203) ^ [_1567747, _1567749, _1567751] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567747, _1567747)), _1567749), _1567751)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567747, _1567747)), _1567749), c_Transitive__Closure_Ortrancl(_1567747, _1567751))))], (29222 ^ _779203) ^ [_1296981, _1296983, _1296985] : [-(hAPP(c_Set_OPow(_1296981), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296981, tc_HOL_Obool)), _1296983), _1296985)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1296981, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1296981), _1296983)), hAPP(c_Set_OPow(_1296981), _1296985)))], (29488 ^ _779203) ^ [_1302419, _1302421, _1302423, _1302425] : [class_Lattices_Osemilattice__inf(_1302419), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302419), _1302421), _1302423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302419), _1302421), _1302425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302419), _1302421), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1302419), _1302423), _1302425))))], (8963 ^ _779203) ^ [_930850, _930852, _930854, _930856, _930858] : [class_Groups_Ocomm__monoid__add(_930850), hBOOL(hAPP(c_Finite__Set_Ofinite(_930852), _930854)), -(hBOOL(hAPP(hAPP(c_member(_930852), _930856), _930854))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_930852, _930850), _930858), hAPP(hAPP(c_Set_Oinsert(_930852), _930856), _930854)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_930850), hAPP(_930858, _930856)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_930852, _930850), _930858), _930854)))], (32037 ^ _779203) ^ [_1357239, _1357241, _1357243, _1357245, _1357247] : [class_Groups_Ocomm__monoid__add(_1357239), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357241), _1357243)), 32044 ^ _779203 : [(32051 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1357241), _1357245), _1357243))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357241, _1357239), hAPP(hAPP(c_COMBC(_1357241, _1357239, _1357239), hAPP(hAPP(c_COMBS(_1357241, _1357239, tc_fun(_1357239, _1357239)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1357239, tc_fun(_1357239, _1357239)), _1357241), c_If(_1357239)), hAPP(hAPP(c_COMBC(_1357241, _1357241, tc_HOL_Obool), c_fequal), _1357245))), _1357247)), c_Groups_Ozero__class_Ozero(_1357239))), _1357243) = c_Groups_Ozero__class_Ozero(_1357239))], (32045 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1357241), _1357245), _1357243)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357241, _1357239), hAPP(hAPP(c_COMBC(_1357241, _1357239, _1357239), hAPP(hAPP(c_COMBS(_1357241, _1357239, tc_fun(_1357239, _1357239)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1357239, tc_fun(_1357239, _1357239)), _1357241), c_If(_1357239)), hAPP(hAPP(c_COMBC(_1357241, _1357241, tc_HOL_Obool), c_fequal), _1357245))), _1357247)), c_Groups_Ozero__class_Ozero(_1357239))), _1357243) = hAPP(_1357247, _1357245))]]], (27010 ^ _779203) ^ [_1254856, _1254858, _1254860] : [class_Divides_Osemiring__div(_1254856), -(_1254858 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1254856), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1254856), _1254858), _1254860)), _1254860)), c_Divides_Odiv__class_Omod(_1254856, _1254858, _1254860)))], (25762 ^ _779203) ^ [_1232522] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1232522), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1232522))], (39508 ^ _779203) ^ [_1547961, _1547963, _1547965, _1547967, _1547969, _1547971] : [-(hAPP(hAPP(c_Fun_Ocomp(_1547961, _1547963, _1547965, _1547967), _1547969), _1547971) = hAPP(_1547967, hAPP(_1547969, _1547971)))], (3248 ^ _779203) ^ [_827581, _827583] : [_827583 = _827581, -(c_Int_OBit1(_827583) = c_Int_OBit1(_827581))], (21563 ^ _779203) ^ [_1158790, _1158792] : [c_Int_OBit1(_1158790) = c_Int_OBit0(_1158792)], (23195 ^ _779203) ^ [_1187261, _1187263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187261)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187263)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1187261), _1187263)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1187261)), hAPP(c_Int_Onat, _1187263)))], (33905 ^ _779203) ^ [_1400416, _1400418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1400416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400418), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1400416), _1400418) = 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), _1400416), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1400418)))))], (25824 ^ _779203) ^ [_1233504, _1233506] : [class_Rings_Oring__1(_1233504), 25827 ^ _779203 : [(25834 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233506), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1233504), _1233506) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1233504), hAPP(c_Int_Onat, _1233506)))], (25828 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1233506), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1233504), _1233506) = hAPP(c_Groups_Ouminus__class_Ouminus(_1233504), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1233504), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1233506)))))]]], (46546 ^ _779203) ^ [_1715153, _1715155] : [-(c_Fun_Oinj__on(tc_List_Olist(_1715153), tc_List_Olist(_1715153), c_List_Orev(_1715153), _1715155))], (25580 ^ _779203) ^ [_1229856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1229856))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1229856)))], (40703 ^ _779203) ^ [_1577269, _1577271] : [c_Wellfounded_Oacyclic(_1577269, hAPP(c_Relation_Oconverse(_1577269, _1577269), _1577271)), -(c_Wellfounded_Oacyclic(_1577269, _1577271))], (17246 ^ _779203) ^ [_1083324, _1083326, _1083328] : [class_Orderings_Olinorder(_1083324), hAPP(_1083326, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1083324), 17251 ^ [_1083324, _1083326, _1083328]), 17252 ^ [_1083324, _1083326, _1083328])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1083324), hAPP(_1083326, 17251 ^ [_1083324, _1083326, _1083328])), hAPP(_1083326, 17252 ^ [_1083324, _1083326, _1083328])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083324), _1083328)), -(_1083328 = c_Orderings_Obot__class_Obot(tc_fun(_1083324, tc_HOL_Obool))), -(hAPP(_1083326, c_Big__Operators_Olinorder__class_OMin(_1083324, _1083328)) = c_Big__Operators_Olinorder__class_OMin(_1083324, hAPP(c_Set_Oimage(_1083324, _1083324, _1083326), _1083328)))], (51131 ^ _779203) ^ [_1814053, _1814055, _1814057] : [class_Rings_Olinordered__idom(_1814053), 51134 ^ _779203 : [(51141 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814053), _1814055), _1814057)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814053), _1814055), hAPP(c_Groups_Oabs__class_Oabs(_1814053), _1814057))))], (51135 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814053), _1814055), hAPP(c_Groups_Oabs__class_Oabs(_1814053), _1814057))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814053), _1814055), _1814057)))]]], (47165 ^ _779203) ^ [_1728264, _1728266, _1728268] : [hBOOL(hAPP(hAPP(c_member(_1728264), _1728266), hAPP(c_List_Oset(_1728264), _1728268))), -(c_List_Oinsert(_1728264, _1728266, _1728268) = _1728268)], (40101 ^ _779203) ^ [_1561965, _1561967, _1561969, _1561971, _1561973] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1561965, _1561967, _1561965, _1561969), hAPP(c_Product__Type_OPair(_1561967, _1561965), _1561971)), _1561973) = hAPP(_1561973, _1561971))], (52269 ^ _779203) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (1840 ^ _779203) ^ [_805163, _805165] : [-(class_Rings_Osemiring__0(_805163)), _805165 = _805163, class_Rings_Osemiring__0(_805165)], (42157 ^ _779203) ^ [_1618768, _1618770, _1618772, _1618774] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1618768, _1618768)), hAPP(hAPP(c_Product__Type_OPair(_1618768, _1618768), _1618770), _1618772)), hAPP(c_List_Oset(tc_prod(_1618768, _1618768)), hAPP(hAPP(c_List_Ozip(_1618768, _1618768), _1618774), _1618774))))), hBOOL(hAPP(hAPP(c_member(_1618768), _1618770), hAPP(c_List_Oset(_1618768), _1618774))), _1618770 = _1618772], (42632 ^ _779203) ^ [_1629199, _1629201, _1629203, _1629205] : [-(_1629199 = _1629201), -(c_List_Oremove1(_1629203, _1629199, hAPP(hAPP(c_List_Olist_OCons(_1629203), _1629201), _1629205)) = hAPP(hAPP(c_List_Olist_OCons(_1629203), _1629201), c_List_Oremove1(_1629203, _1629199, _1629205)))], (20302 ^ _779203) ^ [_1137278, _1137280, _1137282] : [class_Rings_Ocomm__ring__1(_1137278), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137278), _1137280), _1137282) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137278), _1137280), hAPP(c_Groups_Ouminus__class_Ouminus(_1137278), _1137282)))], (23691 ^ _779203) ^ [_1196237, _1196239] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1196237), _1196239) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1196237, _1196239)), _1196239))], (11512 ^ _779203) ^ [_977650, _977652, _977654, _977656] : [class_Rings_Oordered__semiring(_977650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977650), _977652), _977654)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977650), c_Groups_Ozero__class_Ozero(_977650)), _977656)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977650), _977652), _977656)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977650), _977654), _977656))))], (38865 ^ _779203) ^ [_1531965, _1531967, _1531969, _1531971] : [38866 ^ _779203 : [(38867 ^ _779203) ^ [_1532040] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531965, _1531969)), hAPP(hAPP(c_Product__Type_OPair(_1531965, _1531969), _1531967), _1532040)), _1531971))]], -(hBOOL(hAPP(hAPP(c_member(_1531965), _1531967), hAPP(c_Relation_ODomain(_1531965, _1531969), _1531971))))], (15984 ^ _779203) ^ [_1059719, _1059721, _1059723] : [class_Int_Onumber__ring(_1059719), -(hAPP(c_Int_Onumber__class_Onumber__of(_1059719), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1059721), _1059723)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1059719), hAPP(c_Int_Onumber__class_Onumber__of(_1059719), _1059721)), hAPP(c_Int_Onumber__class_Onumber__of(_1059719), _1059723)))], (15496 ^ _779203) ^ [_1050913, _1050915, _1050917] : [class_Orderings_Olinorder(_1050913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050913), _1050915), _1050917)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1050913), _1050917), _1050915) = _1050917)], (42798 ^ _779203) ^ [_1632115, _1632117] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632115), tc_List_Olist(_1632115))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632115), tc_List_Olist(_1632115)), c_List_Olist_ONil(_1632115)), c_List_Olist_ONil(_1632115))), c_List_Olistrel(_1632115, _1632117))))], (48644 ^ _779203) ^ [_1760884, _1760886] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1760884, _1760886), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760884)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7537 ^ _779203) ^ [_903736, _903738, _903740, _903742] : [-(c_Nitpick_Ofold__graph_H(_903736, _903738, _903740, _903742, c_Orderings_Obot__class_Obot(tc_fun(_903736, tc_HOL_Obool)), _903742))], (37783 ^ _779203) ^ [_1497151, _1497153, _1497155, _1497157] : [_1497151 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1497153, _1497155), 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)), _1497157))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1497153), _1497151)))], (7459 ^ _779203) ^ [_902499, _902501, _902503, _902505] : [class_Orderings_Opreorder(_902499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902499), _902501), _902503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902499), _902503), _902505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902499), _902501), _902505)))], (44223 ^ _779203) ^ [_1663738, _1663740, _1663742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663738), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663740)), _1663742))), -(c_List_Olast(_1663740, hAPP(hAPP(c_List_Odrop(_1663740), _1663738), _1663742)) = c_List_Olast(_1663740, _1663742))], (41903 ^ _779203) ^ [_1611046, _1611048, _1611050] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611046, tc_HOL_Obool)), hAPP(c_List_Oset(_1611046), hAPP(hAPP(c_List_Otake(_1611046), _1611048), _1611050))), hAPP(c_List_Oset(_1611046), _1611050))))], (42682 ^ _779203) ^ [_1630023, _1630025, _1630027] : [-(hAPP(hAPP(c_List_Ozip(_1630023, _1630025), c_List_Olist_ONil(_1630023)), _1630027) = c_List_Olist_ONil(tc_prod(_1630023, _1630025)))], (48806 ^ _779203) ^ [_1764910, _1764912] : [-(c_Relation_Otrans(_1764910, c_Relation_OId__on(_1764910, _1764912)))], (17342 ^ _779203) ^ [_1084934, _1084936] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084934), _1084936))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084936), _1084934)))], (14553 ^ _779203) ^ [_1032600, _1032602, _1032604, _1032606] : [class_Fields_Olinordered__field(_1032600), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032600), c_Groups_Ozero__class_Ozero(_1032600)), _1032602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032600), _1032604), _1032602)), _1032606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032600), _1032604), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1032600), _1032606), _1032602))))], (7941 ^ _779203) ^ [_909936, _909938, _909940, _909942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909936, tc_HOL_Obool)), _909938), _909940)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_909936, tc_HOL_Obool)), _909940), _909942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_909936, tc_HOL_Obool)), _909938), _909942)))], (34400 ^ _779203) ^ [_1412592, _1412594, _1412596, _1412598] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1412592, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412594, tc_fun(tc_fun(_1412592, tc_HOL_Obool), tc_HOL_Obool)), _1412596), hAPP(hAPP(c_COMBB(tc_fun(_1412592, tc_HOL_Obool), tc_fun(tc_fun(_1412592, tc_HOL_Obool), tc_HOL_Obool), _1412594), c_Set_OPow(_1412592)), _1412598))), hAPP(c_Set_OPow(_1412592), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412594, tc_fun(_1412592, tc_HOL_Obool)), _1412596), _1412598)))))], (12605 ^ _779203) ^ [_996638, _996640, _996642, _996644] : [class_Rings_Olinordered__ring__strict(_996638), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996638), c_Groups_Ozero__class_Ozero(_996638)), _996640)), 12612 ^ _779203 : [(12619 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996638), _996642), _996644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996638), _996640), _996642)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996638), _996640), _996644))))], (12613 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996638), _996640), _996642)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_996638), _996640), _996644))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996638), _996642), _996644)))]]], (45951 ^ _779203) ^ [_1703819, _1703821] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703819)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703821)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703819), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703821)) = c_List_Olist_ONil(tc_Nat_Onat))], (23735 ^ _779203) ^ [_1197014, _1197016] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197014, _1197016)) = _1197016), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1197014), _1197016) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197014, _1197016)))], (28028 ^ _779203) ^ [_1274054, _1274056] : [28030 ^ _779203 : [(28033 ^ _779203) ^ [] : [hBOOL(hAPP(_1274056, 28029 ^ [_1274054, _1274056]))], (28031 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 28029 ^ [_1274054, _1274056]), _1274054)))]], 28034 ^ _779203 : [(28035 ^ _779203) ^ [_1274204] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1274204), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1274054))), -(hBOOL(hAPP(_1274056, _1274204)))]]], (40322 ^ _779203) ^ [_1567967, _1567969, _1567971, _1567973] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567967, _1567967)), hAPP(hAPP(c_Product__Type_OPair(_1567967, _1567967), _1567969), _1567971)), c_Transitive__Closure_Otrancl(_1567967, _1567973))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567967, _1567967)), hAPP(hAPP(c_Product__Type_OPair(_1567967, _1567967), _1567969), _1567971)), c_Transitive__Closure_Ortrancl(_1567967, _1567973))))], (21979 ^ _779203) ^ [_1166629, _1166631, _1166633, _1166635] : [class_Divides_Osemiring__div(_1166629), -(c_Divides_Odiv__class_Omod(_1166629, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166629), _1166631), _1166633), _1166635) = c_Divides_Odiv__class_Omod(_1166629, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166629), _1166631), c_Divides_Odiv__class_Omod(_1166629, _1166633, _1166635)), _1166635))], (44829 ^ _779203) ^ [_1677439, _1677441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1677439), _1677441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677439)), hAPP(c_Code__Numeral_Onat__of, _1677441))))], (27946 ^ _779203) ^ [_1272433, _1272435] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272433, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272433, tc_HOL_Obool)), _1272435)), _1272435) = c_Orderings_Otop__class_Otop(tc_fun(_1272433, tc_HOL_Obool)))], (5803 ^ _779203) ^ [_871031, _871033, _871035] : [hBOOL(hAPP(hAPP(c_member(_871031), _871033), _871035)), -(hBOOL(hAPP(_871035, _871033)))], (23677 ^ _779203) ^ [_1195937, _1195939] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1195937, _1195939) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1195937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1195937), _1195939)), _1195939)))], (42283 ^ _779203) ^ [_1621385, _1621387, _1621389, _1621391] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621385)), hAPP(hAPP(c_List_Olist__update(_1621385, _1621387), _1621389), _1621391)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621385)), _1621387))], (5454 ^ _779203) ^ [_862630, _862632] : [_862632 = _862630, -(c_Groups_Otimes__class_Otimes(_862632) = c_Groups_Otimes__class_Otimes(_862630))], (11716 ^ _779203) ^ [_981302, _981304, _981306] : [class_Groups_Oordered__comm__monoid__add(_981302), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981302), c_Groups_Ozero__class_Ozero(_981302)), _981304)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981302), c_Groups_Ozero__class_Ozero(_981302)), _981306)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981302), c_Groups_Ozero__class_Ozero(_981302)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981302), _981304), _981306))))], (21683 ^ _779203) ^ [_1160894, _1160896] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1160894)), c_Int_OBit0(_1160896)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1160894), _1160896)))], (868 ^ _779203) ^ [_792139, _792141, _792143, _792145] : [-(c_Equiv__Relations_Opart__equivp(_792143, _792139)), c_Equiv__Relations_Opart__equivp(_792145, _792141), _792145 = _792143, _792141 = _792139], (36796 ^ _779203) ^ [_1472696] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1472696))], (46931 ^ _779203) ^ [_1723161, _1723163] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1723161), _1723163) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1723161)), c_List_Oembed__list(_1723163))))], (37839 ^ _779203) ^ [_1499333, _1499335, _1499337, _1499339] : [-(hAPP(c_Relation_OImage(_1499333, _1499335, _1499337), hAPP(hAPP(c_Set_Oinsert(_1499333), _1499339), c_Orderings_Obot__class_Obot(tc_fun(_1499333, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1499335), hAPP(hAPP(c_COMBC(_1499335, tc_fun(tc_prod(_1499333, _1499335), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1499333, _1499335), tc_fun(tc_fun(tc_prod(_1499333, _1499335), tc_HOL_Obool), tc_HOL_Obool), _1499335), c_member(tc_prod(_1499333, _1499335))), hAPP(c_Product__Type_OPair(_1499333, _1499335), _1499339))), _1499337)))], (1450 ^ _779203) ^ [_800288, _800290] : [-(class_Lattices_Odistrib__lattice(_800288)), _800290 = _800288, class_Lattices_Odistrib__lattice(_800290)], (36210 ^ _779203) ^ [_1460427, _1460429, _1460431, _1460433, _1460435, _1460437] : [c_Fun_Oinj__on(_1460427, _1460429, _1460431, _1460433), hAPP(_1460431, _1460435) = hAPP(_1460431, _1460437), hBOOL(hAPP(hAPP(c_member(_1460427), _1460435), _1460433)), hBOOL(hAPP(hAPP(c_member(_1460427), _1460437), _1460433)), -(_1460435 = _1460437)], (43804 ^ _779203) ^ [_1655467, _1655469, _1655471] : [-(hAPP(c_List_Orotate(_1655467, hAPP(c_Nat_OSuc, _1655469)), _1655471) = hAPP(c_List_Orotate1(_1655467), hAPP(c_List_Orotate(_1655467, _1655469), _1655471)))], (46688 ^ _779203) ^ [_1718064, _1718066, _1718068] : [-(hAPP(c_List_Orev(_1718064), hAPP(hAPP(c_List_Olist_OCons(_1718064), _1718066), _1718068)) = hAPP(hAPP(c_List_Oappend(_1718064), hAPP(c_List_Orev(_1718064), _1718068)), hAPP(hAPP(c_List_Olist_OCons(_1718064), _1718066), c_List_Olist_ONil(_1718064))))], (51903 ^ _779203) ^ [_1827239, _1827241, _1827243, _1827245, _1827247] : [class_Rings_Ocomm__semiring__1(_1827239), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827239), hAPP(hAPP(c_Power_Opower__class_Opower(_1827239), _1827241), _1827243)), _1827245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1827247), _1827243)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827239), hAPP(hAPP(c_Power_Opower__class_Opower(_1827239), _1827241), _1827247)), _1827245)))], (34478 ^ _779203) ^ [_1415089, _1415091, _1415093, _1415095, _1415097] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1415089, tc_HOL_Obool)), _1415091), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1415093, tc_fun(_1415089, tc_HOL_Obool)), _1415095), _1415097)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415093, tc_fun(_1415089, tc_HOL_Obool)), _1415095), hAPP(hAPP(c_COMBB(tc_fun(_1415089, tc_HOL_Obool), tc_fun(_1415089, tc_HOL_Obool), _1415093), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1415089, tc_HOL_Obool)), _1415091)), _1415097)))], (13787 ^ _779203) ^ [_1018727, _1018729, _1018731, _1018733] : [class_Fields_Olinordered__field(_1018727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018727), c_Groups_Ozero__class_Ozero(_1018727)), _1018729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018727), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018727), _1018731), _1018729)), _1018733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018727), _1018731), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1018727), _1018733), _1018729))))], (15536 ^ _779203) ^ [_1051593, _1051595, _1051597, _1051599] : [class_Orderings_Olinorder(_1051593), 15539 ^ _779203 : [(15548 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051593), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1051593), _1051595), _1051597)), _1051599))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051593), _1051595), _1051599)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051593), _1051597), _1051599))], (15540 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051593), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1051593), _1051595), _1051597)), _1051599)), 15543 ^ _779203 : [(15546 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051593), _1051597), _1051599)))], (15544 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051593), _1051595), _1051599)))]]]]], (25312 ^ _779203) ^ [_1225650, _1225652, _1225654] : [class_Rings_Olinordered__semidom(_1225650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225650), c_Groups_Ozero__class_Ozero(_1225650)), _1225652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225650), _1225652), c_Groups_Oone__class_Oone(_1225650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1225650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225650), _1225652), hAPP(hAPP(c_Power_Opower__class_Opower(_1225650), _1225652), _1225654))), hAPP(hAPP(c_Power_Opower__class_Opower(_1225650), _1225652), _1225654))))], (41258 ^ _779203) ^ [_1591728, _1591730, _1591732] : [-(c_Nitpick_Oplus__frac(_1591728, _1591730, _1591732) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1591728), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1591728), _1591730), hAPP(c_Nitpick_Odenom(_1591728), _1591732))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1591728), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1591728), tc_Int_Oint), c_Nitpick_Ofrac(_1591728)), 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(_1591728), _1591730))), 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(_1591728), _1591730))))), 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(_1591728), _1591732))), 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(_1591728), _1591732)))))), c_COMBI(tc_Int_Oint))))], (42199 ^ _779203) ^ [_1619712] : [42201 ^ _779203 : [(42204 ^ _779203) ^ [] : [42200 ^ [_1619712] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (42202 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 42200 ^ [_1619712]), hAPP(c_List_Oset(tc_Nat_Onat), _1619712))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619712) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27960 ^ _779203) ^ [_1272813, _1272815] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1272813, _1272815)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1272813, _1272815), tc_HOL_Obool)))), 27963 ^ _779203 : [(27966 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1272815), c_Orderings_Otop__class_Otop(tc_fun(_1272815, tc_HOL_Obool)))))], (27964 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1272813), c_Orderings_Otop__class_Otop(tc_fun(_1272813, tc_HOL_Obool)))))]]], (35586 ^ _779203) ^ [_1445422] : [-(_1445422 = 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), 35583 ^ [_1445422]), 35584 ^ [_1445422])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (30706 ^ _779203) ^ [_1327846, _1327848, _1327850] : [class_Complete__Lattice_Ocomplete__lattice(_1327846), -(c_Complete__Lattice_OSup__class_OSup(_1327846, hAPP(hAPP(c_Set_Oinsert(_1327846), _1327848), _1327850)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1327846), _1327848), c_Complete__Lattice_OSup__class_OSup(_1327846, _1327850)))], (48236 ^ _779203) ^ [_1752108, _1752110, _1752112, _1752114, _1752116] : [c_List_Oreplicate(_1752108, _1752110, _1752112) = c_List_Oreplicate(_1752108, _1752114, _1752116), 48239 ^ _779203 : [(48242 ^ _779203) ^ [] : [-(_1752110 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1752112 = _1752116)], (48240 ^ _779203) ^ [] : [-(_1752110 = _1752114)]]], (6128 ^ _779203) ^ [_877058, _877060, _877062] : [-(hAPP(c_Set_Oimage(_877058, _877060, _877062), c_Orderings_Obot__class_Obot(tc_fun(_877058, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_877060, tc_HOL_Obool)))], (12416 ^ _779203) ^ [_993319, _993321, _993323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993319), _993321)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993319), _993323)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993321), _993323))))], (49751 ^ _779203) ^ [_1785028, _1785030, _1785032] : [hAPP(c_Set_Oimage(_1785028, _1785030, _1785032), c_Orderings_Otop__class_Otop(tc_fun(_1785028, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1785030, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1785028, _1785030, _1785030, _1785032), c_Hilbert__Choice_Oinv__into(_1785028, _1785030, c_Orderings_Otop__class_Otop(tc_fun(_1785028, tc_HOL_Obool)), _1785032)) = c_Fun_Oid(_1785030))], (25456 ^ _779203) ^ [_1228043] : [c_Int_OMin = c_Int_OBit0(_1228043)], (31508 ^ _779203) ^ [_1344347, _1344349] : [class_Complete__Lattice_Ocomplete__lattice(_1344347), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344347), _1344349)), -(_1344349 = c_Orderings_Obot__class_Obot(tc_fun(_1344347, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1344347, _1344349) = c_Complete__Lattice_OInf__class_OInf(_1344347, _1344349))], (11630 ^ _779203) ^ [_979784, _979786, _979788] : [class_Rings_Olinordered__ring__strict(_979784), 11633 ^ _779203 : [(11648 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979784), c_Groups_Ozero__class_Ozero(_979784)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979784), _979786), _979788)))), 11649 ^ _779203 : [(11656 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979784), _979786), c_Groups_Ozero__class_Ozero(_979784))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979784), _979788), c_Groups_Ozero__class_Ozero(_979784)))], (11650 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979784), c_Groups_Ozero__class_Ozero(_979784)), _979786)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979784), c_Groups_Ozero__class_Ozero(_979784)), _979788))]]], (11634 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979784), c_Groups_Ozero__class_Ozero(_979784)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979784), _979786), _979788))), 11639 ^ _779203 : [(11642 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979784), c_Groups_Ozero__class_Ozero(_979784)), _979788)))], (11640 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979784), c_Groups_Ozero__class_Ozero(_979784)), _979786)))]], 11643 ^ _779203 : [(11646 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979784), _979788), c_Groups_Ozero__class_Ozero(_979784))))], (11644 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979784), _979786), c_Groups_Ozero__class_Ozero(_979784))))]]]]], (43135 ^ _779203) ^ [_1639916, _1639918, _1639920] : [class_Groups_Omonoid__add(_1639916), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1639916), hAPP(hAPP(c_List_Oappend(_1639916), _1639918), _1639920)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1639916), hAPP(c_List_Omonoid__add__class_Olistsum(_1639916), _1639918)), hAPP(c_List_Omonoid__add__class_Olistsum(_1639916), _1639920)))], (10815 ^ _779203) ^ [_966218, _966220] : [class_Rings_Ocomm__semiring__1(_966218), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966218), _966220), c_Groups_Ozero__class_Ozero(_966218)) = _966220)], (35318 ^ _779203) ^ [] : [-(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)))))], (6597 ^ _779203) ^ [_885566, _885568, _885570, _885572] : [c_Finite__Set_Ofolding__one(_885566, _885568, _885570), -(hAPP(_885570, hAPP(hAPP(c_Set_Oinsert(_885566), _885572), c_Orderings_Obot__class_Obot(tc_fun(_885566, tc_HOL_Obool)))) = _885572)], (12789 ^ _779203) ^ [_1000168, _1000170, _1000172, _1000174] : [class_Rings_Olinordered__semiring__strict(_1000168), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000168), _1000170), _1000172)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000168), _1000174), _1000172))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000168), c_Groups_Ozero__class_Ozero(_1000168)), _1000172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000168), _1000170), _1000174)))], (25764 ^ _779203) ^ [_1232554, _1232556] : [c_Nat__Transfer_Onat__set(_1232554), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1232556), _1232554)), -(c_Nat__Transfer_Ois__nat(_1232556))], (43492 ^ _779203) ^ [_1648555, _1648557, _1648559, _1648561] : [-(hAPP(hAPP(c_List_Odrop(_1648555), _1648557), hAPP(hAPP(c_List_Otake(_1648555), _1648559), _1648561)) = hAPP(hAPP(c_List_Otake(_1648555), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1648559), _1648557)), hAPP(hAPP(c_List_Odrop(_1648555), _1648557), _1648561)))], (2702 ^ _779203) ^ [_819064, _819066, _819068, _819070, _819072, _819074] : [-(c_Predicate_ORangeP(_819074, _819070, _819066) = c_Predicate_ORangeP(_819072, _819068, _819064)), _819074 = _819072, _819070 = _819068, _819066 = _819064], (48128 ^ _779203) ^ [_1749408, _1749410, _1749412, _1749414, _1749416] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749408, _1749410, _1749412), _1749414), _1749416)), -(hBOOL(hAPP(hAPP(_1749412, _1749416), _1749414)))], (10769 ^ _779203) ^ [_965502, _965504] : [class_Groups_Ocomm__monoid__add(_965502), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965502), _965504), c_Groups_Ozero__class_Ozero(_965502)) = _965504)], (6245 ^ _779203) ^ [_879586, _879588, _879590, _879592] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879586, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_879586), _879588), _879590)), _879592))), hBOOL(hAPP(hAPP(c_member(_879586), _879588), _879592)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879586, tc_HOL_Obool)), _879590), _879592))], (37397 ^ _779203) ^ [_1486836, _1486838, _1486840, _1486842, _1486844] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1486836, _1486838), _1486840), hAPP(hAPP(c_COMBS(_1486836, tc_fun(_1486838, tc_HOL_Obool), tc_fun(_1486838, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1486838, tc_HOL_Obool), tc_fun(tc_fun(_1486838, tc_HOL_Obool), tc_fun(_1486838, tc_HOL_Obool)), _1486836), c_Groups_Ominus__class_Ominus(tc_fun(_1486838, tc_HOL_Obool))), _1486842)), _1486844)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1486836, _1486838), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1486836, _1486838), _1486840), _1486842)), hAPP(hAPP(c_Product__Type_OSigma(_1486836, _1486838), _1486840), _1486844)))], (49308 ^ _779203) ^ [_1776283, _1776285] : [c_Relation_Osym(_1776283, hAPP(c_Relation_Oconverse(_1776283, _1776283), _1776285)), -(c_Relation_Osym(_1776283, _1776285))], (37441 ^ _779203) ^ [_1487793, _1487795, _1487797] : [-(hAPP(hAPP(c_Set_Oinsert(_1487793), _1487795), hAPP(c_Set_OCollect(_1487793), _1487797)) = hAPP(c_Set_OCollect(_1487793), hAPP(hAPP(c_COMBS(_1487793, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1487793), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1487793), c_fNot), hAPP(hAPP(c_COMBC(_1487793, _1487793, tc_HOL_Obool), c_fequal), _1487795)))), _1487797)))], (17498 ^ _779203) ^ [] : [-(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))))], (48622 ^ _779203) ^ [_1760354, _1760356, _1760358, _1760360, _1760362, _1760364, _1760366] : [48624 ^ _779203 : [(48627 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1760358, 48623 ^ [_1760354, _1760356, _1760358, _1760360, _1760362, _1760364, _1760366]), _1760360), _1760362))], (48625 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760354), 48623 ^ [_1760354, _1760356, _1760358, _1760360, _1760362, _1760364, _1760366]), _1760356)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1760354, tc_fun(_1760364, tc_fun(_1760366, tc_HOL_Obool))), _1760356), _1760358), _1760360), _1760362)))], (2916 ^ _779203) ^ [_822391, _822393, _822395, _822397] : [-(c_Nitpick_Ouminus__frac(_822397, _822393) = c_Nitpick_Ouminus__frac(_822395, _822391)), _822397 = _822395, _822393 = _822391], (44510 ^ _779203) ^ [_1670775, _1670777, _1670779, _1670781] : [hBOOL(hAPP(c_List_Odistinct(_1670775), hAPP(hAPP(c_List_Omap(_1670777, _1670775), _1670779), _1670781))), 44513 ^ _779203 : [(44516 ^ _779203) ^ [] : [-(c_Fun_Oinj__on(_1670777, _1670775, _1670779, hAPP(c_List_Oset(_1670777), _1670781)))], (44514 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1670777), _1670781)))]]], (468 ^ _779203) ^ [_786195, _786197, _786199, _786201, _786203, _786205] : [-(c_Nitpick_Oless__frac(_786203, _786199, _786195)), c_Nitpick_Oless__frac(_786205, _786201, _786197), _786205 = _786203, _786201 = _786199, _786197 = _786195], (17986 ^ _779203) ^ [_1096340, _1096342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096340)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096342)), -(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), _1096340), _1096342))))], (15994 ^ _779203) ^ [_1059909, _1059911] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1059909)), hAPP(c_Nat_OSuc, _1059911)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1059909), _1059911)))], (25674 ^ _779203) ^ [_1231199, _1231201] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1231199), _1231201), hAPP(c_Int_Onumber__class_Onumber__of(_1231199), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1231199), _1231201)), class_Fields_Ofield__inverse__zero(_1231199), class_Int_Onumber__ring(_1231199)], (7681 ^ _779203) ^ [_905851, _905853, _905855] : [class_Orderings_Olinorder(_905851), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905851), _905853), _905855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905851), _905855), _905853)))], (43395 ^ _779203) ^ [_1645957, _1645959, _1645961, _1645963, _1645965, _1645967] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645957), tc_List_Olist(_1645957))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645957), tc_List_Olist(_1645957)), hAPP(hAPP(c_List_Oappend(_1645957), _1645959), hAPP(hAPP(c_List_Olist_OCons(_1645957), _1645961), c_List_Olist_ONil(_1645957)))), hAPP(hAPP(c_List_Oappend(_1645957), _1645963), hAPP(hAPP(c_List_Olist_OCons(_1645957), _1645965), c_List_Olist_ONil(_1645957))))), c_List_Olistrel1(_1645957, _1645967))), 43400 ^ _779203 : [(43403 ^ _779203) ^ [] : [-(_1645961 = _1645965)], (43401 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645957), tc_List_Olist(_1645957))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645957), tc_List_Olist(_1645957)), _1645959), _1645963)), c_List_Olistrel1(_1645957, _1645967))))]], 43404 ^ _779203 : [(43407 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1645957, _1645957)), hAPP(hAPP(c_Product__Type_OPair(_1645957, _1645957), _1645961), _1645965)), _1645967)))], (43405 ^ _779203) ^ [] : [-(_1645959 = _1645963)]]], (13815 ^ _779203) ^ [_1019265, _1019267, _1019269, _1019271] : [class_Fields_Olinordered__field(_1019265), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019265), c_Groups_Ozero__class_Ozero(_1019265)), _1019267)), 13822 ^ _779203 : [(13829 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019265), _1019269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019265), _1019271), _1019267))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019265), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1019265), _1019269), _1019267)), _1019271)))], (13823 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019265), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1019265), _1019269), _1019267)), _1019271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019265), _1019269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019265), _1019271), _1019267))))]]], (43780 ^ _779203) ^ [_1655023, _1655025, _1655027] : [_1655027 = c_List_Olist_ONil(_1655023), -(hAPP(c_List_Orotate(_1655023, _1655025), _1655027) = c_List_Olist_ONil(_1655023))], (49851 ^ _779203) ^ [_1787314] : [-(c_Quickcheck_Obeyond(_1787314, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (52475 ^ _779203) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (27994 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (48292 ^ _779203) ^ [_1753026, _1753028, _1753030] : [_1753028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1753026) = c_List_Oreplicate(_1753026, _1753028, _1753030))], (13307 ^ _779203) ^ [_1009606, _1009608, _1009610, _1009612, _1009614] : [class_Groups_Ocomm__monoid__mult(_1009606), hBOOL(hAPP(c_Finite__Set_Ofinite(_1009608), _1009610)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1009608, _1009606), _1009612), hAPP(hAPP(c_Set_Oinsert(_1009608), _1009614), _1009610)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009606), hAPP(_1009612, _1009614)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1009608, _1009606), _1009612), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1009608, tc_HOL_Obool)), _1009610), hAPP(hAPP(c_Set_Oinsert(_1009608), _1009614), c_Orderings_Obot__class_Obot(tc_fun(_1009608, tc_HOL_Obool)))))))], (27312 ^ _779203) ^ [_1260043, _1260045, _1260047, _1260049] : [class_Lattices_Osemilattice__sup(_1260043), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260043), _1260045), _1260047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1260043), _1260045), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1260043), _1260049), _1260047))))], (6098 ^ _779203) ^ [_876449, _876451, _876453] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_876449), _876453)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_876449), hAPP(hAPP(c_Set_Oinsert(_876449), _876451), _876453))))], (21829 ^ _779203) ^ [] : [-(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))))], (32333 ^ _779203) ^ [_1364377] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1364377)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1364377)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1364377)), 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)))))], (45821 ^ _779203) ^ [_1701137, _1701139, _1701141, _1701143] : [-(c_List_Ofoldr(_1701137, _1701139, _1701141, c_List_Olist_ONil(_1701137), _1701143) = _1701143)], (19670 ^ _779203) ^ [_1126252, _1126254] : [class_Int_Onumber__ring(_1126252), -(hAPP(c_Int_Onumber__class_Onumber__of(_1126252), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1126254)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1126252), hAPP(c_Int_Onumber__class_Onumber__of(_1126252), _1126254)))], (52109 ^ _779203) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (22153 ^ _779203) ^ [_1170341, _1170343] : [class_Divides_Osemiring__div(_1170341), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1170341), c_Groups_Ozero__class_Ozero(_1170341)), _1170343) = c_Groups_Ozero__class_Ozero(_1170341))], (30267 ^ _779203) ^ [_1319050, _1319052, _1319054, _1319056, _1319058] : [class_Groups_Ocomm__monoid__mult(_1319050), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319052), _1319054)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319052), _1319056)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319052, tc_HOL_Obool)), _1319054), _1319056) = c_Orderings_Obot__class_Obot(tc_fun(_1319052, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319052, _1319050), _1319058), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319052, tc_HOL_Obool)), _1319054), _1319056)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319050), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319052, _1319050), _1319058), _1319054)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319052, _1319050), _1319058), _1319056)))], (27332 ^ _779203) ^ [_1260540, _1260542, _1260544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260540, tc_HOL_Obool)), _1260542), _1260544)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260540, tc_HOL_Obool)), _1260542), _1260544) = _1260544)], (45558 ^ _779203) ^ [_1693548, _1693550] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1693548)), c_List_Oconcat(_1693548, _1693550)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1693548), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1693548))), _1693550)))], (44612 ^ _779203) ^ [_1673145, _1673147] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673145)), hAPP(c_Code__Numeral_Oof__nat, _1673147)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1673145), _1673147)))], (24111 ^ _779203) ^ [_1203870, _1203872] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1203870)))), 24114 ^ _779203 : [(24121 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1203872)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203870), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203872)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1203870), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1203872))))], (24115 ^ _779203) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1203872))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203870), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203872)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203870))]]], (43319 ^ _779203) ^ [_1643989, _1643991, _1643993] : [hBOOL(hAPP(c_List_Odistinct(_1643989), hAPP(hAPP(c_List_Oappend(_1643989), _1643991), _1643993))), 43322 ^ _779203 : [(43327 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1643989, tc_HOL_Obool)), hAPP(c_List_Oset(_1643989), _1643991)), hAPP(c_List_Oset(_1643989), _1643993)) = c_Orderings_Obot__class_Obot(tc_fun(_1643989, tc_HOL_Obool)))], (43325 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643989), _1643993)))], (43323 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1643989), _1643991)))]]], (37189 ^ _779203) ^ [_1481414, _1481416, _1481418, _1481420, _1481422] : [hBOOL(hAPP(_1481420, hAPP(_1481418, _1481422))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1481414, _1481416, _1481418), _1481420), _1481422)))], (39471 ^ _779203) ^ [_1547213, _1547215, _1547217, _1547219, _1547221, _1547223] : [-(hAPP(hAPP(c_Fun_Ocomp(_1547213, _1547215, _1547217, hAPP(c_COMBK(_1547215, _1547213), _1547219)), _1547221), _1547223) = _1547219)], (51785 ^ _779203) ^ [_1825058, _1825060] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825060), _1825058)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1825058), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825060))))], (44382 ^ _779203) ^ [_1667630, _1667632, _1667634, _1667636, _1667638] : [class_Groups_Ocomm__monoid__add(_1667630), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667630), hAPP(hAPP(c_List_Omap(_1667632, _1667630), hAPP(hAPP(c_COMBS(_1667632, _1667630, _1667630), hAPP(hAPP(c_COMBB(_1667630, tc_fun(_1667630, _1667630), _1667632), c_Groups_Oplus__class_Oplus(_1667630)), _1667634)), _1667636)), _1667638)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1667630), hAPP(c_List_Omonoid__add__class_Olistsum(_1667630), hAPP(hAPP(c_List_Omap(_1667632, _1667630), _1667634), _1667638))), hAPP(c_List_Omonoid__add__class_Olistsum(_1667630), hAPP(hAPP(c_List_Omap(_1667632, _1667630), _1667636), _1667638))))], (18036 ^ _779203) ^ [] : [-(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))))], (23721 ^ _779203) ^ [_1196815, _1196817, _1196819] : [-(_1196815 = 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), _1196815), _1196817)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196815), _1196819)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1196817), _1196819))], (26236 ^ _779203) ^ [_1240618, _1240620, _1240622, _1240624, _1240626] : [class_Orderings_Oorder(_1240618), 26239 ^ _779203 : [(26252 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1240618, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1240618, _1240620, _1240622)), c_SetInterval_Oord__class_OatLeastAtMost(_1240618, _1240624, _1240626)))), 26253 ^ _779203 : [(26256 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240618), _1240624), _1240620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240618), _1240622), _1240626))], (26254 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240618), _1240620), _1240622)))]]], (26240 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1240618, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1240618, _1240620, _1240622)), c_SetInterval_Oord__class_OatLeastAtMost(_1240618, _1240624, _1240626))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240618), _1240620), _1240622)), 26247 ^ _779203 : [(26250 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240618), _1240622), _1240626)))], (26248 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240618), _1240624), _1240620)))]]]]], (5162 ^ _779203) ^ [_857950, _857952, _857954, _857956, _857958, _857960] : [-(c_Lazy__Sequence_Obind(_857960, _857956, _857952) = c_Lazy__Sequence_Obind(_857958, _857954, _857950)), _857960 = _857958, _857956 = _857954, _857952 = _857950], (8234 ^ _779203) ^ [_916004, _916006, _916008, _916010, _916012, _916014, _916016] : [c_Finite__Set_Ofun__left__comm(_916004, _916006, _916008), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_916004, _916006, _916008, _916010, _916012), _916014)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_916004, _916006, _916008, _916010, _916012), _916016)), -(_916016 = _916014)], (40723 ^ _779203) ^ [_1577718, _1577720, _1577722, _1577724] : [-(hAPP(c_Relation_Oconverse(_1577718, _1577718), hAPP(hAPP(c_Relation_Oinv__image(_1577720, _1577718), _1577722), _1577724)) = hAPP(hAPP(c_Relation_Oinv__image(_1577720, _1577718), hAPP(c_Relation_Oconverse(_1577720, _1577720), _1577722)), _1577724))], (21835 ^ _779203) ^ [_1163617] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1163617), 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, _1163617)))], (40199 ^ _779203) ^ [_1564263, _1564265, _1564267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564263, _1564263), tc_HOL_Obool)), _1564265), _1564267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564263, _1564263), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1564263, _1564263, _1564263), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1564263, _1564263), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1564263, _1564265)), _1564267)), _1564265)), _1564267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564263, _1564263), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1564263, _1564265)), _1564267)))], (29318 ^ _779203) ^ [_1299029, _1299031, _1299033, _1299035] : [class_Lattices_Osemilattice__inf(_1299029), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299029), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299029), _1299031), _1299033)), _1299035) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299029), _1299031), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299029), _1299033), _1299035)))], (18306 ^ _779203) ^ [_1102123, _1102125, _1102127] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1102123)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1102125)), _1102127)) = 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), _1102123), _1102125))), _1102127))], (12134 ^ _779203) ^ [_988905, _988907, _988909, _988911] : [class_Groups_Ocomm__monoid__add(_988905), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_988907), _988909))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_988907, _988905), _988911), _988909) = c_Groups_Ozero__class_Ozero(_988905))], (44807 ^ _779203) ^ [_1677048, _1677050] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1677048), _1677050) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677048)), hAPP(c_Code__Numeral_Onat__of, _1677050))))], (51379 ^ _779203) ^ [_1818030, _1818032] : [_1818030 = _1818032, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818030), _1818032)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818032), _1818030)))], (8021 ^ _779203) ^ [_911682, _911684, _911686, _911688, _911690, _911692, _911694] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911682, _911684, _911686, _911688, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911682, tc_HOL_Obool)), _911690), hAPP(hAPP(c_Set_Oinsert(_911682), _911692), c_Orderings_Obot__class_Obot(tc_fun(_911682, tc_HOL_Obool))))), _911694)), hBOOL(hAPP(hAPP(c_member(_911682), _911692), _911690)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_911682, _911684, _911686, _911688, _911690), hAPP(hAPP(_911686, _911692), _911694))))], (21833 ^ _779203) ^ [_1163585] : [-(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)))), _1163585) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1163585)))], (51283 ^ _779203) ^ [_1816492, _1816494, _1816496] : [_1816492 = _1816494, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816494), _1816496)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816492), _1816496)))], (36346 ^ _779203) ^ [_1462991, _1462993, _1462995, _1462997, _1462999] : [c_Fun_Oinj__on(_1462991, _1462993, _1462995, c_Orderings_Otop__class_Otop(tc_fun(_1462991, tc_HOL_Obool))), hAPP(_1462995, _1462997) = hAPP(_1462995, _1462999), -(_1462997 = _1462999)], (47470 ^ _779203) ^ [_1735508, _1735510, _1735512, _1735514, _1735516] : [-(hAPP(c_List_Ofilter(_1735508, _1735510), _1735512) = hAPP(hAPP(c_List_Olist_OCons(_1735508), _1735514), _1735516)), 47471 ^ _779203 : [(47472 ^ _779203) ^ [_1735636, _1735638] : [_1735512 = hAPP(hAPP(c_List_Oappend(_1735508), _1735638), hAPP(hAPP(c_List_Olist_OCons(_1735508), _1735514), _1735636)), 47478 ^ _779203 : [(47481 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1735510, 47477 ^ [_1735508, _1735510, _1735512, _1735514, _1735516, _1735636, _1735638])))], (47479 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735508), 47477 ^ [_1735508, _1735510, _1735512, _1735514, _1735516, _1735636, _1735638]), hAPP(c_List_Oset(_1735508), _1735638))))]], hBOOL(hAPP(_1735510, _1735514)), _1735516 = hAPP(c_List_Ofilter(_1735508, _1735510), _1735636)]]], (43670 ^ _779203) ^ [_1652888, _1652890, _1652892, _1652894, _1652896] : [-(hAPP(hAPP(c_List_Ozip(_1652888, _1652890), _1652892), hAPP(hAPP(c_List_Oappend(_1652890), _1652894), _1652896)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1652888, _1652890)), hAPP(hAPP(c_List_Ozip(_1652888, _1652890), hAPP(hAPP(c_List_Otake(_1652888), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652890)), _1652894)), _1652892)), _1652894)), hAPP(hAPP(c_List_Ozip(_1652888, _1652890), hAPP(hAPP(c_List_Odrop(_1652888), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652890)), _1652894)), _1652892)), _1652896)))], (25090 ^ _779203) ^ [_1221369, _1221371, _1221373] : [class_Groups_Omonoid__mult(_1221369), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1221369), _1221371), hAPP(c_Nat_OSuc, _1221373)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221369), hAPP(hAPP(c_Power_Opower__class_Opower(_1221369), _1221371), _1221373)), _1221371))], (35266 ^ _779203) ^ [_1436348, _1436350, _1436352, _1436354] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1436348), _1436350)), 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)), _1436352), _1436348)), 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)), _1436354), _1436350)), 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)), _1436352), _1436354)), _1436350)), c_FunDef_Omax__weak)))], (28658 ^ _779203) ^ [] : [-(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))], (30127 ^ _779203) ^ [_1316096, _1316098, _1316100] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1316096), _1316098)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316096), _1316100)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1316096), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316096, tc_HOL_Obool)), _1316098), _1316100))), hAPP(c_Finite__Set_Ocard(_1316096), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316096, tc_HOL_Obool)), _1316098), _1316100))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1316096), _1316098)), hAPP(c_Finite__Set_Ocard(_1316096), _1316100)))], (25888 ^ _779203) ^ [_1234509, _1234511] : [class_Int_Oring__char__0(_1234509), 25891 ^ _779203 : [(25898 ^ _779203) ^ [] : [_1234511 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1234509), _1234511) = c_Groups_Ozero__class_Ozero(_1234509))], (25892 ^ _779203) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1234509), _1234511) = c_Groups_Ozero__class_Ozero(_1234509), -(_1234511 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (46656 ^ _779203) ^ [_1717451, _1717453, _1717455] : [_1717453 = _1717455, -(hAPP(c_List_Orev(_1717451), _1717453) = hAPP(c_List_Orev(_1717451), _1717455))], (42129 ^ _779203) ^ [_1617951, _1617953, _1617955, _1617957, _1617959, _1617961] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617951, _1617953)), hAPP(hAPP(c_Product__Type_OPair(_1617951, _1617953), _1617955), _1617957)), hAPP(c_List_Oset(tc_prod(_1617951, _1617953)), hAPP(hAPP(c_List_Ozip(_1617951, _1617953), _1617959), _1617961)))), 42132 ^ _779203 : [(42135 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617953), _1617957), hAPP(c_List_Oset(_1617953), _1617961))))], (42133 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1617951), _1617955), hAPP(c_List_Oset(_1617951), _1617959))))]]], (40570 ^ _779203) ^ [_1573828, _1573830, _1573832, _1573834] : [hBOOL(hAPP(hAPP(c_member(_1573828), _1573830), c_Wellfounded_Oacc(_1573828, _1573832))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1573828, _1573828)), hAPP(hAPP(c_Product__Type_OPair(_1573828, _1573828), _1573834), _1573830)), c_Transitive__Closure_Ortrancl(_1573828, _1573832))), -(hBOOL(hAPP(hAPP(c_member(_1573828), _1573834), c_Wellfounded_Oacc(_1573828, _1573832))))], (48430 ^ _779203) ^ [_1755674, _1755676, _1755678] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1755674), _1755676))), -(hBOOL(hAPP(hAPP(_1755678, _1755674), _1755676))), 48437 ^ _779203 : [(48440 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 48435 ^ [_1755674, _1755676, _1755678]), 48436 ^ [_1755674, _1755676, _1755678]))), -(hBOOL(hAPP(hAPP(_1755678, 48435 ^ [_1755674, _1755676, _1755678]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 48436 ^ [_1755674, _1755676, _1755678]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48446 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1755678, 48435 ^ [_1755674, _1755676, _1755678]), 48436 ^ [_1755674, _1755676, _1755678]))], (48438 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 48435 ^ [_1755674, _1755676, _1755678]), 48436 ^ [_1755674, _1755676, _1755678]))))]]], (50907 ^ _779203) ^ [_1810148, _1810150] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810148), _1810150))), -(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), _1810148, _1810150))], (51599 ^ _779203) ^ [_1821707, _1821709, _1821711, _1821713] : [class_Divides_Osemiring__div(_1821707), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821707), _1821709), _1821711)), 51606 ^ _779203 : [(51613 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821707), _1821709), _1821713)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821707), _1821709), c_Divides_Odiv__class_Omod(_1821707, _1821713, _1821711))))], (51607 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821707), _1821709), c_Divides_Odiv__class_Omod(_1821707, _1821713, _1821711))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821707), _1821709), _1821713)))]]], (31407 ^ _779203) ^ [_1342333, _1342335, _1342337] : [class_Complete__Lattice_Ocomplete__lattice(_1342333), class_Orderings_Olinorder(_1342333), 31414 ^ _779203 : [(31424 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342333), c_Complete__Lattice_OInf__class_OInf(_1342333, _1342335)), _1342337))), 31425 ^ _779203 : [(31426 ^ _779203) ^ [_1342639] : [hBOOL(hAPP(hAPP(c_member(_1342333), _1342639), _1342335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342333), _1342639), _1342337))]]], (31415 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342333), c_Complete__Lattice_OInf__class_OInf(_1342333, _1342335)), _1342337)), 31419 ^ _779203 : [(31422 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342333), 31418 ^ [_1342333, _1342335, _1342337]), _1342337)))], (31420 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1342333), 31418 ^ [_1342333, _1342335, _1342337]), _1342335)))]]]]], (1510 ^ _779203) ^ [_801038, _801040] : [-(class_Lazy__Sequence_Osmall__lazy(_801038)), _801040 = _801038, class_Lazy__Sequence_Osmall__lazy(_801040)], (23683 ^ _779203) ^ [_1196078, _1196080, _1196082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1196078), _1196080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1196078), _1196082)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1196080), _1196082))))], (13711 ^ _779203) ^ [_1017247, _1017249, _1017251, _1017253] : [class_Fields_Olinordered__field__inverse__zero(_1017247), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017247), _1017249), _1017251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017247), _1017253), c_Groups_Ozero__class_Ozero(_1017247))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017247), c_Groups_Ozero__class_Ozero(_1017247)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017247), _1017249), _1017251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017247), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017247), _1017253), _1017249)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017247), _1017253), _1017251))))], (18889 ^ _779203) ^ [_1112013, _1112015] : [_1112013 = _1112015, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1112013) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1112015))], (50623 ^ _779203) ^ [_1804721, _1804723, _1804725] : [50624 ^ _779203 : [(50627 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1804723), _1804725))], (50625 ^ _779203) ^ [] : [_1804721 = 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), _1804721), _1804723)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1804721), _1804725))))], (46955 ^ _779203) ^ [_1723820, _1723822, _1723824] : [-(hAPP(hAPP(c_List_Oappend(_1723820), c_List_OtakeWhile(_1723820, _1723822, _1723824)), c_List_OdropWhile(_1723820, _1723822, _1723824)) = _1723824)], (25712 ^ _779203) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (16665 ^ _779203) ^ [_1072285, _1072287, _1072289] : [class_Orderings_Olinorder(_1072285), hBOOL(hAPP(c_Finite__Set_Ofinite(_1072285), _1072287)), -(_1072287 = c_Orderings_Obot__class_Obot(tc_fun(_1072285, tc_HOL_Obool))), 16676 ^ _779203 : [(16677 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072285), _1072289), hAPP(c_Finite__Set_Ofold1(_1072285, c_Orderings_Oord__class_Omin(_1072285)), _1072287))), 16680 ^ _779203 : [(16681 ^ _779203) ^ [_1072578] : [hBOOL(hAPP(hAPP(c_member(_1072285), _1072578), _1072287)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072285), _1072289), _1072578)))]]], (16687 ^ _779203) ^ [] : [16689 ^ _779203 : [(16692 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072285), _1072289), 16688 ^ [_1072285, _1072287, _1072289]))], (16690 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1072285), 16688 ^ [_1072285, _1072287, _1072289]), _1072287)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1072285), _1072289), hAPP(c_Finite__Set_Ofold1(_1072285, c_Orderings_Oord__class_Omin(_1072285)), _1072287))))]]], (45855 ^ _779203) ^ [_1702130, _1702132] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1702130), _1702132) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1702130, _1702132)))], (45640 ^ _779203) ^ [_1696302, _1696304, _1696306] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1696302, tc_HOL_Obool)), hAPP(c_List_Oset(_1696302), hAPP(c_List_Ofilter(_1696302, _1696304), _1696306))), hAPP(c_List_Oset(_1696302), _1696306))))], (2292 ^ _779203) ^ [_812701, _812703, _812705, _812707] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_812707, _812703) = c_Code__Numeral_Odiv__mod__code__numeral(_812705, _812701)), _812707 = _812705, _812703 = _812701], (28782 ^ _779203) ^ [_1288217, _1288219] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1288217), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1288219) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1288217, _1288219))], (16052 ^ _779203) ^ [_1061029, _1061031, _1061033, _1061035] : [class_Int_Onumber__ring(_1061029), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061029), hAPP(c_Int_Onumber__class_Onumber__of(_1061029), _1061031)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1061029), hAPP(c_Int_Onumber__class_Onumber__of(_1061029), _1061033)), _1061035)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1061029), hAPP(c_Int_Onumber__class_Onumber__of(_1061029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1061031), _1061033))), _1061035))], (38312 ^ _779203) ^ [_1516907, _1516909, _1516911, _1516913, _1516915, _1516917, _1516919, _1516921, _1516923, _1516925] : [hAPP(c_Set_Oimage(_1516907, _1516909, _1516911), _1516913) = _1516915, hAPP(c_Set_Oimage(_1516917, _1516919, _1516921), _1516923) = _1516925, -(hAPP(c_Set_Oimage(tc_prod(_1516907, _1516917), tc_prod(_1516909, _1516919), c_Product__Type_Omap__pair(_1516907, _1516909, _1516917, _1516919, _1516911, _1516921)), hAPP(hAPP(c_Product__Type_OSigma(_1516907, _1516917), _1516913), hAPP(c_COMBK(tc_fun(_1516917, tc_HOL_Obool), _1516907), _1516923))) = hAPP(hAPP(c_Product__Type_OSigma(_1516909, _1516919), _1516915), hAPP(c_COMBK(tc_fun(_1516919, tc_HOL_Obool), _1516909), _1516925)))], (40685 ^ _779203) ^ [_1576739, _1576741, _1576743, _1576745, _1576747] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576741, _1576739)), hAPP(hAPP(c_Product__Type_OPair(_1576741, _1576739), _1576745), _1576743)), _1576747)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576739, _1576741)), hAPP(hAPP(c_Product__Type_OPair(_1576739, _1576741), _1576743), _1576745)), hAPP(c_Relation_Oconverse(_1576741, _1576739), _1576747))))], (16200 ^ _779203) ^ [_1063630, _1063632, _1063634, _1063636] : [class_Fields_Ofield__inverse__zero(_1063630), class_Int_Onumber(_1063630), 16207 ^ _779203 : [(16208 ^ _779203) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1063630), _1063632), hAPP(c_Int_Onumber__class_Onumber__of(_1063630), _1063634)) = _1063636, 16211 ^ _779203 : [(16218 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1063630), _1063634) = c_Groups_Ozero__class_Ozero(_1063630), -(_1063636 = c_Groups_Ozero__class_Ozero(_1063630))], (16212 ^ _779203) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1063630), _1063634) = c_Groups_Ozero__class_Ozero(_1063630)), -(_1063632 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063630), _1063636), hAPP(c_Int_Onumber__class_Onumber__of(_1063630), _1063634)))]]], (16224 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1063630), _1063632), hAPP(c_Int_Onumber__class_Onumber__of(_1063630), _1063634)) = _1063636), 16227 ^ _779203 : [(16230 ^ _779203) ^ [] : [_1063632 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063630), _1063636), hAPP(c_Int_Onumber__class_Onumber__of(_1063630), _1063634))], (16228 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1063630), _1063634) = c_Groups_Ozero__class_Ozero(_1063630)]], 16231 ^ _779203 : [(16234 ^ _779203) ^ [] : [_1063636 = c_Groups_Ozero__class_Ozero(_1063630)], (16232 ^ _779203) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1063630), _1063634) = c_Groups_Ozero__class_Ozero(_1063630))]]]]], (22434 ^ _779203) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (18349 ^ _779203) ^ [_1102920] : [class_Int_Onumber__ring(_1102920), -(c_Groups_Ozero__class_Ozero(_1102920) = hAPP(c_Int_Onumber__class_Onumber__of(_1102920), c_Int_OPls))], (35163 ^ _779203) ^ [_1433893, _1433895, _1433897, _1433899, _1433901] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433893, tc_fun(_1433895, tc_HOL_Obool)), _1433897), _1433899), _1433901))), 35164 ^ _779203 : [(35165 ^ _779203) ^ [_1433965] : [hBOOL(hAPP(hAPP(c_member(_1433893), _1433965), _1433897)), hBOOL(hAPP(hAPP(_1433899, _1433965), _1433901))]]], (47944 ^ _779203) ^ [_1745210, _1745212, _1745214, _1745216] : [-(c_List_Olist__ex1(_1745210, _1745212, hAPP(hAPP(c_List_Olist_OCons(_1745210), _1745214), _1745216))), 47947 ^ _779203 : [(47950 ^ _779203) ^ [] : [c_List_Olist__all(_1745210, hAPP(hAPP(c_COMBS(_1745210, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1745210), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1745210), c_fNot), _1745212))), hAPP(c_fequal, _1745214)), _1745216)], (47948 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1745212, _1745214)))]], 47951 ^ _779203 : [(47954 ^ _779203) ^ [] : [c_List_Olist__ex1(_1745210, _1745212, _1745216)], (47952 ^ _779203) ^ [] : [hBOOL(hAPP(_1745212, _1745214))]]], (49296 ^ _779203) ^ [_1776082, _1776084, _1776086] : [c_Relation_Osym(_1776082, _1776084), c_Relation_Osym(_1776082, _1776086), -(c_Relation_Osym(_1776082, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1776082, _1776082), tc_HOL_Obool)), _1776084), _1776086)))], (42690 ^ _779203) ^ [_1630172, _1630174] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630172)), _1630174) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1630174 = c_List_Olist_ONil(_1630172))], (40221 ^ _779203) ^ [_1564796, _1564798] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564796, _1564796)), c_Transitive__Closure_Otrancl(_1564796, _1564798))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564796, _1564796)), _1564798)))], (43564 ^ _779203) ^ [_1650266, _1650268, _1650270, _1650272] : [-(hAPP(hAPP(c_List_Oappend(_1650266), _1650268), _1650270) = _1650272), _1650268 = hAPP(hAPP(c_List_Otake(_1650266), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650266)), _1650268)), _1650272), _1650270 = hAPP(hAPP(c_List_Odrop(_1650266), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650266)), _1650268)), _1650272)], (29448 ^ _779203) ^ [_1301676, _1301678, _1301680, _1301682] : [class_Lattices_Osemilattice__inf(_1301676), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301676), _1301678), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1301676), _1301680), _1301682))), 29455 ^ _779203 : [(29458 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301676), _1301678), _1301682)))], (29456 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301676), _1301678), _1301680)))]]], (2986 ^ _779203) ^ [_823514, _823516, _823518, _823520] : [-(c_List_Olexn(_823520, _823516) = c_List_Olexn(_823518, _823514)), _823520 = _823518, _823516 = _823514], (10667 ^ _779203) ^ [_963816, _963818] : [-(_963816 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _963816), _963818) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _963818), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _963816), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _963818)))], (2876 ^ _779203) ^ [_821787, _821789, _821791, _821793] : [-(c_Nitpick_Oinverse__frac(_821793, _821789) = c_Nitpick_Oinverse__frac(_821791, _821787)), _821793 = _821791, _821789 = _821787], (28228 ^ _779203) ^ [_1278108, _1278110, _1278112] : [class_Orderings_Oorder(_1278108), 28231 ^ _779203 : [(28238 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278108), _1278112), _1278110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1278108, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1278108), _1278110)), hAPP(c_SetInterval_Oord__class_OatLeast(_1278108), _1278112))))], (28232 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1278108, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1278108), _1278110)), hAPP(c_SetInterval_Oord__class_OatLeast(_1278108), _1278112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278108), _1278112), _1278110)))]]], (45780 ^ _779203) ^ [_1699356, _1699358] : [45782 ^ _779203 : [(45785 ^ _779203) ^ [] : [45781 ^ [_1699356, _1699358] = c_List_Olist_ONil(_1699356)], (45783 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699356)), 45781 ^ [_1699356, _1699358]), hAPP(c_List_Oset(tc_List_Olist(_1699356)), _1699358))))]], -(c_List_Otranspose(_1699356, _1699358) = c_List_Olist_ONil(tc_List_Olist(_1699356)))], (37675 ^ _779203) ^ [_1494190, _1494192, _1494194, _1494196, _1494198, _1494200] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494190, _1494192)), hAPP(hAPP(c_Product__Type_OPair(_1494190, _1494192), _1494194), _1494196)), hAPP(hAPP(c_Product__Type_OSigma(_1494190, _1494192), _1494198), _1494200))), -(hBOOL(hAPP(hAPP(c_member(_1494190), _1494194), _1494198)))], (52265 ^ _779203) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (51513 ^ _779203) ^ [_1820226, _1820228] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820226), _1820228)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820228), _1820226))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820228), _1820226)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1820226), _1820228)))], (46618 ^ _779203) ^ [_1716613, _1716615, _1716617, _1716619] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716613)), _1716615) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1716617)), _1716619), -(hAPP(hAPP(c_List_Ozip(_1716613, _1716617), hAPP(c_List_Orev(_1716613), _1716615)), hAPP(c_List_Orev(_1716617), _1716619)) = hAPP(c_List_Orev(tc_prod(_1716613, _1716617)), hAPP(hAPP(c_List_Ozip(_1716613, _1716617), _1716615), _1716619)))], (40285 ^ _779203) ^ [_1566354, _1566356, _1566358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566354, _1566354), tc_HOL_Obool)), _1566356), hAPP(hAPP(c_Product__Type_OSigma(_1566354, _1566354), _1566358), hAPP(c_COMBK(tc_fun(_1566354, tc_HOL_Obool), _1566354), _1566358)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566354, _1566354), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1566354, _1566356)), hAPP(hAPP(c_Product__Type_OSigma(_1566354, _1566354), _1566358), hAPP(c_COMBK(tc_fun(_1566354, tc_HOL_Obool), _1566354), _1566358)))))], (19003 ^ _779203) ^ [_1113967, _1113969] : [class_Rings_Osemiring__1(_1113967), -(hBOOL(hAPP(hAPP(c_member(_1113967), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1113967), _1113969)), c_Nat_Osemiring__1__class_ONats(_1113967))))], (29976 ^ _779203) ^ [_1312852, _1312854, _1312856] : [class_Orderings_Oorder(_1312852), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312852, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1312852, _1312854, _1312856)), hAPP(c_SetInterval_Oord__class_OatLeast(_1312852), _1312856)) = c_Orderings_Obot__class_Obot(tc_fun(_1312852, tc_HOL_Obool)))], (5737 ^ _779203) ^ [_869890, _869892, _869894, _869896] : [_869890 = _869892, 5742 ^ _779203 : [(5745 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_869894), _869896), _869892)))], (5743 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_869894), _869896), _869890)))]], 5746 ^ _779203 : [(5749 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_869894), _869896), _869892))], (5747 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_869894), _869896), _869890))]]], (7071 ^ _779203) ^ [_895934, _895936, _895938, _895940, _895942] : [class_Groups_Oordered__ab__group__add(_895934), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_895934), _895936), _895938) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_895934), _895940), _895942), 7078 ^ _779203 : [(7085 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895934), _895940), _895942)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895934), _895936), _895938)))], (7079 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895934), _895936), _895938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_895934), _895940), _895942)))]]], (48717 ^ _779203) ^ [_1762520, _1762522, _1762524, _1762526] : [-(c_Random__Sequence_Omap(_1762520, _1762522, _1762524, _1762526) = c_Random__Sequence_Obind(_1762520, _1762522, _1762526, hAPP(c_Fun_Ocomp(_1762522, 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(_1762522)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1762520, c_Random__Sequence_Osingle(_1762522)), _1762524)))], (37862 ^ _779203) ^ [_1500036, _1500038, _1500040, _1500042, _1500044, _1500046] : [class_Groups_Ocomm__monoid__mult(_1500036), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500038), _1500040)), 37872 ^ _779203 : [(37875 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1500042), hAPP(_1500044, 37871 ^ [_1500036, _1500038, _1500040, _1500042, _1500044, _1500046])))], (37873 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1500038), 37871 ^ [_1500036, _1500038, _1500040, _1500042, _1500044, _1500046]), _1500040)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1500036, _1500038, c_Groups_Otimes__class_Otimes(_1500036)), hAPP(hAPP(c_COMBS(_1500038, tc_fun(_1500042, tc_HOL_Obool), _1500036), hAPP(hAPP(c_COMBC(_1500038, _1500036, tc_fun(tc_fun(_1500042, tc_HOL_Obool), _1500036)), hAPP(hAPP(c_COMBB(tc_fun(_1500042, _1500036), tc_fun(_1500036, tc_fun(tc_fun(_1500042, tc_HOL_Obool), _1500036)), _1500038), c_Finite__Set_Ofold__image(_1500036, _1500042, c_Groups_Otimes__class_Otimes(_1500036))), _1500046)), c_Groups_Oone__class_Oone(_1500036))), _1500044)), c_Groups_Oone__class_Oone(_1500036)), _1500040) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1500036, tc_prod(_1500038, _1500042), c_Groups_Otimes__class_Otimes(_1500036)), hAPP(c_Product__Type_Oprod_Oprod__case(_1500038, _1500042, _1500036), _1500046)), c_Groups_Oone__class_Oone(_1500036)), hAPP(hAPP(c_Product__Type_OSigma(_1500038, _1500042), _1500040), _1500044)))], (18594 ^ _779203) ^ [_1107151] : [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), _1107151))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1107151)))], (5717 ^ _779203) ^ [_869525, _869527, _869529, _869531, _869533] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_869525), _869527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869529, tc_HOL_Obool)), _869531), hAPP(c_Set_Oimage(_869525, _869529, _869533), _869527))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_869529), _869531)))], (49238 ^ _779203) ^ [_1774687, _1774689, _1774691, _1774693, _1774695, _1774697] : [-(c_Partial__Function_Ofun__lub(_1774687, _1774689, _1774691, _1774693, _1774695, _1774697) = hAPP(_1774693, hAPP(c_Set_OCollect(_1774687), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774691, _1774687), tc_HOL_Obool), tc_HOL_Obool, _1774687), c_HOL_OEx(tc_fun(_1774691, _1774687))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1774691, _1774687), tc_HOL_Obool), tc_fun(tc_fun(_1774691, _1774687), tc_HOL_Obool), _1774687), hAPP(c_COMBS(tc_fun(_1774691, _1774687), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1774691, _1774687)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1774691, _1774687), tc_fun(tc_fun(_1774691, _1774687), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1774691, _1774687))), _1774695)))), hAPP(hAPP(c_COMBC(_1774687, tc_fun(tc_fun(_1774691, _1774687), _1774687), tc_fun(tc_fun(_1774691, _1774687), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1774687, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1774691, _1774687), _1774687), tc_fun(tc_fun(_1774691, _1774687), tc_HOL_Obool)), _1774687), c_COMBB(_1774687, tc_HOL_Obool, tc_fun(_1774691, _1774687))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1774691, _1774687), _1774691, _1774687), c_COMBI(tc_fun(_1774691, _1774687))), _1774697)))))))], (40440 ^ _779203) ^ [_1570898] : [-(c_Transitive__Closure_Ortrancl(_1570898, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1570898, _1570898), tc_HOL_Obool))) = c_Relation_OId(_1570898))], (32649 ^ _779203) ^ [_1373630, _1373632, _1373634, _1373636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1373630, tc_fun(_1373632, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1373630, tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_fun(_1373632, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373632, tc_fun(tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_fun(_1373632, tc_HOL_Obool)), _1373630), c_COMBC(_1373632, tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373632, tc_prod(_1373630, _1373632)), tc_fun(_1373632, tc_fun(tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_HOL_Obool)), _1373630), hAPP(c_COMBB(tc_prod(_1373630, _1373632), tc_fun(tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_HOL_Obool), _1373632), c_member(tc_prod(_1373630, _1373632)))), c_Product__Type_OPair(_1373630, _1373632)))), _1373634)), hAPP(hAPP(c_COMBC(_1373630, tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_fun(_1373632, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373632, tc_fun(tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_fun(_1373632, tc_HOL_Obool)), _1373630), c_COMBC(_1373632, tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1373632, tc_prod(_1373630, _1373632)), tc_fun(_1373632, tc_fun(tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_HOL_Obool)), _1373630), hAPP(c_COMBB(tc_prod(_1373630, _1373632), tc_fun(tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool), tc_HOL_Obool), _1373632), c_member(tc_prod(_1373630, _1373632)))), c_Product__Type_OPair(_1373630, _1373632)))), _1373636))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1373630, _1373632), tc_HOL_Obool)), _1373634), _1373636)))], (28798 ^ _779203) ^ [_1288544, _1288546, _1288548] : [class_Orderings_Olinorder(_1288544), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288544), _1288546), _1288548)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288544, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1288544), _1288546)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1288544, _1288546, _1288548)) = hAPP(c_SetInterval_Oord__class_OatMost(_1288544), _1288548))], (7897 ^ _779203) ^ [_909137, _909139, _909141] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_909137, tc_HOL_Obool)), _909139), _909141))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909137, tc_HOL_Obool)), _909139), _909141)), -(_909139 = _909141)], (45925 ^ _779203) ^ [_1703272, _1703274, _1703276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703272), _1703274)), _1703276)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1703274), c_List_Oupt(_1703272, _1703276)) = c_List_Oupt(_1703272, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703272), _1703274)))], (44341 ^ _779203) ^ [_1666618, _1666620, _1666622, _1666624] : [hAPP(hAPP(c_List_Omap(_1666618, _1666620), _1666622), _1666624) = c_List_Olist_ONil(_1666620), -(_1666624 = c_List_Olist_ONil(_1666618))], (33485 ^ _779203) ^ [_1391959, _1391961, _1391963, _1391965, _1391967] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1391959, _1391961), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1391963), _1391965))), -(_1391961 = 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), _1391967), _1391959), _1391961), 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), _1391967), _1391963)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1391967), _1391965)), _1391961))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1391967), _1391965), _1391961)))))], (20829 ^ _779203) ^ [_1146848, _1146850] : [class_Groups_Osgn__if(_1146848), 20832 ^ _779203 : [(20839 ^ _779203) ^ [] : [-(_1146850 = c_Groups_Ozero__class_Ozero(_1146848)), 20842 ^ _779203 : [(20849 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146848), c_Groups_Ozero__class_Ozero(_1146848)), _1146850))), -(c_Groups_Osgn__class_Osgn(_1146848, _1146850) = hAPP(c_Groups_Ouminus__class_Ouminus(_1146848), c_Groups_Oone__class_Oone(_1146848)))], (20843 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146848), c_Groups_Ozero__class_Ozero(_1146848)), _1146850)), -(c_Groups_Osgn__class_Osgn(_1146848, _1146850) = c_Groups_Oone__class_Oone(_1146848))]]], (20833 ^ _779203) ^ [] : [_1146850 = c_Groups_Ozero__class_Ozero(_1146848), -(c_Groups_Osgn__class_Osgn(_1146848, _1146850) = c_Groups_Ozero__class_Ozero(_1146848))]]], (52597 ^ _779203) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (29406 ^ _779203) ^ [_1300743, _1300745, _1300747, _1300749] : [hBOOL(hAPP(hAPP(c_member(_1300743), _1300745), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300743, tc_HOL_Obool)), _1300747), _1300749))), -(hBOOL(hAPP(hAPP(c_member(_1300743), _1300745), _1300749)))], (48298 ^ _779203) ^ [_1753137, _1753139, _1753141] : [c_List_Oreplicate(_1753137, _1753139, _1753141) = c_List_Olist_ONil(_1753137), -(_1753139 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24127 ^ _779203) ^ [_1204143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1204143)), -(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), _1204143), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (16032 ^ _779203) ^ [_1060543, _1060545, _1060547, _1060549] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060543), hAPP(c_Int_Onumber__class_Onumber__of(_1060543), _1060545)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060543), _1060547), _1060549)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1060543), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060543), hAPP(c_Int_Onumber__class_Onumber__of(_1060543), _1060545)), _1060547)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1060543), hAPP(c_Int_Onumber__class_Onumber__of(_1060543), _1060545)), _1060549))), class_Int_Onumber(_1060543), class_Rings_Osemiring(_1060543)], (14161 ^ _779203) ^ [_1025613, _1025615, _1025617, _1025619] : [class_Fields_Ofield__inverse__zero(_1025613), 14164 ^ _779203 : [(14165 ^ _779203) ^ [] : [_1025615 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025613), _1025617), _1025619), 14168 ^ _779203 : [(14175 ^ _779203) ^ [] : [_1025619 = c_Groups_Ozero__class_Ozero(_1025613), -(_1025615 = c_Groups_Ozero__class_Ozero(_1025613))], (14169 ^ _779203) ^ [] : [-(_1025619 = c_Groups_Ozero__class_Ozero(_1025613)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025613), _1025615), _1025619) = _1025617)]]], (14181 ^ _779203) ^ [] : [-(_1025615 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025613), _1025617), _1025619)), 14184 ^ _779203 : [(14187 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1025613), _1025615), _1025619) = _1025617], (14185 ^ _779203) ^ [] : [_1025619 = c_Groups_Ozero__class_Ozero(_1025613)]], 14188 ^ _779203 : [(14191 ^ _779203) ^ [] : [_1025615 = c_Groups_Ozero__class_Ozero(_1025613)], (14189 ^ _779203) ^ [] : [-(_1025619 = c_Groups_Ozero__class_Ozero(_1025613))]]]]], (25510 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6221 ^ _779203) ^ [_879084, _879086, _879088, _879090] : [-(hBOOL(hAPP(hAPP(c_member(_879084), _879086), _879088))), 6224 ^ _779203 : [(6231 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879084, tc_HOL_Obool)), _879088), _879090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879084, tc_HOL_Obool)), _879088), hAPP(hAPP(c_Set_Oinsert(_879084), _879086), _879090))))], (6225 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879084, tc_HOL_Obool)), _879088), hAPP(hAPP(c_Set_Oinsert(_879084), _879086), _879090))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879084, tc_HOL_Obool)), _879088), _879090)))]]], (9405 ^ _779203) ^ [_939542, _939544] : [_939542 = _939544, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939542), _939544)))], (47209 ^ _779203) ^ [_1729028, _1729030] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1729028)), _1729030)), 47215 ^ _779203 : [(47218 ^ _779203) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1729028), 47214 ^ [_1729028, _1729030]))], (47216 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1729028)), 47214 ^ [_1729028, _1729030]), hAPP(c_List_Oset(tc_List_Olist(_1729028)), _1729030))))]], 47222 ^ _779203 : [(47226 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1729028)), 47224 ^ [_1729028, _1729030]), hAPP(c_List_Oset(tc_List_Olist(_1729028)), _1729030))))], (47228 ^ _779203) ^ [] : [47221 ^ [_1729028, _1729030] = 47224 ^ [_1729028, _1729030]], (47230 ^ _779203) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1729028, tc_HOL_Obool)), hAPP(c_List_Oset(_1729028), 47221 ^ [_1729028, _1729030])), hAPP(c_List_Oset(_1729028), 47224 ^ [_1729028, _1729030])) = c_Orderings_Obot__class_Obot(tc_fun(_1729028, tc_HOL_Obool))], (47223 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1729028)), 47221 ^ [_1729028, _1729030]), hAPP(c_List_Oset(tc_List_Olist(_1729028)), _1729030))))]], -(hBOOL(hAPP(c_List_Odistinct(_1729028), c_List_Oconcat(_1729028, _1729030))))], (44185 ^ _779203) ^ [_1663251, _1663253, _1663255] : [-(_1663251 = c_List_Olist_ONil(_1663253)), -(c_List_Olast(_1663253, hAPP(hAPP(c_List_Olist_OCons(_1663253), _1663255), _1663251)) = c_List_Olast(_1663253, _1663251))], (40755 ^ _779203) ^ [_1578410, _1578412, _1578414] : [c_Relation_Orefl__on(_1578410, _1578412, hAPP(c_Relation_Oconverse(_1578410, _1578410), _1578414)), -(c_Relation_Orefl__on(_1578410, _1578412, _1578414))], (51085 ^ _779203) ^ [_1813226, _1813228, _1813230] : [class_Divides_Oring__div(_1813226), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813226), _1813228), _1813230)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813226), hAPP(c_Groups_Ouminus__class_Ouminus(_1813226), _1813230)), _1813228) = hAPP(c_Groups_Ouminus__class_Ouminus(_1813226), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813226), _1813230), _1813228)))], (10675 ^ _779203) ^ [_963915] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _963915)))], (27536 ^ _779203) ^ [_1264359, _1264361, _1264363, _1264365] : [class_Lattices_Osemilattice__sup(_1264359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264359), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264359), _1264361), _1264363)), _1264365)), 27543 ^ 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c_Big__Operators_Olinorder__class_OMax(_1322644, _1322646)), c_Big__Operators_Olinorder__class_OMax(_1322644, _1322648)))], (47985 ^ _779203) ^ [_1746063, _1746065, _1746067] : [-(c_List_Olist__ex1(_1746063, _1746065, _1746067)), 47986 ^ _779203 : [(47987 ^ _779203) ^ [_1746157] : [hBOOL(hAPP(hAPP(c_member(_1746063), _1746157), hAPP(c_List_Oset(_1746063), _1746067))), hBOOL(hAPP(_1746065, _1746157)), 47995 ^ _779203 : [(48000 ^ _779203) ^ [] : [47994 ^ [_1746063, _1746065, _1746067, _1746157] = _1746157], (47998 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1746065, 47994 ^ [_1746063, _1746065, _1746067, _1746157])))], (47996 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1746063), 47994 ^ [_1746063, _1746065, _1746067, _1746157]), hAPP(c_List_Oset(_1746063), _1746067))))]]]]], (27572 ^ _779203) ^ [_1265059, _1265061, _1265063, _1265065] : [27573 ^ _779203 : [(27576 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1265059), _1265061), _1265065))], (27574 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1265059), _1265061), _1265063))]], -(hBOOL(hAPP(hAPP(c_member(_1265059), _1265061), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1265059, tc_HOL_Obool)), _1265063), _1265065))))], (41401 ^ _779203) ^ [_1595893, _1595895, _1595897] : [-(c_List_Oset__Cons(_1595893, _1595895, _1595897) = hAPP(c_Set_OCollect(tc_List_Olist(_1595893)), hAPP(hAPP(c_COMBB(tc_fun(_1595893, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1595893)), c_HOL_OEx(_1595893)), hAPP(hAPP(c_COMBB(tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool)), tc_fun(_1595893, tc_HOL_Obool), tc_List_Olist(_1595893)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool), tc_HOL_Obool, _1595893), c_HOL_OEx(tc_List_Olist(_1595893)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595893), tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool)), tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595893, tc_fun(tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool))), tc_fun(tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool)), tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool))), tc_List_Olist(_1595893)), c_COMBS(_1595893, tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1595893, tc_fun(tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool))), tc_List_Olist(_1595893)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595893), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool)), _1595893), c_COMBS(tc_List_Olist(_1595893), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool)), tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1595893)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595893), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1595893), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1595893)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595893), tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_List_Olist(_1595893))), tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1595893), tc_List_Olist(_1595893)), tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool)), tc_fun(tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_List_Olist(_1595893))), tc_fun(_1595893, tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool))), tc_List_Olist(_1595893)), c_COMBB(tc_fun(tc_List_Olist(_1595893), tc_List_Olist(_1595893)), tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool), _1595893)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1595893), tc_List_Olist(_1595893)), tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool)), tc_List_Olist(_1595893)), c_COMBB(tc_List_Olist(_1595893), tc_HOL_Obool, tc_List_Olist(_1595893))), c_fequal))), c_List_Olist_OCons(_1595893)))))), hAPP(hAPP(c_COMBC(_1595893, tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool), tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool)), _1595893), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1595893))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1595893), c_fconj), hAPP(hAPP(c_COMBC(_1595893, tc_fun(_1595893, tc_HOL_Obool), tc_HOL_Obool), c_member(_1595893)), _1595895)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1595893), tc_fun(tc_List_Olist(_1595893), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1595893))), _1595897)))))))], (50549 ^ _779203) ^ [_1803440, _1803442, _1803444, _1803446, _1803448] : [-(c_New__DSequence_Opos__map(_1803440, _1803442, _1803444, _1803446, _1803448) = c_Lazy__Sequence_Omap(_1803440, _1803442, _1803444, hAPP(_1803446, _1803448)))], (26644 ^ _779203) ^ [_1248223, _1248225, _1248227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1248223)), 26647 ^ _779203 : [(26648 ^ _779203) ^ [_1248357] : [26650 ^ _779203 : [(26656 ^ _779203) ^ [] : [-(_1248357 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26652 ^ [_1248223, _1248225, _1248227, _1248357]), 26649 ^ [_1248223, _1248225, _1248227, _1248357]))], (26654 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26652 ^ [_1248223, _1248225, _1248227, _1248357]), _1248225)))], (26651 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26649 ^ [_1248223, _1248225, _1248227, _1248357]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1248223))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1248357), _1248227)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1248357), _1248223)), _1248227)))]]], (15390 ^ _779203) ^ [_1048953, _1048955] : [class_Orderings_Olinorder(_1048953), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1048953), _1048955), _1048955) = _1048955)], (24016 ^ _779203) ^ [_1202061, _1202063, _1202065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202061)), 24019 ^ _779203 : [(24020 ^ _779203) ^ [] : [-(_1202063 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1202065), _1202061)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1202061), _1202063)), _1202065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1202061), hAPP(c_Nat_OSuc, _1202063))))], (24030 ^ _779203) ^ [] : [_1202063 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1202065), _1202061), 24033 ^ _779203 : [(24036 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1202061), hAPP(c_Nat_OSuc, _1202063)))))], (24034 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1202061), _1202063)), _1202065)))]]]]], (52373 ^ _779203) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (45999 ^ _779203) ^ [_1704664, _1704666] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1704664, _1704666) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1704664), hAPP(c_Nat_OSuc, _1704666))))], (45989 ^ _779203) ^ [_1704463, _1704465] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1704463, _1704465) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704463, hAPP(c_Nat_OSuc, _1704465))))], (17384 ^ _779203) ^ [_1085761, _1085763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085761), _1085763)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085761), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085763), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (22602 ^ _779203) ^ [_1177770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177770), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1177770) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10923 ^ _779203) ^ [_967830, _967832, _967834] : [class_Groups_Oab__group__add(_967830), 10926 ^ _779203 : [(10933 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967830), _967832), _967834) = c_Groups_Ozero__class_Ozero(_967830), -(_967832 = _967834)], (10927 ^ _779203) ^ [] : [_967832 = _967834, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967830), _967832), _967834) = c_Groups_Ozero__class_Ozero(_967830))]]], (31843 ^ _779203) ^ [_1352153, _1352155, _1352157, _1352159, _1352161] : [c_Finite__Set_Ofun__left__comm(_1352153, _1352155, _1352157), -(c_Finite__Set_Ofun__left__comm(_1352159, _1352155, hAPP(hAPP(c_COMBB(_1352153, tc_fun(_1352155, _1352155), _1352159), _1352157), _1352161)))], (6999 ^ _779203) ^ [_894340, _894342, _894344, _894346, _894348, _894350] : [c_Finite__Set_Ofolding__image__simple(_894340, _894342, _894344, _894346, _894348, _894350), -(hAPP(_894350, c_Orderings_Obot__class_Obot(tc_fun(_894342, tc_HOL_Obool))) = _894346)], (31769 ^ _779203) ^ [_1350234, _1350236, _1350238] : [_1350236 = _1350238, -(hAPP(hAPP(c_COMBC(_1350234, tc_fun(_1350234, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350234)), _1350236) = hAPP(hAPP(c_COMBC(_1350234, tc_fun(_1350234, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350234)), _1350238))], (20738 ^ _779203) ^ [_1145275, _1145277, _1145279] : [_1145277 = _1145279, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1145275, tc_HOL_Obool)), _1145277) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1145275, tc_HOL_Obool)), _1145279))], (24085 ^ _779203) ^ [_1203397, _1203399] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1203397, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1203399)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1203397, 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)))), _1203399)))], (26054 ^ _779203) ^ [_1237343, _1237345] : [class_Rings_Olinordered__idom(_1237343), 26057 ^ _779203 : [(26064 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237345), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237343), hAPP(c_Int_Oring__1__class_Oof__int(_1237343), _1237345)), c_Groups_Ozero__class_Ozero(_1237343))))], (26058 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237343), hAPP(c_Int_Oring__1__class_Oof__int(_1237343), _1237345)), c_Groups_Ozero__class_Ozero(_1237343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237345), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (22952 ^ _779203) ^ [_1183396, _1183398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183396), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22955 ^ _779203 : [(22958 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183396), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183398, _1183396))))], (22956 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183398, _1183396)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (29586 ^ _779203) ^ [_1304091, _1304093, _1304095] : [class_Lattices_Olattice(_1304091), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304091), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1304091), _1304093), _1304095)), _1304095)))], (27328 ^ _779203) ^ [_1260426, _1260428, _1260430] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260426, tc_HOL_Obool)), _1260428), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260426, tc_HOL_Obool)), _1260428), _1260430))))], (47244 ^ _779203) ^ [_1730018, _1730020] : [-(c_Wellfounded_Owf(_1730018, c_List_Omeasures(_1730018, _1730020)))], (28192 ^ _779203) ^ [_1277450, _1277452] : [c_Nat__Transfer_Onat__set(_1277450), c_Nat__Transfer_Onat__set(_1277452), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1277450), _1277452) = 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), _1277450)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1277452))))], (31751 ^ _779203) ^ [_1349782, _1349784, _1349786, _1349788, _1349790] : [class_Groups_Ocomm__monoid__mult(_1349782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1349784), _1349786)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1349784, _1349782), hAPP(hAPP(c_COMBS(_1349784, _1349782, _1349782), hAPP(hAPP(c_COMBB(_1349782, tc_fun(_1349782, _1349782), _1349784), c_Groups_Otimes__class_Otimes(_1349782)), _1349788)), _1349790)), _1349786) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349782), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1349784, _1349782), _1349788), _1349786)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1349784, _1349782), _1349790), _1349786)))], (45356 ^ _779203) ^ [_1689677, _1689679, _1689681] : [hBOOL(hAPP(c_List_Odistinct(_1689677), _1689679)), -(hBOOL(hAPP(c_List_Odistinct(_1689677), hAPP(c_List_OremoveAll(_1689677, _1689681), _1689679))))], (44067 ^ _779203) ^ [_1661246, _1661248, _1661250, _1661252, _1661254] : [class_Orderings_Olinorder(_1661246), 44070 ^ _779203 : [(44079 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1661248), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661248, _1661246, _1661250), _1661252), _1661254)))), -(hBOOL(hAPP(hAPP(c_member(_1661248), _1661252), hAPP(c_List_Oset(_1661248), _1661254)))), hBOOL(hAPP(c_List_Odistinct(_1661248), _1661254))], (44071 ^ _779203) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1661248), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661248, _1661246, _1661250), _1661252), _1661254))), 44074 ^ _779203 : [(44077 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1661248), _1661254)))], (44075 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1661248), _1661252), hAPP(c_List_Oset(_1661248), _1661254)))]]]]], (41266 ^ _779203) ^ [_1592023, _1592025, _1592027] : [-(c_Nitpick_Oof__frac(_1592025, _1592023, _1592027) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1592023), hAPP(c_Int_Oring__1__class_Oof__int(_1592023), hAPP(c_Nitpick_Onum(_1592025), _1592027))), hAPP(c_Int_Oring__1__class_Oof__int(_1592023), hAPP(c_Nitpick_Odenom(_1592025), _1592027)))), class_Rings_Oinverse(_1592023), class_Rings_Oring__1(_1592023)], (46120 ^ _779203) ^ [_1707062, _1707064] : [class_Orderings_Olinorder(_1707062), c_List_Olinorder__class_Osorted(_1707062, _1707064), -(c_List_Olinorder__class_Osorted(_1707062, hAPP(c_List_Otl(_1707062), _1707064)))], (24430 ^ _779203) ^ [_1209559, _1209561] : [class_Rings_Oring__1__no__zero__divisors(_1209559), 24433 ^ _779203 : [(24440 ^ _779203) ^ [] : [_1209561 = c_Groups_Ozero__class_Ozero(_1209559), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1209559), _1209561), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1209559))], (24434 ^ _779203) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1209559), _1209561), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1209559), -(_1209561 = c_Groups_Ozero__class_Ozero(_1209559))]]], (3254 ^ _779203) ^ [_827666, _827668, _827670, _827672] : [-(c_List_Olistsp(_827672, _827668) = c_List_Olistsp(_827670, _827666)), _827672 = _827670, _827668 = _827666], (50685 ^ _779203) ^ [_1805779, _1805781, _1805783, _1805785] : [class_Rings_Ocomm__semiring__1(_1805779), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805779), _1805781), _1805783)), _1805785)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805779), _1805781), _1805785)))], (46003 ^ _779203) ^ [_1704743] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1704743) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1704743))))], (19660 ^ _779203) ^ [_1126111, _1126113, _1126115] : [-(hBOOL(hAPP(hAPP(c_member(_1126111), _1126113), _1126115))), -(hBOOL(hAPP(hAPP(c_member(_1126111), _1126113), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1126111, tc_HOL_Obool)), _1126115))))], (24231 ^ _779203) ^ [_1206050, _1206052] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1206050), _1206052)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206050)), _1206052))], (27150 ^ _779203) ^ [_1257145, _1257147, _1257149, _1257151, _1257153] : [class_Orderings_Olinorder(_1257145), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257145, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257145, _1257147), _1257149)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257145, _1257151), _1257153))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257145), _1257149), _1257147))), 27161 ^ _779203 : [(27164 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257145), _1257149), _1257153)))], (27162 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257145), _1257151), _1257147)))]]], (33693 ^ _779203) ^ [_1395970, _1395972, _1395974, _1395976, _1395978] : [hAPP(c_Product__Type_Osnd(_1395970, _1395972), hAPP(hAPP(c_Product__Type_OPair(_1395970, _1395972), _1395974), _1395976)) = _1395978, -(_1395976 = _1395978)], (8154 ^ _779203) ^ [_914657, _914659, _914661, _914663, _914665] : [hAPP(_914661, _914663) = _914665, -(c_Fun_Ofun__upd(_914657, _914659, _914661, _914663, _914665) = _914661)], (11330 ^ _779203) ^ [_974215, _974217, _974219, _974221] : [class_Groups_Oordered__comm__monoid__add(_974215), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974215), c_Groups_Ozero__class_Ozero(_974215)), _974217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974215), _974219), _974221)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974215), _974219), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974215), _974217), _974221))))], (29340 ^ _779203) ^ [_1299438, _1299440] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299438, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1299438, tc_HOL_Obool))), _1299440) = c_Orderings_Obot__class_Obot(tc_fun(_1299438, tc_HOL_Obool)))], (9514 ^ _779203) ^ [_941558, _941560, _941562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941558), _941560)), _941562)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941560), _941562)))], (31440 ^ _779203) ^ [_1342924, _1342926, _1342928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1342924, tc_HOL_Obool), tc_HOL_Obool)), _1342926), _1342928)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1342924, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342924, tc_HOL_Obool), _1342928)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342924, tc_HOL_Obool), _1342926))))], (8115 ^ _779203) ^ [_913814, _913816, _913818, _913820] : [_913818 = _913820, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_913814, _913816, hAPP(hAPP(c_Set_Oinsert(_913814), _913818), c_Orderings_Obot__class_Obot(tc_fun(_913814, tc_HOL_Obool)))), _913820)))], (34019 ^ _779203) ^ [_1402576, _1402578, _1402580, _1402582, _1402584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1402576, _1402578)), hAPP(_1402576, _1402580))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1402582, _1402582)), hAPP(hAPP(c_Product__Type_OPair(_1402582, _1402582), _1402578), _1402580)), _1402584)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1402582, _1402582)), hAPP(hAPP(c_Product__Type_OPair(_1402582, _1402582), _1402578), _1402580)), c_Wellfounded_Omlex__prod(_1402582, _1402576, _1402584))))], (44311 ^ _779203) ^ [_1665401, _1665403, _1665405, _1665407] : [-(hAPP(hAPP(c_List_Omap(_1665401, _1665403), _1665405), hAPP(c_List_Otl(_1665401), _1665407)) = hAPP(c_List_Otl(_1665403), hAPP(hAPP(c_List_Omap(_1665401, _1665403), _1665405), _1665407)))], (31811 ^ _779203) ^ [_1351394, _1351396, _1351398, _1351400, _1351402] : [class_Groups_Ominus(_1351394), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1351396, _1351394)), _1351398), _1351400), _1351402) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351394), hAPP(_1351398, _1351402)), hAPP(_1351400, _1351402)))], (2434 ^ _779203) ^ [_814926, _814928] : [_814928 = _814926, -(c_SetInterval_Oord__class_OatLeast(_814928) = c_SetInterval_Oord__class_OatLeast(_814926))], (36564 ^ _779203) ^ [_1467273, _1467275, _1467277, _1467279, _1467281] : [c_Fun_Oinj__on(_1467273, _1467275, _1467277, c_Orderings_Otop__class_Otop(tc_fun(_1467273, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1467273, _1467275, _1467277), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467273, tc_HOL_Obool)), _1467279), _1467281)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1467275, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1467273, _1467275, _1467277), _1467279)), hAPP(c_Set_Oimage(_1467273, _1467275, _1467277), _1467281)))], (40368 ^ _779203) ^ [_1569156, _1569158, _1569160] : [-(c_Transitive__Closure_Ortrancl(_1569156, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569156, _1569156), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1569156, _1569158)), c_Transitive__Closure_Ortrancl(_1569156, _1569160))) = c_Transitive__Closure_Ortrancl(_1569156, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569156, _1569156), tc_HOL_Obool)), _1569158), _1569160)))], (43742 ^ _779203) ^ [_1654255, _1654257, _1654259] : [-(hAPP(hAPP(c_List_Odrop(_1654255), _1654257), hAPP(c_List_Otl(_1654255), _1654259)) = hAPP(c_List_Otl(_1654255), hAPP(hAPP(c_List_Odrop(_1654255), _1654257), _1654259)))], (43822 ^ _779203) ^ [_1655878, _1655880, _1655882] : [-(hAPP(c_List_Otl(_1655878), hAPP(hAPP(c_List_Otake(_1655878), _1655880), _1655882)) = hAPP(hAPP(c_List_Otake(_1655878), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655880), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1655878), _1655882)))], (19156 ^ _779203) ^ [_1116597] : [class_Groups_Oordered__ab__group__add__abs(_1116597), -(hAPP(c_Groups_Oabs__class_Oabs(_1116597), c_Groups_Ozero__class_Ozero(_1116597)) = c_Groups_Ozero__class_Ozero(_1116597))], (29564 ^ _779203) ^ [_1303728, _1303730, _1303732] : [class_Lattices_Osemilattice__inf(_1303728), 29567 ^ _779203 : [(29574 ^ _779203) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1303728), _1303730), _1303732) = _1303730, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303728), _1303730), _1303732)))], (29568 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303728), _1303730), _1303732)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1303728), _1303730), _1303732) = _1303730)]]], (46851 ^ _779203) ^ [_1721615, _1721617, _1721619, _1721621, _1721623] : [-(c_List_OtakeWhile(_1721615, _1721617, hAPP(hAPP(c_List_Omap(_1721619, _1721615), _1721621), _1721623)) = hAPP(hAPP(c_List_Omap(_1721619, _1721615), _1721621), c_List_OtakeWhile(_1721619, hAPP(c_Fun_Ocomp(_1721615, tc_HOL_Obool, _1721619, _1721617), _1721621), _1721623)))], (21757 ^ _779203) ^ [_1162204, _1162206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162204), _1162206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1162204)), c_Int_OBit0(_1162206))))], (51437 ^ _779203) ^ [_1818958, _1818960] : [_1818960 = _1818958, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818958), _1818960)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818960), _1818958)))], (19354 ^ _779203) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (35610 ^ _779203) ^ [_1446113, _1446115, _1446117] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446113), _1446115), _1446117) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1446113, tc_fun(tc_fun(_1446113, tc_HOL_Obool), tc_HOL_Obool)), _1446115), hAPP(hAPP(c_COMBC(_1446113, tc_fun(tc_fun(_1446113, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1446113, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446113, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1446113, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1446113, tc_HOL_Obool), tc_HOL_Obool)), _1446113), c_Set_Oinsert(tc_fun(_1446113, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1446113, tc_HOL_Obool), tc_fun(_1446113, tc_HOL_Obool), _1446113), c_Relation_OImage(_1446113, _1446113, _1446117)), hAPP(hAPP(c_COMBC(_1446113, tc_fun(_1446113, tc_HOL_Obool), tc_fun(_1446113, tc_HOL_Obool)), c_Set_Oinsert(_1446113)), c_Orderings_Obot__class_Obot(tc_fun(_1446113, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446113, tc_HOL_Obool), tc_HOL_Obool)))))], (44694 ^ _779203) ^ [_1674639, _1674641] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1674639)), hAPP(c_Code__Numeral_Oof__nat, _1674641)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1674639), _1674641)))], (24824 ^ _779203) ^ [_1216678, _1216680, _1216682, _1216684] : [class_Rings_Olinordered__semidom(_1216678), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216678), c_Groups_Oone__class_Oone(_1216678)), _1216680)), 24831 ^ _779203 : [(24838 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1216682), _1216684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1216678), hAPP(hAPP(c_Power_Opower__class_Opower(_1216678), _1216680), _1216682)), hAPP(hAPP(c_Power_Opower__class_Opower(_1216678), _1216680), _1216684))))], (24832 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1216678), hAPP(hAPP(c_Power_Opower__class_Opower(_1216678), _1216680), _1216682)), hAPP(hAPP(c_Power_Opower__class_Opower(_1216678), _1216680), _1216684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1216682), _1216684)))]]], (4418 ^ _779203) ^ [_846260, _846262] : [_846262 = _846260, -(c_List_Olist_ONil(_846262) = c_List_Olist_ONil(_846260))], (7319 ^ _779203) ^ [_900410, _900412, _900414] : [class_Orderings_Olinorder(_900410), -(_900412 = _900414), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900410), _900412), _900414))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900410), _900414), _900412)))], (15354 ^ _779203) ^ [_1048317, _1048319, _1048321] : [class_Orderings_Olinorder(_1048317), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1048317), _1048319), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048317), _1048319), _1048321)) = _1048319)], (42301 ^ _779203) ^ [_1621921, _1621923, _1621925, _1621927] : [-(hAPP(hAPP(c_List_Olist__update(_1621921, hAPP(hAPP(c_List_Olist_OCons(_1621921), _1621923), _1621925)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1621927) = hAPP(hAPP(c_List_Olist_OCons(_1621921), _1621927), _1621925))], (14741 ^ _779203) ^ [_1036126, _1036128, _1036130] : [class_Fields_Olinordered__field(_1036126), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036126), _1036128), _1036130)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036126), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1036126), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036126), _1036128), _1036130)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1036126), c_Groups_Oone__class_Oone(_1036126)), c_Groups_Oone__class_Oone(_1036126)))), _1036130)))], (27928 ^ _779203) ^ [_1272132, _1272134] : [class_Lattices_Olattice(_1272132), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272132), _1272134), _1272134) = _1272134)], (10 ^ _779203) ^ [_779326, _779328, _779330] : [-(_779330 = _779326), _779330 = _779328, _779328 = _779326], (15015 ^ _779203) ^ [_1041597, _1041599] : [class_Int_Oring__char__0(_1041597), hBOOL(hAPP(hAPP(c_member(_1041597), _1041599), c_Int_Oring__1__class_OInts(_1041597))), 15022 ^ _779203 : [(15029 ^ _779203) ^ [] : [_1041599 = c_Groups_Ozero__class_Ozero(_1041597), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041597), _1041599), _1041599) = c_Groups_Ozero__class_Ozero(_1041597))], (15023 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041597), _1041599), _1041599) = c_Groups_Ozero__class_Ozero(_1041597), -(_1041599 = c_Groups_Ozero__class_Ozero(_1041597))]]], (27806 ^ _779203) ^ [_1269542, _1269544] : [class_Lattices_Osemilattice__sup(_1269542), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269542), _1269544), _1269544) = _1269544)], (26038 ^ _779203) ^ [_1237090, _1237092] : [class_Rings_Olinordered__idom(_1237090), 26041 ^ _779203 : [(26048 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237090), c_Groups_Ozero__class_Ozero(_1237090)), hAPP(c_Int_Oring__1__class_Oof__int(_1237090), _1237092))))], (26042 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1237090), c_Groups_Ozero__class_Ozero(_1237090)), hAPP(c_Int_Oring__1__class_Oof__int(_1237090), _1237092))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237092)))]]], (52605 ^ _779203) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (41645 ^ _779203) ^ [_1603762, _1603764, _1603766, _1603768] : [c_List_Olistrelp(_1603762, hAPP(hAPP(c_COMBC(_1603762, tc_fun(tc_prod(_1603762, _1603762), tc_HOL_Obool), tc_fun(_1603762, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603762, tc_fun(tc_fun(tc_prod(_1603762, _1603762), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1603762, _1603762), tc_HOL_Obool), tc_fun(_1603762, tc_HOL_Obool)), _1603762), c_COMBC(_1603762, tc_fun(tc_prod(_1603762, _1603762), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1603762, tc_prod(_1603762, _1603762)), tc_fun(_1603762, tc_fun(tc_fun(tc_prod(_1603762, _1603762), tc_HOL_Obool), tc_HOL_Obool)), _1603762), hAPP(c_COMBB(tc_prod(_1603762, _1603762), tc_fun(tc_fun(tc_prod(_1603762, _1603762), tc_HOL_Obool), tc_HOL_Obool), _1603762), c_member(tc_prod(_1603762, _1603762)))), c_Product__Type_OPair(_1603762, _1603762)))), _1603764), _1603766, _1603768), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603762), tc_List_Olist(_1603762))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603762), tc_List_Olist(_1603762)), _1603766), _1603768)), c_List_Olistrel(_1603762, _1603764))))], (23647 ^ _779203) ^ [_1195422, _1195424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195422)), -(c_SMT_Oz3mod(_1195424, _1195422) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1195424, _1195422))], (6949 ^ _779203) ^ [_892973, _892975, _892977] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892973, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892973, tc_HOL_Obool)), _892975), _892977)), _892975)))], (13089 ^ _779203) ^ [_1005650, _1005652, _1005654] : [13090 ^ _779203 : [(13093 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005650), _1005654))], (13091 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005652)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005650), _1005652)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005654), _1005652))))], (5596 ^ _779203) ^ [_864739, _864741] : [_864741 = _864739, -(c_Orderings_Oord__class_Oless__eq(_864741) = c_Orderings_Oord__class_Oless__eq(_864739))], (44442 ^ _779203) ^ [_1669188, _1669190, _1669192, _1669194] : [-(hAPP(hAPP(c_List_Omap(_1669188, _1669190), _1669192), c_List_Obutlast(_1669188, _1669194)) = c_List_Obutlast(_1669190, hAPP(hAPP(c_List_Omap(_1669188, _1669190), _1669192), _1669194)))], (45111 ^ _779203) ^ [_1684256, _1684258, _1684260, _1684262, _1684264, _1684266, _1684268] : [-(c_List_Olist__all2(_1684256, _1684258, _1684260, hAPP(hAPP(c_List_Olist_OCons(_1684256), _1684262), _1684264), hAPP(hAPP(c_List_Olist_OCons(_1684258), _1684266), _1684268))), hBOOL(hAPP(hAPP(_1684260, _1684262), _1684266)), c_List_Olist__all2(_1684256, _1684258, _1684260, _1684264, _1684268)], (14653 ^ _779203) ^ [_1034527, _1034529, _1034531, _1034533] : [class_Fields_Ofield(_1034527), -(_1034529 = c_Groups_Ozero__class_Ozero(_1034527)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034527), _1034531), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034527), _1034533), _1034529)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034527), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034527), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034527), _1034529), _1034531)), _1034533)), _1034529))], (28416 ^ _779203) ^ [_1281845, _1281847, _1281849] : [class_Orderings_Olinorder(_1281845), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281845), _1281847)), -(_1281847 = c_Orderings_Obot__class_Obot(tc_fun(_1281845, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281845), _1281849)), -(_1281849 = c_Orderings_Obot__class_Obot(tc_fun(_1281845, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1281845, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281845, tc_HOL_Obool)), _1281847), _1281849)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1281845), c_Big__Operators_Olinorder__class_OMin(_1281845, _1281847)), c_Big__Operators_Olinorder__class_OMin(_1281845, _1281849)))], (37914 ^ _779203) ^ [_1502089] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1502089) = 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), _1502089), c_Int_Onat)))))], (50869 ^ _779203) ^ [_1809567, _1809569, _1809571] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809567, _1809569) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1809571), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1809567 = _1809569, _1809569 = _1809571], (49288 ^ _779203) ^ [_1775971, _1775973] : [-(c_Relation_Osym(_1775971, c_Relation_OId__on(_1775971, _1775973)))], (48064 ^ _779203) ^ [_1748040, _1748042, _1748044] : [-(hAPP(c_New__DSequence_Opos__single(_1748040, _1748042), _1748044) = hAPP(c_Lazy__Sequence_Osingle(_1748040), _1748042))], (50545 ^ _779203) ^ [_1803352, _1803354, _1803356, _1803358, _1803360] : [-(c_Lazy__Sequence_Omap(_1803352, _1803354, _1803356, c_Lazy__Sequence_Olazy__sequence_OInsert(_1803352, _1803358, _1803360)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1803354, hAPP(_1803356, _1803358), c_Lazy__Sequence_Omap(_1803352, _1803354, _1803356, _1803360)))], (38058 ^ _779203) ^ [_1507662, _1507664, _1507666] : [class_Groups_Olinordered__ab__semigroup__add(_1507662), hBOOL(hAPP(c_Finite__Set_Ofinite(_1507662), _1507664)), -(_1507664 = c_Orderings_Obot__class_Obot(tc_fun(_1507662, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1507662), _1507666), c_Big__Operators_Olinorder__class_OMax(_1507662, _1507664)) = c_Big__Operators_Olinorder__class_OMax(_1507662, hAPP(c_Set_OCollect(_1507662), hAPP(hAPP(c_COMBB(tc_fun(_1507662, tc_HOL_Obool), tc_HOL_Obool, _1507662), c_HOL_OEx(_1507662)), hAPP(hAPP(c_COMBC(_1507662, tc_fun(_1507662, tc_HOL_Obool), tc_fun(_1507662, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507662, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1507662, tc_HOL_Obool), tc_fun(_1507662, tc_HOL_Obool)), _1507662), c_COMBS(_1507662, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507662, tc_HOL_Obool), tc_fun(_1507662, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1507662), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507662), c_fconj)), hAPP(hAPP(c_COMBC(_1507662, tc_fun(_1507662, _1507662), tc_fun(_1507662, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507662, tc_HOL_Obool), tc_fun(tc_fun(_1507662, _1507662), tc_fun(_1507662, tc_HOL_Obool)), _1507662), c_COMBB(_1507662, tc_HOL_Obool, _1507662)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1507662), _1507666))))), hAPP(hAPP(c_COMBC(_1507662, tc_fun(_1507662, tc_HOL_Obool), tc_HOL_Obool), c_member(_1507662)), _1507664))))))], (43050 ^ _779203) ^ [_1637995, _1637997, _1637999, _1638001] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637995)), hAPP(hAPP(c_List_Oappend(_1637995), _1637997), _1637999)), c_List_Olists(_1637995, _1638001))), 43053 ^ _779203 : [(43056 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637995)), _1637999), c_List_Olists(_1637995, _1638001))))], (43054 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1637995)), _1637997), c_List_Olists(_1637995, _1638001))))]]], (15312 ^ _779203) ^ [_1047422, _1047424, _1047426, _1047428] : [class_Orderings_Olinorder(_1047422), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1047422), _1047424), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1047422), _1047426), _1047428)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1047422), _1047426), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1047422), _1047424), _1047428)))], (27302 ^ _779203) ^ [_1259864, _1259866, _1259868, _1259870] : [class_Lattices_Osemilattice__sup(_1259864), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259864), _1259866), _1259868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259864), _1259866), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1259864), _1259868), _1259870))))], (20290 ^ _779203) ^ [_1137068, _1137070] : [class_Groups_Ogroup__add(_1137068), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137068), _1137070), hAPP(c_Groups_Ouminus__class_Ouminus(_1137068), _1137070)) = c_Groups_Ozero__class_Ozero(_1137068))], (20454 ^ _779203) ^ [_1139897, _1139899] : [_1139899 = c_Orderings_Obot__class_Obot(tc_fun(_1139897, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1139897, tc_HOL_Obool)), _1139899), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1139897, tc_HOL_Obool)), _1139899))))], (32077 ^ _779203) ^ [_1358287, _1358289, _1358291, _1358293, _1358295] : [hBOOL(hAPP(hAPP(c_member(_1358287), _1358289), _1358291)), -(hAPP(c_Set_Oimage(_1358287, _1358293, hAPP(c_COMBK(_1358293, _1358287), _1358295)), _1358291) = hAPP(hAPP(c_Set_Oinsert(_1358293), _1358295), c_Orderings_Obot__class_Obot(tc_fun(_1358293, tc_HOL_Obool))))], (14625 ^ _779203) ^ [_1033990, _1033992, _1033994, _1033996] : [class_Fields_Olinordered__field(_1033990), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033990), _1033992), _1033994)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033990), _1033996), c_Groups_Ozero__class_Ozero(_1033990))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033990), c_Groups_Ozero__class_Ozero(_1033990)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033990), _1033992), _1033994))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033990), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033990), _1033996), _1033992)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033990), _1033996), _1033994))))], (45738 ^ _779203) ^ [_1698229, _1698231] : [-(c_List_OremoveAll(_1698229, _1698231) = c_List_Ofilter(_1698229, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698229), c_fNot), hAPP(c_fequal, _1698231))))], (19096 ^ _779203) ^ [_1115605, _1115607] : [class_Int_Onumber__ring(_1115605), 19099 ^ _779203 : [(19106 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115607)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1115605), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115607)) = hAPP(c_Int_Onumber__class_Onumber__of(_1115605), _1115607))], (19100 ^ _779203) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115607))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1115605), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115607)) = c_Groups_Ozero__class_Ozero(_1115605))]]], (37253 ^ _779203) ^ [_1483032, _1483034, _1483036, _1483038, _1483040] : [-(hAPP(c_Set_Ovimage(_1483032, _1483034, _1483036), hAPP(hAPP(c_Set_Oinsert(_1483034), _1483038), _1483040)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483032, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1483032, _1483034, _1483036), hAPP(hAPP(c_Set_Oinsert(_1483034), _1483038), c_Orderings_Obot__class_Obot(tc_fun(_1483034, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1483032, _1483034, _1483036), _1483040)))], (27134 ^ _779203) ^ [_1256920, _1256922, _1256924] : [class_Orderings_Oorder(_1256920), 27137 ^ _779203 : [(27144 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256920), _1256922), _1256924))), -(c_Orderings_Obot__class_Obot(tc_fun(_1256920, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256920, _1256922), _1256924))], (27138 ^ _779203) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1256920, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256920, _1256922), _1256924), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256920), _1256922), _1256924))]]], (41403 ^ _779203) ^ [_1596443, _1596445, _1596447, _1596449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1596443), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1596445), _1596447))), -(hAPP(c_Random_Opick(_1596445, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1596445)), _1596447), _1596449)), _1596443) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1596445), _1596447))], (46019 ^ _779203) ^ [_1705113, _1705115, _1705117, _1705119, _1705121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1705113), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1705115), _1705117))), -(hAPP(hAPP(c_List_Onth(_1705119), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1705119), _1705121), c_List_Oupt(_1705117, _1705115))), _1705113) = hAPP(_1705121, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1705117), _1705113)))], (25800 ^ _779203) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (38675 ^ _779203) ^ [_1527967, _1527969, _1527971] : [c_Wellfounded_Owf(_1527967, _1527969), -(c_Wellfounded_Owf(_1527967, c_Wellfounded_Omlex__prod(_1527967, _1527971, _1527969)))], (25874 ^ _779203) ^ [_1234285, _1234287] : [class_Int_Onumber__ring(_1234285), -(hAPP(c_Int_Onumber__class_Onumber__of(_1234285), _1234287) = hAPP(c_Int_Oring__1__class_Oof__int(_1234285), _1234287))], (46690 ^ _779203) ^ [_1718148, _1718150, _1718152, _1718154] : [hAPP(c_List_Orev(_1718148), _1718150) = hAPP(hAPP(c_List_Olist_OCons(_1718148), _1718152), _1718154), -(_1718150 = hAPP(hAPP(c_List_Oappend(_1718148), hAPP(c_List_Orev(_1718148), _1718154)), hAPP(hAPP(c_List_Olist_OCons(_1718148), _1718152), c_List_Olist_ONil(_1718148))))], (32922 ^ _779203) ^ [_1382333, _1382335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1382333), 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)), _1382335)), -(c_Divides_OnegDivAlg(_1382333, _1382335) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1382333), _1382335)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1382333, _1382335)))], (27522 ^ _779203) ^ [_1264088, _1264090, _1264092, _1264094, _1264096] : [class_Lattices_Osemilattice__sup(_1264088), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264088), _1264090), _1264092)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264088), _1264094), _1264096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1264088), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264088), _1264090), _1264094)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1264088), _1264092), _1264096))))], (48882 ^ _779203) ^ [_1766464, _1766466] : [48883 ^ _779203 : [(48884 ^ _779203) ^ [_1766530] : [hBOOL(hAPP(_1766466, _1766530))]], 48886 ^ _779203 : [(48889 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1766466, 48885 ^ [_1766464, _1766466])))], (48887 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766464), 48885 ^ [_1766464, _1766466]), c_Orderings_Otop__class_Otop(tc_fun(_1766464, tc_HOL_Obool)))))]]], (21331 ^ _779203) ^ [_1155061, _1155063] : [class_Int_Onumber__ring(_1155061), class_Rings_Olinordered__idom(_1155061), 21338 ^ _779203 : [(21345 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1155063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155061), c_Groups_Oone__class_Oone(_1155061)), hAPP(c_Int_Onumber__class_Onumber__of(_1155061), _1155063))))], (21339 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155061), c_Groups_Oone__class_Oone(_1155061)), hAPP(c_Int_Onumber__class_Onumber__of(_1155061), _1155063))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1155063)))]]], (48268 ^ _779203) ^ [_1752619, _1752621, _1752623, _1752625] : [-(c_List_Oreplicate(_1752619, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1752621), _1752623), _1752625) = hAPP(hAPP(c_List_Oappend(_1752619), c_List_Oreplicate(_1752619, _1752621, _1752625)), c_List_Oreplicate(_1752619, _1752623, _1752625)))], (29778 ^ _779203) ^ [_1308386, _1308388, _1308390, _1308392] : [class_Orderings_Oorder(_1308386), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308386, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1308386, _1308388), _1308390)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1308386, _1308390), _1308392)) = c_Orderings_Obot__class_Obot(tc_fun(_1308386, tc_HOL_Obool)))], (48036 ^ _779203) ^ [_1747203, _1747205, _1747207, _1747209] : [-(c_New__Random__Sequence_Opos__empty(_1747203, _1747205, _1747207, _1747209) = c_New__DSequence_Opos__empty(_1747203))], (48428 ^ _779203) ^ [_1755642] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1755642) = c_Lazy__Sequence_Osmall__lazy_H(_1755642, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1755642)))], (24229 ^ _779203) ^ [_1206007, _1206009] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1206007)), _1206009) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1206007), _1206009)))], (44726 ^ _779203) ^ [_1675386] : [-(_1675386 = 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)), _1675386)))], (2870 ^ _779203) ^ [_821702, _821704] : [_821704 = _821702, -(c_Int_Oring__1__class_Oof__int(_821704) = c_Int_Oring__1__class_Oof__int(_821702))], (42786 ^ _779203) ^ [_1631865, _1631867] : [-(_1631867 = c_List_Olist_ONil(_1631865)), -(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(_1631865)), _1631867))))], (42728 ^ _779203) ^ [_1630822] : [-(hAPP(c_List_Oset(_1630822), c_List_Olist_ONil(_1630822)) = c_Orderings_Obot__class_Obot(tc_fun(_1630822, tc_HOL_Obool)))], (33713 ^ _779203) ^ [_1396468, _1396470, _1396472] : [-(hAPP(c_Product__Type_Osnd(_1396468, _1396470), _1396472) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1396468, _1396470, _1396470), hAPP(c_COMBK(tc_fun(_1396470, _1396470), _1396468), c_COMBI(_1396470))), _1396472))], (20054 ^ _779203) ^ [_1132785, _1132787, _1132789] : [hBOOL(hAPP(hAPP(c_member(_1132785), _1132787), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1132785, tc_HOL_Obool)), _1132789))), hBOOL(hAPP(hAPP(c_member(_1132785), _1132787), _1132789))], (13591 ^ _779203) ^ [_1015398, _1015400] : [class_Rings_Odivision__ring(_1015398), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015398), _1015400), c_Groups_Oone__class_Oone(_1015398)) = _1015400)], (44688 ^ _779203) ^ [_1674528, _1674530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1674528), _1674530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1674528)), hAPP(c_Code__Numeral_Oof__nat, _1674530))))], (34482 ^ _779203) ^ [_1415288, _1415290, _1415292, _1415294, _1415296, _1415298] : [class_Complete__Lattice_Ocomplete__lattice(_1415288), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1415290, _1415288), _1415292), hAPP(hAPP(c_COMBB(tc_fun(_1415294, _1415288), _1415288, _1415290), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1415294, _1415288), _1415296)), _1415298)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1415294, _1415288), _1415296), hAPP(hAPP(c_COMBB(tc_fun(_1415290, _1415288), _1415288, _1415294), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1415290, _1415288), _1415292)), hAPP(c_COMBC(_1415290, _1415294, _1415288), _1415298))))], (102 ^ _779203) ^ [_780720, _780722] : [-(class_Rings_Odivision__ring(_780720)), _780722 = _780720, class_Rings_Odivision__ring(_780722)], (40320 ^ _779203) ^ [_1567921, _1567923] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567921, _1567921)), hAPP(hAPP(c_Product__Type_OPair(_1567921, _1567921), _1567923), _1567923)), c_Relation_OId(_1567921))))], (1530 ^ _779203) ^ [_801288, _801290] : [-(class_Enum_Oenum(_801288)), _801290 = _801288, class_Enum_Oenum(_801290)], (8214 ^ _779203) ^ [_915630, _915632, _915634, _915636, _915638, _915640] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_915630, _915632, _915634, _915636, _915638), _915640)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_915630), _915638)))], (25398 ^ _779203) ^ [_1227235, _1227237] : [c_Nat__Transfer_Ois__nat(_1227235), c_Nat__Transfer_Onat__set(_1227237), 25405 ^ _779203 : [(25412 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1227235)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1227237))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1227235), _1227237)))], (25406 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1227235), _1227237)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1227235)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1227237))))]]], (45793 ^ _779203) ^ [_1699783, _1699785, _1699787, _1699789] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1699783)), c_List_Otranspose__rel(_1699783)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699783)), hAPP(hAPP(c_List_Olist_OCons(_1699783), _1699785), _1699787)), _1699789))), -(c_List_Otranspose(_1699783, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699783)), hAPP(hAPP(c_List_Olist_OCons(_1699783), _1699785), _1699787)), _1699789)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699783)), hAPP(hAPP(c_List_Olist_OCons(_1699783), _1699785), c_List_Oconcat(_1699783, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699783), tc_List_Olist(_1699783)), c_List_Olist_Olist__case(tc_List_Olist(_1699783), _1699783, c_List_Olist_ONil(_1699783), hAPP(hAPP(c_COMBB(tc_List_Olist(_1699783), tc_fun(tc_List_Olist(_1699783), tc_List_Olist(_1699783)), _1699783), c_COMBK(tc_List_Olist(_1699783), tc_List_Olist(_1699783))), hAPP(hAPP(c_COMBC(_1699783, tc_List_Olist(_1699783), tc_List_Olist(_1699783)), c_List_Olist_OCons(_1699783)), c_List_Olist_ONil(_1699783))))), _1699789)))), c_List_Otranspose(_1699783, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1699783)), _1699787), c_List_Oconcat(tc_List_Olist(_1699783), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699783), tc_List_Olist(tc_List_Olist(_1699783))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1699783)), _1699783, c_List_Olist_ONil(tc_List_Olist(_1699783)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1699783), tc_List_Olist(tc_List_Olist(_1699783))), _1699783), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699783), tc_List_Olist(tc_List_Olist(_1699783)), tc_List_Olist(tc_List_Olist(_1699783))), c_List_Olist_OCons(tc_List_Olist(_1699783))), c_List_Olist_ONil(tc_List_Olist(_1699783)))))), _1699789))))))], (35730 ^ _779203) ^ [_1449077, _1449079, _1449081, _1449083] : [c_Equiv__Relations_Oequiv(_1449077, _1449079, _1449081), hBOOL(hAPP(hAPP(c_member(_1449077), _1449083), _1449079)), -(hBOOL(hAPP(hAPP(c_member(_1449077), _1449083), hAPP(c_Relation_OImage(_1449077, _1449077, _1449081), hAPP(hAPP(c_Set_Oinsert(_1449077), _1449083), c_Orderings_Obot__class_Obot(tc_fun(_1449077, tc_HOL_Obool)))))))], (24245 ^ _779203) ^ [_1206391, _1206393, _1206395] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1206391), _1206393)), _1206395) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1206391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206393), _1206395)))], (18182 ^ _779203) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (12472 ^ _779203) ^ [_994318, _994320] : [class_Orderings_Olinorder(_994318), -(c_Big__Operators_Olinorder__class_OMax(_994318, hAPP(hAPP(c_Set_Oinsert(_994318), _994320), c_Orderings_Obot__class_Obot(tc_fun(_994318, tc_HOL_Obool)))) = _994320)], (31883 ^ _779203) ^ [_1352873, _1352875, _1352877, _1352879] : [class_Rings_Oring__1(_1352873), -(hAPP(c_Int_Oring__1__class_Oof__int(_1352873), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352875, tc_Int_Oint), _1352877), _1352879)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1352875, _1352873), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1352873, _1352875), c_Int_Oring__1__class_Oof__int(_1352873)), _1352877)), _1352879))], (32635 ^ _779203) ^ [_1372218, _1372220] : [-(c_Divides_Odivmod__int(_1372218, _1372220) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372218), _1372220)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1372218, _1372220)))], (21195 ^ _779203) ^ [_1152970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1152970)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152970), c_Int_OPls)))], (32273 ^ _779203) ^ [_1363017, _1363019, _1363021] : [class_Groups_Ocomm__monoid__add(_1363017), class_Groups_Ocomm__monoid__mult(_1363017), c_Nat__Transfer_Onat__set(_1363019), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1363017), _1363021), _1363019) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1363017), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1363017, tc_Nat_Onat), _1363021), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1363019)))], (40480 ^ _779203) ^ [_1571850, _1571852, _1571854, _1571856, _1571858] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571850, _1571850)), hAPP(hAPP(c_Product__Type_OPair(_1571850, _1571850), _1571852), _1571854)), c_Transitive__Closure_Ortrancl(_1571850, _1571856))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571850, _1571850)), hAPP(hAPP(c_Product__Type_OPair(_1571850, _1571850), _1571854), _1571858)), _1571856)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571850, _1571850)), hAPP(hAPP(c_Product__Type_OPair(_1571850, _1571850), _1571852), _1571858)), c_Transitive__Closure_Otrancl(_1571850, _1571856))))], (37363 ^ _779203) ^ [_1485972, _1485974, _1485976] : [hBOOL(hAPP(_1485972, _1485974)), -(hBOOL(hAPP(hAPP(c_member(_1485976), _1485974), hAPP(c_Set_OCollect(_1485976), _1485972))))], (35962 ^ _779203) ^ [_1454259, _1454261] : [c_Equiv__Relations_Oequiv(_1454259, c_Orderings_Otop__class_Otop(tc_fun(_1454259, tc_HOL_Obool)), _1454261), -(c_Equiv__Relations_Oequivp(_1454259, hAPP(hAPP(c_COMBC(_1454259, tc_fun(tc_prod(_1454259, _1454259), tc_HOL_Obool), tc_fun(_1454259, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454259, tc_fun(tc_fun(tc_prod(_1454259, _1454259), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1454259, _1454259), tc_HOL_Obool), tc_fun(_1454259, tc_HOL_Obool)), _1454259), c_COMBC(_1454259, tc_fun(tc_prod(_1454259, _1454259), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1454259, tc_prod(_1454259, _1454259)), tc_fun(_1454259, tc_fun(tc_fun(tc_prod(_1454259, _1454259), tc_HOL_Obool), tc_HOL_Obool)), _1454259), hAPP(c_COMBB(tc_prod(_1454259, _1454259), tc_fun(tc_fun(tc_prod(_1454259, _1454259), tc_HOL_Obool), tc_HOL_Obool), _1454259), c_member(tc_prod(_1454259, _1454259)))), c_Product__Type_OPair(_1454259, _1454259)))), _1454261)))], (44546 ^ _779203) ^ [_1671586, _1671588, _1671590] : [c_Fun_Oinj__on(tc_List_Olist(_1671586), tc_List_Olist(_1671588), hAPP(c_List_Omap(_1671586, _1671588), _1671590), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671586), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1671586, _1671588, _1671590, c_Orderings_Otop__class_Otop(tc_fun(_1671586, tc_HOL_Obool))))], (13685 ^ _779203) ^ [_1016911, _1016913] : [class_Rings_Odivision__ring(_1016911), -(_1016913 = c_Groups_Ozero__class_Ozero(_1016911)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1016911), _1016913), _1016913) = c_Groups_Oone__class_Oone(_1016911))], (15306 ^ _779203) ^ [_1047279, _1047281, _1047283, _1047285] : [class_Orderings_Olinorder(_1047279), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047279), _1047281), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047279), _1047283), _1047285)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047279), _1047283), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047279), _1047281), _1047285)))], (21837 ^ _779203) ^ [_1163652] : [-(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)))), _1163652) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1163652), _1163652))], (43119 ^ _779203) ^ [_1639592, _1639594, _1639596, _1639598] : [_1639594 = _1639598, -(hAPP(hAPP(c_List_Oappend(_1639592), _1639594), _1639596) = hAPP(hAPP(c_List_Oappend(_1639592), _1639598), _1639596))], (44191 ^ _779203) ^ [_1663307, _1663309, _1663311] : [_1663307 = c_List_Olist_ONil(_1663309), -(c_List_Olast(_1663309, hAPP(hAPP(c_List_Oappend(_1663309), _1663311), _1663307)) = c_List_Olast(_1663309, _1663311))], (39109 ^ _779203) ^ [_1537876, _1537878, _1537880] : [c_Wellfounded_OwfP(_1537876, _1537878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1537876, tc_fun(_1537876, tc_HOL_Obool))), _1537880), _1537878)), -(c_Wellfounded_OwfP(_1537876, _1537880))], (52021 ^ _779203) ^ [_1829375, _1829377, _1829379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829375)), 52024 ^ _779203 : [(52031 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829377), _1829379)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829375), _1829377)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829375), _1829379))))], (52025 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829375), _1829377)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829375), _1829379))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829377), _1829379)))]]], (20296 ^ _779203) ^ [_1137173, _1137175] : [class_Groups_Ogroup__add(_1137173), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137173), c_Groups_Ozero__class_Ozero(_1137173)), _1137175) = hAPP(c_Groups_Ouminus__class_Ouminus(_1137173), _1137175))], (18566 ^ _779203) ^ [_1106634, _1106636, _1106638] : [class_Rings_Oring__1(_1106634), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1106636), _1106638)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1106634), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1106638), _1106636)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1106634), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1106634), _1106638)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1106634), _1106636)))], (41459 ^ _779203) ^ [_1598013, _1598015, _1598017, _1598019, _1598021, _1598023] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1598013, _1598013)), hAPP(hAPP(c_Product__Type_OPair(_1598013, _1598013), _1598015), _1598017)), c_Transitive__Closure_Ortrancl(_1598013, _1598019))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598013), tc_List_Olist(_1598013))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598013), tc_List_Olist(_1598013)), _1598021), _1598023)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598013), c_List_Olistrel1(_1598013, _1598019)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598013), tc_List_Olist(_1598013))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598013), tc_List_Olist(_1598013)), hAPP(hAPP(c_List_Olist_OCons(_1598013), _1598015), _1598021)), hAPP(hAPP(c_List_Olist_OCons(_1598013), _1598017), _1598023))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598013), c_List_Olistrel1(_1598013, _1598019)))))], (6967 ^ _779203) ^ [_893454, _893456, _893458, _893460] : [hBOOL(hAPP(hAPP(c_member(_893454), _893456), _893458)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893454, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_893454), _893456), _893460)), _893458) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893454, tc_HOL_Obool)), _893460), _893458))], (45945 ^ _779203) ^ [_1703666, _1703668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703666)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703668))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703666), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703668)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703666)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703666)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1703668))))], (52405 ^ _779203) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (8288 ^ _779203) ^ [_917071, _917073, _917075, _917077] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_917071), _917073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_917075), hAPP(c_Set_Oimage(_917071, _917075, _917077), _917073))), hAPP(c_Finite__Set_Ocard(_917071), _917073))))], (4092 ^ _779203) ^ [_841145, _841147, _841149, _841151, _841153, _841155] : [-(c_List_Osplice(_841155, _841151, _841147) = c_List_Osplice(_841153, _841149, _841145)), _841155 = _841153, _841151 = _841149, _841147 = _841145], (26188 ^ _779203) ^ [_1239936, _1239938] : [c_Nat__Transfer_Ois__nat(_1239936), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1239936, _1239938)))], (46598 ^ _779203) ^ [_1716135, _1716137, _1716139] : [hAPP(hAPP(c_List_Olist_OCons(_1716135), _1716137), c_List_Olist_ONil(_1716135)) = hAPP(c_List_Orev(_1716135), _1716139), -(_1716139 = hAPP(hAPP(c_List_Olist_OCons(_1716135), _1716137), c_List_Olist_ONil(_1716135)))], (18909 ^ _779203) ^ [_1112325, _1112327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1112325), _1112327)), -(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)), _1112325)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1112327))))], (43674 ^ _779203) ^ [_1653102, _1653104, _1653106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653102), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653104)), _1653106))), -(_1653106 = hAPP(hAPP(c_List_Oappend(_1653104), hAPP(hAPP(c_List_Otake(_1653104), _1653102), _1653106)), hAPP(hAPP(c_List_Olist_OCons(_1653104), hAPP(hAPP(c_List_Onth(_1653104), _1653106), _1653102)), hAPP(hAPP(c_List_Odrop(_1653104), hAPP(c_Nat_OSuc, _1653102)), _1653106))))], (28854 ^ _779203) ^ [_1289658, _1289660, _1289662] : [class_Lattices_Olattice(_1289658), hBOOL(hAPP(c_Finite__Set_Ofinite(_1289658), _1289660)), hBOOL(hAPP(hAPP(c_member(_1289658), _1289662), _1289660)), 28865 ^ _779203 : [(28872 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289658, tc_HOL_Obool)), _1289660), hAPP(hAPP(c_Set_Oinsert(_1289658), _1289662), c_Orderings_Obot__class_Obot(tc_fun(_1289658, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1289658, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1289658, _1289660) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1289658), _1289662), c_Big__Operators_Olattice__class_OSup__fin(_1289658, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289658, tc_HOL_Obool)), _1289660), hAPP(hAPP(c_Set_Oinsert(_1289658), _1289662), c_Orderings_Obot__class_Obot(tc_fun(_1289658, tc_HOL_Obool)))))))], (28866 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1289658, tc_HOL_Obool)), _1289660), hAPP(hAPP(c_Set_Oinsert(_1289658), _1289662), c_Orderings_Obot__class_Obot(tc_fun(_1289658, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1289658, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1289658, _1289660) = _1289662)]]], (48989 ^ _779203) ^ [_1770157, _1770159, _1770161, _1770163] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1770157), _1770159)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1770157), _1770161)), -(_1770161 = c_Orderings_Obot__class_Obot(tc_fun(_1770157, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1770157, _1770163, _1770159, _1770161)), 49003 ^ _779203 : [(49006 ^ _779203) ^ [_1770502] : [hBOOL(hAPP(hAPP(c_member(_1770157), _1770502), _1770161)), hBOOL(hAPP(hAPP(_1770163, 49002 ^ [_1770157, _1770159, _1770161, _1770163]), _1770502))], (49004 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770157), 49002 ^ [_1770157, _1770159, _1770161, _1770163]), _1770159)))]]], (9055 ^ _779203) ^ [_932668, _932670, _932672, _932674, _932676, _932678] : [class_Rings_Oordered__ring(_932668), 9058 ^ _779203 : [(9065 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932668), _932674), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_932668), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_932668), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_932668), _932676), 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_970535] : [11112 ^ _779203 : [(11115 ^ _779203) ^ [] : [_970533 = _970535], (11113 ^ _779203) ^ [] : [_970531 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970531), _970533) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970531), _970535))], (11254 ^ _779203) ^ [_972923, _972925] : [class_Groups_Olinordered__ab__group__add(_972923), 11257 ^ _779203 : [(11264 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972923), c_Groups_Ozero__class_Ozero(_972923)), _972925)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972923), c_Groups_Ozero__class_Ozero(_972923)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972923), _972925), _972925))))], (11258 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972923), c_Groups_Ozero__class_Ozero(_972923)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972923), _972925), _972925))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_972923), c_Groups_Ozero__class_Ozero(_972923)), _972925)))]]], (48666 ^ _779203) ^ [_1761293, _1761295, _1761297] : [c_List_Olist__ex(tc_Int_Oint, _1761293, c_List_Oupto(_1761295, _1761297)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1761293), _1761295, _1761297)], (47002 ^ _779203) ^ [_1724685, _1724687, _1724689] : [hBOOL(hAPP(c_List_Odistinct(_1724685), _1724687)), -(hBOOL(hAPP(c_List_Odistinct(_1724685), c_List_OdropWhile(_1724685, _1724689, _1724687))))], (19112 ^ _779203) ^ [_1115845, _1115847, _1115849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115845)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1115847), 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), _1115847), _1115849))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1115845))), _1115849)))], (30016 ^ _779203) ^ [_1313674, _1313676, _1313678, _1313680] : [class_Lattices_Osemilattice__inf(_1313674), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313674), _1313676)), hBOOL(hAPP(hAPP(c_member(_1313674), _1313678), _1313676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1313674), hAPP(hAPP(c_Finite__Set_Ofold(_1313674, _1313674, c_Lattices_Osemilattice__inf__class_Oinf(_1313674)), _1313680), _1313676)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313674), _1313678), _1313680))))], (16474 ^ _779203) ^ [_1068722, _1068724, _1068726, _1068728] : [class_Fields_Olinordered__field__inverse__zero(_1068722), class_Int_Onumber(_1068722), 16481 ^ _779203 : [(16482 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1068722), _1068724), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726))), _1068728)), 16485 ^ _779203 : [(16492 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), c_Groups_Ozero__class_Ozero(_1068722)), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726)))), 16495 ^ _779203 : [(16502 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726)), c_Groups_Ozero__class_Ozero(_1068722)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), c_Groups_Ozero__class_Ozero(_1068722)), _1068728)))], (16496 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726)), c_Groups_Ozero__class_Ozero(_1068722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068722), _1068728), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726))), _1068724)))]]], (16486 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), c_Groups_Ozero__class_Ozero(_1068722)), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), _1068724), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068722), _1068728), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726)))))]]], (16508 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1068722), _1068724), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726))), _1068728))), 16511 ^ _779203 : [(16514 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), _1068724), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068722), _1068728), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726))))], (16512 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), c_Groups_Ozero__class_Ozero(_1068722)), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726))))]], 16515 ^ _779203 : [(16518 ^ _779203) ^ [] : [16519 ^ _779203 : [(16522 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1068722), _1068728), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726))), _1068724))], (16520 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726)), c_Groups_Ozero__class_Ozero(_1068722))))]], 16523 ^ _779203 : [(16526 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), c_Groups_Ozero__class_Ozero(_1068722)), _1068728))], (16524 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726)), c_Groups_Ozero__class_Ozero(_1068722)))]]], (16516 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1068722), c_Groups_Ozero__class_Ozero(_1068722)), hAPP(c_Int_Onumber__class_Onumber__of(_1068722), _1068726)))]]]]], (29120 ^ _779203) ^ [_1294640, _1294642, _1294644, _1294646] : [hBOOL(hAPP(hAPP(c_member(_1294640), _1294642), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1294640, tc_HOL_Obool)), _1294644), _1294646))), 29123 ^ _779203 : [(29126 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1294640), _1294642), _1294646)))], (29124 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1294640), _1294642), _1294644)))]]], (29666 ^ _779203) ^ [_1305704, _1305706, _1305708, _1305710] : [class_Lattices_Olattice(_1305704), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305704), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1305704), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1305704), _1305706), _1305708)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1305704), _1305706), _1305710))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1305704), _1305706), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1305704), _1305708), _1305710)))))], (42137 ^ _779203) ^ [_1618186, _1618188, _1618190, _1618192, _1618194, _1618196] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618186, _1618188)), hAPP(hAPP(c_Product__Type_OPair(_1618186, _1618188), _1618190), _1618192)), hAPP(c_List_Oset(tc_prod(_1618186, _1618188)), hAPP(hAPP(c_List_Ozip(_1618186, _1618188), _1618194), _1618196)))), -(hBOOL(hAPP(hAPP(c_member(_1618188), _1618192), hAPP(c_List_Oset(_1618188), _1618196))))], (41797 ^ _779203) ^ [_1608253] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1608253)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1608253), tc_HOL_Obool))))], (14967 ^ _779203) ^ [_1040737, _1040739, _1040741] : [class_Rings_Oring__1(_1040737), hBOOL(hAPP(hAPP(c_member(_1040737), _1040739), c_Int_Oring__1__class_OInts(_1040737))), hBOOL(hAPP(hAPP(c_member(_1040737), _1040741), c_Int_Oring__1__class_OInts(_1040737))), -(hBOOL(hAPP(hAPP(c_member(_1040737), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1040737), _1040739), _1040741)), c_Int_Oring__1__class_OInts(_1040737))))], (44365 ^ _779203) ^ [_1667170, _1667172, _1667174, _1667176, _1667178] : [44367 ^ _779203 : [(44370 ^ _779203) ^ [] : [hAPP(_1667174, 44366 ^ [_1667170, _1667172, _1667174, _1667176, _1667178]) = hAPP(_1667178, 44366 ^ [_1667170, _1667172, _1667174, _1667176, _1667178])], (44368 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1667170), 44366 ^ [_1667170, _1667172, _1667174, _1667176, _1667178]), hAPP(c_List_Oset(_1667170), _1667176))))]], -(hAPP(hAPP(c_List_Omap(_1667170, _1667172), _1667174), _1667176) = hAPP(hAPP(c_List_Omap(_1667170, _1667172), _1667178), _1667176))], (1960 ^ _779203) ^ [_806659, _806661] : [-(hBOOL(_806659)), _806661 = _806659, hBOOL(_806661)], (47315 ^ _779203) ^ [_1731898, _1731900, _1731902] : [class_Enum_Oenum(_1731898), class_Enum_Oenum(_1731900), 47322 ^ _779203 : [(47329 ^ _779203) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731900), hAPP(hAPP(c_COMBB(tc_fun(_1731898, tc_HOL_Obool), tc_HOL_Obool, _1731900), c_Enum_Oenum__class_Oenum__ex(_1731898)), hAPP(hAPP(c_COMBB(tc_fun(_1731898, tc_prod(_1731900, _1731898)), tc_fun(_1731898, tc_HOL_Obool), _1731900), hAPP(c_COMBB(tc_prod(_1731900, _1731898), tc_HOL_Obool, _1731898), _1731902)), c_Product__Type_OPair(_1731900, _1731898))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731900, _1731898)), _1731902)))], (47323 ^ _779203) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1731900, _1731898)), _1731902)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731900), hAPP(hAPP(c_COMBB(tc_fun(_1731898, tc_HOL_Obool), tc_HOL_Obool, _1731900), c_Enum_Oenum__class_Oenum__ex(_1731898)), hAPP(hAPP(c_COMBB(tc_fun(_1731898, tc_prod(_1731900, _1731898)), tc_fun(_1731898, tc_HOL_Obool), _1731900), hAPP(c_COMBB(tc_prod(_1731900, _1731898), tc_HOL_Obool, _1731898), _1731902)), c_Product__Type_OPair(_1731900, _1731898))))))]]], (52419 ^ _779203) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (40606 ^ _779203) ^ [_1574707, _1574709, _1574711, _1574713] : [-(c_Wellfounded_Oacyclic(_1574707, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1574707, _1574707)), hAPP(hAPP(c_Product__Type_OPair(_1574707, _1574707), _1574709), _1574711)), _1574713))), c_Wellfounded_Oacyclic(_1574707, _1574713), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574707, _1574707)), hAPP(hAPP(c_Product__Type_OPair(_1574707, _1574707), _1574711), _1574709)), c_Transitive__Closure_Ortrancl(_1574707, _1574713))))], (47964 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52237 ^ _779203) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (32787 ^ _779203) ^ [_1379335, _1379337, _1379339, _1379341, _1379343, _1379345, _1379347] : [hBOOL(hAPP(hAPP(c_member(_1379335), _1379337), hAPP(hAPP(_1379339, _1379341), _1379343))), -(hBOOL(hAPP(hAPP(c_member(_1379335), _1379337), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1379345, _1379347, tc_fun(_1379335, tc_HOL_Obool)), _1379339), hAPP(hAPP(c_Product__Type_OPair(_1379345, _1379347), _1379341), _1379343)))))], (29610 ^ _779203) ^ [_1304653, _1304655, _1304657, _1304659] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304653, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304653, tc_HOL_Obool)), _1304655), _1304657)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304653, tc_HOL_Obool)), _1304659), _1304657)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304653, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304653, tc_HOL_Obool)), _1304655), _1304657)), _1304659))], (17360 ^ _779203) ^ [_1085214, _1085216] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085214), _1085216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085216), _1085214))], (41337 ^ _779203) ^ [_1594028, _1594030, _1594032] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594028)), c_List_Osublist(_1594028, _1594030, _1594032)) = 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(_1594028)), _1594030)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1594032)))))], (39682 ^ _779203) ^ [_1551986, _1551988, _1551990, _1551992, _1551994, _1551996, _1551998, _1552000] : [c_Finite__Set_Ofolding__image(_1551986, _1551988, _1551990, _1551992, _1551994), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551988), _1551996)), c_Fun_Oinj__on(_1551988, _1551988, _1551998, _1551996), -(hAPP(hAPP(_1551994, _1552000), hAPP(c_Set_Oimage(_1551988, _1551988, _1551998), _1551996)) = hAPP(hAPP(_1551994, hAPP(c_Fun_Ocomp(_1551988, _1551986, _1551988, _1552000), _1551998)), _1551996))], (51817 ^ _779203) ^ [_1825657, _1825659] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1825657), 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)))), _1825659)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825659), _1825657)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825657), _1825659)))], (35653 ^ _779203) ^ [_1447236, _1447238, _1447240, _1447242] : [hBOOL(hAPP(hAPP(c_member(_1447236), _1447238), _1447240)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1447236, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1447236, _1447236, _1447242), hAPP(hAPP(c_Set_Oinsert(_1447236), _1447238), c_Orderings_Obot__class_Obot(tc_fun(_1447236, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447236), _1447240), _1447242))))], (30750 ^ _779203) ^ [_1328807, _1328809, _1328811, _1328813, _1328815] : [class_Groups_Ocomm__monoid__mult(_1328807), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328809), _1328811)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328809), _1328813)), 30764 ^ _779203 : [(30767 ^ _779203) ^ [] : [hAPP(_1328815, 30763 ^ [_1328807, _1328809, _1328811, _1328813, _1328815]) = c_Groups_Oone__class_Oone(_1328807)], (30765 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1328809), 30763 ^ [_1328807, _1328809, _1328811, _1328813, _1328815]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328809, tc_HOL_Obool)), _1328811), _1328813))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1328809, _1328807), _1328815), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328809, tc_HOL_Obool)), _1328811), _1328813)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328807), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1328809, _1328807), _1328815), _1328811)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1328809, _1328807), _1328815), _1328813)))], (22403 ^ _779203) ^ [_1174415, _1174417] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1174415))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1174417))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1174415)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1174417)))], (30343 ^ _779203) ^ [_1320646, _1320648, _1320650] : [class_Lattices_Olattice(_1320646), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320646), _1320648)), -(_1320648 = c_Orderings_Obot__class_Obot(tc_fun(_1320646, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320646), _1320650)), -(_1320650 = c_Orderings_Obot__class_Obot(tc_fun(_1320646, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320646, tc_HOL_Obool)), _1320648), _1320650) = c_Orderings_Obot__class_Obot(tc_fun(_1320646, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1320646, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320646, tc_HOL_Obool)), _1320648), _1320650)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1320646), c_Big__Operators_Olattice__class_OSup__fin(_1320646, _1320648)), c_Big__Operators_Olattice__class_OSup__fin(_1320646, _1320650)))], (51293 ^ _779203) ^ [_1816645, _1816647, _1816649] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816645), _1816647)), _1816647 = _1816649, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816645), _1816649)))], (18441 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (42562 ^ _779203) ^ [_1627871, _1627873, _1627875] : [hBOOL(hAPP(c_List_Odistinct(_1627871), _1627873)), -(hAPP(c_List_Oset(_1627871), c_List_Oremove1(_1627871, _1627875, _1627873)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1627871, tc_HOL_Obool)), hAPP(c_List_Oset(_1627871), _1627873)), hAPP(hAPP(c_Set_Oinsert(_1627871), _1627875), c_Orderings_Obot__class_Obot(tc_fun(_1627871, tc_HOL_Obool)))))], (37098 ^ _779203) ^ [_1479214, _1479216] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1479214), c_Int_OInteg)), hBOOL(hAPP(_1479216, hAPP(c_Int_ORep__Integ, 37103 ^ [_1479214, _1479216]))), -(hBOOL(hAPP(_1479216, _1479214)))], (16760 ^ _779203) ^ [_1073907, _1073909, _1073911] : [class_Orderings_Olinorder(_1073907), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073907), _1073909)), -(c_Big__Operators_Olinorder__class_OMax(_1073907, hAPP(hAPP(c_Set_Oinsert(_1073907), _1073911), _1073909)) = hAPP(hAPP(c_Finite__Set_Ofold(_1073907, _1073907, c_Orderings_Oord__class_Omax(_1073907)), _1073911), _1073909))], (34039 ^ _779203) ^ [_1403099, _1403101, _1403103, _1403105, _1403107, _1403109, _1403111, _1403113] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1403099, _1403101), tc_prod(_1403099, _1403101))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1403099, _1403101), tc_prod(_1403099, _1403101)), hAPP(hAPP(c_Product__Type_OPair(_1403099, _1403101), _1403103), _1403105)), hAPP(hAPP(c_Product__Type_OPair(_1403099, _1403101), _1403107), _1403109))), c_Wellfounded_Olex__prod(_1403099, _1403101, _1403111, _1403113))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1403099, _1403099)), hAPP(hAPP(c_Product__Type_OPair(_1403099, _1403099), _1403103), _1403107)), _1403111))), 34046 ^ _779203 : [(34049 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1403101, _1403101)), hAPP(hAPP(c_Product__Type_OPair(_1403101, _1403101), _1403105), _1403109)), _1403113)))], (34047 ^ _779203) ^ [] : [-(_1403103 = _1403107)]]], (35565 ^ _779203) ^ [_1445015, _1445017, _1445019, _1445021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1445015), _1445021)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1445019), _1445017))), -(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), _1445015), _1445017)), 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), _1445019), _1445021)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (19506 ^ _779203) ^ [_1123098] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1123098)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1123098) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8300 ^ _779203) ^ [_917365, _917367, _917369, _917371] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_917365, _917367, _917369), _917371)), _917369 = c_Orderings_Obot__class_Obot(tc_fun(_917365, tc_HOL_Obool))], (4924 ^ _779203) ^ [_854245, _854247] : [_854247 = _854245, -(c_Fun_Oid(_854247) = c_Fun_Oid(_854245))], (49757 ^ _779203) ^ [_1785177, _1785179, _1785181] : [hAPP(c_Fun_Ocomp(_1785177, _1785179, _1785179, _1785181), c_Hilbert__Choice_Oinv__into(_1785177, _1785179, c_Orderings_Otop__class_Otop(tc_fun(_1785177, tc_HOL_Obool)), _1785181)) = c_Fun_Oid(_1785179), -(hAPP(c_Set_Oimage(_1785177, _1785179, _1785181), c_Orderings_Otop__class_Otop(tc_fun(_1785177, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1785179, tc_HOL_Obool)))], (18325 ^ _779203) ^ [_1102523, _1102525] : [class_Rings_Olinordered__semidom(_1102523), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1102523), c_Groups_Ozero__class_Ozero(_1102523)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1102523), _1102525))))], (37128 ^ _779203) ^ [_1479909, _1479911, _1479913] : [-(c_HOL_OThe(tc_prod(_1479909, _1479911), hAPP(c_Product__Type_Oprod_Oprod__case(_1479909, _1479911, tc_HOL_Obool), _1479913)) = c_HOL_OThe(tc_prod(_1479909, _1479911), hAPP(hAPP(c_COMBS(tc_prod(_1479909, _1479911), _1479911, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1479909, tc_fun(_1479911, tc_HOL_Obool), tc_prod(_1479909, _1479911)), _1479913), c_Product__Type_Ofst(_1479909, _1479911))), c_Product__Type_Osnd(_1479909, _1479911))))], (17132 ^ _779203) ^ [_1080898] : [class_Orderings_Oord(_1080898), -(c_Orderings_Oord__class_Omin(_1080898) = c_Orderings_Oord_Omin(_1080898, c_Orderings_Oord__class_Oless__eq(_1080898)))], (1540 ^ _779203) ^ [_801413, _801415] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_801413)), _801415 = _801413, class_Groups_Oordered__cancel__ab__semigroup__add(_801415)], (35383 ^ _779203) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (52609 ^ _779203) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (46296 ^ _779203) ^ [_1710004, _1710006, _1710008] : [class_Orderings_Olinorder(_1710004), -(c_List_Olinorder__class_Osorted(_1710004, hAPP(c_List_Ofilter(_1710004, hAPP(hAPP(c_COMBC(_1710004, _1710004, tc_HOL_Obool), c_fequal), hAPP(_1710006, _1710008))), _1710008)))], (20036 ^ _779203) ^ [_1132458, _1132460, _1132462] : [class_Rings_Oring(_1132458), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1132458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132458), _1132460), _1132462)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132458), _1132460), hAPP(c_Groups_Ouminus__class_Ouminus(_1132458), _1132462)))], (9570 ^ _779203) ^ [_942618] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _942618), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _942618)], (17812 ^ _779203) ^ [_1093261, _1093263, _1093265] : [class_Orderings_Olinorder(_1093261), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093261), _1093263)), -(hBOOL(hAPP(hAPP(c_member(_1093261), _1093265), _1093263))), -(c_Big__Operators_Olattice_OSup__fin(_1093261, c_Orderings_Oord__class_Omax(_1093261), hAPP(hAPP(c_Set_Oinsert(_1093261), _1093265), _1093263)) = hAPP(hAPP(c_Finite__Set_Ofold(_1093261, _1093261, c_Orderings_Oord__class_Omax(_1093261)), _1093265), _1093263))], (24317 ^ _779203) ^ [_1207825, _1207827] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1207825))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1207825)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1207827)) = 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), _1207827)))], (38808 ^ _779203) ^ [_1530787, _1530789, _1530791] : [-(hAPP(c_Set_Oimage(tc_prod(_1530787, _1530789), _1530787, c_Product__Type_Ofst(_1530787, _1530789)), _1530791) = hAPP(c_Relation_ODomain(_1530787, _1530789), _1530791))], (26000 ^ _779203) ^ [_1236407, _1236409] : [class_Rings_Oring__1(_1236407), -(hBOOL(hAPP(hAPP(c_member(_1236407), hAPP(c_Int_Oring__1__class_Oof__int(_1236407), _1236409)), c_Int_Oring__1__class_OInts(_1236407))))], (22091 ^ _779203) ^ [_1169125, _1169127, _1169129, _1169131, _1169133, _1169135] : [class_Divides_Oring__div(_1169125), c_Divides_Odiv__class_Omod(_1169125, _1169127, _1169129) = c_Divides_Odiv__class_Omod(_1169125, _1169131, _1169129), c_Divides_Odiv__class_Omod(_1169125, _1169133, _1169129) = c_Divides_Odiv__class_Omod(_1169125, _1169135, _1169129), -(c_Divides_Odiv__class_Omod(_1169125, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1169125), _1169127), _1169133), _1169129) = c_Divides_Odiv__class_Omod(_1169125, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1169125), _1169131), _1169135), _1169129))], (36388 ^ _779203) ^ [_1463757, _1463759, _1463761, _1463763, _1463765] : [c_Fun_Oinj__on(_1463757, _1463759, _1463761, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1463757, tc_HOL_Obool)), _1463763), _1463765)), 36391 ^ _779203 : [(36398 ^ _779203) ^ [] : [_1463763 = _1463765, -(hAPP(c_Set_Oimage(_1463757, _1463759, _1463761), _1463763) = hAPP(c_Set_Oimage(_1463757, _1463759, _1463761), _1463765))], (36392 ^ _779203) ^ [] : [hAPP(c_Set_Oimage(_1463757, _1463759, _1463761), _1463763) = hAPP(c_Set_Oimage(_1463757, _1463759, _1463761), _1463765), -(_1463763 = _1463765)]]], (21961 ^ _779203) ^ [_1166320, _1166322] : [class_Divides_Osemiring__div(_1166320), -(c_Divides_Odiv__class_Omod(_1166320, c_Groups_Ozero__class_Ozero(_1166320), _1166322) = c_Groups_Ozero__class_Ozero(_1166320))], (12348 ^ _779203) ^ [_992101, _992103, _992105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992101), _992103)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992101), _992105))), 12351 ^ _779203 : [(12354 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992103), _992105)))], (12352 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992101)))]]], (31907 ^ _779203) ^ [_1353493, _1353495, _1353497, _1353499, _1353501, _1353503, _1353505] : [class_Rings_Osemiring__0(_1353493), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353493), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353495, _1353493), _1353497), _1353499)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353501, _1353493), _1353503), _1353505)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353495, _1353493), hAPP(hAPP(c_COMBC(_1353495, tc_fun(_1353501, tc_HOL_Obool), _1353493), hAPP(hAPP(c_COMBB(tc_fun(_1353501, _1353493), tc_fun(tc_fun(_1353501, tc_HOL_Obool), _1353493), _1353495), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353501, _1353493)), hAPP(hAPP(c_COMBC(_1353495, tc_fun(_1353501, _1353493), tc_fun(_1353501, _1353493)), hAPP(hAPP(c_COMBB(tc_fun(_1353493, _1353493), tc_fun(tc_fun(_1353501, _1353493), tc_fun(_1353501, _1353493)), _1353495), c_COMBB(_1353493, _1353493, _1353501)), hAPP(hAPP(c_COMBB(_1353493, tc_fun(_1353493, _1353493), _1353495), c_Groups_Otimes__class_Otimes(_1353493)), _1353497))), _1353503))), _1353505)), _1353499))], (19584 ^ _779203) ^ [_1124639, _1124641, _1124643] : [19586 ^ _779203 : [(19589 ^ _779203) ^ [] : [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(_1124641, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 19585 ^ [_1124639, _1124641, _1124643]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1124641, 19585 ^ [_1124639, _1124641, _1124643])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19587 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19585 ^ [_1124639, _1124641, _1124643]), _1124639)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1124641, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1124643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124643), hAPP(_1124641, _1124639))), 19599 ^ _779203 : [(19602 ^ _779203) ^ [] : [-(hAPP(_1124641, 19598 ^ [_1124639, _1124641, _1124643]) = _1124643)], (19600 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 19598 ^ [_1124639, _1124641, _1124643]), _1124639)))]]], (36038 ^ _779203) ^ [_1456047, _1456049, _1456051, _1456053, _1456055, _1456057, _1456059, _1456061] : [c_Equiv__Relations_Oequiv(_1456047, _1456049, _1456051), c_Equiv__Relations_Ocongruent2(_1456047, _1456053, _1456055, _1456051, _1456057, _1456059), hBOOL(hAPP(hAPP(c_member(_1456047), _1456061), _1456049)), -(c_Equiv__Relations_Ocongruent(_1456053, _1456055, _1456057, hAPP(_1456059, _1456061)))], (3162 ^ _779203) ^ [_826202, _826204, _826206, _826208, _826210, _826212, _826214, _826216, _826218, _826220] : [-(c_Fun_Ofun__upd(_826220, _826216, _826212, _826208, _826204) = c_Fun_Ofun__upd(_826218, _826214, _826210, _826206, _826202)), _826220 = _826218, _826216 = _826214, _826212 = _826210, _826208 = _826206, _826204 = _826202], (45827 ^ _779203) ^ [_1701292, _1701294, _1701296] : [class_Groups_Oab__semigroup__add(_1701292), -(c_List_Ofoldr(_1701292, _1701292, c_Groups_Oplus__class_Oplus(_1701292), _1701294, _1701296) = hAPP(c_List_Ofoldl(_1701292, _1701292, c_Groups_Oplus__class_Oplus(_1701292), _1701296), _1701294))], (52205 ^ _779203) ^ [_1832059, _1832061] : [class_Groups_Ouminus(_1832059), -(class_Groups_Ouminus(tc_fun(_1832061, _1832059)))], (43614 ^ _779203) ^ [_1651481, _1651483, _1651485, _1651487, _1651489] : [-(hAPP(hAPP(c_List_Oappend(_1651481), _1651483), _1651485) = hAPP(hAPP(c_List_Oappend(_1651481), _1651487), _1651489)), 43617 ^ _779203 : [(43620 ^ _779203) ^ [] : [_1651483 = hAPP(hAPP(c_List_Otake(_1651481), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651481)), _1651483)), _1651487), _1651485 = hAPP(hAPP(c_List_Oappend(_1651481), hAPP(hAPP(c_List_Odrop(_1651481), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651481)), _1651483)), _1651487)), _1651489)], (43618 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651481)), _1651483)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651481)), _1651487))))]], 43625 ^ _779203 : [(43628 ^ _779203) ^ [] : [hAPP(hAPP(c_List_Otake(_1651481), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651481)), _1651487)), _1651483) = _1651487, hAPP(hAPP(c_List_Oappend(_1651481), hAPP(hAPP(c_List_Odrop(_1651481), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651481)), _1651487)), _1651483)), _1651485) = _1651489], (43626 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651481)), _1651483)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651481)), _1651487)))]]], (44374 ^ _779203) ^ [_1667427, _1667429, _1667431, _1667433, _1667435, _1667437, _1667439] : [hAPP(hAPP(c_List_Omap(_1667427, _1667429), _1667431), _1667433) = hAPP(hAPP(c_List_Omap(_1667435, _1667429), _1667437), _1667439), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667427)), _1667433) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667435)), _1667439))], (21167 ^ _779203) ^ [_1152507] : [c_Int_OBit1(_1152507) = c_Int_OPls], (37661 ^ _779203) ^ [_1493824, _1493826, _1493828, _1493830, _1493832, _1493834] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1493824, _1493826)), hAPP(hAPP(c_Product__Type_OPair(_1493824, _1493826), _1493828), _1493830)), hAPP(hAPP(c_Product__Type_OSigma(_1493824, _1493826), _1493832), _1493834))), 37664 ^ _779203 : [(37667 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493826), _1493830), hAPP(_1493834, _1493828))))], (37665 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1493824), _1493828), _1493832)))]]], (34346 ^ _779203) ^ [_1411151, _1411153, _1411155, _1411157, _1411159, _1411161, _1411163] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411151, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411153, tc_fun(_1411151, tc_HOL_Obool)), _1411155), _1411157)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411159, tc_fun(_1411151, tc_HOL_Obool)), _1411161), _1411163)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411153, tc_fun(_1411151, tc_HOL_Obool)), _1411155), hAPP(hAPP(c_COMBB(tc_fun(_1411159, tc_fun(_1411151, tc_HOL_Obool)), tc_fun(_1411151, tc_HOL_Obool), _1411153), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411159, tc_fun(_1411151, tc_HOL_Obool)), _1411161)), hAPP(hAPP(c_COMBC(_1411153, tc_fun(_1411159, tc_fun(_1411151, tc_HOL_Obool)), tc_fun(_1411159, tc_fun(_1411151, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1411151, tc_HOL_Obool), tc_fun(_1411151, tc_HOL_Obool)), tc_fun(tc_fun(_1411159, tc_fun(_1411151, tc_HOL_Obool)), tc_fun(_1411159, tc_fun(_1411151, tc_HOL_Obool))), _1411153), c_COMBB(tc_fun(_1411151, tc_HOL_Obool), tc_fun(_1411151, tc_HOL_Obool), _1411159)), hAPP(hAPP(c_COMBB(tc_fun(_1411151, tc_HOL_Obool), tc_fun(tc_fun(_1411151, tc_HOL_Obool), tc_fun(_1411151, tc_HOL_Obool)), _1411153), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411151, tc_HOL_Obool))), _1411157))), _1411163))))], (21299 ^ _779203) ^ [_1154665, _1154667] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154665), _1154667), hAPP(c_Int_Onumber__class_Onumber__of(_1154665), c_Int_OBit1(c_Int_OPls))) = _1154667), class_Fields_Ofield(_1154665), class_Int_Onumber__ring(_1154665)], (21449 ^ _779203) ^ [_1156904, _1156906] : [class_Fields_Olinordered__field__inverse__zero(_1156904), class_Int_Onumber__ring(_1156904), 21456 ^ _779203 : [(21463 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156904), c_Groups_Ozero__class_Ozero(_1156904)), _1156906)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156904), c_Groups_Ozero__class_Ozero(_1156904)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156904), _1156906), hAPP(c_Int_Onumber__class_Onumber__of(_1156904), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (21457 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156904), c_Groups_Ozero__class_Ozero(_1156904)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156904), _1156906), hAPP(c_Int_Onumber__class_Onumber__of(_1156904), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156904), c_Groups_Ozero__class_Ozero(_1156904)), _1156906)))]]], (24898 ^ _779203) ^ [_1217955, _1217957] : [24899 ^ _779203 : [(24902 ^ _779203) ^ [] : [_1217955 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24900 ^ _779203) ^ [] : [_1217957 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1217955), _1217957) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (50469 ^ _779203) ^ [_1801833, _1801835, _1801837, _1801839] : [50472 ^ _779203 : [(50475 ^ _779203) ^ [] : [hAPP(_1801837, 50470 ^ [_1801833, _1801835, _1801837, _1801839]) = hAPP(_1801837, 50471 ^ [_1801833, _1801835, _1801837, _1801839])], (50473 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801833, _1801833)), hAPP(hAPP(c_Product__Type_OPair(_1801833, _1801833), 50470 ^ [_1801833, _1801835, _1801837, _1801839]), 50471 ^ [_1801833, _1801835, _1801837, _1801839])), _1801835)))]], -(c_Equiv__Relations_Ocongruent(_1801833, _1801839, _1801835, _1801837))], (25592 ^ _779203) ^ [] : [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)], (47335 ^ _779203) ^ [_1732337, _1732339] : [class_Enum_Oenum(_1732337), 47338 ^ _779203 : [(47345 ^ _779203) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732337), _1732339)), -(hBOOL(hAPP(_1732339, 47348 ^ [_1732337, _1732339])))], (47339 ^ _779203) ^ [] : [47340 ^ _779203 : [(47341 ^ _779203) ^ [_1732439] : [hBOOL(hAPP(_1732339, _1732439))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732337), _1732339)))]]], (43229 ^ _779203) ^ [_1641805, _1641807, _1641809] : [c_List_Olist_ONil(_1641805) = hAPP(hAPP(c_List_Oappend(_1641805), _1641807), _1641809), 43232 ^ _779203 : [(43235 ^ _779203) ^ [] : [-(_1641809 = c_List_Olist_ONil(_1641805))], (43233 ^ _779203) ^ [] : [-(_1641807 = c_List_Olist_ONil(_1641805))]]], (49935 ^ _779203) ^ [_1789151, _1789153, _1789155, _1789157, _1789159] : [c_Fun_Obij__betw(_1789151, _1789153, _1789155, c_Orderings_Otop__class_Otop(tc_fun(_1789151, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1789153, tc_HOL_Obool))), c_Fun_Obij__betw(_1789153, _1789157, _1789159, c_Orderings_Otop__class_Otop(tc_fun(_1789153, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1789157, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1789151, _1789157, hAPP(c_Fun_Ocomp(_1789153, _1789157, _1789151, _1789159), _1789155), c_Orderings_Otop__class_Otop(tc_fun(_1789151, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1789157, tc_HOL_Obool))))], (18927 ^ _779203) ^ [_1112661, _1112663] : [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)), _1112661)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1112663))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1112661), _1112663)))], (1976 ^ _779203) ^ [_807667, _807669, _807671, _807673] : [-(c_Option_Othe(_807673, _807669) = c_Option_Othe(_807671, _807667)), _807673 = _807671, _807669 = _807667], (20702 ^ _779203) ^ [_1144549, _1144551, _1144553, _1144555, _1144557] : [-(hBOOL(hAPP(hAPP(c_member(_1144549), _1144551), c_SetInterval_Oord_OgreaterThanLessThan(_1144549, _1144553, _1144555, _1144557)))), hBOOL(hAPP(hAPP(_1144553, _1144555), _1144551)), hBOOL(hAPP(hAPP(_1144553, _1144551), _1144557))], (26894 ^ _779203) ^ [_1252877] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1252877)) = hAPP(c_Nat_OSuc, _1252877))], (29246 ^ _779203) ^ [_1297521, _1297523] : [class_Lattices_Osemilattice__inf(_1297521), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297521), _1297523), _1297523) = _1297523)], (2122 ^ _779203) ^ [_809878, _809880, _809882, _809884] : [-(c_Random_Oinc__shift(_809884, _809880) = c_Random_Oinc__shift(_809882, _809878)), _809884 = _809882, _809880 = _809878], (38416 ^ _779203) ^ [_1520369, _1520371, _1520373] : [_1520373 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520369, _1520371), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1520369, _1520371), _1520373) = c_Orderings_Obot__class_Obot(tc_fun(_1520371, tc_HOL_Obool)))], (45740 ^ _779203) ^ [_1698273, _1698275] : [-(c_List_Otranspose(_1698273, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1698273)), c_List_Olist_ONil(_1698273)), _1698275)) = c_List_Otranspose(_1698273, _1698275))], (5985 ^ _779203) ^ [_874144, _874146, _874148, _874150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874144, tc_HOL_Obool)), _874146), _874148)), hBOOL(hAPP(hAPP(c_member(_874144), _874150), _874146)), -(hBOOL(hAPP(hAPP(c_member(_874144), _874150), _874148)))], (31787 ^ _779203) ^ [_1350636, _1350638, _1350640] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350636, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1350636, tc_fun(_1350636, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350636)), _1350638)), hAPP(hAPP(c_COMBC(_1350636, tc_fun(_1350636, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350636)), _1350640))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350636, tc_HOL_Obool)), _1350638), _1350640)))], (28278 ^ _779203) ^ [_1279137] : [class_Lattices_Oboolean__algebra(_1279137), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1279137), c_Orderings_Otop__class_Otop(_1279137)) = c_Orderings_Obot__class_Obot(_1279137))], (47617 ^ _779203) ^ [_1738723, _1738725, _1738727] : [class_Orderings_Olinorder(_1738723), 47623 ^ _779203 : [(47626 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1738723), _1738727), 47622 ^ [_1738723, _1738725, _1738727]))], (47624 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738723), 47622 ^ [_1738723, _1738725, _1738727]), hAPP(c_List_Oset(_1738723), _1738725))))]], c_List_Olinorder__class_Osorted(_1738723, _1738725), -(c_List_Olinorder__class_Osorted(_1738723, hAPP(hAPP(c_List_Olist_OCons(_1738723), _1738727), _1738725)))], (47848 ^ _779203) ^ [_1743386, _1743388, _1743390] : [c_FunDef_Ois__measure(_1743386, _1743388), -(c_FunDef_Ois__measure(tc_prod(_1743386, _1743390), hAPP(hAPP(c_COMBB(_1743386, tc_Nat_Onat, tc_prod(_1743386, _1743390)), _1743388), c_Product__Type_Ofst(_1743386, _1743390))))], (32954 ^ _779203) ^ [_1382857, _1382859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1382857)), 32957 ^ _779203 : [(32964 ^ _779203) ^ [] : [-(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), _1382859), _1382857)))), -(c_Divides_OnegDivAlg(_1382859, _1382857) = hAPP(c_Divides_Oadjust(_1382857), c_Divides_OnegDivAlg(_1382859, 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)))), _1382857))))], (32958 ^ _779203) ^ [] : [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), _1382859), _1382857))), -(c_Divides_OnegDivAlg(_1382859, _1382857) = 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), _1382859), _1382857)))]]], (36844 ^ _779203) ^ [_1473554, _1473556, _1473558, _1473560] : [c_Fun_Oinj__on(_1473554, _1473556, _1473558, _1473560), -(c_Fun_Oinj__on(_1473556, _1473554, c_Fun_Othe__inv__into(_1473554, _1473556, _1473560, _1473558), hAPP(c_Set_Oimage(_1473554, _1473556, _1473558), _1473560)))], (22257 ^ _779203) ^ [_1172145, _1172147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1172145), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22260 ^ _779203 : [(22267 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1172147), _1172145)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22261 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1172147), _1172145)), 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)), _1172147)))]]], (40233 ^ _779203) ^ [_1565016, _1565018, _1565020, _1565022, _1565024] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565016, _1565016)), hAPP(hAPP(c_Product__Type_OPair(_1565016, _1565016), _1565018), _1565020)), c_Transitive__Closure_Otrancl(_1565016, _1565022))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565016, _1565016)), hAPP(hAPP(c_Product__Type_OPair(_1565016, _1565016), _1565020), _1565024)), c_Transitive__Closure_Otrancl(_1565016, _1565022))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565016, _1565016)), hAPP(hAPP(c_Product__Type_OPair(_1565016, _1565016), _1565018), _1565024)), c_Transitive__Closure_Otrancl(_1565016, _1565022))))], (13579 ^ _779203) ^ [_1015096, _1015098, _1015100, _1015102] : [class_Rings_Odivision__ring(_1015096), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015096), _1015098), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015096), _1015100), _1015102)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015096), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015096), _1015098), _1015100)), _1015102))], (10289 ^ _779203) ^ [_956064, _956066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956064), _956066)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _956066)), _956064) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956066), _956064)))], (46979 ^ _779203) ^ [_1724270, _1724272, _1724274] : [46981 ^ _779203 : [(46984 ^ _779203) ^ [] : [hBOOL(hAPP(_1724272, 46980 ^ [_1724270, _1724272, _1724274]))], (46982 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1724270), 46980 ^ [_1724270, _1724272, _1724274]), hAPP(c_List_Oset(_1724270), _1724274))))]], -(c_List_OdropWhile(_1724270, _1724272, _1724274) = c_List_Olist_ONil(_1724270))], (37647 ^ _779203) ^ [_1493273, _1493275, _1493277, _1493279, _1493281] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1493273, _1493275), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493273, tc_HOL_Obool)), _1493277), _1493279)), _1493281) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1493273, _1493275), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1493273, _1493275), _1493277), _1493281)), hAPP(hAPP(c_Product__Type_OSigma(_1493273, _1493275), _1493279), _1493281)))], (38987 ^ _779203) ^ [_1535361, _1535363] : [c_Wellfounded_Owf(_1535361, _1535363), -(c_Wellfounded_Owf(tc_List_Olist(_1535361), c_List_Olenlex(_1535361, _1535363)))], (15746 ^ _779203) ^ [_1055207, _1055209, _1055211] : [class_Orderings_Olinorder(_1055207), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055207), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1055207), _1055209), _1055211)), _1055209)))], (38879 ^ _779203) ^ [_1532318, _1532320] : [c_FunDef_Oreduction__pair(_1532318, _1532320), 38882 ^ _779203 : [(38885 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1532318, _1532318, _1532318), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool), tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool)), _1532320)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool), tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool)), _1532320))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool), tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool)), _1532320))))], (38883 ^ _779203) ^ [] : [-(c_Wellfounded_Owf(_1532318, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool), tc_fun(tc_prod(_1532318, _1532318), tc_HOL_Obool)), _1532320)))]]], (18405 ^ _779203) ^ [_1103886, _1103888, _1103890] : [class_Rings_Olinordered__semidom(_1103886), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103886), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103886), _1103888)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103886), _1103890))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103888), _1103890)))], (43502 ^ _779203) ^ [_1648857, _1648859] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648857)), hAPP(c_List_Orotate1(_1648857), _1648859)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648857)), _1648859))], (10677 ^ _779203) ^ [_963940] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _963940))))], (26124 ^ _779203) ^ [_1238518, _1238520] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1238518, _1238520)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1238520), _1238518)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (38306 ^ _779203) ^ [_1516698, _1516700, _1516702, _1516704] : [-(c_Product__Type_Oapfst(_1516698, _1516700, _1516702, _1516704) = c_Product__Type_Omap__pair(_1516698, _1516700, _1516702, _1516702, _1516704, c_Fun_Oid(_1516702)))], (4854 ^ _779203) ^ [_853100, _853102, _853104, _853106, _853108, _853110] : [-(c_Finite__Set_Ofold__image(_853110, _853106, _853102) = c_Finite__Set_Ofold__image(_853108, _853104, _853100)), _853110 = _853108, _853106 = _853104, _853102 = _853100], (45133 ^ _779203) ^ [_1684689, _1684691, _1684693] : [c_List_Olist__all2(_1684693, _1684693, c_fequal, _1684689, _1684691), -(_1684689 = _1684691)], (28562 ^ _779203) ^ [_1284380, _1284382] : [class_Groups_Oordered__ab__group__add(_1284380), -(hAPP(c_Set_Oimage(_1284380, _1284380, c_Groups_Ouminus__class_Ouminus(_1284380)), hAPP(c_SetInterval_Oord__class_OatMost(_1284380), _1284382)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1284380), hAPP(c_Groups_Ouminus__class_Ouminus(_1284380), _1284382)))], (27895 ^ _779203) ^ [_1271346, _1271348, _1271350, _1271352] : [27909 ^ _779203 : [(27912 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1271352, 27908 ^ [_1271346, _1271348, _1271350, _1271352])))], (27910 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1271346), 27908 ^ [_1271346, _1271348, _1271350, _1271352]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271346, tc_HOL_Obool)), _1271348), _1271350))))]], 27896 ^ _779203 : [(27903 ^ _779203) ^ [_1271555] : [hBOOL(hAPP(hAPP(c_member(_1271346), _1271555), _1271350)), hBOOL(hAPP(_1271352, _1271555))], (27897 ^ _779203) ^ [_1271459] : [hBOOL(hAPP(hAPP(c_member(_1271346), _1271459), _1271348)), hBOOL(hAPP(_1271352, _1271459))]]], (20744 ^ _779203) ^ [_1145388] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1145388)) = _1145388)], (32321 ^ _779203) ^ [_1364153, _1364155] : [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(_1364155))), 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)), _1364153))))), -(hAPP(c_Nat_OSuc, _1364153) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1364155))], (40394 ^ _779203) ^ [_1569765, _1569767, _1569769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1569765, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1569765, _1569765, _1569767), _1569769)), _1569769)), -(hAPP(c_Relation_OImage(_1569765, _1569765, c_Transitive__Closure_Ortrancl(_1569765, _1569767)), _1569769) = _1569769)], (24482 ^ _779203) ^ [_1210456, _1210458] : [class_Rings_Olinordered__idom(_1210456), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1210456), hAPP(c_Groups_Oabs__class_Oabs(_1210456), _1210458)), 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(_1210456), _1210458), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (36128 ^ _779203) ^ [_1458231, _1458233, _1458235, _1458237, _1458239, _1458241, _1458243, _1458245, _1458247, _1458249, _1458251] : [c_Equiv__Relations_Oequiv(_1458231, _1458233, _1458235), c_Equiv__Relations_Oequiv(_1458237, _1458239, _1458241), c_Equiv__Relations_Ocongruent2(_1458231, _1458237, tc_fun(_1458243, tc_HOL_Obool), _1458235, _1458241, _1458245), hBOOL(hAPP(hAPP(c_member(tc_fun(_1458231, tc_HOL_Obool)), _1458247), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1458231), _1458233), _1458235))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1458237, tc_HOL_Obool)), _1458249), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1458237), _1458239), _1458241))), 36150 ^ _779203 : [(36156 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1458243, tc_HOL_Obool)), hAPP(hAPP(_1458245, 36149 ^ [_1458231, _1458233, _1458235, _1458237, _1458239, _1458241, _1458243, _1458245, _1458247, _1458249, _1458251]), 36152 ^ [_1458231, _1458233, _1458235, _1458237, _1458239, _1458241, _1458243, _1458245, _1458247, _1458249, _1458251])), _1458251))], (36154 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1458237), 36152 ^ [_1458231, _1458233, _1458235, _1458237, _1458239, _1458241, _1458243, _1458245, _1458247, _1458249, _1458251]), _1458239)))], (36151 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1458231), 36149 ^ [_1458231, _1458233, _1458235, _1458237, _1458239, _1458241, _1458243, _1458245, _1458247, _1458249, _1458251]), _1458233)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1458243, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458231, tc_fun(_1458243, tc_HOL_Obool)), _1458247), hAPP(hAPP(c_COMBB(tc_fun(_1458237, tc_fun(_1458243, tc_HOL_Obool)), tc_fun(_1458243, tc_HOL_Obool), _1458231), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1458237, tc_fun(_1458243, tc_HOL_Obool)), _1458249)), _1458245))), _1458251)))], (11730 ^ _779203) ^ [_981557, _981559, _981561] : [class_Groups_Oordered__comm__monoid__add(_981557), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981557), _981559), c_Groups_Ozero__class_Ozero(_981557))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981557), _981561), c_Groups_Ozero__class_Ozero(_981557))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981557), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981557), _981559), _981561)), c_Groups_Ozero__class_Ozero(_981557))))], (44676 ^ _779203) ^ [] : [-(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))], (1940 ^ _779203) ^ [_806413, _806415] : [-(class_Rings_Odvd(_806413)), _806415 = _806413, class_Rings_Odvd(_806415)], (38368 ^ _779203) ^ [_1518869, _1518871, _1518873, _1518875, _1518877, _1518879] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1518869, _1518871, _1518873), _1518875), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518871, _1518873), tc_HOL_Obool)), _1518877), _1518879)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518869, _1518873), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518869, _1518871, _1518873), _1518875), _1518877)), hAPP(hAPP(c_Relation_Orel__comp(_1518869, _1518871, _1518873), _1518875), _1518879)))], (38744 ^ _779203) ^ [_1529289, _1529291, _1529293] : [c_Wellfounded_Owf(_1529289, _1529291), -(hBOOL(hAPP(hAPP(c_member(_1529289), _1529293), c_Wellfounded_Oacc(_1529289, _1529291))))], (11286 ^ _779203) ^ [_973489, _973491, _973493] : [class_Groups_Oordered__comm__monoid__add(_973489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973489), c_Groups_Ozero__class_Ozero(_973489)), _973491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973489), c_Groups_Ozero__class_Ozero(_973489)), _973493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973489), c_Groups_Ozero__class_Ozero(_973489)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973489), _973491), _973493))))], (19244 ^ _779203) ^ [_1118205, _1118207] : [class_Groups_Oordered__ab__group__add__abs(_1118205), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118205), c_Groups_Ozero__class_Ozero(_1118205)), _1118207)), -(hAPP(c_Groups_Oabs__class_Oabs(_1118205), _1118207) = _1118207)], (50931 ^ _779203) ^ [_1810535, _1810537] : [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)))), _1810535, _1810537) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810535), _1810537)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810537), _1810535)))], (36616 ^ _779203) ^ [_1468441, _1468443, _1468445, _1468447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1468441), hAPP(c_Set_Oimage(_1468443, _1468441, _1468445), _1468447))), hAPP(c_Finite__Set_Ocard(_1468443), _1468447))), c_Fun_Oinj__on(_1468443, _1468441, _1468445, _1468447)], (29474 ^ _779203) ^ [_1302170, _1302172, _1302174, _1302176] : [class_Lattices_Osemilattice__inf(_1302170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302170), _1302172), _1302174)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302170), _1302172), _1302176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302170), _1302172), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1302170), _1302174), _1302176))))], (8494 ^ _779203) ^ [_921738, _921740, _921742, _921744, _921746] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_921738, _921740, hAPP(hAPP(c_Set_Oinsert(_921738), _921742), _921744)), _921746)), 8499 ^ _779203 : [(8504 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_921738), 8497 ^ [_921738, _921740, _921742, _921744, _921746]), 8498 ^ [_921738, _921740, _921742, _921744, _921746]))], (8502 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_921738, _921738, _921740, 8497 ^ [_921738, _921740, _921742, _921744, _921746], 8498 ^ [_921738, _921740, _921742, _921744, _921746]), _921746)))], (8500 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_921738), _921742), _921744) = hAPP(hAPP(c_Set_Oinsert(_921738), 8497 ^ [_921738, _921740, _921742, _921744, _921746]), 8498 ^ [_921738, _921740, _921742, _921744, _921746]))]]], (43185 ^ _779203) ^ [_1641032, _1641034, _1641036] : [hAPP(hAPP(c_List_Oappend(_1641032), _1641034), _1641036) = c_List_Olist_ONil(_1641032), 43188 ^ _779203 : [(43191 ^ _779203) ^ [] : [-(_1641036 = c_List_Olist_ONil(_1641032))], (43189 ^ _779203) ^ [] : [-(_1641034 = c_List_Olist_ONil(_1641032))]]], (22145 ^ _779203) ^ [_1170199, _1170201] : [-(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, _1170199, _1170201)), _1170201) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1170199), _1170201))], (32253 ^ _779203) ^ [_1362613, _1362615] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362613), _1362615)), -(hAPP(c_Finite__Set_Ocard(_1362613), _1362615) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1362613, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1362613), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1362615))], (46554 ^ _779203) ^ [_1715300, _1715302] : [hBOOL(hAPP(c_List_Odistinct(_1715300), _1715302)), -(hBOOL(hAPP(c_List_Odistinct(_1715300), hAPP(c_List_Orev(_1715300), _1715302))))], (18147 ^ _779203) ^ [_1099386, _1099388, _1099390, _1099392] : [class_Orderings_Olinorder(_1099386), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099386), _1099388)), 18157 ^ _779203 : [(18160 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099386), _1099390), 18156 ^ [_1099386, _1099388, _1099390, _1099392]))], (18158 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099386), 18156 ^ [_1099386, _1099388, _1099390, _1099392]), _1099388)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099386), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099386), _1099390), _1099392)), hAPP(hAPP(c_Finite__Set_Ofold(_1099386, _1099386, c_Orderings_Oord__class_Omin(_1099386)), _1099392), _1099388))))], (7383 ^ _779203) ^ [_901303, _901305, _901307] : [class_Orderings_Opreorder(_901303), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901303), _901305), _901307)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901303), _901307), _901305))], (12218 ^ _779203) ^ [_990152, _990154] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990152), _990154)), 12219 ^ _779203 : [(12226 ^ _779203) ^ [] : [_990152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _990154 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12220 ^ _779203) ^ [] : [_990152 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _990154 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (48650 ^ _779203) ^ [_1761011, _1761013, _1761015] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1761011) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1761011, _1761013, _1761015)], (50695 ^ _779203) ^ [_1805958, _1805960, _1805962, _1805964] : [class_Rings_Odvd(_1805958), _1805960 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805958), _1805962), _1805964), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805958), _1805962), _1805960)))], (7711 ^ _779203) ^ [_906274, _906276, _906278] : [class_Orderings_Oorder(_906274), -(_906276 = _906278), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906274), _906276), _906278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906274), _906276), _906278)))], (30579 ^ _779203) ^ [_1325193, _1325195, _1325197] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325193, tc_HOL_Obool)), _1325195), _1325197) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1325193, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1325193, tc_HOL_Obool)), _1325195), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1325193, tc_HOL_Obool)), _1325197), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1325193, tc_HOL_Obool), tc_HOL_Obool))))))], (17564 ^ _779203) ^ [_1088812, _1088814, _1088816] : [class_Orderings_Olinorder(_1088812), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088812), _1088814)), hBOOL(hAPP(hAPP(c_member(_1088812), _1088816), _1088814)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1088812), _1088816), c_Big__Operators_Olattice_OSup__fin(_1088812, c_Orderings_Oord__class_Omax(_1088812), _1088814)) = c_Big__Operators_Olattice_OSup__fin(_1088812, c_Orderings_Oord__class_Omax(_1088812), _1088814))], (38788 ^ _779203) ^ [_1530368, _1530370, _1530372, _1530374] : [-(hAPP(c_Relation_ODomain(_1530368, _1530370), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530368, _1530370), tc_HOL_Obool)), _1530372), _1530374)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530368, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1530368, _1530370), _1530372)), hAPP(c_Relation_ODomain(_1530368, _1530370), _1530374)))], (49602 ^ _779203) ^ [_1781610, _1781612, _1781614] : [hAPP(c_Set_Oimage(_1781610, _1781612, _1781614), c_Orderings_Otop__class_Otop(tc_fun(_1781610, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781612, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1781612, _1781610, c_Hilbert__Choice_Oinv__into(_1781610, _1781612, c_Orderings_Otop__class_Otop(tc_fun(_1781610, tc_HOL_Obool)), _1781614), c_Orderings_Otop__class_Otop(tc_fun(_1781612, tc_HOL_Obool))))], (9520 ^ _779203) ^ [_941669, _941671, _941673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941669), _941671)), _941673)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941669), _941673)))], (41369 ^ _779203) ^ [_1594957, _1594959, _1594961] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594957)), hAPP(hAPP(c_List_Olist_OCons(_1594957), _1594959), _1594961)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594957)), _1594961)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31193 ^ _779203) ^ [_1337665, _1337667, _1337669, _1337671, _1337673, _1337675] : [class_Groups_Oab__semigroup__mult(_1337665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337667), _1337669)), -(hBOOL(hAPP(hAPP(c_member(_1337667), _1337671), _1337669))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1337665, _1337667, c_Groups_Otimes__class_Otimes(_1337665)), _1337673), _1337675), hAPP(hAPP(c_Set_Oinsert(_1337667), _1337671), _1337669)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1337665), hAPP(_1337673, _1337671)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1337665, _1337667, c_Groups_Otimes__class_Otimes(_1337665)), _1337673), _1337675), _1337669)))], (28308 ^ _779203) ^ [_1279696, _1279698, _1279700, _1279702] : [hAPP(c_Set_Oimage(_1279696, _1279698, _1279700), c_Orderings_Otop__class_Otop(tc_fun(_1279696, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1279698, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1279698, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1279698, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1279696, _1279698, _1279700), _1279702))), hAPP(c_Set_Oimage(_1279696, _1279698, _1279700), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1279696, tc_HOL_Obool)), _1279702)))))], (44055 ^ _779203) ^ [_1661031, _1661033, _1661035] : [class_Orderings_Olinorder(_1661031), -(c_List_Oremove1(_1661031, _1661033, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661031, _1661031, c_COMBI(_1661031)), _1661033), _1661035)) = _1661035)], (42794 ^ _779203) ^ [_1631982, _1631984, _1631986] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631982), tc_List_Olist(_1631982))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631982), tc_List_Olist(_1631982)), _1631984), c_List_Olist_ONil(_1631982))), c_List_Olistrel1(_1631982, _1631986)))], (2338 ^ _779203) ^ [_813382, _813384] : [_813384 = _813382, -(c_Int_OBit0(_813384) = c_Int_OBit0(_813382))], (17226 ^ _779203) ^ [_1082921, _1082923, _1082925] : [class_Orderings_Olinorder(_1082921), hAPP(_1082923, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1082921), 17231 ^ [_1082921, _1082923, _1082925]), 17232 ^ [_1082921, _1082923, _1082925])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1082921), hAPP(_1082923, 17231 ^ [_1082921, _1082923, _1082925])), hAPP(_1082923, 17232 ^ [_1082921, _1082923, _1082925])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082921), _1082925)), -(_1082925 = c_Orderings_Obot__class_Obot(tc_fun(_1082921, tc_HOL_Obool))), -(hAPP(_1082923, c_Big__Operators_Olinorder__class_OMax(_1082921, _1082925)) = c_Big__Operators_Olinorder__class_OMax(_1082921, hAPP(c_Set_Oimage(_1082921, _1082921, _1082923), _1082925)))], (8889 ^ _779203) ^ [_929425] : [class_Lattices_Oab__semigroup__idem__mult(_929425), -(c_Finite__Set_Ofun__left__comm__idem(_929425, _929425, c_Groups_Otimes__class_Otimes(_929425)))], (29726 ^ _779203) ^ [_1306998, _1307000, _1307002, _1307004] : [-(hBOOL(hAPP(hAPP(c_member(_1306998), _1307000), _1307002))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306998, tc_HOL_Obool)), _1307002), hAPP(hAPP(c_Set_Oinsert(_1306998), _1307000), _1307004)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306998, tc_HOL_Obool)), _1307002), _1307004))], (9544 ^ _779203) ^ [_942164, _942166, _942168] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _942164), _942166)), _942168) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _942164), _942168)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _942166), _942168)))], (32539 ^ _779203) ^ [_1369693, _1369695] : [class_Rings_Osemiring__1(_1369693), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1369693), _1369695) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1369693, hAPP(hAPP(c_COMBC(_1369693, _1369693, _1369693), c_Groups_Oplus__class_Oplus(_1369693)), c_Groups_Oone__class_Oone(_1369693)), _1369695, c_Groups_Ozero__class_Ozero(_1369693)))], (45899 ^ _779203) ^ [_1702918, _1702920] : [c_List_Oupt(_1702918, _1702920) = c_List_Olist_ONil(tc_Nat_Onat), -(_1702920 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702920), _1702918)))], (47550 ^ _779203) ^ [_1737492, _1737494] : [class_Enum_Oenum(_1737492), 47553 ^ _779203 : [(47560 ^ _779203) ^ [] : [hBOOL(hAPP(_1737494, 47561 ^ [_1737492, _1737494])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737492), _1737494)))], (47554 ^ _779203) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737492), _1737494)), 47557 ^ _779203 : [(47558 ^ _779203) ^ [_1737618] : [-(hBOOL(hAPP(_1737494, _1737618)))]]]]], (49332 ^ _779203) ^ [_1776650, _1776652] : [c_Relation_Osym(_1776650, _1776652), -(c_Relation_Osym(tc_List_Olist(_1776650), c_List_Olistrel(_1776650, _1776652)))], (52303 ^ _779203) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (48334 ^ _779203) ^ [_1753828, _1753830, _1753832] : [_1753828 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1753830), c_List_Oreplicate(_1753830, _1753828, _1753832)) = c_Orderings_Obot__class_Obot(tc_fun(_1753830, tc_HOL_Obool)))], (2332 ^ _779203) ^ [_813297, _813299] : [_813299 = _813297, -(c_Divides_Oadjust(_813299) = c_Divides_Oadjust(_813297))], (46612 ^ _779203) ^ [_1716449, _1716451] : [-(hAPP(c_List_Orev(_1716449), c_List_Oconcat(_1716449, _1716451)) = c_List_Oconcat(_1716449, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1716449), tc_List_Olist(_1716449)), c_List_Orev(_1716449)), hAPP(c_List_Orev(tc_List_Olist(_1716449)), _1716451))))], (8264 ^ _779203) ^ [_916635, _916637, _916639] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_916635), _916637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916635, tc_HOL_Obool)), _916639), _916637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_916635), _916637)), hAPP(c_Finite__Set_Ocard(_916635), _916639))), -(_916639 = _916637)], (3796 ^ _779203) ^ [_836149, _836151] : [_836151 = _836149, -(c_Enum_Oenum__class_Oenum__all(_836151) = c_Enum_Oenum__class_Oenum__all(_836149))], (21471 ^ _779203) ^ [] : [-(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)))))], (32667 ^ _779203) ^ [_1375016, _1375018, _1375020, _1375022] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1375016, _1375018)), hAPP(hAPP(c_Product__Type_OPair(_1375016, _1375018), _1375020), _1375022)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1375016, _1375018), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1375016, tc_fun(_1375018, tc_HOL_Obool))), _1375020), _1375022)))], (40460 ^ _779203) ^ [_1571304, _1571306, _1571308, _1571310, _1571312] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571304, _1571304)), hAPP(hAPP(c_Product__Type_OPair(_1571304, _1571304), _1571306), _1571308)), c_Transitive__Closure_Ortrancl(_1571304, _1571310))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571304, _1571304)), hAPP(hAPP(c_Product__Type_OPair(_1571304, _1571304), _1571308), _1571312)), c_Transitive__Closure_Otrancl(_1571304, _1571310))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571304, _1571304)), hAPP(hAPP(c_Product__Type_OPair(_1571304, _1571304), _1571306), _1571312)), c_Transitive__Closure_Otrancl(_1571304, _1571310))))], (34460 ^ _779203) ^ [_1414351, _1414353, _1414355, _1414357, _1414359, _1414361] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414351, tc_fun(_1414353, tc_HOL_Obool)), _1414355), hAPP(hAPP(c_COMBB(_1414357, tc_fun(_1414353, tc_HOL_Obool), _1414351), _1414359), _1414361)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414357, tc_fun(_1414353, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1414351, _1414357, _1414361), _1414355)), _1414359))], (48052 ^ _779203) ^ [_1747752, _1747754, _1747756, _1747758, _1747760] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1747752), _1747754), _1747756), _1747758), _1747760) = c_New__DSequence_Opos__single(_1747752, _1747754))], (1046 ^ _779203) ^ [_794952, _794954, _794956, _794958, _794960, _794962] : [-(c_List_Olist__ex(_794960, _794956, _794952)), c_List_Olist__ex(_794962, _794958, _794954), _794962 = _794960, _794958 = _794956, _794954 = _794952], (8532 ^ _779203) ^ [_922907, _922909, _922911, _922913, _922915, _922917, _922919] : [c_Finite__Set_Ofun__left__comm(_922907, _922909, _922911), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_922907, _922909, _922911, _922913, hAPP(hAPP(c_Set_Oinsert(_922907), _922915), _922917)), _922919)), -(hBOOL(hAPP(hAPP(c_member(_922907), _922915), _922917))), 8544 ^ _779203 : [(8547 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_922907, _922909, _922911, _922913, _922917), 8543 ^ [_922907, _922909, _922911, _922913, _922915, _922917, _922919])))], (8545 ^ _779203) ^ [] : [-(_922919 = hAPP(hAPP(_922911, _922915), 8543 ^ [_922907, _922909, _922911, _922913, _922915, _922917, _922919]))]]], (34621 ^ _779203) ^ [_1419363, _1419365, _1419367, _1419369, _1419371, _1419373] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1419365, _1419367)), hAPP(hAPP(c_Product__Type_OPair(_1419365, _1419367), _1419371), _1419373)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1419363, tc_fun(tc_prod(_1419365, _1419367), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1419363, tc_HOL_Obool))), _1419369))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1419363, tc_fun(_1419365, tc_fun(_1419367, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1419363, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1419365, _1419367), tc_HOL_Obool), tc_fun(_1419365, tc_fun(_1419367, tc_HOL_Obool)), _1419363), hAPP(c_COMBC(_1419365, tc_fun(tc_prod(_1419365, _1419367), tc_HOL_Obool), tc_fun(_1419367, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419367, tc_fun(tc_fun(tc_prod(_1419365, _1419367), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1419365, _1419367), tc_HOL_Obool), tc_fun(_1419367, tc_HOL_Obool)), _1419365), c_COMBC(_1419367, tc_fun(tc_prod(_1419365, _1419367), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419367, tc_prod(_1419365, _1419367)), tc_fun(_1419367, tc_fun(tc_fun(tc_prod(_1419365, _1419367), tc_HOL_Obool), tc_HOL_Obool)), _1419365), hAPP(c_COMBB(tc_prod(_1419365, _1419367), tc_fun(tc_fun(tc_prod(_1419365, _1419367), tc_HOL_Obool), tc_HOL_Obool), _1419367), c_member(tc_prod(_1419365, _1419367)))), c_Product__Type_OPair(_1419365, _1419367))))), _1419369)), _1419371), _1419373)))], (49853 ^ _779203) ^ [_1787340, _1787342, _1787344, _1787346, _1787348, _1787350] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1787340, _1787342, _1787344, _1787346, c_Lazy__Sequence_Olazy__sequence_OInsert(_1787342, _1787348, _1787350)) = hAPP(hAPP(hAPP(_1787346, _1787348), _1787350), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1787340, _1787342, _1787344, _1787346, _1787350)))], (12817 ^ _779203) ^ [_1000706, _1000708, _1000710] : [class_Rings_Olinordered__ring__strict(_1000706), 12820 ^ _779203 : [(12829 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000706), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000706), _1000708), _1000708)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000706), _1000710), _1000710))), c_Groups_Ozero__class_Ozero(_1000706)))), _1000708 = c_Groups_Ozero__class_Ozero(_1000706), _1000710 = c_Groups_Ozero__class_Ozero(_1000706)], (12821 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000706), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1000706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000706), _1000708), _1000708)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000706), _1000710), _1000710))), c_Groups_Ozero__class_Ozero(_1000706))), 12824 ^ _779203 : [(12827 ^ _779203) ^ [] : [-(_1000710 = c_Groups_Ozero__class_Ozero(_1000706))], (12825 ^ _779203) ^ [] : [-(_1000708 = c_Groups_Ozero__class_Ozero(_1000706))]]]]], (10809 ^ _779203) ^ [_966123, _966125] : [class_Rings_Ocomm__semiring__1(_966123), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966123), c_Groups_Ozero__class_Ozero(_966123)), _966125) = _966125)], (672 ^ _779203) ^ [_789275, _789277, _789279, _789281, _789283, _789285, _789287, _789289] : [-(c_Nat__Transfer_Otransfer__morphism(_789287, _789283, _789279, _789275)), c_Nat__Transfer_Otransfer__morphism(_789289, _789285, _789281, _789277), _789289 = _789287, _789285 = _789283, _789281 = _789279, _789277 = _789275], (43070 ^ _779203) ^ [_1638498, _1638500, _1638502, _1638504, _1638506] : [hAPP(hAPP(c_List_Oappend(_1638498), _1638500), _1638502) = hAPP(hAPP(c_List_Oappend(_1638498), _1638504), _1638506), 43076 ^ _779203 : [(43079 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1638498), 43073 ^ [_1638498, _1638500, _1638502, _1638504, _1638506]), _1638502) = _1638506)], (43077 ^ _779203) ^ [] : [-(_1638500 = hAPP(hAPP(c_List_Oappend(_1638498), _1638504), 43073 ^ [_1638498, _1638500, _1638502, _1638504, _1638506]))]], 43080 ^ _779203 : [(43083 ^ _779203) ^ [] : [-(_1638502 = hAPP(hAPP(c_List_Oappend(_1638498), 43073 ^ [_1638498, _1638500, _1638502, _1638504, _1638506]), _1638506))], (43081 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1638498), _1638500), 43073 ^ [_1638498, _1638500, _1638502, _1638504, _1638506]) = _1638504)]]], (27580 ^ _779203) ^ [_1265244, _1265246] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1265244), c_Orderings_Otop__class_Otop(tc_fun(_1265244, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265246), c_Orderings_Otop__class_Otop(tc_fun(_1265246, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1265244, _1265246)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1265244, _1265246), tc_HOL_Obool)))))], (18883 ^ _779203) ^ [_1111928, _1111930] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1111928) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1111930), -(_1111928 = _1111930)], (11956 ^ _779203) ^ [_985681, _985683, _985685, _985687] : [class_Rings_Olinordered__semiring__strict(_985681), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985681), _985683), _985685)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985681), c_Groups_Ozero__class_Ozero(_985681)), _985687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985681), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985681), _985683), _985687)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985681), _985685), _985687))))], (46818 ^ _779203) ^ [_1720848, _1720850, _1720852] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720848)), c_List_OtakeWhile(_1720848, _1720850, _1720852))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720848)), _1720852))))], (27280 ^ _779203) ^ [_1259402, _1259404] : [-(hBOOL(hAPP(hAPP(c_member(_1259402), _1259404), c_Orderings_Otop__class_Otop(tc_fun(_1259402, tc_HOL_Obool)))))], (45967 ^ _779203) ^ [_1704071, _1704073, _1704075, _1704077] : [-(c_List_Oupt(_1704071, _1704073) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1704075), _1704077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1704071), _1704073)), _1704071 = _1704075, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704071), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1704073) = _1704077], (42251 ^ _779203) ^ [_1620777, _1620779, _1620781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1620777), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620779)), _1620781))), -(c_List_Obutlast(_1620779, hAPP(hAPP(c_List_Otake(_1620779), _1620777), _1620781)) = hAPP(hAPP(c_List_Otake(_1620779), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1620777), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1620781))], (38796 ^ _779203) ^ [_1530553] : [-(c_Relation_Orefl__on(_1530553, c_Orderings_Obot__class_Obot(tc_fun(_1530553, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530553, _1530553), tc_HOL_Obool))))], (33031 ^ _779203) ^ [_1384401, _1384403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1384401)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1384403)), -(c_Divides_OposDivAlg(_1384401, _1384403) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1384401), _1384403)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1384401, _1384403)))], (32413 ^ _779203) ^ [_1366312, _1366314] : [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(_1366312))), 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)), _1366314)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366312)), hAPP(c_Nat_OSuc, _1366314))))], (17098 ^ _779203) ^ [_1080383, _1080385, _1080387] : [class_Orderings_Olinorder(_1080383), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080383), _1080385)), -(hBOOL(hAPP(hAPP(c_member(_1080383), _1080387), _1080385))), -(c_Big__Operators_Olinorder__class_OMax(_1080383, hAPP(hAPP(c_Set_Oinsert(_1080383), _1080387), _1080385)) = hAPP(hAPP(c_Finite__Set_Ofold(_1080383, _1080383, c_Orderings_Oord__class_Omax(_1080383)), _1080387), _1080385))], (27376 ^ _779203) ^ [_1261486, _1261488, _1261490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1261486), _1261488)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1261486), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1261488), _1261490)) = 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, _1261486), _1261488)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1261488), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1261488), _1261490))))], (46638 ^ _779203) ^ [_1717110, _1717112, _1717114, _1717116, _1717118] : [c_List_Olist__all2(_1717110, _1717112, _1717114, hAPP(c_List_Orev(_1717110), _1717116), hAPP(c_List_Orev(_1717112), _1717118)), -(c_List_Olist__all2(_1717110, _1717112, _1717114, _1717116, _1717118))], (5124 ^ _779203) ^ [_857351, _857353, _857355, _857357] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_857357, _857353) = c_SetInterval_Oord__class_OatLeastLessThan(_857355, _857351)), _857357 = _857355, _857353 = _857351], (18417 ^ _779203) ^ [] : [-(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)))], (10973 ^ _779203) ^ [_968590] : [hAPP(c_Nat_OSuc, _968590) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37391 ^ _779203) ^ [_1486587, _1486589, _1486591, _1486593] : [-(hAPP(c_Set_Ovimage(_1486587, _1486589, _1486591), hAPP(c_Set_OCollect(_1486589), _1486593)) = hAPP(c_Set_OCollect(_1486587), hAPP(hAPP(c_COMBB(_1486589, tc_HOL_Obool, _1486587), _1486593), _1486591)))], (4752 ^ _779203) ^ [_851479, _851481, _851483, _851485, _851487, _851489, _851491, _851493, _851495, _851497, _851499, _851501] : [-(c_Partial__Function_Ofun__lub(_851501, _851497, _851493, _851489, _851485, _851481) = c_Partial__Function_Ofun__lub(_851499, _851495, _851491, _851487, _851483, _851479)), _851501 = _851499, _851497 = _851495, _851493 = _851491, _851489 = _851487, _851485 = _851483, _851481 = _851479], (17944 ^ _779203) ^ [_1095614, _1095616, _1095618, _1095620, _1095622, _1095624] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1095614), _1095616)), _1095618) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1095620), _1095622)), _1095624), 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), _1095620), _1095622)), _1095624)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095618), _1095614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1095624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1095620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095620), _1095614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095622), _1095616)))], (32633 ^ _779203) ^ [_1372138, _1372140, _1372142] : [-(hAPP(c_Divides_Oadjust(_1372138), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1372140), _1372142)) = 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), _1372142), _1372138)), 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)))), _1372140)), 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)))), _1372140)), _1372142))))], (1560 ^ _779203) ^ [_801663, _801665] : [-(class_Rings_Olinordered__comm__semiring__strict(_801663)), _801665 = _801663, class_Rings_Olinordered__comm__semiring__strict(_801665)], (24247 ^ _779203) ^ [_1206442, _1206444] : [class_Rings_Ocomm__semiring__1(_1206442), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1206442), _1206444), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1206444)], (3748 ^ _779203) ^ [_835401, _835403, _835405, _835407, _835409, _835411] : [-(c_List_OdropWhile(_835411, _835407, _835403) = c_List_OdropWhile(_835409, _835405, _835401)), _835411 = _835409, _835407 = _835405, _835403 = _835401], (20628 ^ _779203) ^ [_1143057, _1143059, _1143061, _1143063] : [hBOOL(hAPP(hAPP(c_member(_1143057), _1143059), c_SetInterval_Oord_OatMost(_1143057, _1143061, _1143063))), -(hBOOL(hAPP(hAPP(_1143061, _1143059), _1143063)))], (45981 ^ _779203) ^ [_1704312, _1704314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1704312), _1704314)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1704312, _1704314)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1704314), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (16742 ^ _779203) ^ [_1073593, _1073595, _1073597] : [class_Orderings_Olinorder(_1073593), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073593), _1073595)), -(_1073597 = c_Orderings_Obot__class_Obot(tc_fun(_1073593, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073593, tc_HOL_Obool)), _1073597), _1073595)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1073593), c_Big__Operators_Olinorder__class_OMin(_1073593, _1073597)), c_Big__Operators_Olinorder__class_OMin(_1073593, _1073595)) = c_Big__Operators_Olinorder__class_OMin(_1073593, _1073595))], (43832 ^ _779203) ^ [_1656089, _1656091] : [class_Lattices_Oab__semigroup__idem__mult(_1656089), -(_1656091 = c_List_Olist_ONil(_1656089)), -(hAPP(c_Finite__Set_Ofold1(_1656089, c_Groups_Otimes__class_Otimes(_1656089)), hAPP(c_List_Oset(_1656089), _1656091)) = hAPP(c_List_Ofoldl(_1656089, _1656089, c_Groups_Otimes__class_Otimes(_1656089), hAPP(c_List_Ohd(_1656089), _1656091)), hAPP(c_List_Otl(_1656089), _1656091)))], (33459 ^ _779203) ^ [_1391497, _1391499, _1391501, _1391503] : [_1391497 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1391499), _1391501)), _1391503), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1391497, _1391499), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1391501), _1391503)))), 33466 ^ _779203 : [(33469 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1391503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1391503), _1391499))], (33467 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1391499)))]], 33474 ^ _779203 : [(33477 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1391499), _1391503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1391503), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33475 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1391499))]]], (14381 ^ _779203) ^ [_1029408, _1029410, _1029412] : [class_Fields_Olinordered__field(_1029408), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029408), _1029410), c_Groups_Ozero__class_Ozero(_1029408))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029408), _1029412), c_Groups_Ozero__class_Ozero(_1029408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029408), c_Groups_Ozero__class_Ozero(_1029408)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1029408), _1029410), _1029412))))], (47289 ^ _779203) ^ [_1731378, _1731380, _1731382, _1731384] : [class_Orderings_Oorder(_1731378), class_Enum_Oenum(_1731380), 47296 ^ _779203 : [(47305 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1731380, _1731378)), _1731382), _1731384))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731380, _1731378)), _1731382), _1731384)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731380), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1731380), c_fNot), hAPP(hAPP(c_COMBS(_1731380, _1731378, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1731378, tc_fun(_1731378, tc_HOL_Obool), _1731380), c_fequal), _1731382)), _1731384))))], (47297 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1731380, _1731378)), _1731382), _1731384)), 47300 ^ _779203 : [(47303 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1731380), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1731380), c_fNot), hAPP(hAPP(c_COMBS(_1731380, _1731378, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1731378, tc_fun(_1731378, tc_HOL_Obool), _1731380), c_fequal), _1731382)), _1731384)))))], (47301 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731380, _1731378)), _1731382), _1731384)))]]]]], (25428 ^ _779203) ^ [_1227658] : [c_Int_OBit1(_1227658) = c_Int_OMin, -(_1227658 = c_Int_OMin)], (29148 ^ _779203) ^ [_1295296, _1295298, _1295300] : [class_Lattices_Obounded__lattice__top(_1295296), 29151 ^ _779203 : [(29160 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295296), _1295298), _1295300) = c_Orderings_Otop__class_Otop(_1295296)), _1295298 = c_Orderings_Otop__class_Otop(_1295296), _1295300 = c_Orderings_Otop__class_Otop(_1295296)], (29152 ^ _779203) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295296), _1295298), _1295300) = c_Orderings_Otop__class_Otop(_1295296), 29155 ^ _779203 : [(29158 ^ _779203) ^ [] : [-(_1295300 = c_Orderings_Otop__class_Otop(_1295296))], (29156 ^ _779203) ^ [] : [-(_1295298 = c_Orderings_Otop__class_Otop(_1295296))]]]]], (15115 ^ _779203) ^ [_1043549, _1043551] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1043549), _1043551)), 15121 ^ _779203 : [(15124 ^ _779203) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15122 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1043549), 15120 ^ [_1043549, _1043551]), _1043551)))]], -(hAPP(c_Finite__Set_Ocard(_1043549), _1043551) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48699 ^ _779203) ^ [_1761868, _1761870, _1761872, _1761874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761868), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1761870, _1761872, _1761868, _1761874) = 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(_1761870)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1761870)))], (38218 ^ _779203) ^ [_1514672, _1514674] : [-(hAPP(c_Fun_Oid(_1514672), _1514674) = _1514674)], (49652 ^ _779203) ^ [_1782602, _1782604, _1782606, _1782608, _1782610, _1782612] : [hAPP(c_Hilbert__Choice_Oinv__into(_1782602, _1782604, _1782606, _1782608), _1782610) = hAPP(c_Hilbert__Choice_Oinv__into(_1782602, _1782604, _1782606, _1782608), _1782612), hBOOL(hAPP(hAPP(c_member(_1782604), _1782610), hAPP(c_Set_Oimage(_1782602, _1782604, _1782608), _1782606))), hBOOL(hAPP(hAPP(c_member(_1782604), _1782612), hAPP(c_Set_Oimage(_1782602, _1782604, _1782608), _1782606))), -(_1782610 = _1782612)], (49666 ^ _779203) ^ [_1782895, _1782897, _1782899, _1782901, _1782903] : [hBOOL(hAPP(hAPP(c_member(_1782895), _1782897), hAPP(c_Set_Oimage(_1782899, _1782895, _1782901), _1782903))), -(hBOOL(hAPP(hAPP(c_member(_1782899), hAPP(c_Hilbert__Choice_Oinv__into(_1782899, _1782895, _1782903, _1782901), _1782897)), _1782903)))], (42900 ^ _779203) ^ [_1634304, _1634306, _1634308, _1634310, _1634312, _1634314] : [-(hAPP(c_List_Olist_Olist__case(_1634304, _1634306, _1634308, _1634310), hAPP(hAPP(c_List_Olist_OCons(_1634306), _1634312), _1634314)) = hAPP(hAPP(_1634310, _1634312), _1634314))], (10067 ^ _779203) ^ [_951282, _951284, _951286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951282), _951284)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951286), _951284)), _951282) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951286), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _951284), _951282)))], (12511 ^ _779203) ^ [_994947, _994949, _994951, _994953] : [c_Finite__Set_Ofolding__one(_994947, _994949, _994951), hBOOL(hAPP(c_Finite__Set_Ofinite(_994947), _994953)), -(hAPP(_994951, _994953) = hAPP(c_Finite__Set_Ofold1(_994947, _994949), _994953))], (21847 ^ _779203) ^ [_1163875, _1163877] : [-(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), _1163875)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1163877)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1163875))) = 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), _1163877)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1163875)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (8043 ^ _779203) ^ [_912228, _912230, _912232, _912234, _912236] : [c_Finite__Set_Ofun__left__comm(_912228, _912230, _912232), hBOOL(hAPP(c_Finite__Set_Ofinite(_912228), _912234)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_912228, _912230, _912232, _912236, _912234), hAPP(hAPP(c_Finite__Set_Ofold(_912228, _912230, _912232), _912236), _912234))))], (24690 ^ _779203) ^ [_1214048, _1214050, _1214052] : [class_Rings_Olinordered__idom(_1214048), 24693 ^ _779203 : [(24694 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214048), c_Groups_Ozero__class_Ozero(_1214048)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214048), hAPP(hAPP(c_Power_Opower__class_Opower(_1214048), _1214050), 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(_1214048), _1214052), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1214050 = c_Groups_Ozero__class_Ozero(_1214048), _1214052 = c_Groups_Ozero__class_Ozero(_1214048)], (24704 ^ _779203) ^ [] : [24705 ^ _779203 : [(24708 ^ _779203) ^ [] : [-(_1214052 = c_Groups_Ozero__class_Ozero(_1214048))], (24706 ^ _779203) ^ [] : [-(_1214050 = c_Groups_Ozero__class_Ozero(_1214048))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214048), c_Groups_Ozero__class_Ozero(_1214048)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214048), hAPP(hAPP(c_Power_Opower__class_Opower(_1214048), _1214050), 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(_1214048), _1214052), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (27590 ^ _779203) ^ [_1265451] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1265451)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1265451), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1265451), c_Orderings_Otop__class_Otop(tc_fun(_1265451, tc_HOL_Obool)))))], (42808 ^ _779203) ^ [_1632494, _1632496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1632494), _1632496)), -(c_List_Oupto(_1632494, _1632496) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1632494), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1632494), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1632496)))], (48983 ^ _779203) ^ [_1769714, _1769716, _1769718, _1769720] : [class_Complete__Lattice_Ocomplete__lattice(_1769714), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1769716, _1769714), _1769718), _1769720) = c_Complete__Lattice_OInf__class_OInf(_1769714, hAPP(c_Set_OCollect(_1769714), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769716, _1769714), tc_HOL_Obool), tc_HOL_Obool, _1769714), c_HOL_OEx(tc_fun(_1769716, _1769714))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769716, _1769714), tc_HOL_Obool), tc_fun(tc_fun(_1769716, _1769714), tc_HOL_Obool), _1769714), hAPP(c_COMBS(tc_fun(_1769716, _1769714), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1769716, _1769714)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1769716, _1769714), tc_fun(tc_fun(_1769716, _1769714), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1769716, _1769714))), _1769718)))), hAPP(hAPP(c_COMBC(_1769714, tc_fun(tc_fun(_1769716, _1769714), _1769714), tc_fun(tc_fun(_1769716, _1769714), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1769714, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1769716, _1769714), _1769714), tc_fun(tc_fun(_1769716, _1769714), tc_HOL_Obool)), _1769714), c_COMBB(_1769714, tc_HOL_Obool, tc_fun(_1769716, _1769714))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1769716, _1769714), _1769716, _1769714), c_COMBI(tc_fun(_1769716, _1769714))), _1769720)))))))], (50526 ^ _779203) ^ [_1802901, _1802903, _1802905, _1802907] : [-(hAPP(c_Lazy__Sequence_Obind(_1802901, _1802903, _1802905), _1802907) = c_Lazy__Sequence_Oflat(_1802903, c_Lazy__Sequence_Omap(_1802901, tc_Lazy__Sequence_Olazy__sequence(_1802903), _1802907, _1802905)))], (21289 ^ _779203) ^ [_1154514, _1154516] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1154514), _1154516), hAPP(c_Int_Onumber__class_Onumber__of(_1154514), c_Int_OBit1(c_Int_OPls))) = _1154516), class_Fields_Ofield(_1154514), class_Int_Onumber__ring(_1154514)], (4906 ^ _779203) ^ [_853944, _853946, _853948, _853950, _853952, _853954, _853956, _853958] : [-(c_Fun_Othe__inv__into(_853958, _853954, _853950, _853946) = c_Fun_Othe__inv__into(_853956, _853952, _853948, _853944)), _853958 = _853956, _853954 = _853952, _853950 = _853948, _853946 = _853944], (18953 ^ _779203) ^ [_1113102, _1113104] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1113102)), _1113104)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113102), _1113104)))], (41911 ^ _779203) ^ [_1611264, _1611266, _1611268] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611264, tc_HOL_Obool)), hAPP(c_List_Oset(_1611264), c_List_Osublist(_1611264, _1611266, _1611268))), hAPP(c_List_Oset(_1611264), _1611266))))], (4180 ^ _779203) ^ [_842459, _842461] : [_842461 = _842459, -(c_Orderings_Oord__class_Omin(_842461) = c_Orderings_Oord__class_Omin(_842459))], (41310 ^ _779203) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29216 ^ _779203) ^ [_1296824, _1296826] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296824, tc_HOL_Obool)), _1296826), c_Orderings_Otop__class_Otop(tc_fun(_1296824, tc_HOL_Obool))) = _1296826)], (40215 ^ _779203) ^ [_1564659] : [-(c_Transitive__Closure_Otrancl(_1564659, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564659, _1564659), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1564659, _1564659), tc_HOL_Obool)))], (9203 ^ _779203) ^ [_936209, _936211, _936213] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936209), _936211)), _936213) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936211), _936213)))], (15276 ^ _779203) ^ [_1046532, _1046534, _1046536, _1046538] : [class_Orderings_Olinorder(_1046532), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046532), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046532), _1046534), _1046536)), _1046538) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046532), _1046534), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046532), _1046536), _1046538)))], (39852 ^ _779203) ^ [_1555820, _1555822, _1555824, _1555826, _1555828, _1555830] : [c_Finite__Set_Ofolding(_1555820, _1555822, _1555824, _1555826), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555820), _1555828)), -(hAPP(_1555826, hAPP(hAPP(c_Set_Oinsert(_1555820), _1555830), _1555828)) = hAPP(c_Fun_Ocomp(_1555822, _1555822, _1555822, hAPP(_1555826, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1555820, tc_HOL_Obool)), _1555828), hAPP(hAPP(c_Set_Oinsert(_1555820), _1555830), c_Orderings_Obot__class_Obot(tc_fun(_1555820, tc_HOL_Obool)))))), hAPP(_1555824, _1555830)))], (23459 ^ _779203) ^ [_1191979, _1191981, _1191983, _1191985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191981), _1191983)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1191983), 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), _1191981), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1191985, _1191979))), _1191983)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39039 ^ _779203) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (10443 ^ _779203) ^ [_959499, _959501, _959503, _959505] : [class_Rings_Ocomm__semiring__1(_959499), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959499), _959501), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959499), _959503), _959505)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959499), _959501), _959503)), _959505))], (29342 ^ _779203) ^ [_1299484, _1299486] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299484, tc_HOL_Obool)), _1299486), c_Orderings_Obot__class_Obot(tc_fun(_1299484, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1299484, tc_HOL_Obool)))], (13113 ^ _779203) ^ [_1006095, _1006097, _1006099] : [class_Orderings_Olinorder(_1006095), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006095), _1006097)), hBOOL(hAPP(hAPP(c_member(_1006095), _1006099), _1006097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006095), c_Big__Operators_Olinorder__class_OMin(_1006095, _1006097)), _1006099)))], (29230 ^ _779203) ^ [_1297139, _1297141] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297139, tc_HOL_Obool)), _1297141), _1297141) = _1297141)], (52641 ^ _779203) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (51347 ^ _779203) ^ [_1817492, _1817494, _1817496] : [_1817492 = _1817494, 51358 ^ _779203 : [(51361 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817496), _1817492))], (51359 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817492), _1817496)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817494), _1817496)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817496), _1817494)))], (42523 ^ _779203) ^ [_1626986, _1626988] : [class_Groups_Ocomm__monoid__add(_1626986), hBOOL(hAPP(c_List_Odistinct(_1626986), _1626988)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1626986), _1626988) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1626986, _1626986), c_COMBI(_1626986)), hAPP(c_List_Oset(_1626986), _1626988)))], (31603 ^ _779203) ^ [_1346255, _1346257, _1346259] : [31605 ^ _779203 : [(31608 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1346255), _1346259), 31604 ^ [_1346255, _1346257, _1346259]))], (31606 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1346255, tc_HOL_Obool)), 31604 ^ [_1346255, _1346257, _1346259]), _1346257)))]], -(hBOOL(hAPP(hAPP(c_member(_1346255), _1346259), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1346255, tc_HOL_Obool), _1346257))))], (24940 ^ _779203) ^ [_1218682, _1218684, _1218686] : [class_Groups_Omonoid__mult(_1218682), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218682), hAPP(hAPP(c_Power_Opower__class_Opower(_1218682), _1218684), _1218686)), _1218684) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218682), _1218684), hAPP(hAPP(c_Power_Opower__class_Opower(_1218682), _1218684), _1218686)))], (45987 ^ _779203) ^ [_1704423, _1704425] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1704423, _1704425)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1704423), hAPP(c_Nat_OSuc, _1704425)))], (24159 ^ _779203) ^ [_1204665] : [-(_1204665 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 24162 ^ _779203 : [(24169 ^ _779203) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1204665, 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, _1204665) = 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), _1204665), 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)))], (24163 ^ _779203) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1204665, 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, _1204665) = 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), _1204665), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (36404 ^ _779203) ^ [_1464050, _1464052, _1464054, _1464056] : [c_Fun_Oinj__on(_1464050, _1464052, _1464054, _1464056), -(hAPP(c_Finite__Set_Ocard(_1464052), hAPP(c_Set_Oimage(_1464050, _1464052, _1464054), _1464056)) = hAPP(c_Finite__Set_Ocard(_1464050), _1464056))], (3928 ^ _779203) ^ [_838485, _838487, _838489, _838491, _838493, _838495, _838497, _838499] : [-(c_New__Random__Sequence_Opos__empty(_838499, _838495, _838491, _838487) = c_New__Random__Sequence_Opos__empty(_838497, _838493, _838489, _838485)), _838499 = _838497, _838495 = _838493, _838491 = _838489, _838487 = _838485], (21913 ^ _779203) ^ [_1165210, _1165212, _1165214] : [class_Divides_Osemiring__div(_1165210), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165210), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165210), _1165212), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1165210), _1165214), _1165212))), c_Divides_Odiv__class_Omod(_1165210, _1165214, _1165212)) = _1165214)], (51747 ^ _779203) ^ [_1824336, _1824338, _1824340, _1824342] : [class_Divides_Osemiring__div(_1824336), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824336), _1824338), _1824340)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1824336), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824336), _1824340), _1824338)), _1824342) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1824336), hAPP(hAPP(c_Power_Opower__class_Opower(_1824336), _1824340), _1824342)), hAPP(hAPP(c_Power_Opower__class_Opower(_1824336), _1824338), _1824342)))], (8001 ^ _779203) ^ [_911161, _911163, _911165, _911167, _911169, _911171, _911173] : [-(c_Nitpick_Ofold__graph_H(_911161, _911163, _911165, _911167, _911169, hAPP(hAPP(_911165, _911171), _911173))), 8002 ^ _779203 : [(8009 ^ _779203) ^ [_911390, _911392] : [hAPP(hAPP(_911165, _911171), _911173) = hAPP(hAPP(_911165, _911392), _911390), hBOOL(hAPP(hAPP(c_member(_911161), _911392), _911169)), c_Nitpick_Ofold__graph_H(_911161, _911163, _911165, _911167, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911161, tc_HOL_Obool)), _911169), hAPP(hAPP(c_Set_Oinsert(_911161), _911392), c_Orderings_Obot__class_Obot(tc_fun(_911161, tc_HOL_Obool)))), _911390)], (8003 ^ _779203) ^ [] : [_911169 = c_Orderings_Obot__class_Obot(tc_fun(_911161, tc_HOL_Obool)), hAPP(hAPP(_911165, _911171), _911173) = _911167]]], (34336 ^ _779203) ^ [_1410652, _1410654, _1410656, _1410658, _1410660] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410652, tc_fun(_1410654, tc_HOL_Obool)), _1410656), hAPP(hAPP(c_COMBS(_1410652, tc_fun(_1410654, tc_HOL_Obool), tc_fun(_1410654, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410654, tc_HOL_Obool), tc_fun(tc_fun(_1410654, tc_HOL_Obool), tc_fun(_1410654, tc_HOL_Obool)), _1410652), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410654, tc_HOL_Obool))), _1410658)), _1410660)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410654, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410652, tc_fun(_1410654, tc_HOL_Obool)), _1410656), _1410658)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410652, tc_fun(_1410654, tc_HOL_Obool)), _1410656), _1410660)))], (20460 ^ _779203) ^ [_1140022, _1140024, _1140026] : [class_Groups_Olinordered__ab__group__add(_1140022), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1140022), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1140022), _1140024), _1140026)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1140022), hAPP(c_Groups_Ouminus__class_Ouminus(_1140022), _1140024)), hAPP(c_Groups_Ouminus__class_Ouminus(_1140022), _1140026)))], (16780 ^ _779203) ^ [_1074277, _1074279, _1074281, _1074283] : [class_Fields_Olinordered__field__inverse__zero(_1074277), class_Int_Onumber(_1074277), 16787 ^ _779203 : [(16788 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074277), _1074279), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1074277), _1074281), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283)))), 16791 ^ _779203 : [(16798 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074277), c_Groups_Ozero__class_Ozero(_1074277)), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283)))), 16801 ^ _779203 : [(16808 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074277), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283)), c_Groups_Ozero__class_Ozero(_1074277)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074277), _1074279), c_Groups_Ozero__class_Ozero(_1074277))))], (16802 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074277), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283)), c_Groups_Ozero__class_Ozero(_1074277))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074277), _1074281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074277), _1074279), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283)))))]]], (16792 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074277), c_Groups_Ozero__class_Ozero(_1074277)), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074277), _1074279), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283))), _1074281)))]]], (16814 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074277), _1074279), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1074277), _1074281), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283))))), 16817 ^ _779203 : [(16820 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074277), _1074279), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283))), _1074281))], (16818 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074277), c_Groups_Ozero__class_Ozero(_1074277)), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283))))]], 16821 ^ _779203 : [(16824 ^ _779203) ^ [] : [16825 ^ _779203 : [(16828 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074277), _1074281), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074277), _1074279), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283))))], (16826 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074277), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283)), c_Groups_Ozero__class_Ozero(_1074277))))]], 16829 ^ _779203 : [(16832 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1074277), _1074279), c_Groups_Ozero__class_Ozero(_1074277)))], (16830 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074277), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283)), c_Groups_Ozero__class_Ozero(_1074277)))]]], (16822 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074277), c_Groups_Ozero__class_Ozero(_1074277)), hAPP(c_Int_Onumber__class_Onumber__of(_1074277), _1074283)))]]]]], (3892 ^ _779203) ^ [_837883, _837885, _837887, _837889, _837891, _837893, _837895, _837897] : [-(c_New__DSequence_Opos__decr__bind(_837897, _837893, _837889, _837885) = c_New__DSequence_Opos__decr__bind(_837895, _837891, _837887, _837883)), _837897 = _837895, _837893 = _837891, _837889 = _837887, _837885 = _837883], (29214 ^ _779203) ^ [_1296740, _1296742, _1296744, _1296746] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296740, tc_HOL_Obool)), _1296742), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296740, tc_HOL_Obool)), _1296744), _1296746)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296740, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296740, tc_HOL_Obool)), _1296742), _1296744)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296740, tc_HOL_Obool)), _1296742), _1296746)))], (36822 ^ _779203) ^ [_1473123, _1473125, _1473127, _1473129, _1473131] : [c_Fun_Oinj__on(_1473123, _1473125, _1473127, _1473129), hBOOL(hAPP(hAPP(c_member(_1473123), _1473131), _1473129)), -(hAPP(c_Fun_Othe__inv__into(_1473123, _1473125, _1473129, _1473127), hAPP(_1473127, _1473131)) = _1473131)], (38366 ^ _779203) ^ [_1518814, _1518816, _1518818, _1518820] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1518814, _1518816, _1518818), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518814, _1518816), tc_HOL_Obool))), _1518820) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518814, _1518818), tc_HOL_Obool)))], (47401 ^ _779203) ^ [_1733856, _1733858] : [class_Orderings_Olinorder(_1733856), hBOOL(hAPP(c_Finite__Set_Ofinite(_1733856), _1733858)), 47409 ^ _779203 : [(47412 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1733856, 47408 ^ [_1733856, _1733858]))], (47414 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1733856), 47408 ^ [_1733856, _1733858])))], (47416 ^ _779203) ^ [_1734182] : [-(_1734182 = 47408 ^ [_1733856, _1733858]), hAPP(c_List_Oset(_1733856), _1734182) = _1733858, c_List_Olinorder__class_Osorted(_1733856, _1734182), hBOOL(hAPP(c_List_Odistinct(_1733856), _1734182))], (47410 ^ _779203) ^ [] : [-(hAPP(c_List_Oset(_1733856), 47408 ^ [_1733856, _1733858]) = _1733858)]]], (45642 ^ _779203) ^ [_1696373, _1696375, _1696377] : [hAPP(c_List_Ofilter(_1696373, _1696375), _1696377) = _1696377, 45645 ^ _779203 : [(45646 ^ _779203) ^ [_1696464] : [hBOOL(hAPP(hAPP(c_member(_1696373), _1696464), hAPP(c_List_Oset(_1696373), _1696377))), -(hBOOL(hAPP(_1696375, _1696464)))]]], (41669 ^ _779203) ^ [_1604938, _1604940, _1604942, _1604944, _1604946, _1604948] : [c_List_Olistrelp(_1604938, _1604940, hAPP(hAPP(c_List_Olist_OCons(_1604938), _1604942), _1604944), hAPP(hAPP(c_List_Olist_OCons(_1604938), _1604946), _1604948)), 41672 ^ _779203 : [(41675 ^ _779203) ^ [] : [-(c_List_Olistrelp(_1604938, _1604940, _1604944, _1604948))], (41673 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1604940, _1604942), _1604946)))]]], (21137 ^ _779203) ^ [_1151945, _1151947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1151945), _1151947)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1151945)), c_Int_OBit1(_1151947))))], (30002 ^ _779203) ^ [_1313439, _1313441, _1313443] : [class_Lattices_Oboolean__algebra(_1313439), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1313439), _1313441), _1313443) = c_Orderings_Obot__class_Obot(_1313439), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1313439), _1313441), _1313443) = c_Orderings_Otop__class_Otop(_1313439), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1313439), _1313441) = _1313443)], (22233 ^ _779203) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52479 ^ _779203) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (33221 ^ _779203) ^ [_1387517, _1387519] : [-(c_Divides_Opdivmod(_1387517, _1387519) = 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), _1387517)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1387519))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1387517), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1387519))))], (20314 ^ _779203) ^ [_1137516, _1137518, _1137520] : [class_Groups_Oab__group__add(_1137516), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137516), _1137518), _1137520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137516), _1137518), hAPP(c_Groups_Ouminus__class_Ouminus(_1137516), _1137520)))], (44897 ^ _779203) ^ [_1679267, _1679269, _1679271, _1679273] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1679267)), _1679269), c_List_Olists(_1679267, _1679271))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1679267)), _1679269), c_List_Olists(_1679267, _1679273))), -(hBOOL(hAPP(c_List_Olistsp(_1679267, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1679267, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1679267, tc_fun(_1679267, tc_HOL_Obool), tc_HOL_Obool), c_member(_1679267)), _1679271)), hAPP(hAPP(c_COMBC(_1679267, tc_fun(_1679267, tc_HOL_Obool), tc_HOL_Obool), c_member(_1679267)), _1679273))), _1679269)))], (41429 ^ _779203) ^ [_1597081, _1597083, _1597085, _1597087, _1597089, _1597091] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597081), tc_List_Olist(_1597081))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597081), tc_List_Olist(_1597081)), hAPP(hAPP(c_List_Olist_OCons(_1597081), _1597083), _1597085)), hAPP(hAPP(c_List_Olist_OCons(_1597081), _1597087), _1597089))), c_List_Olexord(_1597081, _1597091)))), 41430 ^ _779203 : [(41433 ^ _779203) ^ [] : [_1597083 = _1597087, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597081), tc_List_Olist(_1597081))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597081), tc_List_Olist(_1597081)), _1597085), _1597089)), c_List_Olexord(_1597081, _1597091)))], (41431 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597081, _1597081)), hAPP(hAPP(c_Product__Type_OPair(_1597081, _1597081), _1597083), _1597087)), _1597091))]]], (8795 ^ _779203) ^ [_927658, _927660, _927662, _927664] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_927658), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927658), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927658), _927660), _927662)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927658), _927664), _927662))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927658), _927660), _927664)))], (31057 ^ _779203) ^ [_1334706, _1334708, _1334710] : [class_Lattices_Olattice(_1334706), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334706), _1334708)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334706), _1334710)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334706, tc_HOL_Obool)), _1334708), _1334710) = c_Orderings_Obot__class_Obot(tc_fun(_1334706, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334706), c_Big__Operators_Olattice__class_OInf__fin(_1334706, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334706, tc_HOL_Obool)), _1334708), _1334710))), c_Big__Operators_Olattice__class_OInf__fin(_1334706, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334706, tc_HOL_Obool)), _1334708), _1334710))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334706), c_Big__Operators_Olattice__class_OInf__fin(_1334706, _1334708)), c_Big__Operators_Olattice__class_OInf__fin(_1334706, _1334710)))], (9689 ^ _779203) ^ [_944773, _944775] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944773), _944775))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944773), hAPP(c_Nat_OSuc, _944775))), -(_944775 = _944773)], (37723 ^ _779203) ^ [_1495482, _1495484, _1495486, _1495488, _1495490, _1495492, _1495494] : [class_Groups_Ocomm__monoid__add(_1495482), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495484), _1495486)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1495488), _1495490)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495484, _1495482), hAPP(hAPP(c_COMBS(_1495484, tc_fun(_1495488, tc_HOL_Obool), _1495482), hAPP(hAPP(c_COMBB(tc_fun(_1495488, _1495482), tc_fun(tc_fun(_1495488, tc_HOL_Obool), _1495482), _1495484), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495488, _1495482)), _1495492)), hAPP(hAPP(c_COMBB(tc_fun(_1495488, tc_HOL_Obool), tc_fun(_1495488, tc_HOL_Obool), _1495484), c_Set_OCollect(_1495488)), hAPP(hAPP(c_COMBB(tc_fun(_1495488, tc_HOL_Obool), tc_fun(_1495488, tc_HOL_Obool), _1495484), hAPP(c_COMBS(_1495488, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1495488), c_fconj), hAPP(hAPP(c_COMBC(_1495488, tc_fun(_1495488, tc_HOL_Obool), tc_HOL_Obool), c_member(_1495488)), _1495490)))), _1495494)))), _1495486) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495488, _1495482), hAPP(hAPP(c_COMBS(_1495488, tc_fun(_1495484, tc_HOL_Obool), _1495482), hAPP(hAPP(c_COMBB(tc_fun(_1495484, _1495482), tc_fun(tc_fun(_1495484, tc_HOL_Obool), _1495482), _1495488), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1495484, _1495482)), hAPP(c_COMBC(_1495484, _1495488, _1495482), _1495492))), hAPP(hAPP(c_COMBB(tc_fun(_1495484, tc_HOL_Obool), tc_fun(_1495484, tc_HOL_Obool), _1495488), c_Set_OCollect(_1495484)), hAPP(hAPP(c_COMBB(tc_fun(_1495484, tc_HOL_Obool), tc_fun(_1495484, tc_HOL_Obool), _1495488), hAPP(c_COMBS(_1495484, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1495484), c_fconj), hAPP(hAPP(c_COMBC(_1495484, tc_fun(_1495484, tc_HOL_Obool), tc_HOL_Obool), c_member(_1495484)), _1495486)))), hAPP(c_COMBC(_1495484, _1495488, tc_HOL_Obool), _1495494))))), _1495490))], (20652 ^ _779203) ^ [_1143547, _1143549, _1143551, _1143553] : [hBOOL(hAPP(hAPP(c_member(_1143547), _1143549), c_SetInterval_Oord_OlessThan(_1143547, _1143551, _1143553))), -(hBOOL(hAPP(hAPP(_1143551, _1143549), _1143553)))], (40136 ^ _779203) ^ [_1562916, _1562918] : [-(c_Wellfounded_Owf(_1562916, _1562918)), 40139 ^ _779203 : [(40142 ^ _779203) ^ [_1563136] : [hBOOL(hAPP(hAPP(c_member(_1562916), _1563136), 40137 ^ [_1562916, _1562918])), 40146 ^ _779203 : [(40149 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562916), 40145 ^ [_1562916, _1562918, _1563136]), 40137 ^ [_1562916, _1562918])))], (40147 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1562916, _1562916)), hAPP(hAPP(c_Product__Type_OPair(_1562916, _1562916), 40145 ^ [_1562916, _1562918, _1563136]), _1563136)), _1562918)))]]], (40140 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562916), 40138 ^ [_1562916, _1562918]), 40137 ^ [_1562916, _1562918])))]]], (4778 ^ _779203) ^ [_851964, _851966, _851968, _851970, _851972, _851974] : [-(c_Relation_Orel__comp(_851974, _851970, _851966) = c_Relation_Orel__comp(_851972, _851968, _851964)), _851974 = _851972, _851970 = _851968, _851966 = _851964], (44632 ^ _779203) ^ [_1673451, _1673453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673451)), hAPP(c_Code__Numeral_Oof__nat, _1673453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673451), _1673453)))], (854 ^ _779203) ^ [_791946, _791948, _791950, _791952] : [-(c_Predicate_Otransp(_791950, _791946)), c_Predicate_Otransp(_791952, _791948), _791952 = _791950, _791948 = _791946], (26142 ^ _779203) ^ [_1238904, _1238906] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1238904, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1238904, tc_HOL_Obool))), hAPP(c_Set_OPow(_1238904), _1238906))))], (26892 ^ _779203) ^ [_1252839] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1252839)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1252839), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1252839)))], (6355 ^ _779203) ^ [_881605, _881607, _881609, _881611, _881613] : [c_Finite__Set_Ofolding__one__idem(_881605, _881607, _881609), hBOOL(hAPP(c_Finite__Set_Ofinite(_881605), _881611)), -(_881613 = c_Orderings_Obot__class_Obot(tc_fun(_881605, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881605, tc_HOL_Obool)), _881613), _881611)), -(hAPP(hAPP(_881607, hAPP(_881609, _881613)), hAPP(_881609, _881611)) = hAPP(_881609, _881611))], (15816 ^ _779203) ^ [_1056401, _1056403, _1056405, _1056407] : [class_Orderings_Olinorder(_1056401), 15819 ^ _779203 : [(15820 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056401), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1056401), _1056403), _1056405)), _1056407)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056401), _1056403), _1056407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056401), _1056405), _1056407)))], (15830 ^ _779203) ^ [] : [15831 ^ _779203 : [(15834 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056401), _1056405), _1056407))], (15832 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056401), _1056403), _1056407))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056401), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1056401), _1056403), _1056405)), _1056407)))]]], (51635 ^ _779203) ^ [_1822336] : [_1822336 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822336), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (45622 ^ _779203) ^ [_1695796, _1695798] : [-(c_List_Oconcat(_1695796, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695796), tc_List_Olist(_1695796)), c_List_Olist_Olist__case(tc_List_Olist(_1695796), _1695796, c_List_Olist_ONil(_1695796), hAPP(hAPP(c_COMBB(tc_List_Olist(_1695796), tc_fun(tc_List_Olist(_1695796), tc_List_Olist(_1695796)), _1695796), c_COMBK(tc_List_Olist(_1695796), tc_List_Olist(_1695796))), hAPP(hAPP(c_COMBC(_1695796, tc_List_Olist(_1695796), tc_List_Olist(_1695796)), c_List_Olist_OCons(_1695796)), c_List_Olist_ONil(_1695796))))), _1695798)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695796), _1695796), c_List_Ohd(_1695796)), hAPP(c_List_Ofilter(tc_List_Olist(_1695796), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1695796)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695796), tc_List_Olist(_1695796), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1695796)))), _1695798)))], (43786 ^ _779203) ^ [_1655124] : [-(hAPP(c_List_Otl(_1655124), c_List_Olist_ONil(_1655124)) = c_List_Olist_ONil(_1655124))], (29774 ^ _779203) ^ [_1308242, _1308244, _1308246, _1308248] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308242, tc_HOL_Obool)), _1308244), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308242, tc_HOL_Obool)), _1308246), _1308248)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308242, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308242, tc_HOL_Obool)), _1308244), _1308246)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308242, tc_HOL_Obool)), _1308244), _1308248)))], (52423 ^ _779203) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (52369 ^ _779203) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (25756 ^ _779203) ^ [_1232390] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1232390)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1232390)))], (44779 ^ _779203) ^ [_1676608] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1676608)) = _1676608)], (25744 ^ _779203) ^ [_1232255, _1232257] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232255), _1232257) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1232255 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1232255 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (44867 ^ _779203) ^ [_1678079, _1678081] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1678079), _1678081) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1678079, 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)))), _1678081))))], (21189 ^ _779203) ^ [_1152869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1152869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1152869))))], (3762 ^ _779203) ^ [_835622, _835624] : [_835624 = _835622, -(c_List_Odistinct(_835624) = c_List_Odistinct(_835622))], (1920 ^ _779203) ^ [_806163, _806165] : [-(class_Int_Onumber(_806163)), _806165 = _806163, class_Int_Onumber(_806165)], (2070 ^ _779203) ^ [_809058, _809060, _809062, _809064] : [-(c_Nitpick_Onat__lcm(_809064, _809060) = c_Nitpick_Onat__lcm(_809062, _809058)), _809064 = _809062, _809060 = _809058], (9319 ^ _779203) ^ [_938094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938094), _938094))], (52651 ^ _779203) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (36710 ^ _779203) ^ [_1470603, _1470605, _1470607, _1470609] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1470603), _1470605)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1470607), _1470609)), 36717 ^ _779203 : [(36718 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470603), _1470605)), hAPP(c_Finite__Set_Ocard(_1470607), _1470609)))), 36719 ^ _779203 : [(36720 ^ _779203) ^ [_1470814] : [c_Fun_Oinj__on(_1470603, _1470607, _1470814, _1470605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470607, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470603, _1470607, _1470814), _1470605)), _1470609))]]], (36728 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1470603), _1470605)), hAPP(c_Finite__Set_Ocard(_1470607), _1470609))), 36732 ^ _779203 : [(36735 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1470607, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470603, _1470607, 36731 ^ [_1470603, _1470605, _1470607, _1470609]), _1470605)), _1470609)))], (36733 ^ _779203) ^ [] : [-(c_Fun_Oinj__on(_1470603, _1470607, 36731 ^ [_1470603, _1470605, _1470607, _1470609], _1470605))]]]]], (19186 ^ _779203) ^ [_1117242] : [class_Rings_Olinordered__idom(_1117242), -(hAPP(c_Groups_Oabs__class_Oabs(_1117242), c_Groups_Oone__class_Oone(_1117242)) = c_Groups_Oone__class_Oone(_1117242))], (23132 ^ _779203) ^ [_1186195, _1186197] : [-(_1186195 = hAPP(c_Int_Onat, _1186197)), 23135 ^ _779203 : [(23138 ^ _779203) ^ [] : [_1186197 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186195)], (23136 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186197)))]], 23139 ^ _779203 : [(23142 ^ _779203) ^ [] : [_1186195 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23140 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186197))]]], (28640 ^ _779203) ^ [_1285859, _1285861, _1285863, _1285865] : [class_Orderings_Olinorder(_1285859), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285859), _1285861), _1285863)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285859), _1285863), _1285865)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285859, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1285859, _1285861, _1285863)), c_SetInterval_Oord__class_OatLeastAtMost(_1285859, _1285863, _1285865)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1285859, _1285861, _1285865))], (34145 ^ _779203) ^ [_1405608, _1405610, _1405612] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1405608, 34146 ^ [_1405608, _1405610, _1405612])), hAPP(_1405610, 34146 ^ [_1405608, _1405610, _1405612]))), -(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), _1405610), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1405612))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1405608), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1405612))) = 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)), _1405610)), _1405608)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1405612)))], (17418 ^ _779203) ^ [_1086418, _1086420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086418), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086420), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086418), _1086420))), -(_1086418 = _1086420)], (26368 ^ _779203) ^ [_1242975, _1242977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242975), _1242977)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1242977, _1242975) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (51413 ^ _779203) ^ [_1818575, _1818577] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818575), _1818577)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818577), _1818575))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818577), _1818575)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818575), _1818577)))], (10281 ^ _779203) ^ [_955920, _955922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _955920)), _955922)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955920), _955922)))], (25380 ^ _779203) ^ [_1226908] : [class_Power_Opower(_1226908), -(c_Power_Opower__class_Opower(_1226908) = c_Power_Opower_Opower(_1226908, c_Groups_Oone__class_Oone(_1226908), c_Groups_Otimes__class_Otimes(_1226908)))], (52697 ^ _779203) ^ [_1837051, _1837053] : [_1837051 = _1837053, -(hBOOL(hAPP(hAPP(c_fequal, _1837051), _1837053)))], (11031 ^ _779203) ^ [_969358] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969358), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _969358)], (27326 ^ _779203) ^ [_1260366, _1260368, _1260370] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260366, tc_HOL_Obool)), _1260368), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260366, tc_HOL_Obool)), _1260370), _1260368)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260366, tc_HOL_Obool)), _1260368), _1260370))], (35478 ^ _779203) ^ [_1442539, _1442541, _1442543, _1442545, _1442547] : [hBOOL(hAPP(hAPP(c_member(_1442539), _1442541), hAPP(c_Relation_OImage(_1442543, _1442539, _1442545), _1442547))), 35482 ^ _779203 : [(35485 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1442543, _1442539)), hAPP(hAPP(c_Product__Type_OPair(_1442543, _1442539), 35481 ^ [_1442539, _1442541, _1442543, _1442545, _1442547]), _1442541)), _1442545)))], (35483 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1442543), 35481 ^ [_1442539, _1442541, _1442543, _1442545, _1442547]), _1442547)))]]], (13155 ^ _779203) ^ [_1006729, _1006731] : [class_Orderings_Olinorder(_1006729), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006729), _1006731)), -(_1006731 = c_Orderings_Obot__class_Obot(tc_fun(_1006729, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1006729), c_Big__Operators_Olinorder__class_OMax(_1006729, _1006731)), _1006731)))], (44835 ^ _779203) ^ [_1677544, _1677546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677544)), hAPP(c_Code__Numeral_Onat__of, _1677546))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1677544), _1677546)))], (51189 ^ _779203) ^ [_1814993, _1814995] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814993), _1814995))), 51190 ^ _779203 : [(51191 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814993), _1814995)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814995), _1814993)))], (51197 ^ _779203) ^ [] : [_1814993 = _1814995]]], (39506 ^ _779203) ^ [_1547894, _1547896, _1547898, _1547900, _1547902, _1547904, _1547906] : [-(hAPP(c_Fun_Ocomp(_1547894, _1547896, _1547898, _1547900), hAPP(c_Fun_Ocomp(_1547902, _1547894, _1547898, _1547904), _1547906)) = hAPP(c_Fun_Ocomp(_1547902, _1547896, _1547898, hAPP(c_Fun_Ocomp(_1547894, _1547896, _1547902, _1547900), _1547904)), _1547906))], (20104 ^ _779203) ^ [_1133897, _1133899, _1133901] : [class_Fields_Ofield__inverse__zero(_1133897), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133897), hAPP(c_Groups_Ouminus__class_Ouminus(_1133897), _1133899)), hAPP(c_Groups_Ouminus__class_Ouminus(_1133897), _1133901)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133897), _1133899), _1133901))], (52427 ^ _779203) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (33191 ^ _779203) ^ [_1387097] : [-(c_Divides_Odivmod__nat(_1387097, 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)), _1387097))], (28620 ^ _779203) ^ [_1285542, _1285544, _1285546, _1285548] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285542, tc_HOL_Obool)), _1285544), _1285546), _1285548)), -(hBOOL(hAPP(_1285544, _1285548))), -(hBOOL(hAPP(_1285546, _1285548)))], (9213 ^ _779203) ^ [_936456, _936458] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936456), _936458) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936458), _936456))], (44869 ^ _779203) ^ [_1678117, _1678119, _1678121, _1678123, _1678125] : [c_List_Opartition(_1678117, _1678119, _1678121) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1678117), tc_List_Olist(_1678117)), _1678123), _1678125), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1678117, tc_HOL_Obool)), hAPP(c_List_Oset(_1678117), _1678123)), hAPP(c_List_Oset(_1678117), _1678125)) = hAPP(c_List_Oset(_1678117), _1678121))], (9205 ^ _779203) ^ [_936260, _936262, _936264] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936260), _936262)), _936264) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936262), _936264)))], (40334 ^ _779203) ^ [_1568251, _1568253] : [-(c_Transitive__Closure_Otrancl(_1568251, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568251, _1568251), tc_HOL_Obool)), _1568253), c_Relation_OId(_1568251))) = c_Transitive__Closure_Ortrancl(_1568251, _1568253))], (37275 ^ _779203) ^ [_1483560, _1483562, _1483564, _1483566] : [-(hAPP(c_Set_Oimage(_1483560, _1483562, _1483564), hAPP(c_Set_Ovimage(_1483560, _1483562, _1483564), _1483566)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483562, tc_HOL_Obool)), _1483566), hAPP(c_Set_Oimage(_1483560, _1483562, _1483564), c_Orderings_Otop__class_Otop(tc_fun(_1483560, tc_HOL_Obool)))))], (41355 ^ _779203) ^ [_1594682, _1594684, _1594686, _1594688, _1594690] : [-(hAPP(hAPP(c_List_Olist_OCons(_1594682), _1594684), _1594686) = hAPP(hAPP(c_List_Olist_OCons(_1594682), _1594688), _1594690)), _1594684 = _1594688, _1594686 = _1594690], (27264 ^ _779203) ^ [_1259100, _1259102, _1259104, _1259106] : [class_Orderings_Olinorder(_1259100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1259100), _1259102), _1259104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1259100), _1259104), _1259106)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259100, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1259100, _1259102, _1259104)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1259100, _1259104, _1259106)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1259100, _1259102), _1259106))], (48971 ^ _779203) ^ [_1768828, _1768830, _1768832, _1768834] : [class_Complete__Lattice_Ocomplete__lattice(_1768828), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1768830, _1768828), _1768832), _1768834) = c_Complete__Lattice_OSup__class_OSup(_1768828, hAPP(c_Set_OCollect(_1768828), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768830, _1768828), tc_HOL_Obool), tc_HOL_Obool, _1768828), c_HOL_OEx(tc_fun(_1768830, _1768828))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768830, _1768828), tc_HOL_Obool), tc_fun(tc_fun(_1768830, _1768828), tc_HOL_Obool), _1768828), hAPP(c_COMBS(tc_fun(_1768830, _1768828), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768830, _1768828)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768830, _1768828), tc_fun(tc_fun(_1768830, _1768828), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768830, _1768828))), _1768832)))), hAPP(hAPP(c_COMBC(_1768828, tc_fun(tc_fun(_1768830, _1768828), _1768828), tc_fun(tc_fun(_1768830, _1768828), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768828, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768830, _1768828), _1768828), tc_fun(tc_fun(_1768830, _1768828), tc_HOL_Obool)), _1768828), c_COMBB(_1768828, tc_HOL_Obool, tc_fun(_1768830, _1768828))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768830, _1768828), _1768830, _1768828), c_COMBI(tc_fun(_1768830, _1768828))), _1768834)))))))], (28590 ^ _779203) ^ [_1284956, _1284958, _1284960] : [class_Orderings_Olinorder(_1284956), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284956), _1284958), _1284960)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284956, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1284956, _1284958), _1284960)), hAPP(hAPP(c_Set_Oinsert(_1284956), _1284960), c_Orderings_Obot__class_Obot(tc_fun(_1284956, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1284956, _1284958, _1284960))], (19222 ^ _779203) ^ [_1117849, _1117851] : [class_Groups_Oordered__ab__group__add__abs(_1117849), 19225 ^ _779203 : [(19232 ^ _779203) ^ [] : [_1117851 = c_Groups_Ozero__class_Ozero(_1117849), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117849), hAPP(c_Groups_Oabs__class_Oabs(_1117849), _1117851)), c_Groups_Ozero__class_Ozero(_1117849))))], (19226 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117849), hAPP(c_Groups_Oabs__class_Oabs(_1117849), _1117851)), c_Groups_Ozero__class_Ozero(_1117849))), -(_1117851 = c_Groups_Ozero__class_Ozero(_1117849))]]], (30143 ^ _779203) ^ [_1316548, _1316550] : [class_Orderings_Oorder(_1316548), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316548, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1316548), _1316550)), hAPP(c_SetInterval_Oord__class_OatLeast(_1316548), _1316550)) = hAPP(hAPP(c_Set_Oinsert(_1316548), _1316550), c_Orderings_Obot__class_Obot(tc_fun(_1316548, tc_HOL_Obool))))], (35009 ^ _779203) ^ [_1429822, _1429824, _1429826, _1429828, _1429830] : [-(_1429822 = c_Orderings_Obot__class_Obot(tc_fun(_1429824, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429824, tc_fun(_1429826, tc_HOL_Obool)), _1429822), hAPP(hAPP(c_COMBC(_1429824, tc_fun(_1429826, tc_HOL_Obool), tc_fun(_1429826, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429826, tc_HOL_Obool), tc_fun(tc_fun(_1429826, tc_HOL_Obool), tc_fun(_1429826, tc_HOL_Obool)), _1429824), c_Groups_Ominus__class_Ominus(tc_fun(_1429826, tc_HOL_Obool))), _1429828)), _1429830)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1429826, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429824, tc_fun(_1429826, tc_HOL_Obool)), _1429822), _1429828)), _1429830))], (39554 ^ _779203) ^ [_1548996, _1548998, _1549000, _1549002, _1549004, _1549006, _1549008, _1549010, _1549012, _1549014, _1549016] : [-(hAPP(c_Product__Type_Omap__pair(_1548996, _1548998, _1549000, _1549002, _1549004, _1549006), hAPP(c_Product__Type_Omap__pair(_1549008, _1548996, _1549010, _1549000, _1549012, _1549014), _1549016)) = hAPP(c_Product__Type_Omap__pair(_1549008, _1548998, _1549010, _1549002, hAPP(c_Fun_Ocomp(_1548996, _1548998, _1549008, _1549004), _1549012), hAPP(c_Fun_Ocomp(_1549000, _1549002, _1549010, _1549006), _1549014)), _1549016))], (37293 ^ _779203) ^ [_1483945, _1483947, _1483949, _1483951] : [hBOOL(hAPP(hAPP(c_member(_1483945), _1483947), _1483949)), -(hAPP(c_Set_Ovimage(_1483951, _1483945, hAPP(c_COMBK(_1483945, _1483951), _1483947)), _1483949) = c_Orderings_Otop__class_Otop(tc_fun(_1483951, tc_HOL_Obool)))], (21801 ^ _779203) ^ [_1163051] : [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), _1163051))), 21804 ^ _779203 : [(21807 ^ _779203) ^ [] : [-(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(_1163051)))))], (21805 ^ _779203) ^ [] : [-(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(_1163051)))))]]], (48923 ^ _779203) ^ [_1767299, _1767301, _1767303] : [-(c_List_Olist__ex(_1767299, _1767303, _1767301)), 48924 ^ _779203 : [(48925 ^ _779203) ^ [_1767356] : [hBOOL(hAPP(hAPP(c_member(_1767299), _1767356), hAPP(c_List_Oset(_1767299), _1767301))), hBOOL(hAPP(_1767303, _1767356))]]], (13367 ^ _779203) ^ [_1010753, _1010755] : [-(_1010753 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1010753), _1010755) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1010753), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1010755)))], (50347 ^ _779203) ^ [_1797299, _1797301, _1797303, _1797305] : [c_Equiv__Relations_Oequivp(_1797299, _1797301), -(c_Quotient_OBabs(_1797299, _1797303, c_Quotient_ORespects(_1797299, _1797301), _1797305) = _1797305)], (45482 ^ _779203) ^ [_1692000, _1692002, _1692004] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1692000), tc_List_Olist(_1692000), c_List_Oappend(_1692000), _1692002), _1692004) = hAPP(hAPP(c_List_Oappend(_1692000), _1692002), c_List_Oconcat(_1692000, _1692004)))], (30475 ^ _779203) ^ [_1323121, _1323123, _1323125] : [class_Orderings_Olinorder(_1323121), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323121), _1323123)), -(_1323123 = c_Orderings_Obot__class_Obot(tc_fun(_1323121, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323121), _1323125)), -(_1323125 = c_Orderings_Obot__class_Obot(tc_fun(_1323121, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323121, tc_HOL_Obool)), _1323123), _1323125) = c_Orderings_Obot__class_Obot(tc_fun(_1323121, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1323121, c_Orderings_Oord__class_Omin(_1323121), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1323121, tc_HOL_Obool)), _1323123), _1323125)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1323121), c_Big__Operators_Olattice_OInf__fin(_1323121, c_Orderings_Oord__class_Omin(_1323121), _1323123)), c_Big__Operators_Olattice_OInf__fin(_1323121, c_Orderings_Oord__class_Omin(_1323121), _1323125)))], (41949 ^ _779203) ^ [_1612081, _1612083, _1612085] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612081)), hAPP(hAPP(c_List_Otake(_1612081), _1612083), _1612085)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612081)), _1612085)), _1612083))], (4936 ^ _779203) ^ [_854415, _854417] : [_854417 = _854415, -(c_Lattices_Osemilattice__sup__class_Osup(_854417) = c_Lattices_Osemilattice__sup__class_Osup(_854415))], (52451 ^ _779203) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (17702 ^ _779203) ^ [_1091185, _1091187, _1091189] : [class_Orderings_Olinorder(_1091185), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091185), _1091187)), -(c_Big__Operators_Olattice_OInf__fin(_1091185, c_Orderings_Oord__class_Omin(_1091185), hAPP(hAPP(c_Set_Oinsert(_1091185), _1091189), _1091187)) = hAPP(hAPP(c_Finite__Set_Ofold(_1091185, _1091185, c_Orderings_Oord__class_Omin(_1091185)), _1091189), _1091187))], (29438 ^ _779203) ^ [_1301459, _1301461, _1301463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301459, tc_HOL_Obool)), _1301461), _1301463)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301459, tc_HOL_Obool)), _1301461), _1301463) = _1301461)], (25522 ^ _779203) ^ [_1228905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1228905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1228905))))], (52719 ^ _779203) ^ [_1837293, _1837295] : [hBOOL(_1837293), hBOOL(_1837295), -(hBOOL(hAPP(hAPP(c_fconj, _1837293), _1837295)))], (42672 ^ _779203) ^ [_1629840, _1629842] : [-(c_List_Oremove1(_1629840, _1629842, c_List_Olist_ONil(_1629840)) = c_List_Olist_ONil(_1629840))], (49117 ^ _779203) ^ [_1772335, _1772337, _1772339, _1772341] : [-(c_Wellfounded_Omax__extp(_1772335, _1772337, _1772339, _1772341)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1772335), _1772339)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1772335), _1772341)), -(_1772341 = c_Orderings_Obot__class_Obot(tc_fun(_1772335, tc_HOL_Obool))), 49131 ^ _779203 : [(49134 ^ _779203) ^ [_1772680] : [hBOOL(hAPP(hAPP(c_member(_1772335), _1772680), _1772341)), hBOOL(hAPP(hAPP(_1772337, 49130 ^ [_1772335, _1772337, _1772339, _1772341]), _1772680))], (49132 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1772335), 49130 ^ [_1772335, _1772337, _1772339, _1772341]), _1772339)))]]], (9923 ^ _779203) ^ [_948583, _948585] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948583), _948585)), _948583)))], (38993 ^ _779203) ^ [_1535448, _1535450, _1535452, _1535454, _1535456] : [hBOOL(hAPP(hAPP(_1535448, _1535450), _1535452)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1535454, _1535456, _1535448), _1535450)))], (40263 ^ _779203) ^ [_1565823, _1565825, _1565827, _1565829, _1565831] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565823, _1565823)), hAPP(hAPP(c_Product__Type_OPair(_1565823, _1565823), _1565825), _1565827)), _1565829)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565823, _1565823)), hAPP(hAPP(c_Product__Type_OPair(_1565823, _1565823), _1565827), _1565831)), _1565829)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565823, _1565823)), hAPP(hAPP(c_Product__Type_OPair(_1565823, _1565823), _1565825), _1565831)), c_Transitive__Closure_Otrancl(_1565823, _1565829))))], (50148 ^ _779203) ^ [_1793252] : [-(c_Fun_Obij__betw(_1793252, _1793252, c_Fun_Oid(_1793252), c_Orderings_Otop__class_Otop(tc_fun(_1793252, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793252, tc_HOL_Obool))))], (33281 ^ _779203) ^ [_1388644, _1388646, _1388648, _1388650, _1388652] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1388644, _1388646), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1388648), _1388650))), -(_1388646 = 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)), _1388652)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1388644, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1388646), _1388652)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1388648), _1388652)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1388646), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1388648, _1388652))), _1388650)))))], (52375 ^ _779203) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (34156 ^ _779203) ^ [_1406008, _1406010, _1406012, _1406014, _1406016, _1406018] : [hAPP(c_Product__Type_Oapfst(_1406008, _1406010, _1406012, _1406014), _1406016) = hAPP(c_Product__Type_Oapfst(_1406008, _1406010, _1406012, _1406018), _1406016), -(hAPP(_1406014, hAPP(c_Product__Type_Ofst(_1406008, _1406012), _1406016)) = hAPP(_1406018, hAPP(c_Product__Type_Ofst(_1406008, _1406012), _1406016)))], (32309 ^ _779203) ^ [_1363886, _1363888] : [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(_1363886))), 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)), _1363888))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1363886) = hAPP(c_Nat_OSuc, _1363888))], (20796 ^ _779203) ^ [_1146308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1146308), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1146308 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 20799 ^ [_1146308]))))], (47829 ^ _779203) ^ [_1743014, _1743016, _1743018] : [c_List_Olist__all(_1743014, _1743016, _1743018), 47832 ^ _779203 : [(47833 ^ _779203) ^ [_1743095] : [hBOOL(hAPP(hAPP(c_member(_1743014), _1743095), hAPP(c_List_Oset(_1743014), _1743018))), -(hBOOL(hAPP(_1743016, _1743095)))]]], (40628 ^ _779203) ^ [_1575270, _1575272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1575270), _1575272)), -(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), _1575270), _1575272)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (44817 ^ _779203) ^ [_1677232, _1677234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677232)), hAPP(c_Code__Numeral_Onat__of, _1677234))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1677232), _1677234)))], (22516 ^ _779203) ^ [_1176114, _1176116, _1176118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176114), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22519 ^ _779203 : [(22520 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1176116, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1176118), _1176114)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176118, _1176114))), 22523 ^ _779203 : [(22524 ^ _779203) ^ [_1176324, _1176326] : [-(hBOOL(hAPP(hAPP(_1176116, _1176326), _1176324))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176114), _1176324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176324), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1176118 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1176114), _1176326)), _1176324)]]], (22538 ^ _779203) ^ [] : [22541 ^ _779203 : [(22544 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 22540 ^ [_1176114, _1176116, _1176118]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22546 ^ _779203) ^ [] : [-(_1176118 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1176114), 22539 ^ [_1176114, _1176116, _1176118])), 22540 ^ [_1176114, _1176116, _1176118]))], (22548 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1176116, 22539 ^ [_1176114, _1176116, _1176118]), 22540 ^ [_1176114, _1176116, _1176118]))], (22542 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176114), 22540 ^ [_1176114, _1176116, _1176118])))]], -(hBOOL(hAPP(hAPP(_1176116, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1176118), _1176114)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176118, _1176114))))]]], (48211 ^ _779203) ^ [_1751625, _1751627, _1751629, _1751631] : [48213 ^ _779203 : [(48216 ^ _779203) ^ [] : [hBOOL(hAPP(_1751631, 48212 ^ [_1751625, _1751627, _1751629, _1751631]))], (48214 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751625), 48212 ^ [_1751625, _1751627, _1751629, _1751631]), hAPP(c_List_Oset(_1751625), c_List_Oreplicate(_1751625, _1751627, _1751629)))))]], -(hBOOL(hAPP(_1751631, _1751629))), -(_1751627 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6843 ^ _779203) ^ [_890769, _890771, _890773, _890775] : [hBOOL(hAPP(hAPP(c_member(_890769), _890771), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890769, tc_HOL_Obool)), _890773), _890775))), 6846 ^ _779203 : [(6849 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890769), _890771), _890775))], (6847 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_890769), _890771), _890773)))]]], (32527 ^ _779203) ^ [_1369248, _1369250] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369248), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369250)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369248)) = 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), _1369250), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1369248)))), 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)))], (29678 ^ _779203) ^ [_1305982, _1305984] : [class_Lattices_Oboolean__algebra(_1305982), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1305982), hAPP(c_Groups_Ouminus__class_Ouminus(_1305982), _1305984)), _1305984) = c_Orderings_Obot__class_Obot(_1305982))], (25188 ^ _779203) ^ [_1223321, _1223323, _1223325] : [class_Rings_Olinordered__semidom(_1223321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1223321), c_Groups_Oone__class_Oone(_1223321)), _1223323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1223321), hAPP(hAPP(c_Power_Opower__class_Opower(_1223321), _1223323), _1223325)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223321), _1223323), hAPP(hAPP(c_Power_Opower__class_Opower(_1223321), _1223323), _1223325)))))], (46416 ^ _779203) ^ [_1712307, _1712309] : [class_Orderings_Olinorder(_1712307), hBOOL(hAPP(c_Finite__Set_Ofinite(_1712307), _1712309)), 46423 ^ _779203 : [(46428 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1712307), c_List_Olinorder__class_Osorted__list__of__set(_1712307, _1712309))))], (46426 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1712307, c_List_Olinorder__class_Osorted__list__of__set(_1712307, _1712309)))], (46424 ^ _779203) ^ [] : [-(hAPP(c_List_Oset(_1712307), c_List_Olinorder__class_Osorted__list__of__set(_1712307, _1712309)) = _1712309)]]], (17058 ^ _779203) ^ [_1079443, _1079445, _1079447] : [class_Orderings_Olinorder(_1079443), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079443), _1079445)), 17065 ^ _779203 : [(17072 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079443, tc_HOL_Obool)), _1079445), hAPP(hAPP(c_Set_Oinsert(_1079443), _1079447), c_Orderings_Obot__class_Obot(tc_fun(_1079443, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1079443, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1079443, hAPP(hAPP(c_Set_Oinsert(_1079443), _1079447), _1079445)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1079443), _1079447), c_Big__Operators_Olinorder__class_OMax(_1079443, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079443, tc_HOL_Obool)), _1079445), hAPP(hAPP(c_Set_Oinsert(_1079443), _1079447), c_Orderings_Obot__class_Obot(tc_fun(_1079443, tc_HOL_Obool)))))))], (17066 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079443, tc_HOL_Obool)), _1079445), hAPP(hAPP(c_Set_Oinsert(_1079443), _1079447), c_Orderings_Obot__class_Obot(tc_fun(_1079443, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1079443, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1079443, hAPP(hAPP(c_Set_Oinsert(_1079443), _1079447), _1079445)) = _1079447)]]], (36490 ^ _779203) ^ [_1465781, _1465783, _1465785] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465781), _1465783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465781, tc_HOL_Obool)), _1465783), hAPP(c_Set_Oimage(_1465781, _1465781, _1465785), _1465783))), -(c_Fun_Oinj__on(_1465781, _1465781, _1465785, _1465783))], (34857 ^ _779203) ^ [_1425929, _1425931, _1425933, _1425935, _1425937] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1425929, tc_fun(_1425931, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1425929), _1425933), _1425935)), _1425937) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425931, tc_HOL_Obool)), hAPP(_1425937, _1425933)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1425929, tc_fun(_1425931, tc_HOL_Obool)), _1425935), _1425937)))], (27416 ^ _779203) ^ [_1262274, _1262276, _1262278] : [class_Lattices_Osemilattice__sup(_1262274), 27419 ^ _779203 : [(27426 ^ _779203) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262274), _1262276), _1262278) = _1262278, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262274), _1262276), _1262278)))], (27420 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262274), _1262276), _1262278)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262274), _1262276), _1262278) = _1262278)]]], (2440 ^ _779203) ^ [_815011, _815013] : [_815013 = _815011, -(c_SetInterval_Oord__class_OgreaterThan(_815013) = c_SetInterval_Oord__class_OgreaterThan(_815011))], (52211 ^ _779203) ^ [_1832138, _1832140] : [class_Groups_Ominus(_1832138), -(class_Groups_Ominus(tc_fun(_1832140, _1832138)))], (5382 ^ _779203) ^ [_861534, _861536] : [_861536 = _861534, -(c_Groups_Ominus__class_Ominus(_861536) = c_Groups_Ominus__class_Ominus(_861534))], (40919 ^ _779203) ^ [_1582603, _1582605, _1582607, _1582609] : [-(hAPP(_1582603, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1582605, _1582605), _1582607), _1582603), _1582609)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1582605, _1582605), _1582607), _1582603), hAPP(_1582603, _1582609)))], (21119 ^ _779203) ^ [_1151621, _1151623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1151621)), c_Int_OBit1(_1151623))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1151621), _1151623)))], (38907 ^ _779203) ^ [_1533119, _1533121, _1533123, _1533125, _1533127] : [c_Relation_Orefl__on(_1533119, _1533121, _1533123), hBOOL(hAPP(hAPP(c_member(tc_prod(_1533119, _1533119)), hAPP(hAPP(c_Product__Type_OPair(_1533119, _1533119), _1533125), _1533127)), _1533123)), -(hBOOL(hAPP(hAPP(c_member(_1533119), _1533125), _1533121)))], (48804 ^ _779203) ^ [_1764882] : [-(c_Relation_Otrans(tc_fun(_1764882, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1764882)))], (32503 ^ _779203) ^ [_1368649, _1368651, _1368653] : [-(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), _1368649)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1368651))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1368653))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1368653), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1368649), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1368649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1368653), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1368651)))))], (40512 ^ _779203) ^ [_1572667, _1572669, _1572671, _1572673] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572667, _1572667)), hAPP(hAPP(c_Product__Type_OPair(_1572667, _1572667), _1572669), _1572671)), c_Transitive__Closure_Ortrancl(_1572667, _1572673))), -(_1572669 = _1572671), 40519 ^ _779203 : [(40522 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572667, _1572667)), hAPP(hAPP(c_Product__Type_OPair(_1572667, _1572667), _1572669), _1572671)), c_Transitive__Closure_Otrancl(_1572667, _1572673))))], (40520 ^ _779203) ^ [] : [_1572669 = _1572671]]], (37475 ^ _779203) ^ [_1488523, _1488525, _1488527] : [-(hAPP(c_Set_OCollect(_1488523), hAPP(hAPP(c_COMBS(_1488523, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1488523), c_fdisj), _1488525)), _1488527)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1488523, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1488523), _1488525)), hAPP(c_Set_OCollect(_1488523), _1488527)))], (21821 ^ _779203) ^ [_1163424] : [class_Int_Onumber__ring(_1163424), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163424), c_Groups_Oone__class_Oone(_1163424)), c_Groups_Oone__class_Oone(_1163424)) = hAPP(c_Int_Onumber__class_Onumber__of(_1163424), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (11484 ^ _779203) ^ [_977112, _977114, _977116, _977118] : [class_Rings_Oordered__comm__semiring(_977112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977112), _977114), _977116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977112), c_Groups_Ozero__class_Ozero(_977112)), _977118)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977112), _977118), _977114)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977112), _977118), _977116))))], (21859 ^ _779203) ^ [_1164108, _1164110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1164108)), -(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)))), _1164110)), 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)))), _1164108)) = 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, _1164110, _1164108))))], (41895 ^ _779203) ^ [_1610872, _1610874, _1610876] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610872, tc_HOL_Obool)), hAPP(c_List_Oset(_1610872), _1610874)), hAPP(c_List_Oset(_1610872), hAPP(hAPP(c_List_Olist_OCons(_1610872), _1610876), _1610874)))))], (40851 ^ _779203) ^ [_1580678, _1580680, _1580682] : [c_Relation_Ototal__on(_1580678, _1580680, _1580682), 40854 ^ _779203 : [(40855 ^ _779203) ^ [_1580822] : [hBOOL(hAPP(hAPP(c_member(_1580678), _1580822), _1580680)), 40858 ^ _779203 : [(40859 ^ _779203) ^ [_1580962] : [hBOOL(hAPP(hAPP(c_member(_1580678), _1580962), _1580680)), -(_1580822 = _1580962), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580678, _1580678)), hAPP(hAPP(c_Product__Type_OPair(_1580678, _1580678), _1580822), _1580962)), _1580682))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580678, _1580678)), hAPP(hAPP(c_Product__Type_OPair(_1580678, _1580678), _1580962), _1580822)), _1580682)))]]]]], (43313 ^ _779203) ^ [_1643736, _1643738, _1643740, _1643742, _1643744] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643736), tc_List_Olist(_1643736))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643736), tc_List_Olist(_1643736)), _1643738), _1643740)), c_List_Olexord(_1643736, _1643742))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643736), tc_List_Olist(_1643736))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643736), tc_List_Olist(_1643736)), hAPP(hAPP(c_List_Oappend(_1643736), _1643744), _1643738)), hAPP(hAPP(c_List_Oappend(_1643736), _1643744), _1643740))), c_List_Olexord(_1643736, _1643742))))], (9791 ^ _779203) ^ [_946360, _946362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946360), _946362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946360), hAPP(c_Nat_OSuc, _946362))))], (16078 ^ _779203) ^ [_1061684, _1061686] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1061684), _1061686)), _1061686) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1061684), _1061686))], (21973 ^ _779203) ^ [_1166520, _1166522, _1166524] : [class_Divides_Osemiring__div(_1166520), -(c_Divides_Odiv__class_Omod(_1166520, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166520), _1166522), _1166524), _1166522) = c_Divides_Odiv__class_Omod(_1166520, _1166524, _1166522))], (21671 ^ _779203) ^ [_1160686, _1160688] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1160686)), c_Int_OBit0(_1160688))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160686), _1160688)))], (39886 ^ _779203) ^ [_1556812, _1556814, _1556816, _1556818, _1556820, _1556822] : [c_Finite__Set_Ofolding__idem(_1556812, _1556814, _1556816, _1556818), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556812), _1556820)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556812), _1556822)), -(hAPP(_1556818, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1556812, tc_HOL_Obool)), _1556820), _1556822)) = hAPP(c_Fun_Ocomp(_1556814, _1556814, _1556814, hAPP(_1556818, _1556820)), hAPP(_1556818, _1556822)))], (7917 ^ _779203) ^ [_909461, _909463, _909465] : [7918 ^ _779203 : [(7921 ^ _779203) ^ [] : [_909463 = _909465], (7919 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_909461, tc_HOL_Obool)), _909463), _909465))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909461, tc_HOL_Obool)), _909463), _909465)))], (1670 ^ _779203) ^ [_803038, _803040] : [-(class_Groups_Oab__semigroup__mult(_803038)), _803040 = _803038, class_Groups_Oab__semigroup__mult(_803040)], (41118 ^ _779203) ^ [_1587543, _1587545, _1587547, _1587549, _1587551] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587543, _1587543)), hAPP(hAPP(c_Product__Type_OPair(_1587543, _1587543), _1587545), _1587547)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587543, _1587543), tc_HOL_Obool), _1587549), _1587551))), 41123 ^ _779203 : [(41126 ^ _779203) ^ [] : [-(_1587545 = _1587547)], (41124 ^ _779203) ^ [] : [-(_1587549 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41129 ^ _779203 : [(41134 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587543, _1587543)), hAPP(hAPP(c_Product__Type_OPair(_1587543, _1587543), 41127 ^ [_1587543, _1587545, _1587547, _1587549, _1587551]), _1587547)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587543, _1587543), tc_HOL_Obool), 41128 ^ [_1587543, _1587545, _1587547, _1587549, _1587551]), _1587551))))], (41132 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587543, _1587543)), hAPP(hAPP(c_Product__Type_OPair(_1587543, _1587543), _1587545), 41127 ^ [_1587543, _1587545, _1587547, _1587549, _1587551])), _1587551)))], (41130 ^ _779203) ^ [] : [-(_1587549 = hAPP(c_Nat_OSuc, 41128 ^ [_1587543, _1587545, _1587547, _1587549, _1587551]))]]], (47643 ^ _779203) ^ [_1739227, _1739229, _1739231] : [-(c_List_Olist__ex(_1739227, _1739229, _1739231)), 47644 ^ _779203 : [(47645 ^ _779203) ^ [_1739292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1739292), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739227)), _1739231))), hBOOL(hAPP(_1739229, hAPP(hAPP(c_List_Onth(_1739227), _1739231), _1739292)))]]], (50705 ^ _779203) ^ [_1806123, _1806125, _1806127, _1806129, _1806131] : [class_Rings_Ocomm__semiring__1(_1806123), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806123), _1806125), _1806127)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806123), _1806129), _1806131)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806123), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806123), _1806125), _1806129)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806123), _1806127), _1806131))))], (50973 ^ _779203) ^ [_1811282, _1811284] : [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)))), _1811282, _1811284) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811282), _1811284)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811284), _1811282)))], (39570 ^ _779203) ^ [_1549490, _1549492, _1549494, _1549496, _1549498, _1549500] : [class_Groups_Ocomm__monoid__add(_1549490), c_Fun_Oinj__on(_1549492, _1549494, _1549496, _1549498), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1549494, _1549490), _1549500), hAPP(c_Set_Oimage(_1549492, _1549494, _1549496), _1549498)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1549492, _1549490), hAPP(c_Fun_Ocomp(_1549494, _1549490, _1549492, _1549500), _1549496)), _1549498))], (29422 ^ _779203) ^ [_1301119, _1301121, _1301123, _1301125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301119, tc_HOL_Obool)), _1301121), _1301123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301119, tc_HOL_Obool)), _1301121), _1301125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301119, tc_HOL_Obool)), _1301121), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301119, tc_HOL_Obool)), _1301123), _1301125))))], (44907 ^ _779203) ^ [_1679544, _1679546] : [-(hBOOL(hAPP(c_List_Olistsp(_1679544, _1679546), c_List_Olist_ONil(_1679544))))], (26264 ^ _779203) ^ [_1241121, _1241123, _1241125] : [class_Orderings_Oorder(_1241121), _1241123 = _1241125, -(c_SetInterval_Oord__class_OatLeastAtMost(_1241121, _1241123, _1241125) = hAPP(hAPP(c_Set_Oinsert(_1241121), _1241123), c_Orderings_Obot__class_Obot(tc_fun(_1241121, tc_HOL_Obool))))], (32423 ^ _779203) ^ [_1366583, _1366585, _1366587] : [class_Int_Onumber__ring(_1366583), 32426 ^ _779203 : [(32433 ^ _779203) ^ [] : [-(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), _1366585)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1366583), _1366587), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1366585))) = c_Groups_Oone__class_Oone(_1366583))], (32427 ^ _779203) ^ [] : [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), _1366585))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1366583), _1366587), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1366585))) = hAPP(hAPP(c_HOL_OLet(_1366583, _1366583), hAPP(hAPP(c_Power_Opower__class_Opower(_1366583), _1366587), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366585))), hAPP(hAPP(c_COMBS(_1366583, _1366583, _1366583), hAPP(hAPP(c_COMBB(_1366583, tc_fun(_1366583, _1366583), _1366583), c_Groups_Otimes__class_Otimes(_1366583)), hAPP(c_Groups_Otimes__class_Otimes(_1366583), _1366587))), c_COMBI(_1366583))))]]], (52117 ^ _779203) ^ [_1830903, _1830905] : [class_Complete__Lattice_Ocomplete__lattice(_1830903), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1830905, _1830903)))], (6875 ^ _779203) ^ [_891392, _891394, _891396, _891398] : [hBOOL(hAPP(hAPP(c_member(_891392), _891394), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891392, tc_HOL_Obool)), _891396), _891398))), hBOOL(hAPP(hAPP(c_member(_891392), _891394), _891398))], (3134 ^ _779203) ^ [_825760, _825762, _825764, _825766, _825768, _825770] : [-(c_Big__Operators_Olattice_OInf__fin(_825770, _825766, _825762) = c_Big__Operators_Olattice_OInf__fin(_825768, _825764, _825760)), _825770 = _825768, _825766 = _825764, _825762 = _825760], (38774 ^ _779203) ^ [_1530054, _1530056, _1530058] : [_1530058 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530054, _1530056), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1530054, _1530056), _1530058) = c_Orderings_Obot__class_Obot(tc_fun(_1530054, tc_HOL_Obool)))], (24642 ^ _779203) ^ [_1213155] : [c_Nat__Transfer_Onat__set(_1213155), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1213155) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1213155)))], (32986 ^ _779203) ^ [_1383493, _1383495, _1383497, _1383499, _1383501] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1383493, _1383495, _1383497), _1383499), _1383501)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1383493, _1383495)), hAPP(hAPP(c_Product__Type_OPair(_1383493, _1383495), _1383499), _1383501)), _1383497)))], (11053 ^ _779203) ^ [_969673] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _969673), _969673) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52411 ^ _779203) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (28784 ^ _779203) ^ [_1288256, _1288258, _1288260] : [class_Groups_Oordered__ab__group__add(_1288256), -(hAPP(c_Set_Oimage(_1288256, _1288256, c_Groups_Ouminus__class_Ouminus(_1288256)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1288256, _1288258, _1288260)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1288256, hAPP(c_Groups_Ouminus__class_Ouminus(_1288256), _1288260)), hAPP(c_Groups_Ouminus__class_Ouminus(_1288256), _1288258)))], (32847 ^ _779203) ^ [_1380682, _1380684, _1380686, _1380688, _1380690, _1380692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1380682, tc_fun(_1380684, tc_HOL_Obool))), _1380686), _1380688)), hBOOL(hAPP(hAPP(_1380686, _1380690), _1380692)), -(hBOOL(hAPP(hAPP(_1380688, _1380690), _1380692)))], (31805 ^ _779203) ^ [_1351193, _1351195, _1351197, _1351199, _1351201] : [class_Groups_Oab__group__add(_1351193), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351195, _1351193), hAPP(hAPP(c_COMBS(_1351195, _1351193, _1351193), hAPP(hAPP(c_COMBB(_1351193, tc_fun(_1351193, _1351193), _1351195), c_Groups_Ominus__class_Ominus(_1351193)), _1351197)), _1351199)), _1351201) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1351193), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351195, _1351193), _1351197), _1351201)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1351195, _1351193), _1351199), _1351201)))], (32992 ^ _779203) ^ [_1383628, _1383630, _1383632, _1383634, _1383636] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1383628, _1383630)), hAPP(hAPP(c_Product__Type_OPair(_1383628, _1383630), _1383634), _1383636)), _1383632)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1383628, _1383630, _1383632), _1383634), _1383636)))], (40873 ^ _779203) ^ [_1581167, _1581169, _1581171] : [40875 ^ _779203 : [(40876 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1581167), 40874 ^ [_1581167, _1581169, _1581171]), _1581169)))], (40881 ^ _779203) ^ [] : [40874 ^ [_1581167, _1581169, _1581171] = 40877 ^ [_1581167, _1581169, _1581171]], (40885 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581167, _1581167)), hAPP(hAPP(c_Product__Type_OPair(_1581167, _1581167), 40877 ^ [_1581167, _1581169, _1581171]), 40874 ^ [_1581167, _1581169, _1581171])), _1581171))], (40883 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581167, _1581167)), hAPP(hAPP(c_Product__Type_OPair(_1581167, _1581167), 40874 ^ [_1581167, _1581169, _1581171]), 40877 ^ [_1581167, _1581169, _1581171])), _1581171))], (40879 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1581167), 40877 ^ [_1581167, _1581169, _1581171]), _1581169)))]], -(c_Relation_Ototal__on(_1581167, _1581169, _1581171))], (40753 ^ _779203) ^ [_1578351, _1578353] : [-(hAPP(c_Relation_OField(_1578351), hAPP(c_Relation_Oconverse(_1578351, _1578351), _1578353)) = hAPP(c_Relation_OField(_1578351), _1578353))], (23838 ^ _779203) ^ [_1198728, _1198730, _1198732] : [-(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), _1198728), _1198730)), _1198732)), _1198730) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1198732), _1198730))], (36450 ^ _779203) ^ [_1465013, _1465015, _1465017, _1465019, _1465021] : [c_Fun_Oinj__on(_1465013, _1465015, _1465017, c_Orderings_Otop__class_Otop(tc_fun(_1465013, tc_HOL_Obool))), 36453 ^ _779203 : [(36460 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1465013), _1465019), _1465021)), -(hBOOL(hAPP(hAPP(c_member(_1465015), hAPP(_1465017, _1465019)), hAPP(c_Set_Oimage(_1465013, _1465015, _1465017), _1465021))))], (36454 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1465015), hAPP(_1465017, _1465019)), hAPP(c_Set_Oimage(_1465013, _1465015, _1465017), _1465021))), -(hBOOL(hAPP(hAPP(c_member(_1465013), _1465019), _1465021)))]]], (46881 ^ _779203) ^ [_1722130] : [-(c_List_Oreturn__list(_1722130) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1722130))], (19021 ^ _779203) ^ [_1114325, _1114327] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1114325))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1114325)), _1114327)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1114327))], (13349 ^ _779203) ^ [_1010467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1010467)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1010467), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1010467)], (17550 ^ _779203) ^ [_1088565, _1088567, _1088569] : [class_Orderings_Olinorder(_1088565), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088565), _1088567)), hBOOL(hAPP(hAPP(c_member(_1088565), _1088569), _1088567)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1088565), _1088569), c_Big__Operators_Olattice_OInf__fin(_1088565, c_Orderings_Oord__class_Omin(_1088565), _1088567)) = c_Big__Operators_Olattice_OInf__fin(_1088565, c_Orderings_Oord__class_Omin(_1088565), _1088567))], (35145 ^ _779203) ^ [_1433458, _1433460, _1433462, _1433464, _1433466] : [35147 ^ _779203 : [(35150 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1433464, 35146 ^ [_1433458, _1433460, _1433462, _1433464, _1433466]), _1433466))], (35148 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1433458), 35146 ^ [_1433458, _1433460, _1433462, _1433464, _1433466]), _1433462)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1433458, tc_fun(_1433460, tc_HOL_Obool)), _1433462), _1433464), _1433466)))], (8883 ^ _779203) ^ [_929346] : [class_Groups_Oab__semigroup__mult(_929346), -(c_Finite__Set_Ofun__left__comm(_929346, _929346, c_Groups_Otimes__class_Otimes(_929346)))], (31590 ^ _779203) ^ [_1345993, _1345995, _1345997] : [31592 ^ _779203 : [(31595 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1345993, tc_HOL_Obool)), 31591 ^ [_1345993, _1345995, _1345997]), _1345997))], (31593 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1345993, tc_HOL_Obool)), 31591 ^ [_1345993, _1345995, _1345997]), _1345995)))]], -(_1345995 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1345993, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1345993, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1345993, tc_HOL_Obool), _1345995)), _1345997)))], (52123 ^ _779203) ^ [_1830982, _1830984] : [class_Lattices_Obounded__lattice(_1830982), -(class_Lattices_Obounded__lattice__top(tc_fun(_1830984, _1830982)))], (36737 ^ _779203) ^ [_1471130, _1471132, _1471134, _1471136, _1471138] : [c_Fun_Oinj__on(_1471130, _1471132, _1471134, _1471136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471132, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1471130, _1471132, _1471134), _1471136)), _1471138)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1471132), _1471138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1471130), _1471136)), hAPP(c_Finite__Set_Ocard(_1471132), _1471138))))], (16006 ^ _779203) ^ [_1060137] : [class_Orderings_Olinorder(_1060137), -(c_Finite__Set_Ofun__left__comm__idem(_1060137, _1060137, c_Orderings_Oord__class_Omin(_1060137)))], (12264 ^ _779203) ^ [_990818, _990820] : [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), _990818), _990820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _990818))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _990820)))], (40336 ^ _779203) ^ [_1568298, _1568300] : [-(c_Transitive__Closure_Otrancl(_1568298, _1568300) = hAPP(hAPP(c_Relation_Orel__comp(_1568298, _1568298, _1568298), c_Transitive__Closure_Ortrancl(_1568298, _1568300)), _1568300))], (52367 ^ _779203) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (45292 ^ _779203) ^ [_1688205, _1688207] : [-(c_Enum_On__lists(_1688205, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1688207) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1688205)), c_List_Olist_ONil(_1688205)), c_List_Olist_ONil(tc_List_Olist(_1688205))))], (24916 ^ _779203) ^ [_1218205, _1218207] : [24917 ^ _779203 : [(24920 ^ _779203) ^ [] : [_1218207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24918 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218205))]], -(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), _1218205), _1218207))))], (11358 ^ _779203) ^ [_974721, _974723, _974725] : [class_Groups_Oordered__comm__monoid__add(_974721), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974721), _974723), c_Groups_Ozero__class_Ozero(_974721))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974721), _974725), c_Groups_Ozero__class_Ozero(_974721))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974721), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974721), _974723), _974725)), c_Groups_Ozero__class_Ozero(_974721))))], (24906 ^ _779203) ^ [_1218099, _1218101] : [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), _1218099), _1218101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218099))), -(_1218101 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9540 ^ _779203) ^ [_942062, _942064, _942066] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _942062), _942064)), _942066) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _942062), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942064), _942066)))], (46444 ^ _779203) ^ [_1712769, _1712771, _1712773, _1712775] : [class_Orderings_Olinorder(_1712769), c_List_Olinorder__class_Osorted(_1712769, _1712771), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1712773), _1712775)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1712775), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1712769)), _1712771))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1712769), hAPP(hAPP(c_List_Onth(_1712769), _1712771), _1712773)), hAPP(hAPP(c_List_Onth(_1712769), _1712771), _1712775))))], (19406 ^ _779203) ^ [_1121392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1121392)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1121392 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24038 ^ _779203) ^ [_1202463, _1202465, _1202467] : [hBOOL(hAPP(_1202463, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1202465), _1202467))), 24043 ^ _779203 : [(24046 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1202463, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24044 ^ _779203) ^ [] : [-(_1202467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 24048 ^ _779203 : [(24053 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1202463, 24047 ^ [_1202463, _1202465, _1202467])))], (24051 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1202467), hAPP(c_Nat_OSuc, 24047 ^ [_1202463, _1202465, _1202467])))))], (24049 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1202467), 24047 ^ [_1202463, _1202465, _1202467])), _1202465)))]]], (37447 ^ _779203) ^ [_1488124] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1488124, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1488124), hAPP(c_COMBK(tc_HOL_Obool, _1488124), c_fFalse)))], (74 ^ _779203) ^ [_780326, _780328, _780330, _780332, _780334, _780336] : [-(c_Big__Operators_Osemilattice__big(_780334, _780330, _780326)), c_Big__Operators_Osemilattice__big(_780336, _780332, _780328), _780336 = _780334, _780332 = _780330, _780328 = _780326], (42437 ^ _779203) ^ [_1625045, _1625047, _1625049] : [hBOOL(hAPP(c_List_Odistinct(_1625045), hAPP(hAPP(c_List_Olist_OCons(_1625045), _1625047), _1625049))), 42440 ^ _779203 : [(42443 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1625045), _1625049)))], (42441 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1625045), _1625047), hAPP(c_List_Oset(_1625045), _1625049)))]]], (41367 ^ _779203) ^ [_1594922, _1594924, _1594926] : [_1594922 = hAPP(hAPP(c_List_Olist_OCons(_1594924), _1594926), _1594922)], (4136 ^ _779203) ^ [_841821, _841823] : [_841823 = _841821, -(c_List_Orev(_841823) = c_List_Orev(_841821))], (15149 ^ _779203) ^ [_1044121, _1044123, _1044125] : [class_Orderings_Olinorder(_1044121), hBOOL(hAPP(c_Finite__Set_Ofinite(_1044121), _1044123)), 15159 ^ _779203 : [(15162 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044121), 15158 ^ [_1044121, _1044123, _1044125]), _1044125))], (15160 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1044121), 15158 ^ [_1044121, _1044123, _1044125]), _1044123)))]], hBOOL(hAPP(hAPP(c_member(_1044121), _1044125), _1044123)), -(c_Big__Operators_Olinorder__class_OMax(_1044121, _1044123) = _1044125)], (38999 ^ _779203) ^ [_1535553, _1535555, _1535557] : [c_Predicate_Oreflp(_1535553, _1535555), -(hBOOL(hAPP(hAPP(_1535555, _1535557), _1535557)))], (5026 ^ _779203) ^ [_855850, _855852] : [_855852 = _855850, -(c_Finite__Set_Ocard(_855852) = c_Finite__Set_Ocard(_855850))], (44638 ^ _779203) ^ [_1673556, _1673558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673556), _1673558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1673556)), hAPP(c_Code__Numeral_Oof__nat, _1673558))))], (27914 ^ _779203) ^ [_1271749, _1271751, _1271753, _1271755] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271749, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271749, tc_HOL_Obool)), _1271751), _1271753)), _1271755) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271749, tc_HOL_Obool)), _1271751), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271749, tc_HOL_Obool)), _1271753), _1271755)))], (36696 ^ _779203) ^ [_1470264, _1470266, _1470268, _1470270, _1470272] : [-(c_Fun_Oinj__on(_1470264, _1470266, _1470268, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1470264, tc_HOL_Obool)), _1470270), _1470272))), c_Fun_Oinj__on(_1470264, _1470266, _1470268, _1470270), c_Fun_Oinj__on(_1470264, _1470266, _1470268, _1470272), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470266, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1470264, _1470266, _1470268), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470264, tc_HOL_Obool)), _1470270), _1470272))), hAPP(c_Set_Oimage(_1470264, _1470266, _1470268), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1470264, tc_HOL_Obool)), _1470272), _1470270))) = c_Orderings_Obot__class_Obot(tc_fun(_1470266, tc_HOL_Obool))], (37468 ^ _779203) ^ [_1488466, _1488468] : [-(hBOOL(hAPP(_1488468, 37469 ^ [_1488466, _1488468]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1488466, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1488466), _1488468))], (24141 ^ _779203) ^ [_1204379] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1204379, 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, _1204379, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34943 ^ _779203) ^ [_1428183, _1428185, _1428187] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1428183, tc_HOL_Obool)), _1428185), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1428183, tc_HOL_Obool), _1428187)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1428183, tc_HOL_Obool), tc_fun(_1428183, tc_HOL_Obool)), _1428187), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1428183, tc_HOL_Obool)), _1428185)))], (40253 ^ _779203) ^ [_1565556, _1565558, _1565560, _1565562, _1565564] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565556, _1565556)), hAPP(hAPP(c_Product__Type_OPair(_1565556, _1565556), _1565558), _1565560)), _1565562)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1565556, _1565556)), hAPP(hAPP(c_Product__Type_OPair(_1565556, _1565556), _1565560), _1565564)), c_Transitive__Closure_Otrancl(_1565556, _1565562))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565556, _1565556)), hAPP(hAPP(c_Product__Type_OPair(_1565556, _1565556), _1565558), _1565564)), c_Transitive__Closure_Otrancl(_1565556, _1565562))))], (3600 ^ _779203) ^ [_833107, _833109, _833111, _833113] : [-(c_List_Otranspose(_833113, _833109) = c_List_Otranspose(_833111, _833107)), _833113 = _833111, _833109 = _833107], (48977 ^ _779203) ^ [_1769271, _1769273, _1769275, _1769277] : [class_Complete__Lattice_Ocomplete__lattice(_1769271), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1769273, _1769271), _1769275), _1769277) = c_Complete__Lattice_OInf__class_OInf(_1769271, hAPP(c_Set_OCollect(_1769271), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769273, _1769271), tc_HOL_Obool), tc_HOL_Obool, _1769271), c_HOL_OEx(tc_fun(_1769273, _1769271))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1769273, _1769271), tc_HOL_Obool), tc_fun(tc_fun(_1769273, _1769271), tc_HOL_Obool), _1769271), hAPP(c_COMBS(tc_fun(_1769273, _1769271), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1769273, _1769271)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1769273, _1769271), tc_fun(tc_fun(_1769273, _1769271), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1769273, _1769271))), _1769275)))), hAPP(hAPP(c_COMBC(_1769271, tc_fun(tc_fun(_1769273, _1769271), _1769271), tc_fun(tc_fun(_1769273, _1769271), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1769271, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1769273, _1769271), _1769271), tc_fun(tc_fun(_1769273, _1769271), tc_HOL_Obool)), _1769271), c_COMBB(_1769271, tc_HOL_Obool, tc_fun(_1769273, _1769271))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1769273, _1769271), _1769273, _1769271), c_COMBI(tc_fun(_1769273, _1769271))), _1769277)))))))], (37747 ^ _779203) ^ [_1496339, _1496341, _1496343, _1496345] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1496339, _1496341)), hAPP(hAPP(c_Product__Type_OSigma(_1496339, _1496341), _1496343), hAPP(c_COMBK(tc_fun(_1496341, tc_HOL_Obool), _1496339), _1496345)))), -(_1496345 = c_Orderings_Obot__class_Obot(tc_fun(_1496341, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1496339), _1496343)))], (17486 ^ _779203) ^ [_1087533] : [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)), _1087533)), _1087533)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087533), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36372 ^ _779203) ^ [_1463476, _1463478, _1463480, _1463482, _1463484] : [c_Fun_Oinj__on(_1463476, _1463478, _1463480, c_Orderings_Otop__class_Otop(tc_fun(_1463476, tc_HOL_Obool))), 36375 ^ _779203 : [(36382 ^ _779203) ^ [] : [_1463482 = _1463484, -(hAPP(c_Set_Oimage(_1463476, _1463478, _1463480), _1463482) = hAPP(c_Set_Oimage(_1463476, _1463478, _1463480), _1463484))], (36376 ^ _779203) ^ [] : [hAPP(c_Set_Oimage(_1463476, _1463478, _1463480), _1463482) = hAPP(c_Set_Oimage(_1463476, _1463478, _1463480), _1463484), -(_1463482 = _1463484)]]], (45709 ^ _779203) ^ [_1697732, _1697734, _1697736] : [hAPP(c_List_Ofilter(_1697732, _1697734), _1697736) = c_List_Olist_ONil(_1697732), 45712 ^ _779203 : [(45713 ^ _779203) ^ [_1697829] : [hBOOL(hAPP(hAPP(c_member(_1697732), _1697829), hAPP(c_List_Oset(_1697732), _1697736))), hBOOL(hAPP(_1697734, _1697829))]]], (39143 ^ _779203) ^ [_1538866, _1538868] : [-(c_HOL_OThe(_1538866, hAPP(c_fequal, _1538868)) = _1538868)], (9277 ^ _779203) ^ [_937542, _937544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937542), _937544)), _937544))], (25424 ^ _779203) ^ [] : [c_Int_OPls = c_Int_OMin], (51799 ^ _779203) ^ [_1825325, _1825327] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1825325), 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)))), _1825327)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825325), _1825327)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825327), _1825325)))], (49220 ^ _779203) ^ [_1774388, _1774390] : [c_Relation_Oantisym(_1774388, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774388, _1774388), tc_HOL_Obool)), _1774390), c_Relation_OId(_1774388))), -(c_Relation_Oantisym(_1774388, _1774390))], (52379 ^ _779203) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (22029 ^ _779203) ^ [_1167730, _1167732, _1167734, _1167736] : [class_Divides_Osemiring__div(_1167730), -(c_Divides_Odiv__class_Omod(_1167730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167730), _1167732), _1167734), _1167736) = c_Divides_Odiv__class_Omod(_1167730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167730), c_Divides_Odiv__class_Omod(_1167730, _1167732, _1167736)), _1167734), _1167736))], (9735 ^ _779203) ^ [_945435, _945437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _945435)), _945437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945435), _945437)))], (44039 ^ _779203) ^ [_1660666, _1660668, _1660670, _1660672] : [class_Orderings_Olinorder(_1660666), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660666, _1660666, c_COMBI(_1660666)), _1660668), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660666, _1660666, c_COMBI(_1660666)), _1660670), _1660672)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660666, _1660666, c_COMBI(_1660666)), _1660670), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660666, _1660666, c_COMBI(_1660666)), _1660668), _1660672)))], (6531 ^ _779203) ^ [_884554, _884556, _884558] : [class_Orderings_Oorder(_884554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884554), _884556), _884558)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884554), _884558), _884556)), -(_884556 = _884558)], (46800 ^ _779203) ^ [_1720498, _1720500] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1720498), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1720498))), _1720500))), -(c_List_Otranspose(_1720498, c_List_Otranspose(_1720498, _1720500)) = c_List_OtakeWhile(tc_List_Olist(_1720498), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1720498)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1720498), tc_List_Olist(_1720498), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1720498))), _1720500))], (46662 ^ _779203) ^ [_1717570, _1717572, _1717574] : [hAPP(c_List_Orev(_1717570), _1717572) = _1717574, -(_1717572 = hAPP(c_List_Orev(_1717570), _1717574))], (5614 ^ _779203) ^ [_864994, _864996, _864998, _865000] : [-(tc_fun(_865000, _864996) = tc_fun(_864998, _864994)), _865000 = _864998, _864996 = _864994], (8164 ^ _779203) ^ [_914872, _914874, _914876, _914878, _914880, _914882] : [_914872 = _914874, -(hAPP(c_Fun_Ofun__upd(_914876, _914878, _914880, _914874, _914882), _914872) = _914882)], (1340 ^ _779203) ^ [_798913, _798915] : [-(class_Groups_Oabs__if(_798913)), _798915 = _798913, class_Groups_Oabs__if(_798915)], (52769 ^ _779203) ^ [_1837914, _1837916] : [hBOOL(_1837914), -(hBOOL(hAPP(hAPP(c_fimplies, _1837916), _1837914)))], (22722 ^ _779203) ^ [_1179627, _1179629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179627), _1179629)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179627), _1179629) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (39668 ^ _779203) ^ [_1551673, _1551675, _1551677, _1551679, _1551681, _1551683] : [c_Finite__Set_Ofolding(_1551673, _1551675, _1551677, _1551679), hBOOL(hAPP(c_Finite__Set_Ofinite(_1551673), _1551681)), hBOOL(hAPP(hAPP(c_member(_1551673), _1551683), _1551681)), -(hAPP(_1551679, _1551681) = hAPP(c_Fun_Ocomp(_1551675, _1551675, _1551675, hAPP(_1551679, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1551673, tc_HOL_Obool)), _1551681), hAPP(hAPP(c_Set_Oinsert(_1551673), _1551683), c_Orderings_Obot__class_Obot(tc_fun(_1551673, tc_HOL_Obool)))))), hAPP(_1551677, _1551683)))], (41186 ^ _779203) ^ [_1589723, _1589725, _1589727, _1589729, _1589731] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589723, _1589723)), hAPP(hAPP(c_Product__Type_OPair(_1589723, _1589723), _1589725), _1589727)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589723, _1589723), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1589729)), _1589731))), 41190 ^ _779203 : [(41193 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589723, _1589723)), hAPP(hAPP(c_Product__Type_OPair(_1589723, _1589723), 41189 ^ [_1589723, _1589725, _1589727, _1589729, _1589731]), _1589727)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589723, _1589723), tc_HOL_Obool), _1589729), _1589731))))], (41191 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589723, _1589723)), hAPP(hAPP(c_Product__Type_OPair(_1589723, _1589723), _1589725), 41189 ^ [_1589723, _1589725, _1589727, _1589729, _1589731])), _1589731)))]]], (9542 ^ _779203) ^ [_942113, _942115, _942117] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _942113), _942115)), _942117) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _942113), _942117)), _942115))], (29988 ^ _779203) ^ [_1313106, _1313108, _1313110, _1313112, _1313114, _1313116, _1313118, _1313120] : [c_Finite__Set_Ofolding__image__simple(_1313106, _1313108, _1313110, _1313112, _1313114, _1313116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313108), _1313118)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313108), _1313120)), -(hAPP(hAPP(_1313110, hAPP(_1313116, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1313108, tc_HOL_Obool)), _1313118), _1313120))), hAPP(_1313116, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1313108, tc_HOL_Obool)), _1313118), _1313120))) = hAPP(hAPP(_1313110, hAPP(_1313116, _1313118)), hAPP(_1313116, _1313120)))], (49380 ^ _779203) ^ [_1777388, _1777390, _1777392] : [c_Equiv__Relations_Oequiv(_1777388, _1777390, _1777392), 49383 ^ _779203 : [(49388 ^ _779203) ^ [] : [-(c_Relation_Otrans(_1777388, _1777392))], (49386 ^ _779203) ^ [] : [-(c_Relation_Osym(_1777388, _1777392))], (49384 ^ _779203) ^ [] : [-(c_Relation_Orefl__on(_1777388, _1777390, _1777392))]]], (47706 ^ _779203) ^ [_1740486, _1740488, _1740490] : [c_List_Olist__ex(_1740486, _1740488, hAPP(c_List_Orev(_1740486), _1740490)), -(c_List_Olist__ex(_1740486, _1740488, _1740490))], (1440 ^ _779203) ^ [_800163, _800165] : [-(class_Lattices_Osemilattice__inf(_800163)), _800165 = _800163, class_Lattices_Osemilattice__inf(_800165)], (34170 ^ _779203) ^ [_1406366, _1406368, _1406370, _1406372, _1406374] : [-(hAPP(c_Product__Type_Osnd(_1406366, _1406368), hAPP(c_Product__Type_Oapfst(_1406370, _1406366, _1406368, _1406372), _1406374)) = hAPP(c_Product__Type_Osnd(_1406370, _1406368), _1406374))], (48901 ^ _779203) ^ [_1766794] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1766794, tc_HOL_Obool) = c_Set_OBex(_1766794))], (1950 ^ _779203) ^ [_806538, _806540] : [-(class_Nat_Osize(_806538)), _806540 = _806538, class_Nat_Osize(_806540)], (51271 ^ _779203) ^ [_1816296, _1816298] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816296), _1816298)), -(_1816296 = _1816298), 51278 ^ _779203 : [(51281 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816298), _1816296))], (51279 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816296), _1816298)))]]], (21571 ^ _779203) ^ [_1158934, _1158936] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1158934)), c_Int_OBit0(_1158936)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1158934), _1158936)))], (30137 ^ _779203) ^ [_1316353, _1316355, _1316357] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1316353), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316353, tc_HOL_Obool)), _1316355), _1316357))), -(hAPP(c_Finite__Set_Ocard(_1316353), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316353, tc_HOL_Obool)), _1316355), _1316357)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1316353), _1316355)), hAPP(c_Finite__Set_Ocard(_1316353), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316353, tc_HOL_Obool)), _1316355), _1316357))))], (20786 ^ _779203) ^ [_1146115, _1146117, _1146119, _1146121, _1146123, _1146125] : [-(hBOOL(hAPP(hAPP(c_member(_1146115), _1146117), c_SetInterval_Oord_OgreaterThanAtMost(_1146115, _1146119, _1146121, _1146123, _1146125)))), hBOOL(hAPP(hAPP(_1146121, _1146123), _1146117)), hBOOL(hAPP(hAPP(_1146119, _1146117), _1146125))], (24291 ^ _779203) ^ [_1207306, _1207308, _1207310, _1207312] : [class_Rings_Ocomm__semiring__1(_1207306), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207306), hAPP(hAPP(c_Power_Opower__class_Opower(_1207306), _1207308), _1207310)), hAPP(hAPP(c_Power_Opower__class_Opower(_1207306), _1207308), _1207312)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1207306), _1207308), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1207310), _1207312)))], (21997 ^ _779203) ^ [_1167042, _1167044, _1167046, _1167048] : [class_Divides_Osemiring__div(_1167042), -(c_Divides_Odiv__class_Omod(_1167042, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167042), _1167044), c_Divides_Odiv__class_Omod(_1167042, _1167046, _1167048)), _1167048) = c_Divides_Odiv__class_Omod(_1167042, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167042), _1167044), _1167046), _1167048))], (32383 ^ _779203) ^ [_1365563, _1365565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1365563)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365565))), -(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(_1365565))), 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), _1365563)), c_Int_Onat))))))], (37130 ^ _779203) ^ [_1480002, _1480004, _1480006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480002, tc_HOL_Obool)), _1480004), hAPP(hAPP(c_Set_Oinsert(_1480002), _1480006), c_Orderings_Obot__class_Obot(tc_fun(_1480002, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1480002, _1480006, _1480004) = _1480006)], (45183 ^ _779203) ^ [_1685690, _1685692, _1685694, _1685696, _1685698] : [-(c_List_Olist__all2(_1685690, _1685692, _1685694, _1685696, _1685698)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685690)), _1685696) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685692)), _1685698), 45189 ^ _779203 : [(45192 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1685694, hAPP(hAPP(c_List_Onth(_1685690), _1685696), 45188 ^ [_1685690, _1685692, _1685694, _1685696, _1685698])), hAPP(hAPP(c_List_Onth(_1685692), _1685698), 45188 ^ [_1685690, _1685692, _1685694, _1685696, _1685698])))], (45190 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45188 ^ [_1685690, _1685692, _1685694, _1685696, _1685698]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685690)), _1685696))))]]], (45342 ^ _779203) ^ [_1689435, _1689437] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689435)), c_List_Oremdups(_1689435, _1689437))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689435)), _1689437))))], (18756 ^ _779203) ^ [_1109740, _1109742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1109740), _1109742)), -(c_Nat__Transfer_Otsub(_1109742, _1109740) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1109742), _1109740))], (6503 ^ _779203) ^ [_884116, _884118, _884120, _884122] : [class_Orderings_Oord(_884116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884116), _884118), _884120)), _884120 = _884122, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884116), _884118), _884122)))], (9859 ^ _779203) ^ [_947441, _947443] : [9860 ^ _779203 : [(9863 ^ _779203) ^ [] : [_947441 = _947443], (9861 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947441), _947443))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _947441), _947443)))], (27812 ^ _779203) ^ [_1269633, _1269635] : [class_Lattices_Osemilattice__sup(_1269633), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269633), _1269635), _1269635) = _1269635)], (43355 ^ _779203) ^ [_1644758, _1644760, _1644762, _1644764, _1644766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644758), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644760)), _1644762))), -(hAPP(hAPP(c_List_Olist__update(_1644760, hAPP(hAPP(c_List_Oappend(_1644760), _1644762), _1644764)), _1644758), _1644766) = hAPP(hAPP(c_List_Oappend(_1644760), hAPP(hAPP(c_List_Olist__update(_1644760, _1644762), _1644758), _1644766)), _1644764))], (40097 ^ _779203) ^ [_1561792, _1561794, _1561796, _1561798, _1561800, _1561802, _1561804, _1561806, _1561808] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1561792, _1561794, _1561796, _1561798), hAPP(hAPP(c_Product__Type_Oscomp(_1561792, _1561800, _1561802, tc_prod(_1561794, _1561796)), _1561804), _1561806)), _1561808) = hAPP(hAPP(c_Product__Type_Oscomp(_1561792, _1561800, _1561802, _1561798), _1561804), hAPP(hAPP(c_COMBC(_1561800, tc_fun(_1561794, tc_fun(_1561796, _1561798)), tc_fun(_1561802, _1561798)), hAPP(hAPP(c_COMBB(tc_fun(_1561802, tc_prod(_1561794, _1561796)), tc_fun(tc_fun(_1561794, tc_fun(_1561796, _1561798)), tc_fun(_1561802, _1561798)), _1561800), c_Product__Type_Oscomp(_1561802, _1561794, _1561796, _1561798)), _1561806)), _1561808)))], (36410 ^ _779203) ^ [_1464169, _1464171, _1464173, _1464175, _1464177] : [c_Fun_Oinj__on(_1464169, _1464171, _1464173, _1464175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1464169, tc_HOL_Obool)), _1464177), _1464175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1464171, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1464169, _1464171, _1464173), _1464177)), hAPP(c_Set_Oimage(_1464169, _1464171, _1464173), _1464175))))], (35055 ^ _779203) ^ [_1431085, _1431087, _1431089, _1431091] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1431085, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1431087)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1431085, tc_HOL_Obool), tc_Nat_Onat), _1431089), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1431091))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1431085, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1431091, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1431087), _1431091))), _1431089))], (47352 ^ _779203) ^ [_1732580, _1732582] : [class_Enum_Oenum(_1732580), 47355 ^ _779203 : [(47363 ^ _779203) ^ [] : [47364 ^ _779203 : [(47365 ^ _779203) ^ [_1732760] : [hBOOL(hAPP(_1732582, _1732760))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732580), _1732582)))], (47356 ^ _779203) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1732580), _1732582)), -(hBOOL(hAPP(_1732582, 47359 ^ [_1732580, _1732582])))]]], (7473 ^ _779203) ^ [_902732, _902734, _902736, _902738] : [class_Orderings_Oorder(_902732), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902732), _902734), _902736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902732), _902738), _902734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902732), _902738), _902736)))], (24211 ^ _779203) ^ [_1205554, _1205556, _1205558] : [class_Rings_Olinordered__idom(_1205554), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205554), c_Groups_Ozero__class_Ozero(_1205554)), hAPP(hAPP(c_Power_Opower__class_Opower(_1205554), _1205556), 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)))), _1205558))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205554), c_Groups_Ozero__class_Ozero(_1205554)), _1205556)))], (35369 ^ _779203) ^ [] : [-(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)))], (27226 ^ _779203) ^ [_1258516, _1258518] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1258516), _1258518)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1258518), _1258516)))], (36356 ^ _779203) ^ [_1463158, _1463160, _1463162, _1463164] : [c_Fun_Oinj__on(_1463158, _1463160, _1463162, c_Orderings_Otop__class_Otop(tc_fun(_1463158, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1463158, tc_fun(_1463164, _1463160), hAPP(hAPP(c_COMBB(_1463160, tc_fun(_1463164, _1463160), _1463158), c_COMBK(_1463160, _1463164)), _1463162), c_Orderings_Otop__class_Otop(tc_fun(_1463158, tc_HOL_Obool))))], (27166 ^ _779203) ^ [_1257426, _1257428, _1257430, _1257432] : [class_Orderings_Olinorder(_1257426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257426), _1257428), _1257430)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1257426, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257426, _1257428), _1257432)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257426, _1257428), _1257430)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1257426, _1257430), _1257432))], (17368 ^ _779203) ^ [_1085410, _1085412, _1085414] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085410), _1085412)), _1085414) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085412), _1085414)))], (32007 ^ _779203) ^ [_1356449] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1356449)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1356449)), 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))))], (17610 ^ _779203) ^ [_1089611, _1089613, _1089615] : [class_Orderings_Olinorder(_1089611), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089611), _1089613)), -(_1089613 = c_Orderings_Obot__class_Obot(tc_fun(_1089611, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1089611, c_Orderings_Oord__class_Omin(_1089611), hAPP(hAPP(c_Set_Oinsert(_1089611), _1089615), _1089613)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1089611), _1089615), c_Big__Operators_Olattice_OInf__fin(_1089611, c_Orderings_Oord__class_Omin(_1089611), _1089613)))], (34809 ^ _779203) ^ [_1424625, _1424627, _1424629, _1424631, _1424633] : [_1424625 = c_Orderings_Obot__class_Obot(tc_fun(_1424627, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424629, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424627, tc_fun(_1424629, tc_HOL_Obool)), _1424625), _1424631)), _1424633) = _1424633)], (47880 ^ _779203) ^ [_1743970, _1743972, _1743974, _1743976] : [-(c_List_Olist__all(_1743970, _1743972, hAPP(hAPP(c_List_Olist_OCons(_1743970), _1743974), _1743976))), hBOOL(hAPP(_1743972, _1743974)), c_List_Olist__all(_1743970, _1743972, _1743976)], (5354 ^ _779203) ^ [_861092, _861094, _861096, _861098, _861100, _861102] : [-(c_SetInterval_Oord_OlessThan(_861102, _861098, _861094) = c_SetInterval_Oord_OlessThan(_861100, _861096, _861092)), _861102 = _861100, _861098 = _861096, _861094 = _861092], (42792 ^ _779203) ^ [_1631914, _1631916, _1631918] : [-(hAPP(hAPP(c_List_Otake(_1631914), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1631914), _1631916), _1631918)) = hAPP(hAPP(c_List_Olist_OCons(_1631914), _1631916), c_List_Olist_ONil(_1631914)))], (504 ^ _779203) ^ [_786733, _786735] : [-(c_Nat__Transfer_Onat__set(_786733)), _786735 = _786733, c_Nat__Transfer_Onat__set(_786735)], (39163 ^ _779203) ^ [_1539171, _1539173] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539171, _1539171)), _1539173)), 39166 ^ _779203 : [(39173 ^ _779203) ^ [] : [c_Wellfounded_Oacyclic(_1539171, _1539173), -(c_Wellfounded_Owf(_1539171, _1539173))], (39167 ^ _779203) ^ [] : [c_Wellfounded_Owf(_1539171, _1539173), -(c_Wellfounded_Oacyclic(_1539171, _1539173))]]], (21769 ^ _779203) ^ [_1162427, _1162429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1162427), _1162429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1162427)), c_Int_OBit1(_1162429))))], (8805 ^ _779203) ^ [_927853, _927855, _927857, _927859, _927861] : [class_Groups_Oordered__cancel__ab__semigroup__add(_927853), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927853), _927855), _927857)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927853), _927859), _927861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927853), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927853), _927855), _927859)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927853), _927857), _927861))))], (21685 ^ _779203) ^ [_1160937, _1160939] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1160937)), c_Int_OBit1(_1160939)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1160937), _1160939)))], (5687 ^ _779203) ^ [_868986, _868988, _868990, _868992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_868986, tc_HOL_Obool)), _868988), _868990)), hBOOL(hAPP(hAPP(c_member(_868986), _868992), _868988)), -(hBOOL(hAPP(hAPP(c_member(_868986), _868992), _868990)))], (34885 ^ _779203) ^ [_1426622, _1426624, _1426626, _1426628, _1426630] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1426622, tc_fun(_1426624, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426622, tc_HOL_Obool)), _1426626), _1426628)), _1426630) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1426624, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1426622, tc_fun(_1426624, tc_HOL_Obool)), _1426626), _1426630)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1426622, tc_fun(_1426624, tc_HOL_Obool)), _1426628), _1426630)))], (16770 ^ _779203) ^ [_1074092, _1074094, _1074096] : [class_Orderings_Olinorder(_1074092), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074092), _1074094)), -(c_Big__Operators_Olinorder__class_OMin(_1074092, hAPP(hAPP(c_Set_Oinsert(_1074092), _1074096), _1074094)) = hAPP(hAPP(c_Finite__Set_Ofold(_1074092, _1074092, c_Orderings_Oord__class_Omin(_1074092)), _1074096), _1074094))], (49290 ^ _779203) ^ [_1775999, _1776001] : [c_Relation_Osym(_1775999, _1776001), -(c_Relation_Osym(_1775999, c_Transitive__Closure_Otrancl(_1775999, _1776001)))], (36024 ^ _779203) ^ [_1455818, _1455820, _1455822, _1455824, _1455826] : [c_Equiv__Relations_Oequivp(_1455818, _1455820), hBOOL(hAPP(hAPP(_1455820, _1455822), _1455824)), hBOOL(hAPP(hAPP(_1455820, _1455824), _1455826)), -(hBOOL(hAPP(hAPP(_1455820, _1455822), _1455826)))], (6709 ^ _779203) ^ [_887831, _887833, _887835, _887837, _887839, _887841, _887843, _887845] : [c_Finite__Set_Ofolding__image__simple__idem(_887831, _887833, _887835, _887837, _887839, _887841), hBOOL(hAPP(c_Finite__Set_Ofinite(_887833), _887843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887833, tc_HOL_Obool)), _887845), _887843)), -(hAPP(hAPP(_887835, hAPP(_887841, _887845)), hAPP(_887841, _887843)) = hAPP(_887841, _887843))], (13043 ^ _779203) ^ [_1004820, _1004822] : [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), _1004820), _1004822))), 13046 ^ _779203 : [(13049 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1004822)))], (13047 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1004820)))]]], (20634 ^ _779203) ^ [_1143166, _1143168, _1143170, _1143172] : [hBOOL(hAPP(hAPP(_1143170, _1143168), _1143172)), -(hBOOL(hAPP(hAPP(c_member(_1143166), _1143168), c_SetInterval_Oord_OatMost(_1143166, _1143170, _1143172))))], (32713 ^ _779203) ^ [_1378030, _1378032] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1378030), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 32716 ^ _779203 : [(32725 ^ _779203) ^ [] : [-(c_Nitpick_Onorm__frac(_1378032, _1378030) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1378032), _1378030)), 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), _1378032))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1378030)))), -(_1378032 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1378030 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32717 ^ _779203) ^ [] : [32718 ^ _779203 : [(32721 ^ _779203) ^ [] : [_1378030 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (32719 ^ _779203) ^ [] : [_1378032 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1378032, _1378030) = 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)))]]], (21659 ^ _779203) ^ [_1160463, _1160465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1160463)), c_Int_OBit0(_1160465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160463), _1160465)))], (12366 ^ _779203) ^ [_992451, _992453, _992455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992451), _992453)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992455), _992453))), 12369 ^ _779203 : [(12372 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992451), _992455)))], (12370 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992453)))]]], (12971 ^ _779203) ^ [_1003462, _1003464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1003462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1003464)), -(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), _1003464), _1003462))))], (14673 ^ _779203) ^ [_1034883, _1034885, _1034887, _1034889] : [class_Fields_Ofield(_1034883), -(_1034885 = c_Groups_Ozero__class_Ozero(_1034883)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034883), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034883), _1034887), _1034885)), _1034889) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034883), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034883), _1034887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034883), _1034885), _1034889))), _1034885))], (42582 ^ _779203) ^ [_1628300, _1628302, _1628304] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628300), tc_List_Olist(_1628300))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628300), tc_List_Olist(_1628300)), _1628302), c_List_Olist_ONil(_1628300))), c_List_Olistrel(_1628300, _1628304))), -(_1628302 = c_List_Olist_ONil(_1628300))], (50115 ^ _779203) ^ [_1792704, _1792706, _1792708, _1792710] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792704), _1792706)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1792708), _1792710)), 50122 ^ _779203 : [(50129 ^ _779203) ^ [] : [hAPP(c_Finite__Set_Ocard(_1792704), _1792706) = hAPP(c_Finite__Set_Ocard(_1792708), _1792710), -(c_Fun_Obij__betw(_1792704, _1792708, 50132 ^ [_1792704, _1792706, _1792708, _1792710], _1792706, _1792710))], (50123 ^ _779203) ^ [] : [50124 ^ _779203 : [(50125 ^ _779203) ^ [_1792893] : [c_Fun_Obij__betw(_1792704, _1792708, _1792893, _1792706, _1792710)]], -(hAPP(c_Finite__Set_Ocard(_1792704), _1792706) = hAPP(c_Finite__Set_Ocard(_1792708), _1792710))]]], (17282 ^ _779203) ^ [_1084065, _1084067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084065)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084067))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084065), _1084067)))], (17996 ^ _779203) ^ [_1096493, _1096495] : [class_Orderings_Olinorder(_1096493), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096493), _1096495)), -(_1096495 = c_Orderings_Obot__class_Obot(tc_fun(_1096493, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1096493), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1096493), 18009 ^ [_1096493, _1096495]), 18010 ^ [_1096493, _1096495])), hAPP(hAPP(c_Set_Oinsert(_1096493), 18009 ^ [_1096493, _1096495]), hAPP(hAPP(c_Set_Oinsert(_1096493), 18010 ^ [_1096493, _1096495]), c_Orderings_Obot__class_Obot(tc_fun(_1096493, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1096493), c_Big__Operators_Olattice_OSup__fin(_1096493, c_Orderings_Oord__class_Omax(_1096493), _1096495)), _1096495)))], (43856 ^ _779203) ^ [_1656599, _1656601, _1656603] : [class_Groups_Omonoid__add(_1656599), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1656599), _1656601), hAPP(c_List_Ofoldl(_1656599, _1656599, c_Groups_Oplus__class_Oplus(_1656599), c_Groups_Ozero__class_Ozero(_1656599)), _1656603)) = hAPP(c_List_Ofoldl(_1656599, _1656599, c_Groups_Oplus__class_Oplus(_1656599), _1656601), _1656603))], (33341 ^ _779203) ^ [_1389643, _1389645, _1389647] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389643, _1389643), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1389645), _1389647))), -(_1389643 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1389647 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6152 ^ _779203) ^ [_877520, _877522, _877524] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_877520), _877522)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877520, tc_HOL_Obool)), _877524), _877522)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_877520), _877524)))], (21177 ^ _779203) ^ [_1152673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152673), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1152673)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25784 ^ _779203) ^ [_1232870, _1232872] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1232870), hAPP(hAPP(c_Power_Opower__class_Opower(_1232870), hAPP(c_Int_Onumber__class_Onumber__of(_1232870), c_Int_OMin)), _1232872)) = c_Groups_Oone__class_Oone(_1232870)), class_Int_Onumber__ring(_1232870), class_Rings_Olinordered__idom(_1232870)], (8109 ^ _779203) ^ [_913699, _913701, _913703, _913705] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_913699, _913701, hAPP(hAPP(c_Set_Oinsert(_913699), _913703), c_Orderings_Obot__class_Obot(tc_fun(_913699, tc_HOL_Obool)))), _913705)), -(_913703 = _913705)], (50997 ^ _779203) ^ [_1811688, _1811690] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811688), _1811690)), -(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)))), _1811690, _1811688) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (25626 ^ _779203) ^ [_1230443] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1230443), c_Int_OMin) = c_Int_Osucc(_1230443))], (52675 ^ _779203) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (35456 ^ _779203) ^ [_1441819, _1441821, _1441823, _1441825, _1441827, _1441829] : [-(hAPP(c_Relation_OImage(_1441819, _1441821, _1441823), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1441825, tc_fun(_1441819, tc_HOL_Obool)), _1441827), _1441829)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1441825, tc_fun(_1441821, tc_HOL_Obool)), _1441827), hAPP(hAPP(c_COMBB(tc_fun(_1441819, tc_HOL_Obool), tc_fun(_1441821, tc_HOL_Obool), _1441825), c_Relation_OImage(_1441819, _1441821, _1441823)), _1441829)))], (52231 ^ _779203) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (21575 ^ _779203) ^ [_1159022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1159022)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159022), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41790 ^ _779203) ^ [_1608069, _1608071, _1608073] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608069, _1608069)), hAPP(hAPP(c_Product__Type_OPair(_1608069, _1608069), 41791 ^ [_1608069, _1608071, _1608073]), 41791 ^ [_1608069, _1608071, _1608073])), _1608071))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1608069), tc_List_Olist(_1608069))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1608069), tc_List_Olist(_1608069)), _1608073), _1608073)), c_List_Olexord(_1608069, _1608071)))], (43999 ^ _779203) ^ [_1659798, _1659800, _1659802, _1659804] : [class_Orderings_Olinorder(_1659798), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659800, _1659798, _1659802), _1659804), c_List_Olist_ONil(_1659800)) = hAPP(hAPP(c_List_Olist_OCons(_1659800), _1659804), c_List_Olist_ONil(_1659800)))], (28314 ^ _779203) ^ [_1279891] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1279891), hAPP(c_Nat_OSuc, _1279891)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1279891), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (5907 ^ _779203) ^ [_872862, _872864] : [5908 ^ _779203 : [(5909 ^ _779203) ^ [_872915] : [hBOOL(hAPP(hAPP(c_member(_872862), _872915), _872864))]], _872864 = c_Orderings_Obot__class_Obot(tc_fun(_872862, tc_HOL_Obool))], (40783 ^ _779203) ^ [_1578906, _1578908, _1578910] : [-(hAPP(c_Relation_ODomain(_1578906, _1578908), hAPP(c_Relation_Oconverse(_1578908, _1578906), _1578910)) = hAPP(c_Relation_ORange(_1578908, _1578906), _1578910))], (20977 ^ _779203) ^ [_1149132, _1149134] : [class_Rings_Olinordered__idom(_1149132), 20980 ^ _779203 : [(20987 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149132), c_Groups_Ozero__class_Ozero(_1149132)), _1149134)), -(c_Groups_Osgn__class_Osgn(_1149132, _1149134) = c_Groups_Oone__class_Oone(_1149132))], (20981 ^ _779203) ^ [] : [c_Groups_Osgn__class_Osgn(_1149132, _1149134) = c_Groups_Oone__class_Oone(_1149132), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1149132), c_Groups_Ozero__class_Ozero(_1149132)), _1149134)))]]], (26677 ^ _779203) ^ [_1248900, _1248902] : [26679 ^ _779203 : [(26682 ^ _779203) ^ [] : [hBOOL(hAPP(_1248902, 26678 ^ [_1248900, _1248902]))], (26680 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26678 ^ [_1248900, _1248902]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1248900))))]], 26683 ^ _779203 : [(26684 ^ _779203) ^ [_1249055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1249055), _1248900)), -(hBOOL(hAPP(_1248902, _1249055)))]]], (41919 ^ _779203) ^ [_1611454, _1611456, _1611458, _1611460] : [-(hAPP(hAPP(c_List_Otake(_1611454), hAPP(c_Nat_OSuc, _1611456)), hAPP(hAPP(c_List_Olist_OCons(_1611454), _1611458), _1611460)) = hAPP(hAPP(c_List_Olist_OCons(_1611454), _1611458), hAPP(hAPP(c_List_Otake(_1611454), _1611456), _1611460)))], (31492 ^ _779203) ^ [_1344021, _1344023, _1344025] : [class_Complete__Lattice_Ocomplete__lattice(_1344021), -(c_Complete__Lattice_OInf__class_OInf(_1344021, hAPP(hAPP(c_Set_Oinsert(_1344021), _1344023), hAPP(hAPP(c_Set_Oinsert(_1344021), _1344025), c_Orderings_Obot__class_Obot(tc_fun(_1344021, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1344021), _1344023), _1344025))], (30929 ^ _779203) ^ [_1332488, _1332490, _1332492] : [class_Lattices_Olattice(_1332488), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332488), _1332490)), -(_1332492 = c_Orderings_Obot__class_Obot(tc_fun(_1332488, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1332488, tc_HOL_Obool)), _1332492), _1332490)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332488), c_Big__Operators_Olattice__class_OInf__fin(_1332488, _1332492)), c_Big__Operators_Olattice__class_OInf__fin(_1332488, _1332490)) = c_Big__Operators_Olattice__class_OInf__fin(_1332488, _1332490))], (23619 ^ _779203) ^ [_1195062, _1195064] : [-(c_Int_Onat__aux(_1195062, _1195064) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1195062)), _1195064))], (1300 ^ _779203) ^ [_798413, _798415] : [-(class_Rings_Ocomm__ring(_798413)), _798415 = _798413, class_Rings_Ocomm__ring(_798415)], (11141 ^ _779203) ^ [_970971, _970973, _970975] : [class_Groups_Ocomm__monoid__mult(_970971), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_970973, _970971), _970975), c_Orderings_Obot__class_Obot(tc_fun(_970973, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_970971))], (40536 ^ _779203) ^ [_1573191] : [-(hAPP(c_Relation_ODomain(_1573191, _1573191), c_Relation_OId(_1573191)) = c_Orderings_Otop__class_Otop(tc_fun(_1573191, tc_HOL_Obool)))], (30877 ^ _779203) ^ [_1331659, _1331661, _1331663] : [class_Lattices_Olattice(_1331659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331659), _1331661)), hBOOL(hAPP(hAPP(c_member(_1331659), _1331663), _1331661)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1331659), _1331663), c_Big__Operators_Olattice__class_OInf__fin(_1331659, _1331661)) = _1331663)], (33855 ^ _779203) ^ [_1399370, _1399372, _1399374, _1399376, _1399378] : [hAPP(c_Product__Type_Ofst(_1399370, _1399372), hAPP(hAPP(c_Product__Type_OPair(_1399370, _1399372), _1399374), _1399376)) = _1399378, -(_1399374 = _1399378)], (29400 ^ _779203) ^ [_1300612, _1300614, _1300616, _1300618] : [hBOOL(hAPP(hAPP(c_member(_1300612), _1300614), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300612, tc_HOL_Obool)), _1300616), _1300618))), -(hBOOL(hAPP(hAPP(c_member(_1300612), _1300614), _1300616)))], (6973 ^ _779203) ^ [_893603, _893605, _893607, _893609] : [-(hBOOL(hAPP(hAPP(c_member(_893603), _893605), _893607))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893603, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_893603), _893605), _893609)), _893607) = hAPP(hAPP(c_Set_Oinsert(_893603), _893605), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893603, tc_HOL_Obool)), _893609), _893607)))], (49618 ^ _779203) ^ [_1781989, _1781991, _1781993, _1781995, _1781997] : [c_Fun_Oinj__on(_1781989, _1781991, _1781993, c_Orderings_Otop__class_Otop(tc_fun(_1781989, tc_HOL_Obool))), hAPP(_1781993, _1781995) = _1781997, -(hAPP(c_Hilbert__Choice_Oinv__into(_1781989, _1781991, c_Orderings_Otop__class_Otop(tc_fun(_1781989, tc_HOL_Obool)), _1781993), _1781997) = _1781995)], (37229 ^ _779203) ^ [_1482393, _1482395, _1482397, _1482399, _1482401] : [-(hAPP(c_Set_Ovimage(_1482393, _1482395, _1482397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1482395, tc_HOL_Obool)), _1482399), _1482401)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1482393, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1482393, _1482395, _1482397), _1482399)), hAPP(c_Set_Ovimage(_1482393, _1482395, _1482397), _1482401)))], (45384 ^ _779203) ^ [_1690194] : [-(c_List_Oremdups(_1690194, c_List_Olist_ONil(_1690194)) = c_List_Olist_ONil(_1690194))], (25514 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (52661 ^ _779203) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (27242 ^ _779203) ^ [_1258850, _1258852, _1258854] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1258850), _1258852))), -(c_Random_Ominus__shift(_1258854, _1258850, _1258852) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1258850), _1258852))], (25820 ^ _779203) ^ [_1233422] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1233422)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1233422)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (40170 ^ _779203) ^ [_1563713, _1563715] : [c_Wellfounded_Owf(_1563713, _1563715), -(c_Wellfounded_Owf(_1563713, c_Transitive__Closure_Otrancl(_1563713, _1563715)))], (38224 ^ _779203) ^ [_1514773, _1514775] : [-(hAPP(c_Set_Oimage(_1514773, _1514773, c_Fun_Oid(_1514773)), _1514775) = _1514775)], (25120 ^ _779203) ^ [_1221978, _1221980, _1221982, _1221984] : [class_Fields_Ofield(_1221978), -(_1221980 = c_Groups_Ozero__class_Ozero(_1221978)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1221978), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221978), _1221982), _1221980)), _1221984) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1221978), hAPP(hAPP(c_Power_Opower__class_Opower(_1221978), _1221982), _1221984)), hAPP(hAPP(c_Power_Opower__class_Opower(_1221978), _1221980), _1221984)))], (3380 ^ _779203) ^ [_829609, _829611, _829613, _829615] : [-(c_List_OremoveAll(_829615, _829611) = c_List_OremoveAll(_829613, _829609)), _829615 = _829613, _829611 = _829609], (33381 ^ _779203) ^ [_1390177, _1390179, _1390181] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390177, _1390177), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1390179), _1390181))), -(_1390177 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1390179 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (29252 ^ _779203) ^ [_1297612, _1297614, _1297616] : [class_Lattices_Osemilattice__inf(_1297612), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297612), _1297614), _1297616) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297612), _1297616), _1297614))], (31913 ^ _779203) ^ [_1353832, _1353834, _1353836, _1353838, _1353840] : [class_Rings_Osemiring__0(_1353832), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353832), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353834, _1353832), _1353836), _1353838)), _1353840) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353834, _1353832), hAPP(hAPP(c_COMBC(_1353834, _1353832, _1353832), hAPP(hAPP(c_COMBB(_1353832, tc_fun(_1353832, _1353832), _1353834), c_Groups_Otimes__class_Otimes(_1353832)), _1353836)), _1353840)), _1353838))], (29868 ^ _779203) ^ [_1310382, _1310384, _1310386, _1310388, _1310390] : [class_Orderings_Olinorder(_1310382), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310382, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1310382, _1310384), _1310386)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1310382, _1310388), _1310390)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1310382, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1310382), _1310384), _1310388)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1310382), _1310386), _1310390)))], (9241 ^ _779203) ^ [_936873, _936875] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _936873)), _936875) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936873), _936875)))], (41409 ^ _779203) ^ [_1596586, _1596588, _1596590, _1596592] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1596586), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1596588), _1596590)))), -(hAPP(c_Random_Opick(_1596588, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1596588)), _1596590), _1596592)), _1596586) = hAPP(c_Random_Opick(_1596588, _1596592), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1596586), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1596588), _1596590))))], (42744 ^ _779203) ^ [_1631130, _1631132, _1631134] : [-(hAPP(hAPP(c_List_Olist__update(_1631130, c_List_Olist_ONil(_1631130)), _1631132), _1631134) = c_List_Olist_ONil(_1631130))], (44388 ^ _779203) ^ [_1667861, _1667863, _1667865] : [class_Groups_Omonoid__add(_1667861), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667861), hAPP(hAPP(c_List_Omap(_1667863, _1667861), hAPP(c_COMBK(_1667861, _1667863), c_Groups_Ozero__class_Ozero(_1667861))), _1667865)) = c_Groups_Ozero__class_Ozero(_1667861))], (43951 ^ _779203) ^ [_1658588, _1658590, _1658592] : [class_Orderings_Olinorder(_1658588), -(c_Big__Operators_Olattice_OSup__fin(_1658588, c_Orderings_Oord__class_Omax(_1658588), hAPP(c_List_Oset(_1658588), hAPP(hAPP(c_List_Olist_OCons(_1658588), _1658590), _1658592))) = hAPP(c_List_Ofoldl(_1658588, _1658588, c_Orderings_Oord__class_Omax(_1658588), _1658590), _1658592))], (21113 ^ _779203) ^ [_1151519, _1151521] : [_1151519 = _1151521, -(c_Int_OBit1(_1151519) = c_Int_OBit1(_1151521))], (35353 ^ _779203) ^ [_1438860, _1438862, _1438864, _1438866] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1438860, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35354 ^ [_1438860, _1438862, _1438864, _1438866])), _1438862) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1438860, 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), 35354 ^ [_1438860, _1438862, _1438864, _1438866]), _1438864))), _1438866), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1438860, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1438862) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1438860, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1438866))], (29312 ^ _779203) ^ [_1298886, _1298888, _1298890, _1298892] : [class_Lattices_Olattice(_1298886), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298886), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298886), _1298888), _1298890)), _1298892) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298886), _1298888), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298886), _1298890), _1298892)))], (37197 ^ _779203) ^ [_1481561, _1481563, _1481565, _1481567, _1481569, _1481571] : [-(hAPP(c_Set_Ovimage(_1481561, _1481563, _1481565), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481567, tc_fun(_1481563, tc_HOL_Obool)), _1481569), _1481571)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1481567, tc_fun(_1481561, tc_HOL_Obool)), _1481569), hAPP(hAPP(c_COMBB(tc_fun(_1481563, tc_HOL_Obool), tc_fun(_1481561, tc_HOL_Obool), _1481567), c_Set_Ovimage(_1481561, _1481563, _1481565)), _1481571)))], (31364 ^ _779203) ^ [_1341505, _1341507, _1341509, _1341511] : [hBOOL(hAPP(hAPP(c_member(_1341505), _1341507), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1341505, tc_HOL_Obool), _1341509))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1341505, tc_HOL_Obool)), _1341511), _1341509)), -(hBOOL(hAPP(hAPP(c_member(_1341505), _1341507), _1341511)))], (22436 ^ _779203) ^ [_1174962] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1174962)), -(hAPP(c_Int_Onat, _1174962) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38591 ^ _779203) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (45752 ^ _779203) ^ [_1698715, _1698717, _1698719, _1698721] : [hBOOL(hAPP(hAPP(c_member(_1698715), _1698717), hAPP(c_List_Oset(_1698715), _1698719))), -(hBOOL(hAPP(_1698721, _1698717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698715)), hAPP(c_List_Ofilter(_1698715, _1698721), _1698719))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698715)), _1698719))))], (31861 ^ _779203) ^ [_1352497, _1352499, _1352501, _1352503, _1352505, _1352507] : [-(_1352497 = _1352499), -(hAPP(c_Fun_Ofun__upd(_1352501, _1352503, _1352505, _1352499, _1352507), _1352497) = hAPP(_1352505, _1352497))], (39455 ^ _779203) ^ [_1546763, _1546765, _1546767, _1546769, _1546771, _1546773] : [-(hAPP(c_Set_Oimage(_1546763, _1546765, hAPP(c_Fun_Ocomp(_1546767, _1546765, _1546763, _1546769), _1546771)), _1546773) = hAPP(c_Set_Oimage(_1546767, _1546765, _1546769), hAPP(c_Set_Oimage(_1546763, _1546767, _1546771), _1546773)))], (11093 ^ _779203) ^ [_970258, _970260, _970262] : [11094 ^ _779203 : [(11097 ^ _779203) ^ [] : [_970258 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11095 ^ _779203) ^ [] : [_970260 = _970262]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970258), _970260) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970258), _970262))], (41985 ^ _779203) ^ [_1612985, _1612987, _1612989, _1612991, _1612993] : [hBOOL(hAPP(hAPP(c_member(_1612985), _1612987), hAPP(c_List_Oset(_1612985), _1612989))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612991), hAPP(_1612993, _1612987))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612991), c_List_Olist_Olist__size(_1612985, _1612993, _1612989))))], (26896 ^ _779203) ^ [_1252909] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1252909)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1252909)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1252909)))], (48304 ^ _779203) ^ [_1753224, _1753226, _1753228] : [_1753226 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1753224, _1753226, _1753228) = c_List_Olist_ONil(_1753224))], (41276 ^ _779203) ^ [_1592216, _1592218] : [-(c_Nitpick_Oinverse__frac(_1592216, _1592218) = hAPP(hAPP(c_Nitpick_Ofrac(_1592216), hAPP(c_Nitpick_Odenom(_1592216), _1592218)), hAPP(c_Nitpick_Onum(_1592216), _1592218)))], (26946 ^ _779203) ^ [_1253778, _1253780, _1253782] : [class_Orderings_Oorder(_1253778), 26949 ^ _779203 : [(26956 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253778), _1253780), _1253782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1253778, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1253778), _1253780)), hAPP(c_SetInterval_Oord__class_OatMost(_1253778), _1253782))))], (26950 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1253778, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1253778), _1253780)), hAPP(c_SetInterval_Oord__class_OatMost(_1253778), _1253782))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253778), _1253780), _1253782)))]]], (45151 ^ _779203) ^ [_1685005, _1685007, _1685009, _1685011] : [_1685011 = c_List_Olist_ONil(_1685005), -(c_List_Olist__all2(_1685005, _1685007, _1685009, _1685011, c_List_Olist_ONil(_1685007)))], (4106 ^ _779203) ^ [_841366, _841368, _841370, _841372] : [-(c_New__DSequence_Opos__single(_841372, _841368) = c_New__DSequence_Opos__single(_841370, _841366)), _841372 = _841370, _841368 = _841366], (18357 ^ _779203) ^ [_1103053, _1103055] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103053), _1103055)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1103053)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1103055)))], (37759 ^ _779203) ^ [_1496666, _1496668, _1496670, _1496672] : [_1496666 = c_Orderings_Obot__class_Obot(tc_fun(_1496668, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1496670, _1496668), _1496670, c_Product__Type_Ofst(_1496670, _1496668)), hAPP(hAPP(c_Product__Type_OSigma(_1496670, _1496668), _1496672), hAPP(c_COMBK(tc_fun(_1496668, tc_HOL_Obool), _1496670), _1496666))) = c_Orderings_Obot__class_Obot(tc_fun(_1496670, tc_HOL_Obool)))], (51779 ^ _779203) ^ [_1824957, _1824959] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1824957), c_SetInterval_Oord_OatLeast(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824959))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824959), _1824957)))], (15880 ^ _779203) ^ [_1057488, _1057490, _1057492] : [class_Int_Onumber__ring(_1057488), class_Rings_Olinordered__idom(_1057488), 15887 ^ _779203 : [(15894 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1057490), _1057492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057488), hAPP(c_Int_Onumber__class_Onumber__of(_1057488), _1057490)), hAPP(c_Int_Onumber__class_Onumber__of(_1057488), _1057492))))], (15888 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1057488), hAPP(c_Int_Onumber__class_Onumber__of(_1057488), _1057490)), hAPP(c_Int_Onumber__class_Onumber__of(_1057488), _1057492))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1057490), _1057492)))]]], (22660 ^ _779203) ^ [_1178645, _1178647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178645)), 22663 ^ _779203 : [(22670 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178645), _1178647)), -(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), _1178647), _1178645))))], (22664 ^ _779203) ^ [] : [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), _1178647), _1178645))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178645), _1178647)))]]], (6545 ^ _779203) ^ [_884767, _884769, _884771, _884773] : [class_Orderings_Opreorder(_884767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884767), _884769), _884771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884767), _884771), _884773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884767), _884769), _884773)))], (21094 ^ _779203) ^ [_1151127, _1151129, _1151131, _1151133] : [class_Rings_Olinordered__semidom(_1151127), 21100 ^ _779203 : [(21103 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151127), c_Groups_Ozero__class_Ozero(_1151127)), hAPP(_1151133, 21099 ^ [_1151127, _1151129, _1151131, _1151133])))], (21101 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1151129), 21099 ^ [_1151127, _1151129, _1151131, _1151133]), _1151131)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1151127), c_Groups_Ozero__class_Ozero(_1151127)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1151129, _1151127), _1151133), _1151131))))], (18997 ^ _779203) ^ [_1113872] : [class_Rings_Osemiring__1(_1113872), -(hBOOL(hAPP(hAPP(c_member(_1113872), c_Groups_Oone__class_Oone(_1113872)), c_Nat_Osemiring__1__class_ONats(_1113872))))], (40328 ^ _779203) ^ [_1568136, _1568138] : [-(c_Transitive__Closure_Ortrancl(_1568136, c_Transitive__Closure_Otrancl(_1568136, _1568138)) = c_Transitive__Closure_Ortrancl(_1568136, _1568138))], (42950 ^ _779203) ^ [_1635579, _1635581, _1635583, _1635585, _1635587] : [-(_1635579 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1635581, _1635583, _1635585), _1635579), _1635587) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1635583), _1635581), tc_prod(_1635583, _1635581), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635583), _1635581), c_List_Olist_ONil(_1635583)), _1635587), hAPP(c_Product__Type_Oprod_Oprod__case(_1635583, _1635581, tc_prod(tc_List_Olist(_1635583), _1635581)), hAPP(hAPP(c_COMBC(_1635583, tc_fun(_1635581, tc_prod(tc_List_Olist(_1635583), _1635581)), tc_fun(_1635581, tc_prod(tc_List_Olist(_1635583), _1635581))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1635583), _1635581), tc_prod(tc_List_Olist(_1635583), _1635581)), tc_fun(tc_fun(_1635581, tc_prod(tc_List_Olist(_1635583), _1635581)), tc_fun(_1635581, tc_prod(tc_List_Olist(_1635583), _1635581))), _1635583), c_COMBB(tc_prod(tc_List_Olist(_1635583), _1635581), tc_prod(tc_List_Olist(_1635583), _1635581), _1635581)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1635583), tc_fun(_1635581, tc_prod(tc_List_Olist(_1635583), _1635581))), tc_fun(tc_prod(tc_List_Olist(_1635583), _1635581), tc_prod(tc_List_Olist(_1635583), _1635581)), _1635583), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1635583), _1635581, tc_prod(tc_List_Olist(_1635583), _1635581))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1635583), tc_List_Olist(_1635583)), tc_fun(tc_List_Olist(_1635583), tc_fun(_1635581, tc_prod(tc_List_Olist(_1635583), _1635581))), _1635583), hAPP(c_COMBB(tc_List_Olist(_1635583), tc_fun(_1635581, tc_prod(tc_List_Olist(_1635583), _1635581)), tc_List_Olist(_1635583)), c_Product__Type_OPair(tc_List_Olist(_1635583), _1635581))), c_List_Olist_OCons(_1635583))))), hAPP(c_Lazy__Sequence_Oanamorph(_1635581, _1635583, _1635585), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1635579), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1635585, _1635587)))], (25292 ^ _779203) ^ [_1225220, _1225222, _1225224, _1225226] : [class_Rings_Olinordered__semidom(_1225220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1225222), _1225224)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225220), c_Groups_Oone__class_Oone(_1225220)), _1225226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225220), hAPP(hAPP(c_Power_Opower__class_Opower(_1225220), _1225226), _1225222)), hAPP(hAPP(c_Power_Opower__class_Opower(_1225220), _1225226), _1225224))))], (45400 ^ _779203) ^ [_1690469, _1690471] : [c_List_Oremdups(_1690469, _1690471) = c_List_Olist_ONil(_1690469), -(_1690471 = c_List_Olist_ONil(_1690469))], (6174 ^ _779203) ^ [_877979, _877981, _877983] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877979, tc_HOL_Obool)), _877981), hAPP(hAPP(c_Set_Oinsert(_877979), _877983), _877981))))], (24494 ^ _779203) ^ [_1210690] : [c_Nat__Transfer_Onat__set(_1210690), -(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), _1210690)) = _1210690)], (10407 ^ _779203) ^ [_958573, _958575, _958577] : [class_Rings_Ocomm__semiring__1(_958573), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958573), _958575), _958577) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958573), _958577), _958575))], (28174 ^ _779203) ^ [_1277073, _1277075] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1277073), _1277075)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1277073)), hAPP(c_Nat_OSuc, _1277075)))], (49208 ^ _779203) ^ [_1774052, _1774054] : [49211 ^ _779203 : [(49216 ^ _779203) ^ [] : [49209 ^ [_1774052, _1774054] = 49210 ^ [_1774052, _1774054]], (49214 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774052, _1774052)), hAPP(hAPP(c_Product__Type_OPair(_1774052, _1774052), 49210 ^ [_1774052, _1774054]), 49209 ^ [_1774052, _1774054])), _1774054)))], (49212 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774052, _1774052)), hAPP(hAPP(c_Product__Type_OPair(_1774052, _1774052), 49209 ^ [_1774052, _1774054]), 49210 ^ [_1774052, _1774054])), _1774054)))]], -(c_Relation_Oantisym(_1774052, _1774054))], (22247 ^ _779203) ^ [_1171980, _1171982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1171980), 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)), _1171982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1171980), _1171982)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33945 ^ _779203) ^ [_1401269, _1401271] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401269), _1401271) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1401269, _1401271)))], (41717 ^ _779203) ^ [_1606159, _1606161, _1606163] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1606159, tc_HOL_Obool)), _1606161), _1606163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1606159), tc_HOL_Obool)), c_List_Olists(_1606159, _1606161)), c_List_Olists(_1606159, _1606163))))], (29142 ^ _779203) ^ [_1295137, _1295139, _1295141, _1295143] : [class_Lattices_Odistrib__lattice(_1295137), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295137), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1295137), _1295139), _1295141)), _1295143) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1295137), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295137), _1295139), _1295143)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295137), _1295141), _1295143)))], (44045 ^ _779203) ^ [_1660841, _1660843, _1660845, _1660847, _1660849, _1660851] : [class_Orderings_Olinorder(_1660841), -(hAPP(_1660843, _1660845) = hAPP(_1660843, _1660847)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660849, _1660841, _1660843), _1660847), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660849, _1660841, _1660843), _1660845), _1660851)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660849, _1660841, _1660843), _1660845), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660849, _1660841, _1660843), _1660847), _1660851)))], (37581 ^ _779203) ^ [_1491717, _1491719, _1491721] : [hBOOL(hAPP(_1491717, _1491719)), -(hAPP(c_Set_OCollect(_1491721), hAPP(hAPP(c_COMBS(_1491721, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1491721), c_fconj), hAPP(c_fequal, _1491719))), _1491717)) = hAPP(hAPP(c_Set_Oinsert(_1491721), _1491719), c_Orderings_Obot__class_Obot(tc_fun(_1491721, tc_HOL_Obool))))], (44303 ^ _779203) ^ [_1665239, _1665241, _1665243, _1665245] : [-(_1665239 = c_List_Olist_ONil(_1665241)), -(c_List_Olast(_1665243, hAPP(hAPP(c_List_Omap(_1665241, _1665243), _1665245), _1665239)) = hAPP(_1665245, c_List_Olast(_1665241, _1665239)))], (21487 ^ _779203) ^ [_1157506, _1157508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1157506)), c_Int_OBit0(_1157508))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1157506), _1157508)))], (27548 ^ _779203) ^ [_1264582, _1264584] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264582, tc_HOL_Obool)), _1264584), c_Orderings_Otop__class_Otop(tc_fun(_1264582, tc_HOL_Obool)))))], (35075 ^ _779203) ^ [_1431553, _1431555, _1431557, _1431559, _1431561] : [class_Complete__Lattice_Ocomplete__lattice(_1431553), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431555), _1431557)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1431553), _1431559), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1431555, _1431553), _1431557), _1431561)) = hAPP(hAPP(c_Finite__Set_Ofold(_1431555, _1431553, hAPP(hAPP(c_COMBB(_1431553, tc_fun(_1431553, _1431553), _1431555), c_Lattices_Osemilattice__inf__class_Oinf(_1431553)), _1431561)), _1431559), _1431557))], (5186 ^ _779203) ^ [_858320, _858322, _858324, _858326, _858328, _858330] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_858330, _858326, _858322) = c_Lazy__Sequence_Olazy__sequence_OInsert(_858328, _858324, _858320)), _858330 = _858328, _858326 = _858324, _858322 = _858320], (14981 ^ _779203) ^ [_1040992, _1040994, _1040996] : [class_Rings_Oring__1(_1040992), hBOOL(hAPP(hAPP(c_member(_1040992), _1040994), c_Int_Oring__1__class_OInts(_1040992))), hBOOL(hAPP(hAPP(c_member(_1040992), _1040996), c_Int_Oring__1__class_OInts(_1040992))), -(hBOOL(hAPP(hAPP(c_member(_1040992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040992), _1040994), _1040996)), c_Int_Oring__1__class_OInts(_1040992))))], (42297 ^ _779203) ^ [_1621756, _1621758, _1621760, _1621762, _1621764] : [-(hAPP(hAPP(c_List_Olist__update(_1621756, hAPP(hAPP(c_List_Olist_OCons(_1621756), _1621758), _1621760)), _1621762), _1621764) = c_Nat_Onat_Onat__case(tc_List_Olist(_1621756), hAPP(hAPP(c_List_Olist_OCons(_1621756), _1621764), _1621760), hAPP(hAPP(c_COMBB(tc_List_Olist(_1621756), tc_List_Olist(_1621756), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1621756), _1621758)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1621756, tc_List_Olist(_1621756)), c_List_Olist__update(_1621756, _1621760)), _1621764)), _1621762))], (37969 ^ _779203) ^ [_1503641, _1503643, _1503645] : [class_Orderings_Olinorder(_1503641), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503641), _1503643)), -(_1503643 = c_Orderings_Obot__class_Obot(tc_fun(_1503641, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1503641), _1503645)), -(_1503645 = c_Orderings_Obot__class_Obot(tc_fun(_1503641, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1503641), c_Big__Operators_Olattice_OSup__fin(_1503641, c_Orderings_Oord__class_Omax(_1503641), _1503643)), c_Big__Operators_Olattice_OSup__fin(_1503641, c_Orderings_Oord__class_Omax(_1503641), _1503645)) = c_Big__Operators_Olattice_OSup__fin(_1503641, c_Orderings_Oord__class_Omax(_1503641), hAPP(c_Set_OCollect(_1503641), hAPP(hAPP(c_COMBB(tc_fun(_1503641, tc_HOL_Obool), tc_HOL_Obool, _1503641), c_HOL_OEx(_1503641)), hAPP(hAPP(c_COMBB(tc_fun(_1503641, tc_fun(_1503641, tc_HOL_Obool)), tc_fun(_1503641, tc_HOL_Obool), _1503641), hAPP(c_COMBB(tc_fun(_1503641, tc_HOL_Obool), tc_HOL_Obool, _1503641), c_HOL_OEx(_1503641))), hAPP(hAPP(c_COMBC(_1503641, tc_fun(_1503641, tc_fun(_1503641, tc_HOL_Obool)), tc_fun(_1503641, tc_fun(_1503641, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1503641, tc_fun(tc_fun(_1503641, tc_HOL_Obool), tc_fun(_1503641, tc_HOL_Obool))), tc_fun(tc_fun(_1503641, tc_fun(_1503641, tc_HOL_Obool)), tc_fun(_1503641, tc_fun(_1503641, tc_HOL_Obool))), _1503641), c_COMBS(_1503641, tc_fun(_1503641, tc_HOL_Obool), tc_fun(_1503641, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1503641, tc_fun(_1503641, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1503641, tc_fun(tc_fun(_1503641, tc_HOL_Obool), tc_fun(_1503641, tc_HOL_Obool))), _1503641), hAPP(c_COMBB(tc_fun(_1503641, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1503641, tc_HOL_Obool), tc_fun(_1503641, tc_HOL_Obool)), _1503641), c_COMBS(_1503641, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1503641, tc_fun(_1503641, tc_HOL_Obool)), tc_fun(_1503641, tc_fun(_1503641, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1503641), hAPP(c_COMBB(tc_fun(_1503641, tc_HOL_Obool), tc_fun(_1503641, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1503641), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1503641), c_fconj))), hAPP(hAPP(c_COMBC(_1503641, tc_fun(_1503641, tc_fun(_1503641, _1503641)), tc_fun(_1503641, tc_fun(_1503641, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1503641, _1503641), tc_fun(_1503641, tc_HOL_Obool)), tc_fun(tc_fun(_1503641, tc_fun(_1503641, _1503641)), tc_fun(_1503641, tc_fun(_1503641, tc_HOL_Obool))), _1503641), c_COMBB(tc_fun(_1503641, _1503641), tc_fun(_1503641, tc_HOL_Obool), _1503641)), hAPP(hAPP(c_COMBB(tc_fun(_1503641, tc_HOL_Obool), tc_fun(tc_fun(_1503641, _1503641), tc_fun(_1503641, tc_HOL_Obool)), _1503641), c_COMBB(_1503641, tc_HOL_Obool, _1503641)), c_fequal))), c_Orderings_Oord__class_Omin(_1503641)))))), hAPP(hAPP(c_COMBC(_1503641, tc_fun(_1503641, tc_HOL_Obool), tc_fun(_1503641, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1503641, tc_HOL_Obool), tc_fun(_1503641, tc_HOL_Obool)), _1503641), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1503641)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1503641), c_fconj), hAPP(hAPP(c_COMBC(_1503641, tc_fun(_1503641, tc_HOL_Obool), tc_HOL_Obool), c_member(_1503641)), _1503643)))), hAPP(hAPP(c_COMBC(_1503641, tc_fun(_1503641, tc_HOL_Obool), tc_HOL_Obool), c_member(_1503641)), _1503645))))))))], (19604 ^ _779203) ^ [_1125089, _1125091] : [class_Groups_Olinordered__ab__group__add(_1125089), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125089), _1125091)), -(_1125091 = c_Orderings_Obot__class_Obot(tc_fun(_1125089, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1125089), c_Big__Operators_Olinorder__class_OMin(_1125089, _1125091)) = c_Big__Operators_Olinorder__class_OMax(_1125089, hAPP(c_Set_Oimage(_1125089, _1125089, c_Groups_Ouminus__class_Ouminus(_1125089)), _1125091)))], (35559 ^ _779203) ^ [_1444822, _1444824, _1444826, _1444828] : [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), _1444822), _1444824)), 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), _1444826), _1444828)), 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), _1444822), _1444828)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444826), _1444824))))], (23164 ^ _779203) ^ [_1186735, _1186737] : [hBOOL(hAPP(_1186735, hAPP(c_Int_Onat, _1186737))), 23167 ^ _779203 : [(23174 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1186737), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1186735, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (23168 ^ _779203) ^ [_1186835] : [_1186737 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186835), -(hBOOL(hAPP(_1186735, _1186835)))]]], (11866 ^ _779203) ^ [_984025, _984027, _984029] : [class_Rings_Olinordered__semiring__strict(_984025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984025), c_Groups_Ozero__class_Ozero(_984025)), _984027)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984025), _984029), c_Groups_Ozero__class_Ozero(_984025))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984025), _984029), _984027)), c_Groups_Ozero__class_Ozero(_984025))))], (13573 ^ _779203) ^ [_1014937, _1014939, _1014941, _1014943] : [class_Rings_Odivision__ring(_1014937), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014937), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014937), _1014939), _1014941)), _1014943) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014937), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014937), _1014939), _1014943)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014937), _1014941), _1014943)))], (7031 ^ _779203) ^ [_895004, _895006, _895008, _895010, _895012] : [c_Finite__Set_Ofolding__one__idem(_895004, _895006, _895008), hBOOL(hAPP(c_Finite__Set_Ofinite(_895004), _895010)), -(hAPP(_895008, hAPP(hAPP(c_Set_Oinsert(_895004), _895012), _895010)) = hAPP(hAPP(c_Finite__Set_Ofold(_895004, _895004, _895006), _895012), _895010))], (34013 ^ _779203) ^ [_1402469, _1402471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1402469)), -(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(_1402469), _1402471))), _1402469)))], (39738 ^ _779203) ^ [_1553354, _1553356, _1553358, _1553360, _1553362, _1553364, _1553366, _1553368] : [c_Finite__Set_Ofolding__image(_1553354, _1553356, _1553358, _1553360, _1553362), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553356), _1553364)), -(hAPP(hAPP(_1553362, hAPP(hAPP(c_COMBS(_1553356, _1553354, _1553354), hAPP(hAPP(c_COMBB(_1553354, tc_fun(_1553354, _1553354), _1553356), _1553358), _1553366)), _1553368)), _1553364) = hAPP(hAPP(_1553358, hAPP(hAPP(_1553362, _1553366), _1553364)), hAPP(hAPP(_1553362, _1553368), _1553364)))], (52305 ^ _779203) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (40305 ^ _779203) ^ [_1567675, _1567677] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567675, _1567675)), hAPP(hAPP(c_Product__Type_OPair(_1567675, _1567675), 40306 ^ [_1567675, _1567677]), 40306 ^ [_1567675, _1567677])), c_Transitive__Closure_Otrancl(_1567675, _1567677)))), -(c_Wellfounded_Oacyclic(_1567675, _1567677))], (15672 ^ _779203) ^ [_1053945, _1053947, _1053949] : [class_Orderings_Olinorder(_1053945), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053945), _1053947), _1053949)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1053945), _1053947), _1053949) = _1053947)], (14065 ^ _779203) ^ [_1023923, _1023925, _1023927] : [class_Fields_Olinordered__field(_1023923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023923), c_Groups_Ozero__class_Ozero(_1023923)), _1023925)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023923), _1023927), c_Groups_Ozero__class_Ozero(_1023923))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023923), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1023923), _1023925), _1023927)), c_Groups_Ozero__class_Ozero(_1023923))))], (46790 ^ _779203) ^ [_1720189, _1720191, _1720193] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1720189), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1720189))), _1720191))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1720193), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1720189))), _1720191))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1720189))), hAPP(c_List_Ofilter(tc_List_Olist(_1720189), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1720189)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1720193)), c_Nat_Osize__class_Osize(tc_List_Olist(_1720189)))), c_List_Otranspose(_1720189, _1720191))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720189)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1720189)), _1720191), _1720193)))], (34468 ^ _779203) ^ [_1414659, _1414661, _1414663, _1414665] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1414659, tc_HOL_Obool), tc_fun(_1414661, tc_HOL_Obool)), _1414663), hAPP(hAPP(c_COMBC(tc_fun(_1414659, tc_HOL_Obool), tc_fun(_1414659, tc_fun(_1414661, tc_HOL_Obool)), tc_fun(_1414661, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414659, tc_fun(_1414661, tc_HOL_Obool))), _1414665)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414659, tc_fun(_1414661, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1414659, tc_HOL_Obool), _1414663)), _1414665))], (32145 ^ _779203) ^ [_1360115] : [class_Orderings_Olinorder(_1360115), -(c_Orderings_Oord_Omax(_1360115, hAPP(c_COMBC(_1360115, _1360115, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1360115))) = c_Orderings_Oord__class_Omin(_1360115))], (10073 ^ _779203) ^ [_951419, _951421, _951423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951419), _951421)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _951421), _951419)), _951423) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951421), _951423)), _951419))], (7779 ^ _779203) ^ [_907281, _907283, _907285] : [class_Orderings_Oorder(_907281), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907281), _907283), _907285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907281), _907283), _907285))), -(_907283 = _907285)], (8170 ^ _779203) ^ [_914969, _914971, _914973, _914975, _914977, _914979] : [-(_914969 = _914971), -(hAPP(c_Fun_Ofun__upd(_914973, _914975, _914977, _914971, _914979), _914969) = hAPP(_914977, _914969))], (2312 ^ _779203) ^ [_812999, _813001, _813003, _813005] : [-(c_Divides_Opdivmod(_813005, _813001) = c_Divides_Opdivmod(_813003, _812999)), _813005 = _813003, _813001 = _812999], (32547 ^ _779203) ^ [_1369854, _1369856, _1369858, _1369860] : [-(hAPP(c_Nat_Onat_Onat__rec(_1369854, _1369856, _1369858), hAPP(c_Nat_OSuc, _1369860)) = hAPP(hAPP(_1369858, _1369860), hAPP(c_Nat_Onat_Onat__rec(_1369854, _1369856, _1369858), _1369860)))], (22385 ^ _779203) ^ [_1174112, _1174114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1174112, _1174114)), _1174112)))], (52507 ^ _779203) ^ [_1834866] : [class_Lazy__Sequence_Osmall__lazy(_1834866), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1834866)))], (11101 ^ _779203) ^ [_970419, _970421, _970423] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970419), _970421) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970419), _970423), -(_970419 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_970421 = _970423)], (48903 ^ _779203) ^ [_1766822, _1766824] : [c_Relation_Otrans(_1766822, _1766824), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1766822, _1766822), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1766822, _1766822, _1766822), _1766824), _1766824)), _1766824)))], (18212 ^ _779203) ^ [_1100412] : [-(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), _1100412))))], (47890 ^ _779203) ^ [_1744151, _1744153, _1744155] : [47892 ^ _779203 : [(47895 ^ _779203) ^ [] : [hBOOL(hAPP(_1744155, 47891 ^ [_1744151, _1744153, _1744155]))], (47893 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744151), 47891 ^ [_1744151, _1744153, _1744155]), hAPP(c_List_Oset(_1744151), _1744153))))]], -(c_List_Olist__all(_1744151, _1744155, _1744153))], (38346 ^ _779203) ^ [_1518291, _1518293, _1518295, _1518297, _1518299, _1518301, _1518303, _1518305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1518291, _1518293)), hAPP(hAPP(c_Product__Type_OPair(_1518291, _1518293), _1518295), _1518297)), _1518299)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1518293, _1518301)), hAPP(hAPP(c_Product__Type_OPair(_1518293, _1518301), _1518297), _1518303)), _1518305)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1518291, _1518301)), hAPP(hAPP(c_Product__Type_OPair(_1518291, _1518301), _1518295), _1518303)), hAPP(hAPP(c_Relation_Orel__comp(_1518291, _1518293, _1518301), _1518299), _1518305))))], (36924 ^ _779203) ^ [_1474976, _1474978, _1474980, _1474982, _1474984, _1474986] : [c_Typedef_Otype__definition(_1474976, _1474978, _1474980, _1474982, _1474984), hBOOL(hAPP(hAPP(c_member(_1474978), _1474986), _1474984)), -(hAPP(_1474980, hAPP(_1474982, _1474986)) = _1474986)], (18536 ^ _779203) ^ [_1106113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106113), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106113))], (24446 ^ _779203) ^ [_1209800] : [class_Rings_Osemiring__1(_1209800), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1209800), c_Groups_Ozero__class_Ozero(_1209800)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1209800))], (18473 ^ _779203) ^ [_1105011] : [_1105011 = 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), _1105011)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11021 ^ _779203) ^ [_969215, _969217] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969215), _969217) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _969215 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _969217 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18264 ^ _779203) ^ [_1101319, _1101321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101319), _1101321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101319)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101321))))], (38949 ^ _779203) ^ [_1534074, _1534076] : [-(hAPP(c_Relation_OField(_1534074), _1534076) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1534074, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1534074, _1534074), _1534076)), hAPP(c_Relation_ORange(_1534074, _1534074), _1534076)))], (42966 ^ _779203) ^ [_1636161, _1636163, _1636165, _1636167, _1636169] : [-(hAPP(hAPP(c_List_Oappend(_1636161), _1636163), hAPP(hAPP(c_List_Olist_OCons(_1636161), _1636165), c_List_Olist_ONil(_1636161))) = hAPP(hAPP(c_List_Oappend(_1636161), _1636167), hAPP(hAPP(c_List_Olist_OCons(_1636161), _1636169), c_List_Olist_ONil(_1636161)))), _1636163 = _1636167, _1636165 = _1636169], (37577 ^ _779203) ^ [_1491606, _1491608] : [-(hAPP(c_Set_OCollect(_1491606), hAPP(c_fequal, _1491608)) = hAPP(hAPP(c_Set_Oinsert(_1491606), _1491608), c_Orderings_Obot__class_Obot(tc_fun(_1491606, tc_HOL_Obool))))], (40444 ^ _779203) ^ [_1570968, _1570970, _1570972] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1570968, _1570968, _1570970), c_Relation_OId(_1570968)), _1570972) = _1570972)], (34344 ^ _779203) ^ [_1411042, _1411044, _1411046, _1411048, _1411050] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411042, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411044, tc_fun(_1411042, tc_HOL_Obool)), _1411046), _1411048)), _1411050) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1411044, tc_fun(_1411042, tc_HOL_Obool)), _1411046), hAPP(hAPP(c_COMBC(_1411044, tc_fun(_1411042, tc_HOL_Obool), tc_fun(_1411042, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1411042, tc_HOL_Obool), tc_fun(tc_fun(_1411042, tc_HOL_Obool), tc_fun(_1411042, tc_HOL_Obool)), _1411044), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1411042, tc_HOL_Obool))), _1411048)), _1411050)))], (43022 ^ _779203) ^ [_1637357, _1637359, _1637361, _1637363, _1637365] : [-(hAPP(hAPP(c_List_Oappend(_1637357), _1637359), _1637361) = hAPP(hAPP(c_List_Olist_OCons(_1637357), _1637363), _1637365)), 43023 ^ _779203 : [(43030 ^ _779203) ^ [_1637540] : [_1637359 = hAPP(hAPP(c_List_Olist_OCons(_1637357), _1637363), _1637540), hAPP(hAPP(c_List_Oappend(_1637357), _1637540), _1637361) = _1637365], (43024 ^ _779203) ^ [] : [_1637359 = c_List_Olist_ONil(_1637357), _1637361 = hAPP(hAPP(c_List_Olist_OCons(_1637357), _1637363), _1637365)]]], (28768 ^ _779203) ^ [_1287952, _1287954, _1287956, _1287958] : [class_Orderings_Olinorder(_1287952), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287952), _1287954), _1287956)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287952), _1287956), _1287958)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287952, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1287952, _1287954, _1287956)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1287952, _1287956, _1287958)) = c_SetInterval_Oord__class_OatLeastAtMost(_1287952, _1287954, _1287958))], (49855 ^ _779203) ^ [_1787398, _1787400, _1787402, _1787404] : [c_Fun_Obij__betw(_1787398, _1787400, _1787402, c_Orderings_Otop__class_Otop(tc_fun(_1787398, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1787400, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1787398, _1787400, _1787402), hAPP(c_Set_OCollect(_1787398), _1787404)) = hAPP(c_Set_OCollect(_1787400), hAPP(hAPP(c_COMBB(_1787398, tc_HOL_Obool, _1787400), _1787404), c_Hilbert__Choice_Oinv__into(_1787398, _1787400, c_Orderings_Otop__class_Otop(tc_fun(_1787398, tc_HOL_Obool)), _1787402))))], (51641 ^ _779203) ^ [_1822438, _1822440] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822438), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1822440), _1822438))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822438), _1822440)))], (38332 ^ _779203) ^ [_1517435, _1517437, _1517439, _1517441, _1517443, _1517445, _1517447, _1517449] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1517435, _1517437)), _1517439), hAPP(c_Set_Oimage(tc_prod(_1517441, _1517443), tc_prod(_1517435, _1517437), c_Product__Type_Omap__pair(_1517441, _1517435, _1517443, _1517437, _1517445, _1517447)), _1517449))), 38337 ^ _779203 : [(38340 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517441, _1517443)), hAPP(hAPP(c_Product__Type_OPair(_1517441, _1517443), 38335 ^ [_1517435, _1517437, _1517439, _1517441, _1517443, _1517445, _1517447, _1517449]), 38336 ^ [_1517435, _1517437, _1517439, _1517441, _1517443, _1517445, _1517447, _1517449])), _1517449)))], (38338 ^ _779203) ^ [] : [-(_1517439 = hAPP(hAPP(c_Product__Type_OPair(_1517435, _1517437), hAPP(_1517445, 38335 ^ [_1517435, _1517437, _1517439, _1517441, _1517443, _1517445, _1517447, _1517449])), hAPP(_1517447, 38336 ^ [_1517435, _1517437, _1517439, _1517441, _1517443, _1517445, _1517447, _1517449])))]]], (33717 ^ _779203) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3808 ^ _779203) ^ [_836319, _836321] : [_836321 = _836319, -(c_Lazy__Sequence_Ohit__bound(_836321) = c_Lazy__Sequence_Ohit__bound(_836319))], (34985 ^ _779203) ^ [_1429137, _1429139, _1429141, _1429143, _1429145] : [-(_1429137 = c_Orderings_Obot__class_Obot(tc_fun(_1429139, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429139, tc_fun(_1429141, tc_HOL_Obool)), _1429137), hAPP(hAPP(c_COMBB(tc_fun(_1429141, tc_HOL_Obool), tc_fun(_1429141, tc_HOL_Obool), _1429139), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429141, tc_HOL_Obool)), _1429143)), _1429145)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429141, tc_HOL_Obool)), _1429143), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429139, tc_fun(_1429141, tc_HOL_Obool)), _1429137), _1429145)))], (29238 ^ _779203) ^ [_1297357, _1297359, _1297361, _1297363] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297357, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297357, tc_HOL_Obool)), _1297359), _1297361)), _1297363) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297357, tc_HOL_Obool)), _1297359), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297357, tc_HOL_Obool)), _1297361), _1297363)))], (48066 ^ _779203) ^ [_1748093, _1748095] : [c_Wellfounded_Oacyclic(_1748093, hAPP(c_Set_OCollect(tc_prod(_1748093, _1748093)), hAPP(c_Product__Type_Oprod_Oprod__case(_1748093, _1748093, tc_HOL_Obool), c_Predicate_Oconversep(_1748093, _1748093, _1748095)))), -(c_Wellfounded_Oacyclic(_1748093, hAPP(c_Set_OCollect(tc_prod(_1748093, _1748093)), hAPP(c_Product__Type_Oprod_Oprod__case(_1748093, _1748093, tc_HOL_Obool), _1748095))))], (7835 ^ _779203) ^ [_908034, _908036, _908038, _908040] : [class_Orderings_Oorder(_908034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908034), _908036), _908038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908034), _908040), _908036)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908034), _908040), _908038)))], (32769 ^ _779203) ^ [_1378959, _1378961, _1378963, _1378965, _1378967, _1378969] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1378959, tc_fun(_1378961, tc_HOL_Obool))), _1378963), _1378965), _1378967), _1378969)), 32772 ^ _779203 : [(32775 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1378965, _1378967), _1378969)))], (32773 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1378963, _1378967), _1378969)))]]], (136 ^ _779203) ^ [_781163, _781165, _781167, _781169, _781171, _781173, _781175, _781177, _781179, _781181, _781183, _781185] : [-(c_Finite__Set_Ofolding__image__simple__idem(_781183, _781179, _781175, _781171, _781167, _781163)), c_Finite__Set_Ofolding__image__simple__idem(_781185, _781181, _781177, _781173, _781169, _781165), _781185 = _781183, _781181 = _781179, _781177 = _781175, _781173 = _781171, _781169 = _781167, _781165 = _781163], (46088 ^ _779203) ^ [_1706601, _1706603, _1706605] : [class_Orderings_Olinorder(_1706601), c_List_Olinorder__class_Osorted(_1706601, _1706603), -(c_List_Olinorder__class_Osorted(_1706601, hAPP(hAPP(c_List_Odrop(_1706601), _1706605), _1706603)))], (8855 ^ _779203) ^ [_928821, _928823, _928825, _928827] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_928821), 8858 ^ _779203 : [(8865 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928821), _928823), _928827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928821), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928821), _928823), _928825)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928821), _928827), _928825))))], (8859 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928821), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928821), _928823), _928825)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928821), _928827), _928825))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928821), _928823), _928827)))]]], (34334 ^ _779203) ^ [_1410543, _1410545, _1410547, _1410549, _1410551] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410543, tc_fun(_1410545, tc_HOL_Obool)), _1410547), hAPP(hAPP(c_COMBC(_1410543, tc_fun(_1410545, tc_HOL_Obool), tc_fun(_1410545, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1410545, tc_HOL_Obool), tc_fun(tc_fun(_1410545, tc_HOL_Obool), tc_fun(_1410545, tc_HOL_Obool)), _1410543), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410545, tc_HOL_Obool))), _1410549)), _1410551)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410545, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410543, tc_fun(_1410545, tc_HOL_Obool)), _1410547), _1410549)), _1410551))], (25574 ^ _779203) ^ [_1229743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1229743), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1229743)), c_Int_OMin)))], (45328 ^ _779203) ^ [_1689073, _1689075, _1689077, _1689079, _1689081] : [c_Finite__Set_Ofun__left__comm(_1689073, _1689075, _1689077), -(hAPP(hAPP(c_Finite__Set_Ofold(_1689073, _1689075, _1689077), _1689079), hAPP(c_List_Oset(_1689073), _1689081)) = hAPP(c_List_Ofoldl(_1689075, _1689073, hAPP(c_COMBC(_1689073, _1689075, _1689075), _1689077), _1689079), c_List_Oremdups(_1689073, _1689081)))], (38298 ^ _779203) ^ [_1516466, _1516468, _1516470, _1516472, _1516474, _1516476, _1516478, _1516480] : [-(hAPP(c_Product__Type_Omap__pair(_1516466, _1516468, _1516470, _1516472, _1516474, _1516476), hAPP(hAPP(c_Product__Type_OPair(_1516466, _1516470), _1516478), _1516480)) = hAPP(hAPP(c_Product__Type_OPair(_1516468, _1516472), hAPP(_1516474, _1516478)), hAPP(_1516476, _1516480)))], (52295 ^ _779203) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (35623 ^ _779203) ^ [_1446557, _1446559, _1446561] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446557, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446557), _1446559), _1446561), -(_1446559 = c_Orderings_Obot__class_Obot(tc_fun(_1446557, tc_HOL_Obool)))], (35029 ^ _779203) ^ [_1430349, _1430351] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430349, 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(_1430349, tc_HOL_Obool)), tc_fun(_1430349, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1430349, tc_HOL_Obool)), tc_fun(_1430349, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430349, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1430351)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1430349, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1430351))], (4646 ^ _779203) ^ [_849872, _849874] : [_849874 = _849872, -(c_Random__Sequence_Osingle(_849874) = c_Random__Sequence_Osingle(_849872))], (39258 ^ _779203) ^ [_1541607, _1541609, _1541611] : [hBOOL(hAPP(c_Predicate_OPowp(_1541607, _1541609), _1541611)), 39261 ^ _779203 : [(39262 ^ _779203) ^ [_1541691] : [hBOOL(hAPP(hAPP(c_member(_1541607), _1541691), _1541611)), -(hBOOL(hAPP(_1541609, _1541691)))]]], (7151 ^ _779203) ^ [_897541, _897543, _897545, _897547, _897549, _897551] : [c_Finite__Set_Ofun__left__comm__idem(_897541, _897543, _897545), hBOOL(hAPP(c_Finite__Set_Ofinite(_897541), _897547)), -(hAPP(hAPP(c_Finite__Set_Ofold(_897541, _897543, _897545), _897549), hAPP(hAPP(c_Set_Oinsert(_897541), _897551), _897547)) = hAPP(hAPP(_897545, _897551), hAPP(hAPP(c_Finite__Set_Ofold(_897541, _897543, _897545), _897549), _897547)))], (40807 ^ _779203) ^ [_1579582, _1579584, _1579586, _1579588] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579582, _1579582)), hAPP(hAPP(c_Product__Type_OPair(_1579582, _1579582), _1579584), _1579586)), c_Transitive__Closure_Otrancl(_1579582, hAPP(c_Relation_Oconverse(_1579582, _1579582), _1579588)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579582, _1579582)), hAPP(hAPP(c_Product__Type_OPair(_1579582, _1579582), _1579584), _1579586)), hAPP(c_Relation_Oconverse(_1579582, _1579582), c_Transitive__Closure_Otrancl(_1579582, _1579588)))))], (44518 ^ _779203) ^ [_1670926, _1670928, _1670930, _1670932] : [-(hBOOL(hAPP(c_List_Odistinct(_1670926), hAPP(hAPP(c_List_Omap(_1670928, _1670926), _1670930), _1670932)))), hBOOL(hAPP(c_List_Odistinct(_1670928), _1670932)), c_Fun_Oinj__on(_1670928, _1670926, _1670930, hAPP(c_List_Oset(_1670928), _1670932))], (40741 ^ _779203) ^ [_1578115, _1578117, _1578119] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1578115, _1578117)), hAPP(c_Relation_Oconverse(_1578117, _1578115), _1578119))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1578117, _1578115)), _1578119)))], (3626 ^ _779203) ^ [_833490, _833492] : [_833492 = _833490, -(c_List_Oembed__list(_833492) = c_List_Oembed__list(_833490))], (30167 ^ _779203) ^ [_1317047, _1317049, _1317051, _1317053, _1317055] : [c_Finite__Set_Ofolding__one(_1317047, _1317049, _1317051), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317047), _1317053)), -(_1317053 = c_Orderings_Obot__class_Obot(tc_fun(_1317047, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317047), _1317055)), -(_1317055 = c_Orderings_Obot__class_Obot(tc_fun(_1317047, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317047, tc_HOL_Obool)), _1317053), _1317055) = c_Orderings_Obot__class_Obot(tc_fun(_1317047, tc_HOL_Obool)), -(hAPP(_1317051, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317047, tc_HOL_Obool)), _1317053), _1317055)) = hAPP(hAPP(_1317049, hAPP(_1317051, _1317053)), hAPP(_1317051, _1317055)))], (44446 ^ _779203) ^ [_1669296, _1669298, _1669300, _1669302, _1669304] : [-(hAPP(hAPP(c_List_Omap(_1669296, _1669298), _1669300), hAPP(hAPP(c_List_Olist_OCons(_1669296), _1669302), _1669304)) = hAPP(hAPP(c_List_Olist_OCons(_1669298), hAPP(_1669300, _1669302)), hAPP(hAPP(c_List_Omap(_1669296, _1669298), _1669300), _1669304)))], (13325 ^ _779203) ^ [_1010031, _1010033] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1010031), _1010033)))), -(_1010033 = c_Orderings_Obot__class_Obot(tc_fun(_1010031, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1010031), _1010033))], (12274 ^ _779203) ^ [_990928, _990930] : [12275 ^ _779203 : [(12278 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _990930))], (12276 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _990928))]], -(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), _990928), _990930))))], (23772 ^ _779203) ^ [_1197555, _1197557] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197555), _1197557))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197555, _1197557) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1197555), _1197557), _1197557))], (31985 ^ _779203) ^ [_1355828, _1355830, _1355832, _1355834] : [hBOOL(hAPP(hAPP(c_member(_1355828), _1355834), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1355828, tc_HOL_Obool)), _1355830), _1355832))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1355828, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1355828, tc_fun(_1355828, tc_HOL_Obool), tc_HOL_Obool), c_member(_1355828)), _1355830)), hAPP(hAPP(c_COMBC(_1355828, tc_fun(_1355828, tc_HOL_Obool), tc_HOL_Obool), c_member(_1355828)), _1355832)), _1355834)))], (33369 ^ _779203) ^ [_1389951, _1389953, _1389955, _1389957] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1389951, _1389953), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1389955), _1389957))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1389951, _1389953) = _1389957)], (42015 ^ _779203) ^ [_1613628, _1613630, _1613632] : [42017 ^ _779203 : [(42020 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1613628), 42016 ^ [_1613628, _1613630, _1613632]), _1613632))], (42018 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613628), 42016 ^ [_1613628, _1613630, _1613632]), hAPP(c_List_Oset(_1613628), _1613630))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1613628)), _1613630), c_List_Olists(_1613628, _1613632))))], (34893 ^ _779203) ^ [_1426898, _1426900, _1426902, _1426904, _1426906] : [-(_1426898 = c_Orderings_Obot__class_Obot(tc_fun(_1426900, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426900, tc_fun(_1426902, tc_HOL_Obool)), _1426898), hAPP(hAPP(c_COMBB(tc_fun(_1426902, tc_HOL_Obool), tc_fun(_1426902, tc_HOL_Obool), _1426900), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426902, tc_HOL_Obool)), _1426904)), _1426906)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426902, tc_HOL_Obool)), _1426904), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426900, tc_fun(_1426902, tc_HOL_Obool)), _1426898), _1426906)))], (40725 ^ _779203) ^ [_1577795, _1577797, _1577799] : [c_Relation_Ototal__on(_1577795, _1577797, hAPP(c_Relation_Oconverse(_1577795, _1577795), _1577799)), -(c_Relation_Ototal__on(_1577795, _1577797, _1577799))], (48400 ^ _779203) ^ [_1755237, _1755239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755237), _1755239)), -(c_Lazy__Sequence_Osmall__lazy_H(_1755237, _1755239) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (11470 ^ _779203) ^ [_976843, _976845, _976847, _976849] : [class_Rings_Oordered__ring(_976843), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976843), _976845), _976847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976843), _976849), c_Groups_Ozero__class_Ozero(_976843))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976843), _976847), _976849)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976843), _976845), _976849))))], (49839 ^ _779203) ^ [_1787181, _1787183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1787181), _1787183)), -(c_Quickcheck_Obeyond(_1787181, _1787183) = _1787183)], (43862 ^ _779203) ^ [_1656736, _1656738, _1656740, _1656742] : [class_Groups_Osemigroup__add(_1656736), -(hAPP(c_List_Ofoldl(_1656736, _1656736, c_Groups_Oplus__class_Oplus(_1656736), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1656736), _1656738), _1656740)), _1656742) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1656736), _1656738), hAPP(c_List_Ofoldl(_1656736, _1656736, c_Groups_Oplus__class_Oplus(_1656736), _1656740), _1656742)))], (18824 ^ _779203) ^ [_1110855] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110855), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110855)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1110855)))], (48332 ^ _779203) ^ [_1753767, _1753769, _1753771] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1753767), hAPP(c_COMBK(_1753767, tc_Nat_Onat), _1753769)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1753771)) = c_List_Oreplicate(_1753767, _1753771, _1753769))], (45274 ^ _779203) ^ [_1687926, _1687928, _1687930] : [hBOOL(hAPP(c_List_Odistinct(_1687926), _1687928)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1687926)), c_Enum_On__lists(_1687926, _1687930, _1687928))))], (31434 ^ _779203) ^ [_1342793, _1342795, _1342797] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1342793, tc_HOL_Obool)), _1342795), _1342797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1342793, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1342793, tc_HOL_Obool), _1342797)), _1342795)))], (7041 ^ _779203) ^ [_895197, _895199, _895201, _895203, _895205, _895207] : [c_Finite__Set_Ofun__left__comm(_895197, _895199, _895201), hBOOL(hAPP(c_Finite__Set_Ofinite(_895197), _895203)), hBOOL(hAPP(hAPP(c_member(_895197), _895205), _895203)), -(hAPP(hAPP(c_Finite__Set_Ofold(_895197, _895199, _895201), _895207), _895203) = hAPP(hAPP(_895201, _895205), hAPP(hAPP(c_Finite__Set_Ofold(_895197, _895199, _895201), _895207), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895197, tc_HOL_Obool)), _895203), hAPP(hAPP(c_Set_Oinsert(_895197), _895205), c_Orderings_Obot__class_Obot(tc_fun(_895197, tc_HOL_Obool)))))))], (50200 ^ _779203) ^ [_1794325, _1794327, _1794329, _1794331] : [-(c_Product__Type_Ocurry(_1794325, _1794327, _1794329, hAPP(c_Product__Type_Oprod_Oprod__case(_1794325, _1794327, _1794329), _1794331)) = _1794331)], (48352 ^ _779203) ^ [_1754047, _1754049, _1754051] : [-(hAPP(c_List_Oset(_1754047), c_List_Oreplicate(_1754047, hAPP(c_Nat_OSuc, _1754049), _1754051)) = hAPP(hAPP(c_Set_Oinsert(_1754047), _1754051), c_Orderings_Obot__class_Obot(tc_fun(_1754047, tc_HOL_Obool))))], (43085 ^ _779203) ^ [_1638829, _1638831, _1638833, _1638835, _1638837] : [-(hAPP(hAPP(c_List_Oappend(_1638829), _1638831), _1638833) = hAPP(hAPP(c_List_Oappend(_1638829), _1638835), _1638837)), 43086 ^ _779203 : [(43093 ^ _779203) ^ [_1639053] : [hAPP(hAPP(c_List_Oappend(_1638829), _1638831), _1639053) = _1638835, _1638833 = hAPP(hAPP(c_List_Oappend(_1638829), _1639053), _1638837)], (43087 ^ _779203) ^ [_1638941] : [_1638831 = hAPP(hAPP(c_List_Oappend(_1638829), _1638835), _1638941), hAPP(hAPP(c_List_Oappend(_1638829), _1638941), _1638833) = _1638837]]], (27278 ^ _779203) ^ [_1259369, _1259371] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1259369), _1259371))))], (32355 ^ _779203) ^ [_1364835, _1364837, _1364839, _1364841] : [class_Groups_Oab__group__add(_1364835), 32358 ^ _779203 : [(32365 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1364837), _1364839))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1364835), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1364835, _1364835), hAPP(hAPP(c_COMBB(_1364835, tc_fun(_1364835, _1364835), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1364835)), _1364841)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1364835, tc_Nat_Onat), _1364841), 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, _1364837, _1364839)) = c_Groups_Ozero__class_Ozero(_1364835))], (32359 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1364837), _1364839)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1364835), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1364835, _1364835), hAPP(hAPP(c_COMBB(_1364835, tc_fun(_1364835, _1364835), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1364835)), _1364841)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1364835, tc_Nat_Onat), _1364841), 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, _1364837, _1364839)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1364835), hAPP(_1364841, _1364837)), hAPP(_1364841, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1364839), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (10341 ^ _779203) ^ [_957204, _957206, _957208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957204), _957206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957204), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957208), _957206))))], (45847 ^ _779203) ^ [_1701724, _1701726] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1701724))), c_List_Otranspose(_1701724, _1701726)) = c_List_Ofoldr(tc_List_Olist(_1701724), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1701724)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1701724))), _1701726, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4212 ^ _779203) ^ [_842927, _842929] : [_842929 = _842927, -(c_List_Oappend(_842929) = c_List_Oappend(_842927))], (34369 ^ _779203) ^ [_1411907, _1411909, _1411911, _1411913] : [_1411907 = c_Orderings_Obot__class_Obot(tc_fun(_1411909, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411909, tc_fun(_1411911, tc_HOL_Obool)), _1411907), hAPP(c_COMBK(tc_fun(_1411911, tc_HOL_Obool), _1411909), _1411913)) = c_Orderings_Obot__class_Obot(tc_fun(_1411911, tc_HOL_Obool)))], (38681 ^ _779203) ^ [_1528054, _1528056, _1528058] : [c_Wellfounded_Owf(_1528054, _1528056), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528054, _1528054)), hAPP(hAPP(c_Product__Type_OPair(_1528054, _1528054), _1528058), _1528058)), _1528056))], (19990 ^ _779203) ^ [_1131633, _1131635, _1131637] : [class_Groups_Ogroup__add(_1131633), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131633), hAPP(c_Groups_Ouminus__class_Ouminus(_1131633), _1131635)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131633), _1131635), _1131637)) = _1131637)], (45638 ^ _779203) ^ [_1696226, _1696228, _1696230] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696226)), hAPP(c_List_Ofilter(_1696226, _1696228), _1696230))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696226)), hAPP(c_List_Ofilter(_1696226, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1696226), c_fNot), _1696228)), _1696230))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696226)), _1696230))], (44448 ^ _779203) ^ [_1669364, _1669366, _1669368, _1669370, _1669372] : [-(hAPP(hAPP(c_List_Omap(_1669364, _1669366), _1669368), hAPP(hAPP(c_List_Oappend(_1669364), _1669370), _1669372)) = hAPP(hAPP(c_List_Oappend(_1669366), hAPP(hAPP(c_List_Omap(_1669364, _1669366), _1669368), _1669370)), hAPP(hAPP(c_List_Omap(_1669364, _1669366), _1669368), _1669372)))], (31167 ^ _779203) ^ [_1337200, _1337202, _1337204, _1337206, _1337208, _1337210, _1337212] : [c_Finite__Set_Ofolding__image__simple(_1337200, _1337202, _1337204, _1337206, _1337208, _1337210), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337202), _1337212)), -(hAPP(_1337210, _1337212) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1337200, _1337202, _1337204), _1337208), _1337206), _1337212))], (33865 ^ _779203) ^ [_1399575, _1399577, _1399579] : [-(_1399575 = hAPP(hAPP(c_Product__Type_OPair(_1399577, _1399579), hAPP(c_Product__Type_Ofst(_1399577, _1399579), _1399575)), hAPP(c_Product__Type_Osnd(_1399577, _1399579), _1399575)))], (44670 ^ _779203) ^ [_1674121, _1674123, _1674125, _1674127] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674121)), _1674123) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674125)), _1674127), -(hAPP(hAPP(c_List_Omap(tc_prod(_1674121, _1674125), _1674125), c_Product__Type_Osnd(_1674121, _1674125)), hAPP(hAPP(c_List_Ozip(_1674121, _1674125), _1674123), _1674127)) = _1674127)], (47207 ^ _779203) ^ [_1728968, _1728970, _1728972, _1728974, _1728976] : [-(c_List_Omaps(_1728968, _1728970, _1728972, hAPP(hAPP(c_List_Olist_OCons(_1728968), _1728974), _1728976)) = hAPP(hAPP(c_List_Oappend(_1728970), hAPP(_1728972, _1728974)), c_List_Omaps(_1728968, _1728970, _1728972, _1728976)))], (44472 ^ _779203) ^ [_1669967, _1669969, _1669971, _1669973, _1669975] : [c_Fun_Oinj__on(_1669967, _1669969, _1669971, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1669967, tc_HOL_Obool)), hAPP(c_List_Oset(_1669967), _1669973)), hAPP(c_List_Oset(_1669967), _1669975))), 44475 ^ _779203 : [(44482 ^ _779203) ^ [] : [_1669973 = _1669975, -(hAPP(hAPP(c_List_Omap(_1669967, _1669969), _1669971), _1669973) = hAPP(hAPP(c_List_Omap(_1669967, _1669969), _1669971), _1669975))], (44476 ^ _779203) ^ [] : [hAPP(hAPP(c_List_Omap(_1669967, _1669969), _1669971), _1669973) = hAPP(hAPP(c_List_Omap(_1669967, _1669969), _1669971), _1669975), -(_1669973 = _1669975)]]], (38422 ^ _779203) ^ [_1520488, _1520490] : [-(hAPP(c_Relation_ORange(_1520488, _1520490), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520488, _1520490), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1520490, tc_HOL_Obool)))], (33634 ^ _779203) ^ [_1394865, _1394867, _1394869] : [33636 ^ _779203 : [(33639 ^ _779203) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1394865, _1394867), 33635 ^ [_1394865, _1394867, _1394869]))], (33637 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1394867, 33635 ^ [_1394865, _1394867, _1394869]), _1394869)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1394865, _1394867), _1394869)))], (48810 ^ _779203) ^ [_1764966, _1764968] : [c_Relation_Otrans(_1764966, _1764968), -(c_Transitive__Closure_Otrancl(_1764966, _1764968) = _1764968)], (52689 ^ _779203) ^ [_1836907, _1836909, _1836911, _1836913, _1836915, _1836917] : [-(hAPP(hAPP(hAPP(c_COMBS(_1836907, _1836909, _1836911), _1836913), _1836915), _1836917) = hAPP(hAPP(_1836913, _1836917), hAPP(_1836915, _1836917)))], (4130 ^ _779203) ^ [_841736, _841738] : [_841738 = _841736, -(c_List_Otl(_841738) = c_List_Otl(_841736))], (52229 ^ _779203) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (10245 ^ _779203) ^ [_955265, _955267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955265), _955267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955265), hAPP(c_Nat_OSuc, _955267))))], (44504 ^ _779203) ^ [_1670674, _1670676, _1670678, _1670680, _1670682, _1670684] : [-(hBOOL(hAPP(hAPP(c_member(_1670674), _1670676), hAPP(c_List_Oset(_1670674), _1670678)))), -(hAPP(hAPP(c_List_Omap(_1670674, _1670680), c_Fun_Ofun__upd(_1670674, _1670680, _1670682, _1670676, _1670684)), _1670678) = hAPP(hAPP(c_List_Omap(_1670674, _1670680), _1670682), _1670678))], (52397 ^ _779203) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (13521 ^ _779203) ^ [_1013957, _1013959] : [class_Groups_Olinordered__ab__group__add(_1013957), 13524 ^ _779203 : [(13531 ^ _779203) ^ [] : [_1013959 = c_Groups_Ozero__class_Ozero(_1013957), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013957), _1013959), _1013959) = c_Groups_Ozero__class_Ozero(_1013957))], (13525 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1013957), _1013959), _1013959) = c_Groups_Ozero__class_Ozero(_1013957), -(_1013959 = c_Groups_Ozero__class_Ozero(_1013957))]]], (4878 ^ _779203) ^ [_853470, _853472, _853474, _853476, _853478, _853480, _853482, _853484, _853486, _853488] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_853488, _853484, _853480, _853476, _853472) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_853486, _853482, _853478, _853474, _853470)), _853488 = _853486, _853484 = _853482, _853480 = _853478, _853476 = _853474, _853472 = _853470], (18234 ^ _779203) ^ [_1100812] : [-(hBOOL(hAPP(_1100812, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 18241 ^ [_1100812])))), 18235 ^ _779203 : [(18236 ^ _779203) ^ [_1100864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100864)), hBOOL(hAPP(_1100812, _1100864))]]], (33149 ^ _779203) ^ [_1386258, _1386260] : [-(_1386258 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 33152 ^ _779203 : [(33159 ^ _779203) ^ [] : [-(_1386260 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1386258, _1386260) = 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, _1386260))), 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)), _1386260)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1386258))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1386260), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1386258), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1386258, _1386260)), 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), _1386260))))), c_Divides_Opdivmod(_1386258, _1386260)))))], (33153 ^ _779203) ^ [] : [_1386260 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1386258, _1386260) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1386258))]]], (52535 ^ _779203) ^ [_1835223, _1835225] : [-(class_Nat_Osize(tc_sum(_1835223, _1835225)))], (1850 ^ _779203) ^ [_805288, _805290] : [-(class_Rings_Omult__zero(_805288)), _805290 = _805288, class_Rings_Omult__zero(_805290)], (22349 ^ _779203) ^ [_1173605] : [22350 ^ _779203 : [(22351 ^ _779203) ^ [_1173662] : [hBOOL(hAPP(_1173605, _1173662))]], 22353 ^ _779203 : [(22356 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1173605, hAPP(c_Int_Onat, 22352 ^ [_1173605]))))], (22354 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22352 ^ [_1173605])))]]], (52361 ^ _779203) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (9121 ^ _779203) ^ [_934456, _934458] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934456), hAPP(c_Nat_OSuc, _934458)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _934456), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _934458))], (40747 ^ _779203) ^ [_1578230, _1578232, _1578234] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1578232, _1578230)), _1578234)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1578230, _1578232)), hAPP(c_Relation_Oconverse(_1578232, _1578230), _1578234))))], (47369 ^ _779203) ^ [_1732823, _1732825, _1732827, _1732829, _1732831] : [47370 ^ _779203 : [(47373 ^ _779203) ^ [] : [hBOOL(hAPP(_1732831, hAPP(hAPP(c_List_Ozip(_1732823, _1732827), hAPP(hAPP(c_List_Otake(_1732823), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732823)), _1732825)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732827)), _1732829))), _1732825)), hAPP(hAPP(c_List_Otake(_1732827), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732823)), _1732825)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732827)), _1732829))), _1732829))))], (47371 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732823)), hAPP(hAPP(c_List_Otake(_1732823), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732823)), _1732825)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732827)), _1732829))), _1732825)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732827)), hAPP(hAPP(c_List_Otake(_1732827), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732823)), _1732825)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732827)), _1732829))), _1732829)))]], -(hBOOL(hAPP(_1732831, hAPP(hAPP(c_List_Ozip(_1732823, _1732827), _1732825), _1732829))))], (38790 ^ _779203) ^ [_1530440, _1530442, _1530444] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1530440, _1530442)), _1530444)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1530440), hAPP(c_Relation_ODomain(_1530440, _1530442), _1530444))))], (42059 ^ _779203) ^ [_1614758, _1614760, _1614762] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1614758), _1614760)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1614758)), hAPP(c_Set_OCollect(tc_List_Olist(_1614758)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1614758), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1614758)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614758), tc_fun(_1614758, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614758, tc_HOL_Obool), tc_fun(tc_fun(_1614758, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614758)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614758, tc_HOL_Obool))), c_List_Oset(_1614758))), _1614760))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614758), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1614758)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1614758)))), _1614762))))))], (29306 ^ _779203) ^ [_1298743, _1298745, _1298747, _1298749] : [class_Lattices_Osemilattice__inf(_1298743), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298743), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298743), _1298745), _1298747)), _1298749) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298743), _1298745), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298743), _1298747), _1298749)))], (12851 ^ _779203) ^ [_1001389, _1001391, _1001393] : [class_Rings_Olinordered__ring__strict(_1001389), 12854 ^ _779203 : [(12855 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001389), c_Groups_Ozero__class_Ozero(_1001389)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001389), _1001391), _1001391)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001389), _1001393), _1001393)))), _1001391 = c_Groups_Ozero__class_Ozero(_1001389), _1001393 = c_Groups_Ozero__class_Ozero(_1001389)], (12865 ^ _779203) ^ [] : [12866 ^ _779203 : [(12869 ^ _779203) ^ [] : [-(_1001393 = c_Groups_Ozero__class_Ozero(_1001389))], (12867 ^ _779203) ^ [] : [-(_1001391 = c_Groups_Ozero__class_Ozero(_1001389))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001389), c_Groups_Ozero__class_Ozero(_1001389)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001389), _1001391), _1001391)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001389), _1001393), _1001393)))))]]], (6789 ^ _779203) ^ [_889575, _889577, _889579, _889581, _889583] : [c_Finite__Set_Ofolding__one(_889575, _889577, _889579), hBOOL(hAPP(c_Finite__Set_Ofinite(_889575), _889581)), -(hBOOL(hAPP(hAPP(c_member(_889575), _889583), _889581))), -(hAPP(_889579, hAPP(hAPP(c_Set_Oinsert(_889575), _889583), _889581)) = hAPP(hAPP(c_Finite__Set_Ofold(_889575, _889575, _889577), _889583), _889581))], (15944 ^ _779203) ^ [_1058786, _1058788, _1058790, _1058792] : [class_Int_Onumber__ring(_1058786), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058786), hAPP(c_Int_Onumber__class_Onumber__of(_1058786), _1058788)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058786), hAPP(c_Int_Onumber__class_Onumber__of(_1058786), _1058790)), _1058792)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058786), hAPP(c_Int_Onumber__class_Onumber__of(_1058786), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1058788), _1058790))), _1058792))], (51721 ^ _779203) ^ [_1823929, _1823931, _1823933] : [class_Divides_Osemiring__div(_1823929), 51724 ^ _779203 : [(51731 ^ _779203) ^ [] : [c_Divides_Odiv__class_Omod(_1823929, _1823933, _1823931) = c_Groups_Ozero__class_Ozero(_1823929), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823929), _1823931), _1823933)))], (51725 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1823929), _1823931), _1823933)), -(c_Divides_Odiv__class_Omod(_1823929, _1823933, _1823931) = c_Groups_Ozero__class_Ozero(_1823929))]]], (19124 ^ _779203) ^ [_1116097, _1116099, _1116101] : [class_Groups_Oordered__ab__group__add__abs(_1116097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116097), hAPP(c_Groups_Oabs__class_Oabs(_1116097), _1116099)), _1116101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116097), _1116099), _1116101)))], (24976 ^ _779203) ^ [_1219474, _1219476] : [class_Groups_Omonoid__mult(_1219474), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1219474), _1219476), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1219476)], (15938 ^ _779203) ^ [_1058627, _1058629, _1058631, _1058633] : [class_Groups_Oordered__ab__group__add(_1058627), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058627), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1058627), _1058629), _1058631)), _1058633) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1058627), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058627), _1058629), _1058633)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058627), _1058631), _1058633)))], (39568 ^ _779203) ^ [_1549453, _1549455, _1549457] : [-(hAPP(c_Fun_Ocomp(_1549453, _1549455, _1549453, _1549457), c_Fun_Oid(_1549453)) = _1549457)], (52647 ^ _779203) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (19555 ^ _779203) ^ [_1124010] : [19557 ^ _779203 : [(19560 ^ _779203) ^ [_1124120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19556 ^ [_1124010, _1124120]), _1124120))], (19558 ^ _779203) ^ [_1124086] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 19556 ^ [_1124010, _1124086]), _1124010)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1124010)))], (27602 ^ _779203) ^ [_1265687, _1265689] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1265687, _1265689)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1265687, _1265689), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1265689), c_Orderings_Otop__class_Otop(tc_fun(_1265689, tc_HOL_Obool)))))], (19472 ^ _779203) ^ [_1122476, _1122478, _1122480] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122476))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1122476)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1122478)), _1122480)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1122478)), _1122480))], (46724 ^ _779203) ^ [_1718852, _1718854, _1718856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1718852), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718854)), _1718856))), -(hAPP(hAPP(c_List_Onth(_1718854), hAPP(c_List_Orev(_1718854), _1718856)), _1718852) = hAPP(hAPP(c_List_Onth(_1718854), _1718856), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718854)), _1718856)), hAPP(c_Nat_OSuc, _1718852))))], (35419 ^ _779203) ^ [_1441088, _1441090] : [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)), _1441088), 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)), _1441090), 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)), _1441088), _1441090)), c_Int_Ointrel)))], (26484 ^ _779203) ^ [_1244987, _1244989] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1244987, _1244989)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1244987), hAPP(c_Nat_OSuc, _1244989)))], (51009 ^ _779203) ^ [_1811880] : [_1811880 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811880), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (28790 ^ _779203) ^ [_1288391, _1288393, _1288395] : [class_Groups_Oordered__ab__group__add(_1288391), -(hAPP(c_Set_Oimage(_1288391, _1288391, c_Groups_Ouminus__class_Ouminus(_1288391)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1288391, _1288393), _1288395)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1288391, hAPP(c_Groups_Ouminus__class_Ouminus(_1288391), _1288395), hAPP(c_Groups_Ouminus__class_Ouminus(_1288391), _1288393)))], (31687 ^ _779203) ^ [_1348050, _1348052, _1348054, _1348056, _1348058, _1348060] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1348050, _1348052, _1348054, _1348056, c_Nitpick_Opair__box_OPairBox(_1348050, _1348052, _1348058, _1348060)) = hAPP(hAPP(_1348056, _1348058), _1348060))], (23102 ^ _779203) ^ [_1185764, _1185766] : [-(hAPP(c_Int_Onat, _1185764) = _1185766), 23105 ^ _779203 : [(23108 ^ _779203) ^ [] : [_1185764 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185766)], (23106 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185764)))]], 23109 ^ _779203 : [(23112 ^ _779203) ^ [] : [_1185766 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23110 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185764))]]], (51993 ^ _779203) ^ [_1828861, _1828863, _1828865, _1828867, _1828869] : [class_Groups_Ocomm__monoid__mult(_1828861), class_Rings_Odvd(_1828861), hBOOL(hAPP(c_Finite__Set_Ofinite(_1828863), _1828865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1828863, tc_HOL_Obool)), _1828867), _1828865)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828861), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1828863, _1828861), _1828869), _1828867)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1828863, _1828861), _1828869), _1828865))))], (12909 ^ _779203) ^ [_1002410] : [class_Rings_Olinordered__semidom(_1002410), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002410), c_Groups_Ozero__class_Ozero(_1002410)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1002410), c_Groups_Oone__class_Oone(_1002410)), c_Groups_Oone__class_Oone(_1002410)))))], (5052 ^ _779203) ^ [_856233, _856235, _856237, _856239, _856241, _856243, _856245, _856247] : [-(c_Quotient_OBabs(_856247, _856243, _856239, _856235) = c_Quotient_OBabs(_856245, _856241, _856237, _856233)), _856247 = _856245, _856243 = _856241, _856239 = _856237, _856235 = _856233], (13585 ^ _779203) ^ [_1015239, _1015241, _1015243, _1015245] : [class_Rings_Odivision__ring(_1015239), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015239), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1015239), _1015241), _1015243)), _1015245) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1015239), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015239), _1015241), _1015245)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015239), _1015243), _1015245)))], (35173 ^ _779203) ^ [_1434147, _1434149, _1434151, _1434153, _1434155, _1434157, _1434159] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1434147, tc_fun(_1434149, tc_fun(_1434151, tc_HOL_Obool))), _1434153), _1434155), _1434157), _1434159)), 35176 ^ _779203 : [(35177 ^ _779203) ^ [_1434275] : [hBOOL(hAPP(hAPP(c_member(_1434147), _1434275), _1434153)), -(hBOOL(hAPP(hAPP(hAPP(_1434155, _1434275), _1434157), _1434159)))]]], (4186 ^ _779203) ^ [_842544, _842546] : [_842546 = _842544, -(c_List_Onth(_842546) = c_List_Onth(_842544))], (41286 ^ _779203) ^ [_1592441, _1592443, _1592445] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592441), c_Nitpick_Oplus__frac(_1592441, _1592443, c_Nitpick_Ouminus__frac(_1592441, _1592445)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1592441, _1592443, _1592445))], (46722 ^ _779203) ^ [_1718779, _1718781, _1718783] : [-(hAPP(c_List_Orotate(_1718779, _1718781), hAPP(c_List_Orev(_1718779), _1718783)) = hAPP(c_List_Orev(_1718779), hAPP(c_List_Orotate(_1718779, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718779)), _1718783)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1718781, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718779)), _1718783)))), _1718783)))], (2354 ^ _779203) ^ [_813616, _813618] : [_813618 = _813616, -(c_Nat_Onat_Onat__size(_813618) = c_Nat_Onat_Onat__size(_813616))], (24470 ^ _779203) ^ [_1210208, _1210210] : [class_Rings_Oring__1(_1210208), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1210208), hAPP(c_Groups_Ouminus__class_Ouminus(_1210208), _1210210)), 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(_1210208), _1210210), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (2468 ^ _779203) ^ [_815415, _815417, _815419, _815421] : [-(c_Nitpick_Onumber__of__frac(_815421, _815417) = c_Nitpick_Onumber__of__frac(_815419, _815415)), _815421 = _815419, _815417 = _815415], (39297 ^ _779203) ^ [_1542636, _1542638, _1542640, _1542642] : [39299 ^ _779203 : [(39302 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1542636, _1542636, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1542636, tc_fun(_1542636, _1542638), tc_fun(_1542636, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542638, tc_HOL_Obool), tc_fun(tc_fun(_1542636, _1542638), tc_fun(_1542636, tc_HOL_Obool)), _1542636), c_COMBB(_1542638, tc_HOL_Obool, _1542636)), hAPP(hAPP(c_COMBB(_1542638, tc_fun(_1542638, tc_HOL_Obool), _1542636), c_fequal), _1542642))), _1542642)), 39298 ^ [_1542636, _1542638, _1542640, _1542642]))], (39300 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542636, _1542636)), 39298 ^ [_1542636, _1542638, _1542640, _1542642]), _1542640)))]], -(c_Equiv__Relations_Ocongruent(_1542636, _1542638, _1542640, _1542642))], (8322 ^ _779203) ^ [_917877, _917879, _917881] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_917877), _917879)), hBOOL(hAPP(hAPP(c_member(_917877), _917881), _917879)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_917877), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917877, tc_HOL_Obool)), _917879), hAPP(hAPP(c_Set_Oinsert(_917877), _917881), c_Orderings_Obot__class_Obot(tc_fun(_917877, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_917877), _917879))))], (6867 ^ _779203) ^ [_891225, _891227, _891229] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891225, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891225, tc_HOL_Obool)), _891227), _891229)), _891229) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891225, tc_HOL_Obool)), _891227), _891229))], (43993 ^ _779203) ^ [_1659614, _1659616, _1659618] : [43994 ^ _779203 : [(43995 ^ _779203) ^ [_1659703, _1659705] : [_1659616 = hAPP(hAPP(c_List_Olist_OCons(_1659614), _1659705), _1659703)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659614), tc_List_Olist(_1659614))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659614), tc_List_Olist(_1659614)), c_List_Olist_ONil(_1659614)), _1659616)), c_List_Olexord(_1659614, _1659618))))], (49280 ^ _779203) ^ [_1775843, _1775845] : [-(c_Relation_Osym(_1775843, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1775843, _1775843), tc_HOL_Obool)), _1775845), hAPP(c_Relation_Oconverse(_1775843, _1775843), _1775845))))], (18806 ^ _779203) ^ [_1110609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110609), 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), _1110609)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10605 ^ _779203) ^ [_962789, _962791, _962793, _962795, _962797, _962799, _962801] : [c_Big__Operators_Ocomm__monoid__big(_962789, _962791, _962793, _962795, _962797), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_962791), _962799))), -(hAPP(hAPP(_962797, _962801), _962799) = _962795)], (21543 ^ _779203) ^ [_1158488] : [c_Int_OPls = _1158488, -(c_Int_OPls = c_Int_OBit0(_1158488))], (40436 ^ _779203) ^ [_1570825, _1570827] : [-(hAPP(c_Relation_ODomain(_1570825, _1570825), c_Transitive__Closure_Ortrancl(_1570825, _1570827)) = c_Orderings_Otop__class_Otop(tc_fun(_1570825, tc_HOL_Obool)))], (49366 ^ _779203) ^ [_1777179, _1777181, _1777183] : [c_Relation_Orefl__on(_1777179, _1777181, _1777183), c_Relation_Osym(_1777179, _1777183), c_Relation_Otrans(_1777179, _1777183), -(c_Equiv__Relations_Oequiv(_1777179, _1777181, _1777183))], (7671 ^ _779203) ^ [_905731, _905733, _905735] : [class_Orderings_Olinorder(_905731), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905731), _905733), _905735))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905731), _905735), _905733)))], (9361 ^ _779203) ^ [_938834, _938836, _938838, _938840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938834), _938836)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938838), _938836) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938834), _938840), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938838), _938840)))], (39413 ^ _779203) ^ [_1545962, _1545964, _1545966, _1545968, _1545970] : [c_Fun_Oinj__on(_1545962, _1545964, _1545966, c_Orderings_Otop__class_Otop(tc_fun(_1545962, tc_HOL_Obool))), c_Fun_Oinj__on(_1545968, _1545962, _1545970, c_Orderings_Otop__class_Otop(tc_fun(_1545968, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1545968, _1545964, hAPP(c_Fun_Ocomp(_1545962, _1545964, _1545968, _1545966), _1545970), c_Orderings_Otop__class_Otop(tc_fun(_1545968, tc_HOL_Obool))))], (20274 ^ _779203) ^ [_1136812, _1136814, _1136816] : [class_Groups_Ogroup__add(_1136812), 20277 ^ _779203 : [(20284 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136812), _1136814), _1136816) = c_Groups_Ozero__class_Ozero(_1136812), -(_1136814 = hAPP(c_Groups_Ouminus__class_Ouminus(_1136812), _1136816))], (20278 ^ _779203) ^ [] : [_1136814 = hAPP(c_Groups_Ouminus__class_Ouminus(_1136812), _1136816), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136812), _1136814), _1136816) = c_Groups_Ozero__class_Ozero(_1136812))]]], (46070 ^ _779203) ^ [_1706337, _1706339] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1706337, _1706339)))], (43349 ^ _779203) ^ [_1644649, _1644651, _1644653, _1644655] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644649), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644651)), _1644653)))), -(hAPP(hAPP(c_List_Onth(_1644651), hAPP(hAPP(c_List_Oappend(_1644651), _1644653), _1644655)), _1644649) = hAPP(hAPP(c_List_Onth(_1644651), _1644655), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644649), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644651)), _1644653))))], (5809 ^ _779203) ^ [_871124, _871126, _871128] : [hBOOL(hAPP(_871128, _871126)), -(hBOOL(hAPP(hAPP(c_member(_871124), _871126), _871128)))], (30431 ^ _779203) ^ [_1322296, _1322298, _1322300] : [class_Orderings_Olinorder(_1322296), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322296), _1322298)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322296), _1322300)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322296, tc_HOL_Obool)), _1322298), _1322300) = c_Orderings_Obot__class_Obot(tc_fun(_1322296, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322296), c_Big__Operators_Olinorder__class_OMax(_1322296, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322296, tc_HOL_Obool)), _1322298), _1322300))), c_Big__Operators_Olinorder__class_OMax(_1322296, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322296, tc_HOL_Obool)), _1322298), _1322300))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322296), c_Big__Operators_Olinorder__class_OMax(_1322296, _1322298)), c_Big__Operators_Olinorder__class_OMax(_1322296, _1322300)))], (15962 ^ _779203) ^ [_1059225, _1059227, _1059229, _1059231] : [class_Int_Onumber__ring(_1059225), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059225), hAPP(c_Int_Onumber__class_Onumber__of(_1059225), _1059227)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059225), hAPP(c_Int_Onumber__class_Onumber__of(_1059225), _1059229)), _1059231)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059225), hAPP(c_Int_Onumber__class_Onumber__of(_1059225), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1059227), _1059229))), _1059231))], (52617 ^ _779203) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (39920 ^ _779203) ^ [_1557485, _1557487, _1557489, _1557491, _1557493, _1557495, _1557497] : [c_Finite__Set_Ofolding__idem(_1557485, _1557487, _1557489, _1557491), -(hAPP(c_Fun_Ocomp(_1557487, _1557487, _1557493, hAPP(_1557489, _1557495)), hAPP(c_Fun_Ocomp(_1557487, _1557487, _1557493, hAPP(_1557489, _1557495)), _1557497)) = hAPP(c_Fun_Ocomp(_1557487, _1557487, _1557493, hAPP(_1557489, _1557495)), _1557497))], (31207 ^ _779203) ^ [_1337943, _1337945, _1337947, _1337949] : [class_Groups_Ocomm__monoid__add(_1337943), 31210 ^ _779203 : [(31217 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1337945), _1337947))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1337945, _1337943), _1337949), _1337947) = c_Groups_Ozero__class_Ozero(_1337943))], (31211 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1337945), _1337947)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1337945, _1337943), _1337949), _1337947) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1337943, _1337945, c_Groups_Oplus__class_Oplus(_1337943)), _1337949), c_Groups_Ozero__class_Ozero(_1337943)), _1337947))]]], (19972 ^ _779203) ^ [_1131236, _1131238, _1131240] : [class_Groups_Oab__group__add(_1131236), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1131236), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131236), _1131238), _1131240)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131236), hAPP(c_Groups_Ouminus__class_Ouminus(_1131236), _1131238)), hAPP(c_Groups_Ouminus__class_Ouminus(_1131236), _1131240)))], (9612 ^ _779203) ^ [_943400, _943402] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943402), hAPP(c_Nat_OSuc, _943400))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943400), _943402))], (49696 ^ _779203) ^ [_1783647, _1783649, _1783651] : [hAPP(_1783651, hAPP(c_Hilbert__Choice_Oinv__into(_1783647, _1783649, c_Orderings_Otop__class_Otop(tc_fun(_1783647, tc_HOL_Obool)), _1783651), 49697 ^ [_1783647, _1783649, _1783651])) = 49697 ^ [_1783647, _1783649, _1783651], -(hAPP(c_Set_Oimage(_1783647, _1783649, _1783651), c_Orderings_Otop__class_Otop(tc_fun(_1783647, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1783649, tc_HOL_Obool)))], (38310 ^ _779203) ^ [_1516784, _1516786, _1516788, _1516790, _1516792, _1516794] : [-(c_Product__Type_Omap__pair(_1516784, _1516786, _1516788, _1516790, _1516792, _1516794) = hAPP(c_Product__Type_Oprod_Oprod__case(_1516784, _1516788, tc_prod(_1516786, _1516790)), hAPP(hAPP(c_COMBC(_1516784, tc_fun(_1516788, _1516790), tc_fun(_1516788, tc_prod(_1516786, _1516790))), hAPP(hAPP(c_COMBB(tc_fun(_1516790, tc_prod(_1516786, _1516790)), tc_fun(tc_fun(_1516788, _1516790), tc_fun(_1516788, tc_prod(_1516786, _1516790))), _1516784), c_COMBB(_1516790, tc_prod(_1516786, _1516790), _1516788)), hAPP(hAPP(c_COMBB(_1516786, tc_fun(_1516790, tc_prod(_1516786, _1516790)), _1516784), c_Product__Type_OPair(_1516786, _1516790)), _1516792))), _1516794)))], (6573 ^ _779203) ^ [_885213, _885215, _885217, _885219] : [class_Orderings_Oorder(_885213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885213), _885215), _885217)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885213), _885219), _885215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885213), _885219), _885217)))], (24362 ^ _779203) ^ [_1208532, _1208534] : [c_Nat__Transfer_Onat__set(_1208532), c_Nat__Transfer_Onat__set(_1208534), 24369 ^ _779203 : [(24376 ^ _779203) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1208532) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1208534), -(_1208532 = _1208534)], (24370 ^ _779203) ^ [] : [_1208532 = _1208534, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1208532) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1208534))]]], (13729 ^ _779203) ^ [_1017606, _1017608, _1017610, _1017612] : [class_Fields_Olinordered__field(_1017606), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017606), _1017608), _1017610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017606), c_Groups_Ozero__class_Ozero(_1017606)), _1017612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017606), c_Groups_Ozero__class_Ozero(_1017606)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017606), _1017610), _1017608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017606), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017606), _1017612), _1017610)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017606), _1017612), _1017608))))], (46686 ^ _779203) ^ [_1718007, _1718009, _1718011, _1718013, _1718015] : [-(c_List_Ofoldr(_1718007, _1718009, _1718011, _1718013, _1718015) = hAPP(c_List_Ofoldl(_1718009, _1718007, hAPP(c_COMBC(_1718007, _1718009, _1718009), _1718011), _1718015), hAPP(c_List_Orev(_1718007), _1718013)))], (37031 ^ _779203) ^ [_1477626, _1477628, _1477630] : [hBOOL(hAPP(hAPP(c_member(_1477626), _1477628), c_Wellfounded_Oacc(_1477626, _1477630))), 37034 ^ _779203 : [(37035 ^ _779203) ^ [_1477740] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1477626, _1477626)), hAPP(hAPP(c_Product__Type_OPair(_1477626, _1477626), _1477740), _1477628)), _1477630)), -(hBOOL(hAPP(hAPP(c_member(_1477626), _1477740), c_Wellfounded_Oacc(_1477626, _1477630))))]]], (42185 ^ _779203) ^ [_1619462, _1619464] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619462, _1619464)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1619462, _1619464))], (8765 ^ _779203) ^ [_927073, _927075, _927077, _927079] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_927073), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927073), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927073), _927075), _927077)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927073), _927079), _927077))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927073), _927075), _927079)))], (38798 ^ _779203) ^ [_1530590, _1530592, _1530594, _1530596, _1530598] : [c_Relation_Orefl__on(_1530590, _1530592, _1530594), c_Relation_Orefl__on(_1530590, _1530596, _1530598), -(c_Relation_Orefl__on(_1530590, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1530590, tc_HOL_Obool)), _1530592), _1530596), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530590, _1530590), tc_HOL_Obool)), _1530594), _1530598)))], (2554 ^ _779203) ^ [_816770, _816772, _816774, _816776, _816778, _816780] : [-(c_Partial__Function_Oflat__lub(_816780, _816776, _816772) = c_Partial__Function_Oflat__lub(_816778, _816774, _816770)), _816780 = _816778, _816776 = _816774, _816772 = _816770], (25534 ^ _779203) ^ [_1229101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1229101), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1229101)), c_Int_OMin)))], (35111 ^ _779203) ^ [_1432340, _1432342, _1432344, _1432346] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1432340), _1432342)), 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)), _1432344), _1432340)), 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)), _1432346), _1432342)), 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)), _1432344), _1432346)), _1432342)), c_FunDef_Omax__strict)))], (6651 ^ _779203) ^ [_886630, _886632, _886634, _886636, _886638] : [c_Finite__Set_Ofolding__one__idem(_886630, _886632, _886634), hAPP(_886636, hAPP(hAPP(_886632, 6656 ^ [_886630, _886632, _886634, _886636, _886638]), 6657 ^ [_886630, _886632, _886634, _886636, _886638])) = hAPP(hAPP(_886632, hAPP(_886636, 6656 ^ [_886630, _886632, _886634, _886636, _886638])), hAPP(_886636, 6657 ^ [_886630, _886632, _886634, _886636, _886638])), hBOOL(hAPP(c_Finite__Set_Ofinite(_886630), _886638)), -(_886638 = c_Orderings_Obot__class_Obot(tc_fun(_886630, tc_HOL_Obool))), -(hAPP(_886636, hAPP(_886634, _886638)) = hAPP(_886634, hAPP(c_Set_Oimage(_886630, _886630, _886636), _886638)))], (44109 ^ _779203) ^ [_1661976, _1661978, _1661980, _1661982, _1661984] : [class_Orderings_Olinorder(_1661976), hBOOL(hAPP(c_List_Odistinct(_1661978), _1661980)), -(hBOOL(hAPP(c_List_Odistinct(_1661978), c_List_Olinorder__class_Oinsort__insert__key(_1661978, _1661976, _1661982, _1661984, _1661980))))], (43808 ^ _779203) ^ [_1655600, _1655602, _1655604] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655600, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655602)), _1655604)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1655602, _1655600), _1655604) = _1655604)], (41927 ^ _779203) ^ [_1611641, _1611643, _1611645, _1611647] : [hBOOL(hAPP(hAPP(c_member(_1611641), _1611643), hAPP(c_List_Oset(_1611641), hAPP(hAPP(c_List_Otake(_1611641), _1611645), _1611647)))), -(hBOOL(hAPP(hAPP(c_member(_1611641), _1611643), hAPP(c_List_Oset(_1611641), _1611647))))], (24390 ^ _779203) ^ [_1208973, _1208975] : [_1208973 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1208975), _1208973) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (3690 ^ _779203) ^ [_834480, _834482, _834484, _834486] : [-(c_List_Omeasures(_834486, _834482) = c_List_Omeasures(_834484, _834480)), _834486 = _834484, _834482 = _834480], (48652 ^ _779203) ^ [_1761044, _1761046, _1761048, _1761050] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1761044, _1761046, _1761048, _1761050, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1761046)) = _1761048)], (37173 ^ _779203) ^ [_1480999, _1481001, _1481003, _1481005, _1481007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480999, tc_HOL_Obool)), _1481001), _1481003)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1481005, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1481005, _1480999, _1481007), _1481001)), hAPP(c_Set_Ovimage(_1481005, _1480999, _1481007), _1481003))))], (13317 ^ _779203) ^ [_1009890, _1009892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1009890), _1009892))), 13320 ^ _779203 : [(13323 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1009890), _1009892)))], (13321 ^ _779203) ^ [] : [_1009892 = c_Orderings_Obot__class_Obot(tc_fun(_1009890, tc_HOL_Obool))]]], (22626 ^ _779203) ^ [_1178109, _1178111] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1178109), _1178111) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22627 ^ _779203 : [(22636 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178109), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178111), _1178109))], (22630 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178109)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178109), _1178111))], (22628 ^ _779203) ^ [] : [_1178111 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (33863 ^ _779203) ^ [_1399527, _1399529, _1399531] : [-(hAPP(hAPP(c_Product__Type_OPair(_1399527, _1399529), hAPP(c_Product__Type_Ofst(_1399527, _1399529), _1399531)), hAPP(c_Product__Type_Osnd(_1399527, _1399529), _1399531)) = _1399531)], (45256 ^ _779203) ^ [_1687329, _1687331] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1687329), tc_fun(_1687329, tc_HOL_Obool), c_List_Oset(_1687329)), hAPP(c_List_Oset(tc_List_Olist(_1687329)), c_Enum_Osublists(_1687329, _1687331))) = hAPP(c_Set_OPow(_1687329), hAPP(c_List_Oset(_1687329), _1687331)))], (45719 ^ _779203) ^ [_1697937, _1697939, _1697941] : [45721 ^ _779203 : [(45724 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1697939, 45720 ^ [_1697937, _1697939, _1697941])))], (45722 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1697937), 45720 ^ [_1697937, _1697939, _1697941]), hAPP(c_List_Oset(_1697937), _1697941))))]], -(hAPP(c_List_Ofilter(_1697937, _1697939), _1697941) = c_List_Olist_ONil(_1697937))], (32193 ^ _779203) ^ [_1361120, _1361122, _1361124] : [class_Groups_Ocomm__monoid__add(_1361120), class_Groups_Ocomm__monoid__mult(_1361120), c_Nat__Transfer_Onat__set(_1361122), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1361120), _1361124), _1361122) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1361120), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1361120, tc_Nat_Onat), _1361124), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1361122)))], (33495 ^ _779203) ^ [_1392181, _1392183] : [-(c_Divides_Odivmod__int__rel(_1392181, _1392183) = 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, _1392181))), 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), _1392183)))))), 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)), _1392183))), 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)), _1392183))))), 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)), _1392183)))), 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), _1392183))), 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))))))))], (17688 ^ _779203) ^ [_1090950, _1090952, _1090954] : [class_Orderings_Olinorder(_1090950), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090950), _1090952)), hBOOL(hAPP(hAPP(c_member(_1090950), _1090954), _1090952)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090950), _1090954), c_Big__Operators_Olattice_OSup__fin(_1090950, c_Orderings_Oord__class_Omax(_1090950), _1090952)) = _1090954)], (52665 ^ _779203) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (25286 ^ _779203) ^ [_1225099, _1225101, _1225103] : [class_Rings_Olinordered__idom(_1225099), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225099), c_Groups_Ozero__class_Ozero(_1225099)), hAPP(hAPP(c_Power_Opower__class_Opower(_1225099), hAPP(c_Groups_Oabs__class_Oabs(_1225099), _1225101)), _1225103))))], (25516 ^ _779203) ^ [_1228822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1228822))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1228822)))], (18070 ^ _779203) ^ [_1097980, _1097982, _1097984] : [class_Orderings_Olinorder(_1097980), hAPP(_1097982, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1097980), 18075 ^ [_1097980, _1097982, _1097984]), 18076 ^ [_1097980, _1097982, _1097984])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1097980), hAPP(_1097982, 18075 ^ [_1097980, _1097982, _1097984])), hAPP(_1097982, 18076 ^ [_1097980, _1097982, _1097984])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097980), _1097984)), -(_1097984 = c_Orderings_Obot__class_Obot(tc_fun(_1097980, tc_HOL_Obool))), -(hAPP(_1097982, c_Big__Operators_Olattice_OInf__fin(_1097980, c_Orderings_Oord__class_Omin(_1097980), _1097984)) = c_Big__Operators_Olattice_OInf__fin(_1097980, c_Orderings_Oord__class_Omin(_1097980), hAPP(c_Set_Oimage(_1097980, _1097980, _1097982), _1097984)))], (26572 ^ _779203) ^ [_1246829, _1246831, _1246833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246829)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1246831), _1246833)), 26579 ^ _779203 : [(26580 ^ _779203) ^ [_1247019] : [26582 ^ _779203 : [(26588 ^ _779203) ^ [] : [-(_1247019 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26584 ^ [_1246829, _1246831, _1246833, _1247019]), 26581 ^ [_1246829, _1246831, _1246833, _1247019]))], (26586 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26584 ^ [_1246829, _1246831, _1246833, _1247019]), _1246833)))], (26583 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26581 ^ [_1246829, _1246831, _1246833, _1247019]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1246829))))]], -(_1247019 = _1246831), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1247019), _1246829) = _1246831]]], (10085 ^ _779203) ^ [_951693, _951695, _951697, _951699, _951701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951693), _951695)), 10088 ^ _779203 : [(10095 ^ _779203) ^ [] : [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), _951695), _951693)), _951697)), _951699)), _951701)), -(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), _951695), _951697)), _951699)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951693), _951697)), _951701))))], (10089 ^ _779203) ^ [] : [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), _951695), _951697)), _951699)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _951693), _951697)), _951701))), -(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), _951695), _951693)), _951697)), _951699)), _951701)))]]], (11582 ^ _779203) ^ [_978939, _978941, _978943] : [class_Rings_Oordered__cancel__semiring(_978939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978939), c_Groups_Ozero__class_Ozero(_978939)), _978941)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978939), c_Groups_Ozero__class_Ozero(_978939)), _978943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978939), c_Groups_Ozero__class_Ozero(_978939)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978939), _978941), _978943))))], (13079 ^ _779203) ^ [_1005473, _1005475, _1005477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005473), _1005475)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005477), _1005475))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005473), _1005477)))], (16162 ^ _779203) ^ [_1063035, _1063037, _1063039, _1063041] : [class_Fields_Ofield__inverse__zero(_1063035), class_Int_Onumber(_1063035), 16169 ^ _779203 : [(16170 ^ _779203) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1063035), _1063037), _1063039) = hAPP(c_Int_Onumber__class_Onumber__of(_1063035), _1063041), 16173 ^ _779203 : [(16180 ^ _779203) ^ [] : [_1063039 = c_Groups_Ozero__class_Ozero(_1063035), -(hAPP(c_Int_Onumber__class_Onumber__of(_1063035), _1063041) = c_Groups_Ozero__class_Ozero(_1063035))], (16174 ^ _779203) ^ [] : [-(_1063039 = c_Groups_Ozero__class_Ozero(_1063035)), -(_1063037 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063035), hAPP(c_Int_Onumber__class_Onumber__of(_1063035), _1063041)), _1063039))]]], (16186 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1063035), _1063037), _1063039) = hAPP(c_Int_Onumber__class_Onumber__of(_1063035), _1063041)), 16189 ^ _779203 : [(16192 ^ _779203) ^ [] : [_1063037 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063035), hAPP(c_Int_Onumber__class_Onumber__of(_1063035), _1063041)), _1063039)], (16190 ^ _779203) ^ [] : [_1063039 = c_Groups_Ozero__class_Ozero(_1063035)]], 16193 ^ _779203 : [(16196 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1063035), _1063041) = c_Groups_Ozero__class_Ozero(_1063035)], (16194 ^ _779203) ^ [] : [-(_1063039 = c_Groups_Ozero__class_Ozero(_1063035))]]]]], (44229 ^ _779203) ^ [_1663890, _1663892, _1663894, _1663896] : [hAPP(hAPP(c_List_Oappend(_1663890), _1663892), hAPP(hAPP(c_List_Olist_OCons(_1663890), _1663894), c_List_Olist_ONil(_1663890))) = _1663896, 44232 ^ _779203 : [(44237 ^ _779203) ^ [] : [-(c_List_Olast(_1663890, _1663896) = _1663894)], (44235 ^ _779203) ^ [] : [-(c_List_Obutlast(_1663890, _1663896) = _1663892)], (44233 ^ _779203) ^ [] : [_1663896 = c_List_Olist_ONil(_1663890)]]], (51031 ^ _779203) ^ [_1812235, _1812237, _1812239] : [class_Rings_Ocomm__ring__1(_1812235), 51034 ^ _779203 : [(51041 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812235), _1812237), _1812239)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812235), hAPP(c_Groups_Ouminus__class_Ouminus(_1812235), _1812237)), _1812239)))], (51035 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812235), hAPP(c_Groups_Ouminus__class_Ouminus(_1812235), _1812237)), _1812239)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812235), _1812237), _1812239)))]]], (40841 ^ _779203) ^ [_1580505, _1580507] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1580505, _1580505)), _1580507)), c_Wellfounded_Oacyclic(_1580505, _1580507), -(c_Wellfounded_Owf(_1580505, hAPP(c_Relation_Oconverse(_1580505, _1580505), _1580507)))], (10625 ^ _779203) ^ [_963112, _963114, _963116] : [class_Orderings_Olinorder(_963112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_963112, tc_HOL_Obool)), _963114), _963116)), -(_963114 = c_Orderings_Obot__class_Obot(tc_fun(_963112, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_963112), _963116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963112), c_Big__Operators_Olinorder__class_OMax(_963112, _963114)), c_Big__Operators_Olinorder__class_OMax(_963112, _963116))))], (45683 ^ _779203) ^ [_1697133, _1697135, _1697137] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1697133), tc_List_Olist(_1697133)), c_List_Opartition(_1697133, _1697135, _1697137)) = hAPP(c_List_Ofilter(_1697133, _1697135), _1697137))], (3184 ^ _779203) ^ [_826591, _826593, _826595, _826597, _826599, _826601, _826603, _826605] : [-(c_Nitpick_Osetsum_H(_826605, _826601, _826597, _826593) = c_Nitpick_Osetsum_H(_826603, _826599, _826595, _826591)), _826605 = _826603, _826601 = _826599, _826597 = _826595, _826593 = _826591], (33423 ^ _779203) ^ [_1390750, _1390752] : [-(_1390750 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390752, _1390750), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1390752), _1390750)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390752, _1390750)))))], (41319 ^ _779203) ^ [_1593070, _1593072] : [-(c_List_Olenlex(_1593070, _1593072) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1593070)), tc_List_Olist(_1593070)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1593070), c_Wellfounded_Oless__than, c_List_Olex(_1593070, _1593072))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1593070), tc_List_Olist(_1593070), tc_prod(tc_Nat_Onat, tc_List_Olist(_1593070))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1593070), tc_prod(tc_Nat_Onat, tc_List_Olist(_1593070))), tc_List_Olist(_1593070)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1593070))), c_Nat_Osize__class_Osize(tc_List_Olist(_1593070)))), c_COMBI(tc_List_Olist(_1593070)))))], (8949 ^ _779203) ^ [_930610, _930612, _930614, _930616, _930618] : [class_Groups_Oab__semigroup__mult(_930610), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_930610, _930610, c_Groups_Otimes__class_Otimes(_930610), _930612, _930614), _930616)), -(hBOOL(hAPP(hAPP(c_member(_930610), _930612), _930614))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_930610, _930610, c_Groups_Otimes__class_Otimes(_930610), _930618, hAPP(hAPP(c_Set_Oinsert(_930610), _930612), _930614)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_930610), _930618), _930616))))], (48050 ^ _779203) ^ [_1747689, _1747691, _1747693, _1747695] : [-(c_New__Random__Sequence_Opos__map(_1747689, _1747691, _1747693, _1747695) = c_New__Random__Sequence_Opos__bind(_1747689, _1747691, _1747695, hAPP(c_Fun_Ocomp(_1747691, 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(_1747691))))), _1747689, c_New__Random__Sequence_Opos__single(_1747691)), _1747693)))], (49050 ^ _779203) ^ [_1771262, _1771264] : [-(c_Equiv__Relations_Oequivp(_1771262, _1771264)), c_Predicate_Oreflp(_1771262, _1771264), c_Predicate_Osymp(_1771262, _1771264), c_Predicate_Otransp(_1771262, _1771264)], (42065 ^ _779203) ^ [_1615061, _1615063, _1615065] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1615061), _1615063)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1615061)), hAPP(c_Set_OCollect(tc_List_Olist(_1615061)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1615061), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1615061)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1615061), tc_fun(_1615061, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1615061, tc_HOL_Obool), tc_fun(tc_fun(_1615061, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1615061)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1615061, tc_HOL_Obool))), c_List_Oset(_1615061))), _1615063))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1615061), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1615061)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1615061)))), _1615065))))))], (44590 ^ _779203) ^ [_1672584, _1672586, _1672588, _1672590] : [class_Groups_Ocomm__monoid__add(_1672584), 44593 ^ _779203 : [(44600 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1672586), _1672588))), -(c_Nitpick_Osetsum_H(_1672586, _1672584, _1672590, _1672588) = c_Groups_Ozero__class_Ozero(_1672584))], (44594 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1672586), _1672588)), -(c_Nitpick_Osetsum_H(_1672586, _1672584, _1672590, _1672588) = hAPP(c_List_Omonoid__add__class_Olistsum(_1672584), hAPP(hAPP(c_List_Omap(_1672586, _1672584), _1672590), c_Hilbert__Choice_OEps(tc_List_Olist(_1672586), hAPP(hAPP(c_COMBS(tc_List_Olist(_1672586), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1672586)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1672586), tc_fun(_1672586, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1672586, tc_HOL_Obool), tc_fun(tc_fun(_1672586, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1672586)), c_fequal), c_List_Oset(_1672586))), _1672588))), c_List_Odistinct(_1672586))))))]]], (11035 ^ _779203) ^ [_969413] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _969413)))], (43161 ^ _779203) ^ [_1640604, _1640606, _1640608] : [hAPP(hAPP(c_List_Oappend(_1640604), _1640606), _1640608) = _1640608, -(_1640606 = c_List_Olist_ONil(_1640604))], (22442 ^ _779203) ^ [_1175043] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1175043))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1175043)) = _1175043)], (26296 ^ _779203) ^ [_1241630, _1241632] : [class_Orderings_Oorder(_1241630), -(c_SetInterval_Oord__class_OatLeastAtMost(_1241630, _1241632, _1241632) = hAPP(hAPP(c_Set_Oinsert(_1241630), _1241632), c_Orderings_Obot__class_Obot(tc_fun(_1241630, tc_HOL_Obool))))], (32349 ^ _779203) ^ [_1364634, _1364636] : [class_Rings_Ocomm__semiring__1(_1364634), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364634), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364634), c_Groups_Oone__class_Oone(_1364634)), c_Groups_Oone__class_Oone(_1364634))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1364634), c_Nat_Osemiring__1__class_Oof__nat(_1364634)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1364636))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364634), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1364634), _1364636)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364634), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1364634), _1364636)), c_Groups_Oone__class_Oone(_1364634))))], (19134 ^ _779203) ^ [_1116266, _1116268] : [class_Groups_Oordered__ab__group__add__abs(_1116266), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1116266), _1116268), hAPP(c_Groups_Oabs__class_Oabs(_1116266), _1116268))))], (20640 ^ _779203) ^ [_1143302, _1143304, _1143306, _1143308] : [hBOOL(hAPP(hAPP(c_member(_1143302), _1143304), c_SetInterval_Oord_OatLeast(_1143302, _1143306, _1143308))), -(hBOOL(hAPP(hAPP(_1143306, _1143308), _1143304)))], (39479 ^ _779203) ^ [_1547397, _1547399] : [hBOOL(hAPP(_1547397, c_Hilbert__Choice_OEps(_1547399, _1547397))), -(hBOOL(hAPP(_1547397, 39482 ^ [_1547397, _1547399])))], (37205 ^ _779203) ^ [_1481847, _1481849, _1481851, _1481853, _1481855] : [hBOOL(hAPP(hAPP(c_member(_1481847), hAPP(_1481849, _1481851)), _1481853)), -(hBOOL(hAPP(hAPP(c_member(_1481855), _1481851), hAPP(c_Set_Ovimage(_1481855, _1481847, _1481849), _1481853))))], (35612 ^ _779203) ^ [_1446269, _1446271, _1446273, _1446275, _1446277] : [hBOOL(hAPP(hAPP(c_member(_1446269), _1446271), hAPP(c_Relation_OImage(_1446273, _1446269, _1446275), _1446277))), 35616 ^ _779203 : [(35619 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1446273), 35615 ^ [_1446269, _1446271, _1446273, _1446275, _1446277]), _1446277)))], (35617 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1446273, _1446269)), hAPP(hAPP(c_Product__Type_OPair(_1446273, _1446269), 35615 ^ [_1446269, _1446271, _1446273, _1446275, _1446277]), _1446271)), _1446275)))]]], (14995 ^ _779203) ^ [_1041247, _1041249, _1041251] : [class_Rings_Oring__1(_1041247), hBOOL(hAPP(hAPP(c_member(_1041247), _1041249), c_Int_Oring__1__class_OInts(_1041247))), hBOOL(hAPP(hAPP(c_member(_1041247), _1041251), c_Int_Oring__1__class_OInts(_1041247))), -(hBOOL(hAPP(hAPP(c_member(_1041247), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1041247), _1041249), _1041251)), c_Int_Oring__1__class_OInts(_1041247))))], (49180 ^ _779203) ^ [_1773443, _1773445, _1773447, _1773449] : [c_Relation_Oantisym(_1773443, _1773445), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773443, _1773443)), hAPP(hAPP(c_Product__Type_OPair(_1773443, _1773443), _1773447), _1773449)), _1773445)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773443, _1773443)), hAPP(hAPP(c_Product__Type_OPair(_1773443, _1773443), _1773449), _1773447)), _1773445)), -(_1773447 = _1773449)], (39049 ^ _779203) ^ [_1536511, _1536513, _1536515, _1536517] : [hBOOL(hAPP(hAPP(c_member(_1536511), _1536513), hAPP(c_Relation_ODomain(_1536511, _1536515), _1536517))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1536511, _1536515)), hAPP(hAPP(c_Product__Type_OPair(_1536511, _1536515), _1536513), 39052 ^ [_1536511, _1536513, _1536515, _1536517])), _1536517)))], (44986 ^ _779203) ^ [_1681179, _1681181, _1681183, _1681185] : [-(hBOOL(hAPP(c_List_Olistsp(_1681179, _1681181), hAPP(hAPP(c_List_Oappend(_1681179), _1681183), _1681185)))), hBOOL(hAPP(c_List_Olistsp(_1681179, _1681181), _1681183)), hBOOL(hAPP(c_List_Olistsp(_1681179, _1681181), _1681185))], (29750 ^ _779203) ^ [_1307490, _1307492, _1307494, _1307496, _1307498] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307490, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1307492, _1307490, _1307494), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307492, tc_HOL_Obool)), _1307496), _1307498))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307490, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1307492, _1307490, _1307494), _1307496)), hAPP(c_Set_Oimage(_1307492, _1307490, _1307494), _1307498)))))], (27920 ^ _779203) ^ [_1271955, _1271957, _1271959] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271955, tc_HOL_Obool)), _1271957), _1271959) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271955, tc_HOL_Obool)), _1271959), _1271957))], (48824 ^ _779203) ^ [_1765176, _1765178] : [c_Relation_Otrans(_1765176, hAPP(c_Relation_Oconverse(_1765176, _1765176), _1765178)), -(c_Relation_Otrans(_1765176, _1765178))], (12535 ^ _779203) ^ [_995367, _995369, _995371] : [class_Groups_Oordered__comm__monoid__add(_995367), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995367), c_Groups_Ozero__class_Ozero(_995367)), _995369)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995367), c_Groups_Ozero__class_Ozero(_995367)), _995371)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995367), c_Groups_Ozero__class_Ozero(_995367)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995367), _995369), _995371))))], (1210 ^ _779203) ^ [_797288, _797290] : [-(class_Groups_Oordered__ab__group__add(_797288)), _797290 = _797288, class_Groups_Oordered__ab__group__add(_797290)], (52193 ^ _779203) ^ [_1831901, _1831903] : [class_Orderings_Oord(_1831901), -(class_Orderings_Oord(tc_fun(_1831903, _1831901)))], (51327 ^ _779203) ^ [_1817180, _1817182] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817180), _1817182)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817182), _1817180)), -(_1817180 = _1817182)], (32751 ^ _779203) ^ [_1378618, _1378620, _1378622, _1378624, _1378626, _1378628] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1378618, tc_fun(_1378620, tc_HOL_Obool))), _1378622), _1378624), _1378626), _1378628)), -(hBOOL(hAPP(hAPP(_1378622, _1378626), _1378628))), -(hBOOL(hAPP(hAPP(_1378624, _1378626), _1378628)))], (34375 ^ _779203) ^ [_1412044, _1412046, _1412048, _1412050] : [-(_1412044 = c_Orderings_Obot__class_Obot(tc_fun(_1412046, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412046, tc_fun(_1412048, tc_HOL_Obool)), _1412044), hAPP(c_COMBK(tc_fun(_1412048, tc_HOL_Obool), _1412046), _1412050)) = _1412050)], (25420 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (50237 ^ _779203) ^ [_1795208, _1795210, _1795212, _1795214, _1795216, _1795218] : [c_Fun_Oinj__on(_1795208, _1795210, _1795212, _1795214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1795210, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1795208, _1795210, _1795212), _1795214)), _1795216)), c_Fun_Oinj__on(_1795210, _1795208, _1795218, _1795216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1795208, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1795210, _1795208, _1795218), _1795216)), _1795214)), -(c_Fun_Obij__betw(_1795208, _1795210, 50252 ^ [_1795208, _1795210, _1795212, _1795214, _1795216, _1795218], _1795214, _1795216))], (33259 ^ _779203) ^ [_1388297, _1388299] : [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), _1388297), _1388299))), 33262 ^ _779203 : [(33271 ^ _779203) ^ [] : [-(c_Divides_OnegDivAlg(_1388297, _1388299) = hAPP(c_Divides_Oadjust(_1388299), c_Divides_OnegDivAlg(_1388297, 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)))), _1388299)))), -(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), _1388297), _1388299)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1388299), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33263 ^ _779203) ^ [] : [33264 ^ _779203 : [(33267 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1388299), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33265 ^ _779203) ^ [] : [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), _1388297), _1388299)))]], -(c_Divides_OnegDivAlg(_1388297, _1388299) = 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), _1388297), _1388299)))]]], (33624 ^ _779203) ^ [_1394679, _1394681, _1394683] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1394679, _1394681), _1394683)), 33627 ^ _779203 : [(33628 ^ _779203) ^ [_1394764] : [hBOOL(hAPP(hAPP(_1394681, _1394764), _1394683)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1394679, _1394681), _1394764)))]]], (51537 ^ _779203) ^ [_1820605, _1820607, _1820609, _1820611] : [class_Divides_Osemiring__div(_1820605), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820605), _1820607), _1820609)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820605), _1820607), _1820611)), 51548 ^ _779203 : [(51555 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820605), _1820609), _1820611)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820605), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820605), _1820609), _1820607)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820605), _1820611), _1820607))))], (51549 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820605), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820605), _1820609), _1820607)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1820605), _1820611), _1820607))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820605), _1820609), _1820611)))]]], (28008 ^ _779203) ^ [_1273649, _1273651, _1273653] : [class_Orderings_Olinorder(_1273649), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273649), _1273651), _1273653)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273649, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1273649, _1273651, _1273653)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1273649), _1273653)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1273649), _1273651))], (4518 ^ _779203) ^ [_847806, _847808] : [_847808 = _847806, -(c_Code__Numeral_OSuc__code__numeral(_847808) = c_Code__Numeral_OSuc__code__numeral(_847806))], (21827 ^ _779203) ^ [] : [-(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))))], (36310 ^ _779203) ^ [_1462390, _1462392, _1462394, _1462396, _1462398] : [c_Fun_Oinj__on(_1462390, _1462392, _1462394, _1462396), c_Fun_Oinj__on(_1462390, _1462392, _1462394, _1462398), -(c_Fun_Oinj__on(_1462390, _1462392, _1462394, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1462390, tc_HOL_Obool)), _1462396), _1462398)))], (17840 ^ _779203) ^ [_1093710, _1093712, _1093714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1093710)), _1093710 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1093712), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1093710), _1093714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093712), _1093710)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1093714)))], (51167 ^ _779203) ^ [_1814637, _1814639] : [-(_1814637 = _1814639), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814637), _1814639)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814639), _1814637))], (42057 ^ _779203) ^ [_1614632, _1614634] : [-(hAPP(c_List_Oset(_1614632), _1614634) = hAPP(c_Set_OCollect(_1614632), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1614632), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1614632, 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)), _1614632), 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)), _1614632), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1614632, tc_fun(tc_Nat_Onat, _1614632), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614632, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1614632), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1614632), c_COMBB(_1614632, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1614632), _1614634))))), 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(_1614632)), _1614634))))))], (48148 ^ _779203) ^ [_1750370, _1750372, _1750374, _1750376] : [-(c_Lazy__Sequence_Oproduct(_1750370, _1750372, _1750374, _1750376) = hAPP(c_Lazy__Sequence_Obind(_1750370, tc_prod(_1750370, _1750372), _1750374), hAPP(hAPP(c_COMBB(tc_fun(_1750372, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750370, _1750372))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750370, _1750372)), _1750370), c_Lazy__Sequence_Obind(_1750372, tc_prod(_1750370, _1750372), _1750376)), hAPP(hAPP(c_COMBB(tc_fun(_1750372, tc_prod(_1750370, _1750372)), tc_fun(_1750372, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750370, _1750372))), _1750370), hAPP(c_COMBB(tc_prod(_1750370, _1750372), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1750370, _1750372)), _1750372), c_Lazy__Sequence_Osingle(tc_prod(_1750370, _1750372)))), c_Product__Type_OPair(_1750370, _1750372)))))], (28120 ^ _779203) ^ [_1276006, _1276008] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1276006), hAPP(c_Nat_OSuc, _1276008)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1276006, _1276008))], (37183 ^ _779203) ^ [_1481307, _1481309, _1481311, _1481313, _1481315] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1481307, _1481309, _1481311), _1481313), _1481315)), -(hBOOL(hAPP(_1481313, hAPP(_1481311, _1481315))))], (32761 ^ _779203) ^ [_1378776, _1378778, _1378780, _1378782, _1378784, _1378786] : [32762 ^ _779203 : [(32765 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1378782, _1378778), _1378780))], (32763 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1378776, _1378778), _1378780))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1378784, tc_fun(_1378786, tc_HOL_Obool))), _1378782), _1378776), _1378778), _1378780)))], (28574 ^ _779203) ^ [_1284626, _1284628, _1284630, _1284632] : [class_Groups_Ocomm__monoid__add(_1284626), 28577 ^ _779203 : [(28584 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1284628), _1284630))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1284626), _1284632), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1284630), hAPP(c_Nat_OSuc, _1284628))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1284626), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1284626), _1284632), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1284630), _1284628))), hAPP(_1284632, _1284628)))], (28578 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1284628), _1284630)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1284626), _1284632), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1284630), hAPP(c_Nat_OSuc, _1284628))) = c_Groups_Ozero__class_Ozero(_1284626))]]], (33165 ^ _779203) ^ [_1386627, _1386629] : [_1386627 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1386627, _1386629) = 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)))], (49390 ^ _779203) ^ [_1777517, _1777519, _1777521] : [-(c_Equiv__Relations_Oequiv(_1777517, _1777519, _1777521)), c_Relation_Orefl__on(_1777517, _1777519, _1777521), c_Relation_Osym(_1777517, _1777521), c_Relation_Otrans(_1777517, _1777521)], (26012 ^ _779203) ^ [_1236635, _1236637, _1236639] : [class_Orderings_Oorder(_1236635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1236635), _1236637), _1236639)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1236635, _1236639, _1236637) = c_Orderings_Obot__class_Obot(tc_fun(_1236635, tc_HOL_Obool)))], (29856 ^ _779203) ^ [_1310092, _1310094, _1310096, _1310098] : [class_Orderings_Oorder(_1310092), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310092, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1310092, _1310094), _1310096)), c_SetInterval_Oord__class_OatLeastAtMost(_1310092, _1310096, _1310098)) = c_Orderings_Obot__class_Obot(tc_fun(_1310092, tc_HOL_Obool)))], (14946 ^ _779203) ^ [_1040293, _1040295, _1040297] : [class_Fields_Olinordered__field__inverse__zero(_1040293), 14952 ^ _779203 : [(14957 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1040293), 14951 ^ [_1040293, _1040295, _1040297]), _1040295)), _1040297))], (14955 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040293), 14951 ^ [_1040293, _1040295, _1040297]), c_Groups_Oone__class_Oone(_1040293))))], (14953 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1040293), c_Groups_Ozero__class_Ozero(_1040293)), 14951 ^ [_1040293, _1040295, _1040297])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1040293), _1040295), _1040297)))], (46146 ^ _779203) ^ [_1707446, _1707448] : [class_Orderings_Olinorder(_1707446), -(_1707448 = c_List_Olist_ONil(_1707446)), c_List_Olinorder__class_Osorted(_1707446, _1707448), -(c_List_Olinorder__class_Osorted(_1707446, c_List_Obutlast(_1707446, _1707448)))], (26176 ^ _779203) ^ [_1239640, _1239642, _1239644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239640, tc_HOL_Obool)), _1239642), _1239644)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1239640, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1239640), _1239642)), hAPP(c_Set_OPow(_1239640), _1239644))))], (45863 ^ _779203) ^ [_1702305, _1702307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702305), _1702307)), -(c_List_Oupt(_1702305, hAPP(c_Nat_OSuc, _1702307)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1702305, _1702307)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702307), c_List_Olist_ONil(tc_Nat_Onat))))], (47067 ^ _779203) ^ [_1726179, _1726181] : [class_Orderings_Olinorder(_1726179), 47074 ^ _779203 : [(47079 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1726179), hAPP(hAPP(c_List_Onth(_1726179), _1726181), 47072 ^ [_1726179, _1726181])), hAPP(hAPP(c_List_Onth(_1726179), _1726181), 47073 ^ [_1726179, _1726181])))], (47077 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47073 ^ [_1726179, _1726181]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726179)), _1726181))))], (47075 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47072 ^ [_1726179, _1726181]), 47073 ^ [_1726179, _1726181])))]], -(c_List_Olinorder__class_Osorted(_1726179, _1726181))], (27608 ^ _779203) ^ [_1265812, _1265814, _1265816] : [class_Lattices_Obounded__lattice__bot(_1265812), 27611 ^ _779203 : [(27620 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265812), _1265814), _1265816) = c_Orderings_Obot__class_Obot(_1265812)), _1265814 = c_Orderings_Obot__class_Obot(_1265812), _1265816 = c_Orderings_Obot__class_Obot(_1265812)], (27612 ^ _779203) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1265812), _1265814), _1265816) = c_Orderings_Obot__class_Obot(_1265812), 27615 ^ _779203 : [(27618 ^ _779203) ^ [] : [-(_1265816 = c_Orderings_Obot__class_Obot(_1265812))], (27616 ^ _779203) ^ [] : [-(_1265814 = c_Orderings_Obot__class_Obot(_1265812))]]]]], (2008 ^ _779203) ^ [_808135, _808137, _808139, _808141] : [-(c_SMT_Oz3div(_808141, _808137) = c_SMT_Oz3div(_808139, _808135)), _808141 = _808139, _808137 = _808135], (35902 ^ _779203) ^ [_1452806, _1452808, _1452810, _1452812, _1452814] : [c_Equiv__Relations_Oequiv(_1452806, _1452808, _1452810), hBOOL(hAPP(hAPP(c_member(_1452806), _1452812), _1452808)), hBOOL(hAPP(hAPP(c_member(_1452806), _1452814), _1452808)), 35913 ^ _779203 : [(35920 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1452806, _1452806)), hAPP(hAPP(c_Product__Type_OPair(_1452806, _1452806), _1452812), _1452814)), _1452810)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1452806), hAPP(hAPP(c_Set_Oinsert(_1452806), _1452812), c_Orderings_Obot__class_Obot(tc_fun(_1452806, tc_HOL_Obool)))), _1452810) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1452806), hAPP(hAPP(c_Set_Oinsert(_1452806), _1452814), c_Orderings_Obot__class_Obot(tc_fun(_1452806, tc_HOL_Obool)))), _1452810))], (35914 ^ _779203) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1452806), hAPP(hAPP(c_Set_Oinsert(_1452806), _1452812), c_Orderings_Obot__class_Obot(tc_fun(_1452806, tc_HOL_Obool)))), _1452810) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1452806), hAPP(hAPP(c_Set_Oinsert(_1452806), _1452814), c_Orderings_Obot__class_Obot(tc_fun(_1452806, tc_HOL_Obool)))), _1452810), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1452806, _1452806)), hAPP(hAPP(c_Product__Type_OPair(_1452806, _1452806), _1452812), _1452814)), _1452810)))]]], (15216 ^ _779203) ^ [_1045392, _1045394, _1045396] : [class_Int_Onumber__ring(_1045392), class_Int_Oring__char__0(_1045392), 15223 ^ _779203 : [(15230 ^ _779203) ^ [] : [_1045394 = _1045396, -(hAPP(c_Int_Onumber__class_Onumber__of(_1045392), _1045394) = hAPP(c_Int_Onumber__class_Onumber__of(_1045392), _1045396))], (15224 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1045392), _1045394) = hAPP(c_Int_Onumber__class_Onumber__of(_1045392), _1045396), -(_1045394 = _1045396)]]], (40620 ^ _779203) ^ [_1575109, _1575111] : [-(c_Relation_Oirrefl(_1575109, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1575109, _1575109), tc_HOL_Obool)), _1575111), c_Relation_OId(_1575109))))], (32598 ^ _779203) ^ [_1370995, _1370997, _1370999] : [32600 ^ _779203 : [(32603 ^ _779203) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1370999, 32599 ^ [_1370995, _1370997, _1370999]))], (32601 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1370995), 32599 ^ [_1370995, _1370997, _1370999]), _1370997)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1370995, tc_Int_Oint), _1370999), _1370997) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1370995, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1370995), c_Int_Onat), _1370999)), _1370997)))], (22177 ^ _779203) ^ [_1170745, _1170747, _1170749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1170745)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1170747, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1170749), _1170745)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1170749), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1170747), _1170749), _1170745))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1170747, _1170749)))], (9526 ^ _779203) ^ [_941780, _941782, _941784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941780), _941782)), _941784)), 9529 ^ _779203 : [(9532 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941782), _941784)))], (9530 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941780), _941784)))]]], (52607 ^ _779203) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (27855 ^ _779203) ^ [_1270462, _1270464, _1270466, _1270468] : [27859 ^ _779203 : [(27862 ^ _779203) ^ [] : [hBOOL(hAPP(_1270468, 27858 ^ [_1270462, _1270464, _1270466, _1270468]))], (27860 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1270462), 27858 ^ [_1270462, _1270464, _1270466, _1270468]), _1270464)))]], 27864 ^ _779203 : [(27867 ^ _779203) ^ [] : [hBOOL(hAPP(_1270468, 27863 ^ [_1270462, _1270464, _1270466, _1270468]))], (27865 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1270462), 27863 ^ [_1270462, _1270464, _1270466, _1270468]), _1270466)))]], 27868 ^ _779203 : [(27869 ^ _779203) ^ [_1270795] : [hBOOL(hAPP(hAPP(c_member(_1270462), _1270795), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270462, tc_HOL_Obool)), _1270464), _1270466))), -(hBOOL(hAPP(_1270468, _1270795)))]]], (12179 ^ _779203) ^ [_989551, _989553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989551), hAPP(c_Nat_OSuc, _989553))), -(_989551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 12187 ^ _779203 : [(12190 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 12186 ^ [_989551, _989553]), _989553)))], (12188 ^ _779203) ^ [] : [-(_989551 = hAPP(c_Nat_OSuc, 12186 ^ [_989551, _989553]))]]], (35608 ^ _779203) ^ [_1445989, _1445991] : [-(c_Relation_OId__on(_1445989, _1445991) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1445989, tc_fun(tc_prod(_1445989, _1445989), tc_HOL_Obool)), _1445991), hAPP(hAPP(c_COMBC(_1445989, tc_fun(tc_prod(_1445989, _1445989), tc_HOL_Obool), tc_fun(tc_prod(_1445989, _1445989), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1445989, _1445989), tc_fun(tc_fun(tc_prod(_1445989, _1445989), tc_HOL_Obool), tc_fun(tc_prod(_1445989, _1445989), tc_HOL_Obool)), _1445989), c_Set_Oinsert(tc_prod(_1445989, _1445989))), hAPP(hAPP(c_COMBS(_1445989, _1445989, tc_prod(_1445989, _1445989)), c_Product__Type_OPair(_1445989, _1445989)), c_COMBI(_1445989)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1445989, _1445989), tc_HOL_Obool)))))], (5847 ^ _779203) ^ [_871730, _871732, _871734] : [-(hAPP(hAPP(c_Set_Oinsert(_871730), _871732), hAPP(hAPP(c_Set_Oinsert(_871730), _871732), _871734)) = hAPP(hAPP(c_Set_Oinsert(_871730), _871732), _871734))], (52585 ^ _779203) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (47746 ^ _779203) ^ [_1741223, _1741225, _1741227] : [-(hBOOL(hAPP(hAPP(c_member(_1741223), _1741225), hAPP(c_List_Oset(_1741223), _1741227)))), 47747 ^ _779203 : [(47748 ^ _779203) ^ [_1741312] : [47749 ^ _779203 : [(47750 ^ _779203) ^ [_1741385] : [_1741227 = hAPP(hAPP(c_List_Oappend(_1741223), _1741312), hAPP(hAPP(c_List_Olist_OCons(_1741223), _1741225), _1741385))]], -(hBOOL(hAPP(hAPP(c_member(_1741223), _1741225), hAPP(c_List_Oset(_1741223), _1741312))))]]], (22448 ^ _779203) ^ [_1175085, _1175087, _1175089, _1175091] : [class_Divides_Osemiring__div(_1175085), 22451 ^ _779203 : [(22458 ^ _779203) ^ [] : [-(_1175087 = c_Groups_Ozero__class_Ozero(_1175085)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1175085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175085), _1175087), _1175089)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175085), _1175087), _1175091)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1175085), _1175089), _1175091))], (22452 ^ _779203) ^ [] : [_1175087 = c_Groups_Ozero__class_Ozero(_1175085), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1175085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175085), _1175087), _1175089)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175085), _1175087), _1175091)) = c_Groups_Ozero__class_Ozero(_1175085))]]], (10005 ^ _779203) ^ [_950127, _950129, _950131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950127), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _950131), _950129))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _950127), _950129)), _950131)))], (18210 ^ _779203) ^ [] : [-(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)))], (10163 ^ _779203) ^ [_953628] : [-(hAPP(c_Nat_OSuc, _953628) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _953628), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (37896 ^ _779203) ^ [_1501283, _1501285] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1501283), _1501285)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1501283, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1501283, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1501283, tc_HOL_Obool), tc_fun(_1501283, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1501283, tc_HOL_Obool))), _1501285)))))], (34154 ^ _779203) ^ [_1405919, _1405921, _1405923, _1405925, _1405927, _1405929] : [-(hAPP(c_Product__Type_Oapfst(_1405919, _1405921, _1405923, _1405925), hAPP(hAPP(c_Product__Type_OPair(_1405919, _1405923), _1405927), _1405929)) = hAPP(hAPP(c_Product__Type_OPair(_1405921, _1405923), hAPP(_1405925, _1405927)), _1405929))], (17366 ^ _779203) ^ [_1085359, _1085361, _1085363] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085359), _1085361)), _1085363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085359), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085361), _1085363)))], (43496 ^ _779203) ^ [_1648689, _1648691] : [-(hAPP(hAPP(c_List_Odrop(_1648689), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1648691) = _1648691)], (52663 ^ _779203) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (20732 ^ _779203) ^ [_1145168, _1145170, _1145172] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1145168, tc_HOL_Obool)), _1145170) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1145168, tc_HOL_Obool)), _1145172), -(_1145170 = _1145172)], (17378 ^ _779203) ^ [_1085656, _1085658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085656), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085658), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085656), _1085658)))], (27042 ^ _779203) ^ [_1255433, _1255435, _1255437, _1255439, _1255441] : [class_Orderings_Olinorder(_1255433), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255433), _1255435), _1255437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255433), _1255439), _1255441)), 27053 ^ _779203 : [(27062 ^ _779203) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255433, _1255435), _1255437) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255433, _1255439), _1255441)), _1255435 = _1255439, _1255437 = _1255441], (27054 ^ _779203) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255433, _1255435), _1255437) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255433, _1255439), _1255441), 27057 ^ _779203 : [(27060 ^ _779203) ^ [] : [-(_1255437 = _1255441)], (27058 ^ _779203) ^ [] : [-(_1255435 = _1255439)]]]]], (42533 ^ _779203) ^ [_1627172, _1627174] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1627172), _1627174)), -(c_Nitpick_Ocard_H(_1627172, _1627174) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627172)), c_Hilbert__Choice_OEps(tc_List_Olist(_1627172), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627172), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1627172)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627172), tc_fun(_1627172, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1627172, tc_HOL_Obool), tc_fun(tc_fun(_1627172, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1627172)), c_fequal), c_List_Oset(_1627172))), _1627174))), c_List_Odistinct(_1627172)))))], (50315 ^ _779203) ^ [_1796731, _1796733, _1796735] : [hBOOL(hAPP(c_Quotient_ORespects(_1796731, _1796733), _1796735)), -(hBOOL(hAPP(hAPP(_1796733, _1796735), _1796735)))], (19081 ^ _779203) ^ [_1115423] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115423)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115423)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1115423)))], (42387 ^ _779203) ^ [_1623890, _1623892, _1623894, _1623896] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623890), tc_List_Olist(_1623890))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623890), tc_List_Olist(_1623890)), _1623892), _1623894)), c_List_Olistrel1(_1623890, _1623896)))), 42388 ^ _779203 : [(42389 ^ _779203) ^ [_1624023, _1624025] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1623890, _1623890)), hAPP(hAPP(c_Product__Type_OPair(_1623890, _1623890), hAPP(hAPP(c_List_Onth(_1623890), _1623892), _1624023)), _1624025)), _1623896)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1624023), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623890)), _1623892))), _1623894 = hAPP(hAPP(c_List_Olist__update(_1623890, _1623892), _1624023), _1624025)]]], (42840 ^ _779203) ^ [_1633028, _1633030, _1633032, _1633034] : [-(_1633028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1633030), _1633028), hAPP(hAPP(c_List_Olist_OCons(_1633030), _1633032), _1633034)) = hAPP(hAPP(c_List_Olist_OCons(_1633030), _1633032), hAPP(hAPP(c_List_Otake(_1633030), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1633028), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1633034)))], (35280 ^ _779203) ^ [_1436629, _1436631, _1436633, _1436635] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1436629), _1436631)), 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)), _1436629), _1436633)), 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)), _1436631), _1436635)), 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)), _1436631), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1436633), _1436635))), c_FunDef_Omin__weak)))], (45750 ^ _779203) ^ [_1698632, _1698634, _1698636] : [-(hAPP(c_List_Oset(_1698632), hAPP(c_List_Ofilter(_1698632, _1698634), _1698636)) = hAPP(c_Set_OCollect(_1698632), hAPP(hAPP(c_COMBS(_1698632, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1698632), c_fconj), hAPP(hAPP(c_COMBC(_1698632, tc_fun(_1698632, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698632)), hAPP(c_List_Oset(_1698632), _1698636)))), _1698634)))], (35154 ^ _779203) ^ [_1433705, _1433707, _1433709, _1433711, _1433713] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433705, tc_fun(_1433707, tc_HOL_Obool)), _1433709), _1433711), _1433713)), 35158 ^ _779203 : [(35161 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1433711, 35157 ^ [_1433705, _1433707, _1433709, _1433711, _1433713]), _1433713)))], (35159 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1433705), 35157 ^ [_1433705, _1433707, _1433709, _1433711, _1433713]), _1433709)))]]], (47872 ^ _779203) ^ [_1743843, _1743845, _1743847, _1743849] : [c_List_Olist__all(_1743843, _1743845, hAPP(hAPP(c_List_Olist_OCons(_1743843), _1743847), _1743849)), 47875 ^ _779203 : [(47878 ^ _779203) ^ [] : [-(c_List_Olist__all(_1743843, _1743845, _1743849))], (47876 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1743845, _1743847)))]]], (11119 ^ _779203) ^ [_970689, _970691] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970689), _970691) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_970689 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_970691 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21549 ^ _779203) ^ [_1158581] : [c_Int_OBit0(_1158581) = c_Int_OPls, -(_1158581 = c_Int_OPls)], (50224 ^ _779203) ^ [_1794932, _1794934, _1794936, _1794938] : [c_Fun_Obij__betw(_1794932, _1794934, _1794936, c_Orderings_Otop__class_Otop(tc_fun(_1794932, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794934, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1794932, _1794934, _1794936), _1794938) = hAPP(c_Set_Oimage(_1794934, _1794932, c_Hilbert__Choice_Oinv__into(_1794932, _1794934, c_Orderings_Otop__class_Otop(tc_fun(_1794932, tc_HOL_Obool)), _1794936)), _1794938))], (31482 ^ _779203) ^ [_1343746, _1343748, _1343750] : [class_Complete__Lattice_Ocomplete__lattice(_1343746), -(c_Complete__Lattice_OInf__class_OInf(_1343746, hAPP(hAPP(c_Set_Oinsert(_1343746), _1343748), _1343750)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1343746), _1343748), c_Complete__Lattice_OInf__class_OInf(_1343746, _1343750)))], (43287 ^ _779203) ^ [_1643015, _1643017, _1643019, _1643021] : [43288 ^ _779203 : [(43291 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1643015), _1643017), hAPP(c_List_Oset(_1643015), c_List_Obutlast(_1643015, _1643021))))], (43289 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1643015), _1643017), hAPP(c_List_Oset(_1643015), c_List_Obutlast(_1643015, _1643019))))]], -(hBOOL(hAPP(hAPP(c_member(_1643015), _1643017), hAPP(c_List_Oset(_1643015), c_List_Obutlast(_1643015, hAPP(hAPP(c_List_Oappend(_1643015), _1643019), _1643021))))))], (50775 ^ _779203) ^ [_1807500, _1807502, _1807504] : [class_Divides_Osemiring__div(_1807500), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807500), _1807502), _1807504)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807500), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807500), _1807504), _1807502)), _1807502) = _1807504)], (43870 ^ _779203) ^ [_1656950, _1656952, _1656954, _1656956, _1656958, _1656960] : [-(hAPP(c_List_Ofoldl(_1656950, _1656952, _1656954, _1656956), hAPP(hAPP(c_List_Oappend(_1656952), _1656958), _1656960)) = hAPP(c_List_Ofoldl(_1656950, _1656952, _1656954, hAPP(c_List_Ofoldl(_1656950, _1656952, _1656954, _1656956), _1656958)), _1656960))], (25016 ^ _779203) ^ [_1220200, _1220202, _1220204] : [class_Power_Opower(_1220200), class_Rings_Omult__zero(_1220200), class_Rings_Ono__zero__divisors(_1220200), class_Rings_Ozero__neq__one(_1220200), 25031 ^ _779203 : [(25040 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1220200), _1220202), _1220204) = c_Groups_Ozero__class_Ozero(_1220200)), _1220202 = c_Groups_Ozero__class_Ozero(_1220200), -(_1220204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (25032 ^ _779203) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1220200), _1220202), _1220204) = c_Groups_Ozero__class_Ozero(_1220200), 25035 ^ _779203 : [(25038 ^ _779203) ^ [] : [_1220204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25036 ^ _779203) ^ [] : [-(_1220202 = c_Groups_Ozero__class_Ozero(_1220200))]]]]], (17276 ^ _779203) ^ [_1083939, _1083941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1083939), _1083941)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083939)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083941))))], (8080 ^ _779203) ^ [_913034, _913036, _913038, _913040, _913042] : [class_Rings_Oring(_913034), hBOOL(hAPP(c_Finite__Set_Ofinite(_913036), _913038)), hBOOL(hAPP(hAPP(c_member(_913036), _913040), _913038)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_913036, _913034), _913042), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913036, tc_HOL_Obool)), _913038), hAPP(hAPP(c_Set_Oinsert(_913036), _913040), c_Orderings_Obot__class_Obot(tc_fun(_913036, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_913034), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_913036, _913034), _913042), _913038)), hAPP(_913042, _913040)))], (39020 ^ _779203) ^ [_1535914, _1535916] : [c_Wellfounded_Owf(_1535914, _1535916), -(c_Wellfounded_Owf(tc_List_Olist(_1535914), c_List_Olex(_1535914, _1535916)))], (25964 ^ _779203) ^ [_1235737, _1235739] : [class_Int_Onumber__ring(_1235737), -(hAPP(c_Int_Oring__1__class_Oof__int(_1235737), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1235739)) = hAPP(c_Int_Onumber__class_Onumber__of(_1235737), _1235739))], (37349 ^ _779203) ^ [_1485468, _1485470, _1485472, _1485474, _1485476, _1485478] : [-(hAPP(c_Set_Oimage(_1485468, tc_prod(_1485470, _1485472), hAPP(hAPP(c_COMBS(_1485468, _1485472, tc_prod(_1485470, _1485472)), hAPP(hAPP(c_COMBB(_1485470, tc_fun(_1485472, tc_prod(_1485470, _1485472)), _1485468), c_Product__Type_OPair(_1485470, _1485472)), _1485474)), _1485476)), _1485478) = hAPP(hAPP(c_Product__Type_OSigma(_1485470, _1485472), hAPP(c_Set_Oimage(_1485468, _1485470, _1485474), _1485478)), hAPP(hAPP(c_COMBB(tc_fun(_1485468, tc_HOL_Obool), tc_fun(_1485472, tc_HOL_Obool), _1485470), c_Set_Oimage(_1485468, _1485472, _1485476)), hAPP(hAPP(c_COMBC(_1485470, tc_fun(_1485468, tc_HOL_Obool), tc_fun(_1485468, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485468, tc_HOL_Obool), tc_fun(tc_fun(_1485468, tc_HOL_Obool), tc_fun(_1485468, tc_HOL_Obool)), _1485470), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485468, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1485470, tc_HOL_Obool), tc_fun(_1485468, tc_HOL_Obool), _1485470), c_Set_Ovimage(_1485468, _1485470, _1485474)), hAPP(hAPP(c_COMBC(_1485470, tc_fun(_1485470, tc_HOL_Obool), tc_fun(_1485470, tc_HOL_Obool)), c_Set_Oinsert(_1485470)), c_Orderings_Obot__class_Obot(tc_fun(_1485470, tc_HOL_Obool)))))), _1485478))))], (21665 ^ _779203) ^ [_1160564, _1160566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160564), _1160566)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1160564)), c_Int_OBit0(_1160566))))], (26134 ^ _779203) ^ [_1238725, _1238727] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1238725, _1238727))))], (50013 ^ _779203) ^ [_1790857, _1790859, _1790861, _1790863, _1790865, _1790867, _1790869] : [c_Fun_Obij__betw(_1790857, _1790859, _1790861, _1790863, _1790865), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1790857, tc_HOL_Obool)), _1790867), _1790863)), hAPP(c_Set_Oimage(_1790857, _1790859, _1790861), _1790867) = _1790869, -(c_Fun_Obij__betw(_1790857, _1790859, _1790861, _1790867, _1790869))], (48378 ^ _779203) ^ [_1754826, _1754828, _1754830, _1754832, _1754834] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1754826, _1754828, _1754830) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754826, _1754832, _1754834), 48381 ^ _779203 : [(48384 ^ _779203) ^ [] : [-(_1754830 = _1754834)], (48382 ^ _779203) ^ [] : [-(_1754828 = _1754832)]]], (27018 ^ _779203) ^ [_1255036, _1255038] : [class_Groups_Oordered__ab__group__add(_1255036), -(hAPP(c_Set_Oimage(_1255036, _1255036, c_Groups_Ouminus__class_Ouminus(_1255036)), hAPP(c_SetInterval_Oord__class_OlessThan(_1255036), _1255038)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1255036), hAPP(c_Groups_Ouminus__class_Ouminus(_1255036), _1255038)))], (43458 ^ _779203) ^ [_1647846, _1647848, _1647850] : [-(hAPP(hAPP(c_List_Oappend(_1647846), hAPP(hAPP(c_List_Otake(_1647846), _1647848), _1647850)), hAPP(hAPP(c_List_Odrop(_1647846), _1647848), _1647850)) = _1647850)], (3292 ^ _779203) ^ [_828265, _828267, _828269, _828271] : [-(c_Product__Type_OSigma(_828271, _828267) = c_Product__Type_OSigma(_828269, _828265)), _828271 = _828269, _828267 = _828265], (18871 ^ _779203) ^ [_1111737, _1111739] : [_1111737 = _1111739, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1111737) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1111739))], (16710 ^ _779203) ^ [_1073071, _1073073, _1073075] : [class_Orderings_Olinorder(_1073071), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073071), _1073073)), -(_1073073 = c_Orderings_Obot__class_Obot(tc_fun(_1073071, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1073071, hAPP(hAPP(c_Set_Oinsert(_1073071), _1073075), _1073073)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1073071), _1073075), c_Big__Operators_Olinorder__class_OMin(_1073071, _1073073)))], (40176 ^ _779203) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (50765 ^ _779203) ^ [_1807287, _1807289, _1807291, _1807293] : [class_Divides_Osemiring__div(_1807287), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807287), _1807289), _1807291)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807287), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807287), _1807291), _1807289)), _1807293) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807287), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807287), _1807291), _1807293)), _1807289))], (9261 ^ _779203) ^ [_937239, _937241, _937243] : [_937241 = _937243, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _937239)), _937241) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _937239)), _937243))], (5448 ^ _779203) ^ [_862545, _862547] : [_862547 = _862545, -(c_Groups_Ozero__class_Ozero(_862547) = c_Groups_Ozero__class_Ozero(_862545))], (45917 ^ _779203) ^ [_1703153, _1703155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1703153), _1703155)), -(c_List_Oupt(_1703155, _1703153) = c_List_Olist_ONil(tc_Nat_Onat))], (9887 ^ _779203) ^ [_947917, _947919, _947921] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _947917)), _947919)), hAPP(c_Nat_OSuc, _947921)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947917), _947919)), _947921))], (1930 ^ _779203) ^ [_806288, _806290] : [-(class_Groups_Oone(_806288)), _806290 = _806288, class_Groups_Oone(_806290)], (27550 ^ _779203) ^ [_1264622, _1264624, _1264626, _1264628] : [hBOOL(hAPP(hAPP(c_member(_1264622), _1264624), _1264626)), -(hBOOL(hAPP(hAPP(c_member(_1264622), _1264624), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264622, tc_HOL_Obool)), _1264628), _1264626))))], (41828 ^ _779203) ^ [_1609008, _1609010, _1609012, _1609014] : [-(hAPP(hAPP(c_List_Onth(_1609008), hAPP(hAPP(c_List_Olist_OCons(_1609008), _1609010), _1609012)), _1609014) = c_Nat_Onat_Onat__case(_1609008, _1609010, hAPP(c_List_Onth(_1609008), _1609012), _1609014))], (33797 ^ _779203) ^ [_1398174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398174)), 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), _1398174)) = 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), _1398174))))))], (31448 ^ _779203) ^ [_1343115, _1343117, _1343119] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1343115, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1343115, tc_HOL_Obool)), _1343117), _1343119)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343115, tc_HOL_Obool)), _1343117), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1343115, tc_HOL_Obool), _1343119)))], (32885 ^ _779203) ^ [_1381460, _1381462, _1381464, _1381466, _1381468, _1381470] : [-(hAPP(hAPP(c_Product__Type_OPair(_1381460, _1381462), _1381464), _1381466) = hAPP(hAPP(c_Product__Type_OPair(_1381460, _1381462), _1381468), _1381470)), _1381464 = _1381468, _1381466 = _1381470], (52455 ^ _779203) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (40422 ^ _779203) ^ [_1570472, _1570474, _1570476, _1570478, _1570480] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570472, _1570472)), hAPP(hAPP(c_Product__Type_OPair(_1570472, _1570472), _1570474), _1570476)), _1570478)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1570472, _1570472)), hAPP(hAPP(c_Product__Type_OPair(_1570472, _1570472), _1570476), _1570480)), c_Transitive__Closure_Ortrancl(_1570472, _1570478))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570472, _1570472)), hAPP(hAPP(c_Product__Type_OPair(_1570472, _1570472), _1570474), _1570480)), c_Transitive__Closure_Ortrancl(_1570472, _1570478))))], (44789 ^ _779203) ^ [_1676766, _1676768] : [_1676766 = _1676768, -(hAPP(c_Code__Numeral_Onat__of, _1676766) = hAPP(c_Code__Numeral_Onat__of, _1676768))], (12873 ^ _779203) ^ [_1001764, _1001766, _1001768] : [class_Rings_Olinordered__idom(_1001764), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001764), c_Groups_Ozero__class_Ozero(_1001764)), _1001766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001764), c_Groups_Ozero__class_Ozero(_1001764)), _1001768)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001764), _1001768), c_Groups_Oone__class_Oone(_1001764))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001764), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001764), _1001768), _1001766)), _1001766)))], (12318 ^ _779203) ^ [_991586, _991588] : [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), _991586), _991588))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991588), _991586)))], (41469 ^ _779203) ^ [_1598374, _1598376, _1598378, _1598380] : [-(c_List_Olist_Olist__size(_1598374, _1598376, hAPP(hAPP(c_List_Olist_OCons(_1598374), _1598378), _1598380)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1598376, _1598378)), c_List_Olist_Olist__size(_1598374, _1598376, _1598380))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (15574 ^ _779203) ^ [_1052229, _1052231, _1052233] : [class_Orderings_Olinorder(_1052229), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052229), _1052231), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1052229), _1052233), _1052231))))], (23515 ^ _779203) ^ [_1193039, _1193041, _1193043] : [hBOOL(hAPP(_1193039, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1193041, _1193043))), 23518 ^ _779203 : [(23543 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193043), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23546 ^ _779203 : [(23547 ^ _779203) ^ [_1193661, _1193663] : [-(hBOOL(hAPP(_1193039, _1193661))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193043), _1193661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1193661), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1193041 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193043), _1193663)), _1193661)]]], (23525 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193043)), 23528 ^ _779203 : [(23529 ^ _779203) ^ [_1193369, _1193371] : [-(hBOOL(hAPP(_1193039, _1193369))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1193369)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1193369), _1193043)), _1193041 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1193043), _1193371)), _1193369)]]], (23519 ^ _779203) ^ [] : [_1193043 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1193039, _1193041)))]]], (6343 ^ _779203) ^ [_881373, _881375] : [class_Orderings_Obot(_881373), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881373), c_Orderings_Obot__class_Obot(_881373)), _881375)))], (43909 ^ _779203) ^ [_1657707, _1657709] : [class_Complete__Lattice_Ocomplete__lattice(_1657707), -(c_Complete__Lattice_OSup__class_OSup(_1657707, hAPP(c_List_Oset(_1657707), _1657709)) = hAPP(c_List_Ofoldl(_1657707, _1657707, c_Lattices_Osemilattice__sup__class_Osup(_1657707), c_Orderings_Obot__class_Obot(_1657707)), _1657709))], (38687 ^ _779203) ^ [_1528172, _1528174, _1528176, _1528178] : [c_Wellfounded_Owf(_1528172, _1528174), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528172, _1528172)), hAPP(hAPP(c_Product__Type_OPair(_1528172, _1528172), _1528176), _1528178)), _1528174)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528172, _1528172)), hAPP(hAPP(c_Product__Type_OPair(_1528172, _1528172), _1528178), _1528176)), _1528174))], (43267 ^ _779203) ^ [_1642521, _1642523, _1642525, _1642527, _1642529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642521), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642523)), _1642525))), -(hAPP(hAPP(c_List_Olist__update(_1642523, hAPP(hAPP(c_List_Oappend(_1642523), _1642525), _1642527)), _1642521), _1642529) = hAPP(hAPP(c_List_Oappend(_1642523), hAPP(hAPP(c_List_Olist__update(_1642523, _1642525), _1642521), _1642529)), _1642527))], (44313 ^ _779203) ^ [_1665458, _1665460, _1665462, _1665464, _1665466] : [-(hAPP(c_List_Orotate(_1665458, _1665460), hAPP(hAPP(c_List_Omap(_1665462, _1665458), _1665464), _1665466)) = hAPP(hAPP(c_List_Omap(_1665462, _1665458), _1665464), hAPP(c_List_Orotate(_1665462, _1665460), _1665466)))], (51237 ^ _779203) ^ [_1815783, _1815785] : [_1815783 = _1815785, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815783), _1815785)))], (422 ^ _779203) ^ [_785532, _785534, _785536, _785538, _785540, _785542] : [-(c_Relation_Ototal__on(_785540, _785536, _785532)), c_Relation_Ototal__on(_785542, _785538, _785534), _785542 = _785540, _785538 = _785536, _785534 = _785532], (45909 ^ _779203) ^ [_1703020, _1703022] : [45910 ^ _779203 : [(45913 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1703022), _1703020))], (45911 ^ _779203) ^ [] : [_1703022 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1703020, _1703022) = c_List_Olist_ONil(tc_Nat_Onat))], (33143 ^ _779203) ^ [_1386180, _1386182] : [_1386180 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1386180, _1386182) = 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)))], (50455 ^ _779203) ^ [_1801269, _1801271, _1801273, _1801275, _1801277, _1801279] : [50458 ^ _779203 : [(50465 ^ _779203) ^ [] : [hAPP(hAPP(_1801277, 50456 ^ [_1801269, _1801271, _1801273, _1801275, _1801277, _1801279]), 50460 ^ [_1801269, _1801271, _1801273, _1801275, _1801277, _1801279]) = hAPP(hAPP(_1801277, 50457 ^ [_1801269, _1801271, _1801273, _1801275, _1801277, _1801279]), 50461 ^ [_1801269, _1801271, _1801273, _1801275, _1801277, _1801279])], (50463 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801273, _1801273)), hAPP(hAPP(c_Product__Type_OPair(_1801273, _1801273), 50460 ^ [_1801269, _1801271, _1801273, _1801275, _1801277, _1801279]), 50461 ^ [_1801269, _1801271, _1801273, _1801275, _1801277, _1801279])), _1801275)))], (50459 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801269, _1801269)), hAPP(hAPP(c_Product__Type_OPair(_1801269, _1801269), 50456 ^ [_1801269, _1801271, _1801273, _1801275, _1801277, _1801279]), 50457 ^ [_1801269, _1801271, _1801273, _1801275, _1801277, _1801279])), _1801271)))]], -(c_Equiv__Relations_Ocongruent2(_1801269, _1801273, _1801279, _1801271, _1801275, _1801277))], (52493 ^ _779203) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (41601 ^ _779203) ^ [_1602393, _1602395, _1602397, _1602399, _1602401] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602393), tc_List_Olist(_1602393))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602393), tc_List_Olist(_1602393)), _1602395), _1602397)), c_List_Olistrel(_1602393, c_Transitive__Closure_Ortrancl(_1602393, _1602399)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602393), tc_List_Olist(_1602393))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602393), tc_List_Olist(_1602393)), _1602397), _1602401)), c_List_Olistrel(_1602393, c_Transitive__Closure_Ortrancl(_1602393, _1602399)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602393), tc_List_Olist(_1602393))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602393), tc_List_Olist(_1602393)), _1602395), _1602401)), c_List_Olistrel(_1602393, c_Transitive__Closure_Ortrancl(_1602393, _1602399)))))], (18606 ^ _779203) ^ [_1107327, _1107329, _1107331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1107327), _1107329)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1107331)), -(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), _1107331)), _1107327)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1107331)), _1107329))))], (34494 ^ _779203) ^ [_1415706, _1415708, _1415710, _1415712, _1415714, _1415716] : [class_Complete__Lattice_Ocomplete__lattice(_1415706), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1415708, tc_fun(_1415710, _1415706)), _1415712), _1415714), _1415716) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1415708, _1415706), _1415712), hAPP(hAPP(c_COMBC(_1415708, _1415710, _1415706), _1415714), _1415716)))], (48412 ^ _779203) ^ [_1755386, _1755388] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint, tc_Int_Oint), c_Lazy__Sequence_Osmall__lazy_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1755386), _1755388))), 48415 ^ _779203 : [(48422 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755386), _1755388))), -(c_Lazy__Sequence_Osmall__lazy_H(_1755386, _1755388) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1755388), c_Lazy__Sequence_Osmall__lazy_H(_1755386, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1755388), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (48416 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1755386), _1755388)), -(c_Lazy__Sequence_Osmall__lazy_H(_1755386, _1755388) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (19700 ^ _779203) ^ [_1126781, _1126783, _1126785] : [class_Groups_Ogroup__add(_1126781), 19703 ^ _779203 : [(19710 ^ _779203) ^ [] : [_1126785 = hAPP(c_Groups_Ouminus__class_Ouminus(_1126781), _1126783), -(_1126783 = hAPP(c_Groups_Ouminus__class_Ouminus(_1126781), _1126785))], (19704 ^ _779203) ^ [] : [_1126783 = hAPP(c_Groups_Ouminus__class_Ouminus(_1126781), _1126785), -(_1126785 = hAPP(c_Groups_Ouminus__class_Ouminus(_1126781), _1126783))]]], (43058 ^ _779203) ^ [_1638186, _1638188, _1638190, _1638192] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1638186)), hAPP(hAPP(c_List_Oappend(_1638186), _1638188), _1638190)), c_List_Olists(_1638186, _1638192)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1638186)), _1638188), c_List_Olists(_1638186, _1638192))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1638186)), _1638190), c_List_Olists(_1638186, _1638192)))], (12154 ^ _779203) ^ [_989165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _989165)), -(_989165 = hAPP(c_Nat_OSuc, 12157 ^ [_989165]))], (4604 ^ _779203) ^ [_849185, _849187] : [_849187 = _849185, -(c_DSequence_Osingle(_849187) = c_DSequence_Osingle(_849185))], (20646 ^ _779203) ^ [_1143411, _1143413, _1143415, _1143417] : [hBOOL(hAPP(hAPP(_1143415, _1143417), _1143413)), -(hBOOL(hAPP(hAPP(c_member(_1143411), _1143413), c_SetInterval_Oord_OatLeast(_1143411, _1143415, _1143417))))], (41995 ^ _779203) ^ [_1613184, _1613186, _1613188, _1613190, _1613192] : [hBOOL(hAPP(hAPP(c_member(_1613184), _1613186), hAPP(c_List_Oset(_1613184), _1613188))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1613190), hAPP(_1613192, _1613186))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1613190), c_List_Olist_Olist__size(_1613184, _1613192, _1613188))))], (37906 ^ _779203) ^ [_1501619] : [-(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)))), _1501619))))], (29444 ^ _779203) ^ [_1301580, _1301582, _1301584] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301580, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301580, tc_HOL_Obool)), _1301582), _1301584)), _1301584)))], (42030 ^ _779203) ^ [_1613987, _1613989, _1613991] : [hBOOL(hAPP(hAPP(c_member(_1613987), _1613989), hAPP(c_List_Oset(_1613987), _1613991))), 42034 ^ _779203 : [(42037 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1613987), _1613991), 42033 ^ [_1613987, _1613989, _1613991]) = _1613989)], (42035 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42033 ^ [_1613987, _1613989, _1613991]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1613987)), _1613991))))]]], (12839 ^ _779203) ^ [_1001102, _1001104, _1001106] : [class_Rings_Olinordered__ring(_1001102), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1001102), c_Groups_Ozero__class_Ozero(_1001102)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1001102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001102), _1001104), _1001104)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1001102), _1001106), _1001106)))))], (26848 ^ _779203) ^ [_1252192] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1252192))))], (42445 ^ _779203) ^ [_1625212, _1625214, _1625216] : [-(hBOOL(hAPP(c_List_Odistinct(_1625212), hAPP(hAPP(c_List_Olist_OCons(_1625212), _1625214), _1625216)))), -(hBOOL(hAPP(hAPP(c_member(_1625212), _1625214), hAPP(c_List_Oset(_1625212), _1625216)))), hBOOL(hAPP(c_List_Odistinct(_1625212), _1625216))], (21075 ^ _779203) ^ [_1150708, _1150710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1150708)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1150710)), _1150708) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1150710), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1150708), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (40030 ^ _779203) ^ [_1560201, _1560203, _1560205, _1560207] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1560201, tc_HOL_Obool), tc_fun(_1560201, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1560201, tc_HOL_Obool), tc_fun(_1560201, tc_HOL_Obool)), _1560203), _1560205)), c_Wellfounded_Omax__ext(_1560201, _1560207)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560201), _1560203)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1560201), _1560205)), -(_1560205 = c_Orderings_Obot__class_Obot(tc_fun(_1560201, tc_HOL_Obool))), 40044 ^ _779203 : [(40047 ^ _779203) ^ [_1560606] : [hBOOL(hAPP(hAPP(c_member(_1560201), _1560606), _1560205)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1560201, _1560201)), hAPP(hAPP(c_Product__Type_OPair(_1560201, _1560201), 40043 ^ [_1560201, _1560203, _1560205, _1560207]), _1560606)), _1560207))], (40045 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1560201), 40043 ^ [_1560201, _1560203, _1560205, _1560207]), _1560203)))]]], (29810 ^ _779203) ^ [_1309163, _1309165] : [c_Nat__Transfer_Onat__set(_1309163), c_Nat__Transfer_Onat__set(_1309165), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1309163), _1309165) = 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), _1309163)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1309165))))], (44801 ^ _779203) ^ [_1676957, _1676959] : [_1676957 = _1676959, -(hAPP(c_Code__Numeral_Onat__of, _1676957) = hAPP(c_Code__Numeral_Onat__of, _1676959))], (19984 ^ _779203) ^ [_1131514, _1131516, _1131518] : [class_Groups_Ogroup__add(_1131514), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131514), _1131516), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131514), hAPP(c_Groups_Ouminus__class_Ouminus(_1131514), _1131516)), _1131518)) = _1131518)], (29844 ^ _779203) ^ [_1309800, _1309802, _1309804] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309800, tc_HOL_Obool)), _1309802), _1309804) = c_Orderings_Obot__class_Obot(tc_fun(_1309800, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309800, tc_HOL_Obool)), _1309802), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1309800, tc_HOL_Obool)), _1309804))))], (5905 ^ _779203) ^ [_872810, _872812] : [hBOOL(hAPP(hAPP(c_member(_872810), _872812), c_Orderings_Obot__class_Obot(tc_fun(_872810, tc_HOL_Obool))))], (52429 ^ _779203) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (34949 ^ _779203) ^ [_1428364, _1428366, _1428368, _1428370] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428364, tc_fun(_1428366, tc_HOL_Obool)), _1428368), _1428370) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1428366, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428364, tc_fun(_1428366, tc_HOL_Obool), _1428370), _1428368)))], (34308 ^ _779203) ^ [_1409549, _1409551, _1409553, _1409555, _1409557] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409549, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409551, tc_fun(_1409549, tc_HOL_Obool)), _1409553), _1409555)), _1409557) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409551, tc_fun(_1409549, tc_HOL_Obool)), _1409553), hAPP(hAPP(c_COMBC(_1409551, tc_fun(_1409549, tc_HOL_Obool), tc_fun(_1409549, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409549, tc_HOL_Obool), tc_fun(tc_fun(_1409549, tc_HOL_Obool), tc_fun(_1409549, tc_HOL_Obool)), _1409551), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409549, tc_HOL_Obool))), _1409555)), _1409557)))], (29648 ^ _779203) ^ [_1305341, _1305343, _1305345, _1305347] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305341, tc_HOL_Obool)), _1305343), _1305345), _1305347)), -(hBOOL(hAPP(_1305345, _1305347)))], (45833 ^ _779203) ^ [_1701405, _1701407, _1701409, _1701411, _1701413, _1701415, _1701417] : [-(c_List_Ofoldr(_1701405, _1701407, _1701409, hAPP(hAPP(c_List_Omap(_1701411, _1701405), _1701413), _1701415), _1701417) = c_List_Ofoldr(_1701411, _1701407, hAPP(c_Fun_Ocomp(_1701405, tc_fun(_1701407, _1701407), _1701411, _1701409), _1701413), _1701415, _1701417))], (29288 ^ _779203) ^ [_1298314, _1298316, _1298318, _1298320] : [class_Lattices_Osemilattice__inf(_1298314), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298314), _1298316), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298314), _1298318), _1298320)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298314), _1298318), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298314), _1298316), _1298320)))], (12308 ^ _779203) ^ [_991412, _991414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _991412)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _991414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _991414), _991412)), _991414)))], (21425 ^ _779203) ^ [_1156565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1156565), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1156565 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1156565 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (52613 ^ _779203) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (38457 ^ _779203) ^ [_1521460, _1521462, _1521464, _1521466, _1521468] : [-(hAPP(c_Relation_ORange(_1521460, _1521462), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1521460, _1521462)), hAPP(hAPP(c_Product__Type_OPair(_1521460, _1521462), _1521464), _1521466)), _1521468)) = hAPP(hAPP(c_Set_Oinsert(_1521462), _1521466), hAPP(c_Relation_ORange(_1521460, _1521462), _1521468)))], (41308 ^ _779203) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34911 ^ _779203) ^ [_1427376, _1427378, _1427380, _1427382, _1427384] : [_1427376 = c_Orderings_Obot__class_Obot(tc_fun(_1427378, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427380, tc_HOL_Obool)), _1427382), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427378, tc_fun(_1427380, tc_HOL_Obool)), _1427376), _1427384)) = _1427382)], (21937 ^ _779203) ^ [_1165810, _1165812, _1165814] : [-(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), _1165810), _1165812)), _1165812)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1165810, _1165812))), _1165814) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1165810), _1165814))], (16248 ^ _779203) ^ [_1064463, _1064465, _1064467, _1064469] : [class_Orderings_Olinorder(_1064463), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064463), _1064465)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1064463, _1064463, c_Orderings_Oord__class_Omin(_1064463)), _1064467), hAPP(hAPP(c_Set_Oinsert(_1064463), _1064469), _1064465)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064463), _1064469), hAPP(hAPP(c_Finite__Set_Ofold(_1064463, _1064463, c_Orderings_Oord__class_Omin(_1064463)), _1064467), _1064465)))], (6881 ^ _779203) ^ [_891524, _891526, _891528, _891530] : [hBOOL(hAPP(hAPP(c_member(_891524), _891526), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891524, tc_HOL_Obool)), _891528), _891530))), -(hBOOL(hAPP(hAPP(c_member(_891524), _891526), _891528)))], (41491 ^ _779203) ^ [_1598929, _1598931, _1598933, _1598935, _1598937] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598929), tc_List_Olist(_1598929))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598929), tc_List_Olist(_1598929)), _1598931), _1598933)), c_List_Olistrel1(_1598929, _1598935))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1598929), tc_List_Olist(_1598929))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1598929), tc_List_Olist(_1598929)), hAPP(hAPP(c_List_Olist_OCons(_1598929), _1598937), _1598931)), hAPP(hAPP(c_List_Olist_OCons(_1598929), _1598937), _1598933))), c_List_Olistrel1(_1598929, _1598935))))], (4704 ^ _779203) ^ [_850777, _850779] : [_850779 = _850777, -(c_Wellfounded_Ofinite__psubset(_850779) = c_Wellfounded_Ofinite__psubset(_850777))], (48062 ^ _779203) ^ [_1747991, _1747993, _1747995] : [-(c_List_Osplice(_1747991, hAPP(hAPP(c_List_Olist_OCons(_1747991), _1747993), _1747995), c_List_Olist_ONil(_1747991)) = hAPP(hAPP(c_List_Olist_OCons(_1747991), _1747993), _1747995))], (40978 ^ _779203) ^ [_1583929, _1583931, _1583933] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583929, _1583929)), hAPP(hAPP(c_Product__Type_OPair(_1583929, _1583929), _1583931), _1583931)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583929, _1583929), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1583933))))], (6040 ^ _779203) ^ [_875231, _875233, _875235, _875237, _875239] : [-(hBOOL(hAPP(hAPP(c_member(_875231), _875233), hAPP(c_Set_Oimage(_875235, _875231, _875237), _875239)))), 6041 ^ _779203 : [(6042 ^ _779203) ^ [_875301] : [hBOOL(hAPP(hAPP(c_member(_875235), _875301), _875239)), _875233 = hAPP(_875237, _875301)]]], (11984 ^ _779203) ^ [_986219, _986221, _986223, _986225] : [class_Rings_Olinordered__comm__semiring__strict(_986219), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986219), _986221), _986223)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986219), c_Groups_Ozero__class_Ozero(_986219)), _986225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986219), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986219), _986225), _986221)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986219), _986225), _986223))))], (184 ^ _779203) ^ [_781977, _781979, _781981, _781983, _781985, _781987] : [-(c_Finite__Set_Ofolding__one(_781985, _781981, _781977)), c_Finite__Set_Ofolding__one(_781987, _781983, _781979), _781987 = _781985, _781983 = _781981, _781979 = _781977], (39900 ^ _779203) ^ [_1557093, _1557095, _1557097, _1557099, _1557101, _1557103] : [c_Finite__Set_Ofolding__idem(_1557093, _1557095, _1557097, _1557099), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557093), _1557101)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1557093, tc_HOL_Obool)), _1557103), _1557101)), -(hAPP(c_Fun_Ocomp(_1557095, _1557095, _1557095, hAPP(_1557099, _1557101)), hAPP(_1557099, _1557103)) = hAPP(_1557099, _1557101))], (24844 ^ _779203) ^ [_1217053, _1217055, _1217057, _1217059] : [class_Rings_Olinordered__semidom(_1217053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1217053), c_Groups_Oone__class_Oone(_1217053)), _1217055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217053), hAPP(hAPP(c_Power_Opower__class_Opower(_1217053), _1217055), _1217057)), hAPP(hAPP(c_Power_Opower__class_Opower(_1217053), _1217055), _1217059))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1217057), _1217059)))], (29862 ^ _779203) ^ [_1310223, _1310225, _1310227, _1310229, _1310231] : [class_Orderings_Olinorder(_1310223), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310223, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1310223, _1310225, _1310227)), c_SetInterval_Oord__class_OatLeastAtMost(_1310223, _1310229, _1310231)) = c_SetInterval_Oord__class_OatLeastAtMost(_1310223, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1310223), _1310225), _1310229), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1310223), _1310227), _1310231)))], (43542 ^ _779203) ^ [_1649740, _1649742, _1649744] : [hAPP(hAPP(c_List_Odrop(_1649740), _1649742), _1649744) = c_List_Olist_ONil(_1649740), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649740)), _1649744)), _1649742)))], (52355 ^ _779203) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (35474 ^ _779203) ^ [_1442397, _1442399, _1442401, _1442403, _1442405] : [-(hAPP(c_Relation_OImage(_1442397, _1442399, _1442401), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442397, tc_HOL_Obool)), _1442403), _1442405)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442399, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442397, _1442399, _1442401), _1442403)), hAPP(c_Relation_OImage(_1442397, _1442399, _1442401), _1442405)))], (14051 ^ _779203) ^ [_1023668, _1023670, _1023672] : [class_Fields_Olinordered__field(_1023668), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023668), _1023670), c_Groups_Ozero__class_Ozero(_1023668))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023668), c_Groups_Ozero__class_Ozero(_1023668)), _1023672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023668), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1023668), _1023670), _1023672)), c_Groups_Ozero__class_Ozero(_1023668))))], (38917 ^ _779203) ^ [_1533314, _1533316, _1533318, _1533320, _1533322] : [c_Relation_Orefl__on(_1533314, _1533316, _1533318), hBOOL(hAPP(hAPP(c_member(tc_prod(_1533314, _1533314)), hAPP(hAPP(c_Product__Type_OPair(_1533314, _1533314), _1533320), _1533322)), _1533318)), -(hBOOL(hAPP(hAPP(c_member(_1533314), _1533322), _1533316)))], (32918 ^ _779203) ^ [_1382217, _1382219, _1382221, _1382223, _1382225, _1382227] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1382217, _1382219, _1382221), _1382223), hAPP(hAPP(c_Product__Type_OPair(_1382217, _1382219), _1382225), _1382227)) = hAPP(hAPP(_1382223, _1382225), _1382227))], (42908 ^ _779203) ^ [_1634647, _1634649, _1634651] : [class_Orderings_Olinorder(_1634647), hBOOL(hAPP(c_Finite__Set_Ofinite(_1634647), _1634649)), -(c_List_Olinorder__class_Osorted__list__of__set(_1634647, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1634647, tc_HOL_Obool)), _1634649), hAPP(hAPP(c_Set_Oinsert(_1634647), _1634651), c_Orderings_Obot__class_Obot(tc_fun(_1634647, tc_HOL_Obool))))) = c_List_Oremove1(_1634647, _1634651, c_List_Olinorder__class_Osorted__list__of__set(_1634647, _1634649)))], (24341 ^ _779203) ^ [_1208202] : [c_Nat__Transfer_Onat__set(_1208202), 24344 ^ _779203 : [(24345 ^ _779203) ^ [_1208268] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1208268), _1208202)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1208268)))]]], (47388 ^ _779203) ^ [_1733498, _1733500, _1733502, _1733504, _1733506] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733498)), _1733500) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733502)), _1733504), 47394 ^ _779203 : [(47397 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1733506, hAPP(hAPP(c_List_Onth(_1733498), _1733500), 47393 ^ [_1733498, _1733500, _1733502, _1733504, _1733506])), hAPP(hAPP(c_List_Onth(_1733502), _1733504), 47393 ^ [_1733498, _1733500, _1733502, _1733504, _1733506])))], (47395 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47393 ^ [_1733498, _1733500, _1733502, _1733504, _1733506]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1733498)), _1733500))))]], -(c_List_Olist__all2(_1733498, _1733502, _1733506, _1733500, _1733504))], (6475 ^ _779203) ^ [_883678, _883680, _883682, _883684] : [class_Orderings_Oord(_883678), _883680 = _883682, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883678), _883682), _883684)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883678), _883680), _883684)))], (27410 ^ _779203) ^ [_1262167, _1262169, _1262171] : [class_Lattices_Osemilattice__sup(_1262167), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262167), _1262169), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262167), _1262171), _1262169))))], (32207 ^ _779203) ^ [_1361383, _1361385, _1361387] : [hBOOL(hAPP(c_Predicate_OPowp(_1361383, hAPP(hAPP(c_COMBC(_1361383, tc_fun(_1361383, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361383)), _1361385)), _1361387)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1361383, tc_HOL_Obool)), _1361387), hAPP(c_Set_OPow(_1361383), _1361385))))], (29294 ^ _779203) ^ [_1298457, _1298459, _1298461, _1298463] : [class_Lattices_Olattice(_1298457), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298457), _1298459), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298457), _1298461), _1298463)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298457), _1298461), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298457), _1298459), _1298463)))], (12436 ^ _779203) ^ [_993681, _993683] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _993681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _993681), _993683)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10145 ^ _779203) ^ [_953238, _953240, _953242, _953244, _953246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _953238), _953240)), 10148 ^ _779203 : [(10155 ^ _779203) ^ [] : [_953244 = 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), _953240), _953238)), _953242)), _953246), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953238), _953242)), _953244) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953240), _953242)), _953246))], (10149 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953238), _953242)), _953244) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953240), _953242)), _953246), -(_953244 = 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), _953240), _953238)), _953242)), _953246))]]], (24778 ^ _779203) ^ [_1215824, _1215826, _1215828, _1215830] : [class_Rings_Olinordered__semidom(_1215824), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215824), _1215826), _1215828)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215824), c_Groups_Ozero__class_Ozero(_1215824)), _1215826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1215830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1215824), hAPP(hAPP(c_Power_Opower__class_Opower(_1215824), _1215826), _1215830)), hAPP(hAPP(c_Power_Opower__class_Opower(_1215824), _1215828), _1215830))))], (10967 ^ _779203) ^ [_968485] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _968485)], (50053 ^ _779203) ^ [_1791642, _1791644, _1791646, _1791648, _1791650] : [-(c_Fun_Obij__betw(_1791642, _1791644, _1791646, _1791648, _1791650)), c_Fun_Oinj__on(_1791642, _1791644, _1791646, _1791648), hAPP(c_Set_Oimage(_1791642, _1791644, _1791646), _1791648) = _1791650], (48600 ^ _779203) ^ [_1759867, _1759869, _1759871] : [-(c_FunDef_OTHE__default(_1759869, _1759871, _1759867) = _1759871), 48602 ^ _779203 : [(48605 ^ _779203) ^ [_1759989] : [hBOOL(hAPP(_1759867, _1759989)), -(_1759989 = 48601 ^ [_1759867, _1759869, _1759871])], (48603 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1759867, 48601 ^ [_1759867, _1759869, _1759871])))]]], (38342 ^ _779203) ^ [_1517768, _1517770, _1517772, _1517774, _1517776] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1517768, _1517770, _1517772), _1517774), _1517776) = hAPP(c_Set_OCollect(tc_prod(_1517768, _1517772)), hAPP(c_Product__Type_Oprod_Oprod__case(_1517768, _1517772, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1517772, tc_fun(_1517770, tc_HOL_Obool)), tc_fun(_1517772, tc_HOL_Obool), _1517768), hAPP(c_COMBB(tc_fun(_1517770, tc_HOL_Obool), tc_HOL_Obool, _1517772), c_HOL_OEx(_1517770))), hAPP(hAPP(c_COMBC(_1517768, tc_fun(_1517772, tc_fun(_1517770, tc_HOL_Obool)), tc_fun(_1517772, tc_fun(_1517770, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1517770, tc_HOL_Obool), tc_fun(_1517770, tc_HOL_Obool)), tc_fun(tc_fun(_1517772, tc_fun(_1517770, tc_HOL_Obool)), tc_fun(_1517772, tc_fun(_1517770, tc_HOL_Obool))), _1517768), c_COMBB(tc_fun(_1517770, tc_HOL_Obool), tc_fun(_1517770, tc_HOL_Obool), _1517772)), hAPP(hAPP(c_COMBB(tc_fun(_1517770, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1517770, tc_HOL_Obool), tc_fun(_1517770, tc_HOL_Obool)), _1517768), c_COMBS(_1517770, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517770, tc_HOL_Obool), tc_fun(_1517770, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1517768), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1517770), c_fconj)), hAPP(hAPP(c_COMBC(_1517768, tc_fun(tc_prod(_1517768, _1517770), tc_HOL_Obool), tc_fun(_1517770, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517770, tc_fun(tc_fun(tc_prod(_1517768, _1517770), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1517768, _1517770), tc_HOL_Obool), tc_fun(_1517770, tc_HOL_Obool)), _1517768), c_COMBC(_1517770, tc_fun(tc_prod(_1517768, _1517770), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517770, tc_prod(_1517768, _1517770)), tc_fun(_1517770, tc_fun(tc_fun(tc_prod(_1517768, _1517770), tc_HOL_Obool), tc_HOL_Obool)), _1517768), hAPP(c_COMBB(tc_prod(_1517768, _1517770), tc_fun(tc_fun(tc_prod(_1517768, _1517770), tc_HOL_Obool), tc_HOL_Obool), _1517770), c_member(tc_prod(_1517768, _1517770)))), c_Product__Type_OPair(_1517768, _1517770)))), _1517774))))), hAPP(hAPP(c_COMBC(_1517772, tc_fun(tc_prod(_1517770, _1517772), tc_HOL_Obool), tc_fun(_1517770, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517770, tc_fun(tc_fun(tc_prod(_1517770, _1517772), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1517770, _1517772), tc_HOL_Obool), tc_fun(_1517770, tc_HOL_Obool)), _1517772), c_COMBC(_1517770, tc_fun(tc_prod(_1517770, _1517772), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1517770, tc_prod(_1517770, _1517772)), tc_fun(_1517770, tc_fun(tc_fun(tc_prod(_1517770, _1517772), tc_HOL_Obool), tc_HOL_Obool)), _1517772), hAPP(c_COMBB(tc_prod(_1517770, _1517772), tc_fun(tc_fun(tc_prod(_1517770, _1517772), tc_HOL_Obool), tc_HOL_Obool), _1517770), c_member(tc_prod(_1517770, _1517772)))), hAPP(c_COMBC(_1517770, _1517772, tc_prod(_1517770, _1517772)), c_Product__Type_OPair(_1517770, _1517772))))), _1517776))))))], (26690 ^ _779203) ^ [_1249171, _1249173] : [26698 ^ _779203 : [(26701 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1249173, 26697 ^ [_1249171, _1249173])))], (26699 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 26697 ^ [_1249171, _1249173]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1249171))))]], 26691 ^ _779203 : [(26692 ^ _779203) ^ [_1249240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1249240), _1249171)), hBOOL(hAPP(_1249173, _1249240))]]], (39750 ^ _779203) ^ [_1553692, _1553694, _1553696, _1553698, _1553700, _1553702, _1553704, _1553706] : [c_Finite__Set_Ofolding(_1553692, _1553694, _1553696, _1553698), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553692), _1553700)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1553692), _1553702)), -(hAPP(c_Fun_Ocomp(_1553694, _1553694, _1553704, hAPP(_1553698, _1553702)), hAPP(c_Fun_Ocomp(_1553694, _1553694, _1553704, hAPP(_1553698, _1553700)), _1553706)) = hAPP(c_Fun_Ocomp(_1553694, _1553694, _1553704, hAPP(_1553698, _1553700)), hAPP(c_Fun_Ocomp(_1553694, _1553694, _1553704, hAPP(_1553698, _1553702)), _1553706)))], (21517 ^ _779203) ^ [_1158053, _1158055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1158053), _1158055)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1158053)), c_Int_OBit0(_1158055))))], (52011 ^ _779203) ^ [_1829194, _1829196, _1829198] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829194), _1829196)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1829194), _1829198))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829194)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829196), _1829198)))], (40372 ^ _779203) ^ [_1569270, _1569272, _1569274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569270, _1569270), tc_HOL_Obool)), _1569272), c_Transitive__Closure_Ortrancl(_1569270, _1569274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569270, _1569270), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1569270, _1569272)), c_Transitive__Closure_Ortrancl(_1569270, _1569274))))], (19015 ^ _779203) ^ [_1114189, _1114191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1114189)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1114191)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1114189)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1114191), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1114189))))], (27678 ^ _779203) ^ [_1267025, _1267027, _1267029] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267025, tc_HOL_Obool)), _1267027), _1267029) = c_Orderings_Obot__class_Obot(tc_fun(_1267025, tc_HOL_Obool))), _1267027 = c_Orderings_Obot__class_Obot(tc_fun(_1267025, tc_HOL_Obool)), _1267029 = c_Orderings_Obot__class_Obot(tc_fun(_1267025, tc_HOL_Obool))], (26703 ^ _779203) ^ [_1249401, _1249403] : [26711 ^ _779203 : [(26714 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1249403, 26710 ^ [_1249401, _1249403])))], (26712 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26710 ^ [_1249401, _1249403]), _1249401)))]], 26704 ^ _779203 : [(26705 ^ _779203) ^ [_1249470] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1249470), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1249401))), hBOOL(hAPP(_1249403, _1249470))]]], (5556 ^ _779203) ^ [_864127, _864129, _864131, _864133, _864135, _864137] : [-(c_COMBC(_864137, _864133, _864129) = c_COMBC(_864135, _864131, _864127)), _864137 = _864135, _864133 = _864131, _864129 = _864127], (50136 ^ _779203) ^ [_1793076, _1793078, _1793080] : [c_Fun_Obij__betw(_1793076, _1793076, c_Fun_Oid(_1793076), _1793078, _1793080), -(_1793078 = _1793080)], (48915 ^ _779203) ^ [_1767044, _1767046] : [c_Relation_Otrans(_1767044, _1767046), -(c_Relation_Otrans(_1767044, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1767044, _1767044), tc_HOL_Obool)), _1767046), c_Relation_OId(_1767044))))], (36872 ^ _779203) ^ [_1474088, _1474090, _1474092, _1474094, _1474096, _1474098] : [c_Typedef_Otype__definition(_1474088, _1474090, _1474092, _1474094, _1474096), -(hBOOL(hAPP(hAPP(c_member(_1474090), hAPP(_1474092, _1474098)), _1474096)))], (17268 ^ _779203) ^ [_1083773, _1083775] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083773)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083775)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1083773), _1083775)))], (42702 ^ _779203) ^ [_1630360] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630360)), c_List_Olist_ONil(_1630360)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37287 ^ _779203) ^ [_1483807, _1483809, _1483811, _1483813] : [c_Fun_Oinj__on(_1483807, _1483809, _1483811, c_Orderings_Otop__class_Otop(tc_fun(_1483807, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1483807, _1483809, _1483811), hAPP(c_Set_Oimage(_1483807, _1483809, _1483811), _1483813)) = _1483813)], (32213 ^ _779203) ^ [_1361528, _1361530, _1361532] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1361528, tc_HOL_Obool)), _1361532), hAPP(c_Set_OPow(_1361528), _1361530))), -(hBOOL(hAPP(c_Predicate_OPowp(_1361528, hAPP(hAPP(c_COMBC(_1361528, tc_fun(_1361528, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361528)), _1361530)), _1361532)))], (39788 ^ _779203) ^ [_1554551, _1554553, _1554555, _1554557, _1554559, _1554561] : [c_Finite__Set_Ofolding(_1554551, _1554553, _1554555, _1554557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554551), _1554559)), -(hAPP(c_Fun_Ocomp(_1554553, _1554553, _1554553, hAPP(_1554555, _1554561)), hAPP(_1554557, _1554559)) = hAPP(c_Fun_Ocomp(_1554553, _1554553, _1554553, hAPP(_1554557, _1554559)), hAPP(_1554555, _1554561)))], (19418 ^ _779203) ^ [_1121572] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1121572))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1121572) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42680 ^ _779203) ^ [_1629980, _1629982, _1629984] : [-(hAPP(hAPP(c_List_Ozip(_1629980, _1629982), _1629984), c_List_Olist_ONil(_1629982)) = c_List_Olist_ONil(tc_prod(_1629980, _1629982)))], (19330 ^ _779203) ^ [_1119877] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1119877))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1119877)))], (35367 ^ _779203) ^ [] : [-(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)))], (15648 ^ _779203) ^ [_1053535, _1053537, _1053539, _1053541] : [class_Orderings_Olinorder(_1053535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053535), _1053537), _1053539)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053535), _1053537), _1053541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053535), _1053537), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1053535), _1053539), _1053541))))], (27926 ^ _779203) ^ [_1272086, _1272088] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272086, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1272086, tc_HOL_Obool))), _1272088) = c_Orderings_Otop__class_Otop(tc_fun(_1272086, tc_HOL_Obool)))], (35602 ^ _779203) ^ [_1445880, _1445882] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1445880, _1445880)), _1445882)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1445880), hAPP(c_Relation_OField(_1445880), _1445882))))], (49559 ^ _779203) ^ [_1780401, _1780403] : [c_Equiv__Relations_Opart__equivp(_1780401, _1780403), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1780401, tc_HOL_Obool)), 49562 ^ [_1780401, _1780403]), hAPP(hAPP(c_COMBB(tc_fun(_1780401, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1780401, tc_HOL_Obool)), c_HOL_OEx(_1780401)), hAPP(hAPP(c_COMBB(tc_fun(_1780401, tc_HOL_Obool), tc_fun(_1780401, tc_HOL_Obool), tc_fun(_1780401, tc_HOL_Obool)), hAPP(c_COMBS(_1780401, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1780401), c_fconj), hAPP(hAPP(c_COMBS(_1780401, _1780401, tc_HOL_Obool), _1780403), c_COMBI(_1780401))))), hAPP(hAPP(c_COMBC(tc_fun(_1780401, tc_HOL_Obool), tc_fun(_1780401, tc_fun(_1780401, tc_HOL_Obool)), tc_fun(_1780401, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1780401, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1780401, tc_fun(_1780401, tc_HOL_Obool)), tc_fun(_1780401, tc_HOL_Obool)), tc_fun(_1780401, tc_HOL_Obool)), c_COMBB(tc_fun(_1780401, tc_HOL_Obool), tc_HOL_Obool, _1780401)), c_fequal)), _1780403))))))], (37255 ^ _779203) ^ [_1483116, _1483118, _1483120, _1483122] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1483116), hAPP(c_Set_Ovimage(_1483116, _1483118, _1483120), _1483122))), hAPP(c_Set_Oimage(_1483116, _1483118, _1483120), c_Orderings_Otop__class_Otop(tc_fun(_1483116, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1483118, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1483118), _1483122)))], (18188 ^ _779203) ^ [_1100094] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1100094), c_Int_OPls) = _1100094)], (47776 ^ _779203) ^ [_1742069, _1742071, _1742073] : [c_List_Olist__all(_1742069, _1742071, _1742073), 47779 ^ _779203 : [(47780 ^ _779203) ^ [_1742158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1742158), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742069)), _1742073))), -(hBOOL(hAPP(_1742071, hAPP(hAPP(c_List_Onth(_1742069), _1742073), _1742158))))]]], (44857 ^ _779203) ^ [_1677944, _1677946] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1677944), _1677946) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677944)), hAPP(c_Code__Numeral_Onat__of, _1677946))))], (49154 ^ _779203) ^ [_1773037] : [-(c_Relation_Oantisym(_1773037, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1773037, _1773037), tc_HOL_Obool))))], (26120 ^ _779203) ^ [_1238447, _1238449, _1238451, _1238453] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1238447, _1238449, _1238451, c_Code__Numeral_OSuc__code__numeral(_1238453)) = hAPP(_1238451, _1238453))], (7225 ^ _779203) ^ [_899225, _899227, _899229, _899231] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_899225, tc_HOL_Obool)), _899227), _899229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_899225, tc_HOL_Obool)), _899229), _899231)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_899225, tc_HOL_Obool)), _899227), _899231)))], (49240 ^ _779203) ^ [_1774900, _1774902] : [c_Relation_Osym(_1774900, _1774902), c_Relation_Otrans(_1774900, _1774902), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1774900, _1774900), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1774900, _1774900, _1774900), hAPP(c_Relation_Oconverse(_1774900, _1774900), _1774902)), _1774902)), _1774902)))], (34338 ^ _779203) ^ [_1410773, _1410775, _1410777, _1410779, _1410781] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410773, tc_HOL_Obool)), _1410775), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410777, tc_fun(_1410773, tc_HOL_Obool)), _1410779), _1410781)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410777, tc_fun(_1410773, tc_HOL_Obool)), _1410779), hAPP(hAPP(c_COMBB(tc_fun(_1410773, tc_HOL_Obool), tc_fun(_1410773, tc_HOL_Obool), _1410777), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410773, tc_HOL_Obool)), _1410775)), _1410781)))], (18455 ^ _779203) ^ [_1104722] : [class_Rings_Osemiring__1(_1104722), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104722), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1104722))], (2996 ^ _779203) ^ [_823663, _823665, _823667, _823669] : [-(c_Wellfounded_Oacc(_823669, _823665) = c_Wellfounded_Oacc(_823667, _823663)), _823669 = _823667, _823665 = _823663], (2676 ^ _779203) ^ [_818673, _818675] : [_818675 = _818673, -(c_Set_OBall(_818675) = c_Set_OBall(_818673))], (37639 ^ _779203) ^ [_1493058, _1493060, _1493062, _1493064] : [-(hAPP(c_Set_Ovimage(_1493058, _1493060, _1493062), _1493064) = hAPP(c_Set_OCollect(_1493058), hAPP(hAPP(c_COMBC(_1493058, tc_fun(_1493060, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1493060, tc_fun(tc_fun(_1493060, tc_HOL_Obool), tc_HOL_Obool), _1493058), c_member(_1493060)), _1493062)), _1493064)))], (20524 ^ _779203) ^ [_1141195, _1141197] : [class_Groups_Oabs__if(_1141195), 20527 ^ _779203 : [(20534 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141195), _1141197), c_Groups_Ozero__class_Ozero(_1141195)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1141195), _1141197) = _1141197)], (20528 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141195), _1141197), c_Groups_Ozero__class_Ozero(_1141195))), -(hAPP(c_Groups_Oabs__class_Oabs(_1141195), _1141197) = hAPP(c_Groups_Ouminus__class_Ouminus(_1141195), _1141197))]]], (9087 ^ _779203) ^ [_933546, _933548, _933550, _933552, _933554, _933556] : [class_Rings_Oordered__ring(_933546), 9090 ^ _779203 : [(9097 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933546), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933546), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933546), _933548), _933554)), _933550)), _933552)), _933556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933546), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933546), _933548), _933550)), _933552)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933546), _933554), _933550)), _933556))))], (9091 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933546), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933546), _933548), _933550)), _933552)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933546), _933554), _933550)), _933556))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933546), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933546), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933546), _933548), _933554)), _933550)), _933552)), _933556)))]]], (4652 ^ _779203) ^ [_849957, _849959, _849961, _849963] : [-(c_Product__Type_Osnd(_849963, _849959) = c_Product__Type_Osnd(_849961, _849957)), _849963 = _849961, _849959 = _849957], (23249 ^ _779203) ^ [_1188234, _1188236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1188234), _1188236)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1188234, _1188236) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1188234), _1188236))], (22928 ^ _779203) ^ [_1183003, _1183005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183003)), 22931 ^ _779203 : [(22934 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183005, _1183003)), _1183003)))], (22932 ^ _779203) ^ [] : [-(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, _1183005, _1183003))))]]], (32895 ^ _779203) ^ [_1381661, _1381663, _1381665] : [hBOOL(hAPP(_1381661, 32896 ^ [_1381661, _1381663, _1381665])), 32899 ^ _779203 : [(32900 ^ _779203) ^ [_1381772, _1381774] : [-(hBOOL(hAPP(_1381661, hAPP(hAPP(c_Product__Type_OPair(_1381663, _1381665), _1381774), _1381772))))]]], (24886 ^ _779203) ^ [_1217816] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1217816) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (41415 ^ _779203) ^ [_1596674, _1596676, _1596678] : [-(c_Random_Oselect__weight(_1596674, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1596674)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1596674), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1596676)), _1596678)) = c_Random_Oselect__weight(_1596674, _1596678))], (25458 ^ _779203) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (37757 ^ _779203) ^ [_1496503, _1496505, _1496507, _1496509, _1496511, _1496513] : [-(hAPP(c_Set_Oimage(_1496503, _1496505, hAPP(hAPP(c_COMBS(_1496503, _1496505, _1496505), hAPP(hAPP(c_COMBS(_1496503, _1496505, tc_fun(_1496505, _1496505)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1496505, tc_fun(_1496505, _1496505)), _1496503), c_If(_1496505)), _1496507)), _1496509)), _1496511)), _1496513) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1496505, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1496503, _1496505, _1496509), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496503, tc_HOL_Obool)), _1496513), hAPP(c_Set_OCollect(_1496503), _1496507)))), hAPP(c_Set_Oimage(_1496503, _1496505, _1496511), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1496503, tc_HOL_Obool)), _1496513), hAPP(c_Set_OCollect(_1496503), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1496503), c_fNot), _1496507))))))], (3078 ^ _779203) ^ [_824930, _824932] : [_824932 = _824930, -(c_List_Orotate1(_824932) = c_List_Orotate1(_824930))], (25434 ^ _779203) ^ [_1227733] : [_1227733 = c_Int_OMin, -(c_Int_OBit1(_1227733) = c_Int_OMin)], (28886 ^ _779203) ^ [_1290338, _1290340, _1290342] : [class_Lattices_Olattice(_1290338), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290338), _1290340)), -(hBOOL(hAPP(hAPP(c_member(_1290338), _1290342), _1290340))), -(c_Big__Operators_Olattice__class_OSup__fin(_1290338, hAPP(hAPP(c_Set_Oinsert(_1290338), _1290342), _1290340)) = hAPP(hAPP(c_Finite__Set_Ofold(_1290338, _1290338, c_Lattices_Osemilattice__sup__class_Osup(_1290338)), _1290342), _1290340))], (27916 ^ _779203) ^ [_1271822, _1271824, _1271826, _1271828] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271822, tc_HOL_Obool)), _1271824), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271822, tc_HOL_Obool)), _1271826), _1271828)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271822, tc_HOL_Obool)), _1271826), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271822, tc_HOL_Obool)), _1271824), _1271828)))], (33683 ^ _779203) ^ [_1395755] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1395755)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1395755)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38288 ^ _779203) ^ [_1516165, _1516167, _1516169, _1516171, _1516173, _1516175, _1516177, _1516179, _1516181] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1516165, _1516167)), hAPP(hAPP(c_Product__Type_OPair(_1516165, _1516167), _1516169), _1516171)), _1516173)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516175, _1516177)), hAPP(hAPP(c_Product__Type_OPair(_1516175, _1516177), hAPP(_1516179, _1516169)), hAPP(_1516181, _1516171))), hAPP(c_Set_Oimage(tc_prod(_1516165, _1516167), tc_prod(_1516175, _1516177), c_Product__Type_Omap__pair(_1516165, _1516175, _1516167, _1516177, _1516179, _1516181)), _1516173))))], (31667 ^ _779203) ^ [_1347714, _1347716, _1347718, _1347720, _1347722, _1347724] : [c_Nitpick_Opair__box_OPairBox(_1347714, _1347716, _1347718, _1347720) = c_Nitpick_Opair__box_OPairBox(_1347714, _1347716, _1347722, _1347724), 31670 ^ _779203 : [(31673 ^ _779203) ^ [] : [-(_1347720 = _1347724)], (31671 ^ _779203) ^ [] : [-(_1347718 = _1347722)]]], (52415 ^ _779203) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (26816 ^ _779203) ^ [_1251595] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1251595)) = 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), _1251595))))], (17364 ^ _779203) ^ [_1085302, _1085304, _1085306] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085302), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085304), _1085306)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085302), _1085304)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085302), _1085306)))], (42834 ^ _779203) ^ [_1632917, _1632919, _1632921, _1632923] : [_1632917 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1632919), _1632917), hAPP(hAPP(c_List_Olist_OCons(_1632919), _1632921), _1632923)) = c_List_Olist_ONil(_1632919))], (42373 ^ _779203) ^ [_1623472, _1623474] : [-(c_List_Obutlast(_1623472, _1623474) = hAPP(hAPP(c_List_Otake(_1623472), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623472)), _1623474)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1623474))], (17396 ^ _779203) ^ [_1085992, _1085994] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085992), _1085994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085992), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1085994)))], (1690 ^ _779203) ^ [_803288, _803290] : [-(class_Groups_Oab__semigroup__add(_803288)), _803290 = _803288, class_Groups_Oab__semigroup__add(_803290)], (42580 ^ _779203) ^ [_1628261, _1628263] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1628261)), c_List_Olist_ONil(_1628261)), c_List_Olists(_1628261, _1628263))))], (8176 ^ _779203) ^ [_915023, _915025, _915027, _915029, _915031, _915033, _915035] : [-(_915023 = _915025), -(c_Fun_Ofun__upd(_915027, _915029, c_Fun_Ofun__upd(_915027, _915029, _915031, _915023, _915033), _915025, _915035) = c_Fun_Ofun__upd(_915027, _915029, c_Fun_Ofun__upd(_915027, _915029, _915031, _915025, _915035), _915023, _915033))], (5520 ^ _779203) ^ [_863587, _863589] : [_863589 = _863587, -(tc_Lazy__Sequence_Olazy__sequence(_863589) = tc_Lazy__Sequence_Olazy__sequence(_863587))], (10885 ^ _779203) ^ [_967270, _967272, _967274] : [class_Rings_Ono__zero__divisors(_967270), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967270), _967272), _967274) = c_Groups_Ozero__class_Ozero(_967270), -(_967272 = c_Groups_Ozero__class_Ozero(_967270)), -(_967274 = c_Groups_Ozero__class_Ozero(_967270))], (31490 ^ _779203) ^ [_1343941, _1343943, _1343945] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1343941, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1343941, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1343941, tc_HOL_Obool), _1343943)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1343941, tc_HOL_Obool), _1343945))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1343941, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1343941, tc_HOL_Obool), tc_HOL_Obool)), _1343943), _1343945)))))], (34206 ^ _779203) ^ [_1407195, _1407197, _1407199, _1407201, _1407203, _1407205] : [hBOOL(hAPP(hAPP(c_member(_1407195), _1407197), _1407199)), hBOOL(hAPP(hAPP(_1407201, _1407197), _1407203)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407195, tc_fun(_1407205, tc_HOL_Obool)), _1407199), _1407201), _1407203)))], (52623 ^ _779203) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (18016 ^ _779203) ^ [_1096943, _1096945] : [class_Orderings_Olinorder(_1096943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1096943), _1096945)), -(_1096945 = c_Orderings_Obot__class_Obot(tc_fun(_1096943, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1096943), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1096943), 18029 ^ [_1096943, _1096945]), 18030 ^ [_1096943, _1096945])), hAPP(hAPP(c_Set_Oinsert(_1096943), 18029 ^ [_1096943, _1096945]), hAPP(hAPP(c_Set_Oinsert(_1096943), 18030 ^ [_1096943, _1096945]), c_Orderings_Obot__class_Obot(tc_fun(_1096943, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1096943), c_Big__Operators_Olattice_OInf__fin(_1096943, c_Orderings_Oord__class_Omin(_1096943), _1096945)), _1096945)))], (44628 ^ _779203) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3910 ^ _779203) ^ [_838184, _838186, _838188, _838190, _838192, _838194, _838196, _838198] : [-(c_Lazy__Sequence_Ohb__bind(_838198, _838194, _838190, _838186) = c_Lazy__Sequence_Ohb__bind(_838196, _838192, _838188, _838184)), _838198 = _838196, _838194 = _838192, _838190 = _838188, _838186 = _838184], (48284 ^ _779203) ^ [_1752890, _1752892] : [-(c_List_Oreplicate(_1752890, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1752892) = c_List_Olist_ONil(_1752890))], (15069 ^ _779203) ^ [_1042600, _1042602, _1042604] : [class_Orderings_Olinorder(_1042600), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042600), _1042602)), hBOOL(hAPP(hAPP(c_member(_1042600), _1042604), _1042602)), 15080 ^ _779203 : [(15087 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042600, tc_HOL_Obool)), _1042602), hAPP(hAPP(c_Set_Oinsert(_1042600), _1042604), c_Orderings_Obot__class_Obot(tc_fun(_1042600, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1042600, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1042600, _1042602) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1042600), _1042604), c_Big__Operators_Olinorder__class_OMax(_1042600, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042600, tc_HOL_Obool)), _1042602), hAPP(hAPP(c_Set_Oinsert(_1042600), _1042604), c_Orderings_Obot__class_Obot(tc_fun(_1042600, tc_HOL_Obool)))))))], (15081 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042600, tc_HOL_Obool)), _1042602), hAPP(hAPP(c_Set_Oinsert(_1042600), _1042604), c_Orderings_Obot__class_Obot(tc_fun(_1042600, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1042600, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1042600, _1042602) = _1042604)]]], (18945 ^ _779203) ^ [_1112963] : [-(c_Int_Osucc(c_Int_Opred(_1112963)) = _1112963)], (48248 ^ _779203) ^ [_1752244, _1752246, _1752248, _1752250, _1752252] : [-(c_List_Oreplicate(_1752244, _1752246, _1752248) = c_List_Oreplicate(_1752244, _1752250, _1752252)), _1752246 = _1752250, 48253 ^ _779203 : [(48256 ^ _779203) ^ [] : [_1752248 = _1752252], (48254 ^ _779203) ^ [] : [_1752246 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (30813 ^ _779203) ^ [_1330292, _1330294, _1330296, _1330298, _1330300] : [class_Groups_Ocomm__monoid__add(_1330292), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330294), _1330296)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1330294), _1330298)), 30827 ^ _779203 : [(30830 ^ _779203) ^ [] : [hAPP(_1330300, 30826 ^ [_1330292, _1330294, _1330296, _1330298, _1330300]) = c_Groups_Ozero__class_Ozero(_1330292)], (30828 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1330294), 30826 ^ [_1330292, _1330294, _1330296, _1330298, _1330300]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1330294, tc_HOL_Obool)), _1330296), _1330298))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1330294, _1330292), _1330300), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1330294, tc_HOL_Obool)), _1330296), _1330298)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1330292), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1330294, _1330292), _1330300), _1330296)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1330294, _1330292), _1330300), _1330298)))], (8619 ^ _779203) ^ [_924356, _924358, _924360] : [class_Lattices_Oab__semigroup__idem__mult(_924356), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924356), _924358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924356), _924358), _924360)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924356), _924358), _924360))], (49306 ^ _779203) ^ [_1776243] : [-(c_Relation_Osym(_1776243, c_Relation_OId(_1776243)))], (42265 ^ _779203) ^ [_1621093, _1621095, _1621097, _1621099, _1621101] : [-(_1621093 = _1621095), -(hAPP(hAPP(c_List_Onth(_1621097), hAPP(hAPP(c_List_Olist__update(_1621097, _1621099), _1621093), _1621101)), _1621095) = hAPP(hAPP(c_List_Onth(_1621097), _1621099), _1621095))], (52463 ^ _779203) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (15692 ^ _779203) ^ [_1054285, _1054287, _1054289, _1054291] : [class_Orderings_Olinorder(_1054285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054285), _1054287), _1054289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054285), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1054285), _1054287), _1054291)), _1054289)))], (12733 ^ _779203) ^ [_999092, _999094, _999096, _999098] : [class_Rings_Olinordered__semiring(_999092), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999092), _999094), _999096)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999092), _999098), _999096))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999092), c_Groups_Ozero__class_Ozero(_999092)), _999096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999092), _999094), _999098)))], (24201 ^ _779203) ^ [_1205359, _1205361, _1205363] : [class_Rings_Olinordered__idom(_1205359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205359), _1205361), c_Groups_Ozero__class_Ozero(_1205359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1205359), hAPP(hAPP(c_Power_Opower__class_Opower(_1205359), _1205361), 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)))), _1205363)))), c_Groups_Ozero__class_Ozero(_1205359))))], (34935 ^ _779203) ^ [_1427895, _1427897, _1427899, _1427901, _1427903] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427895, tc_fun(_1427897, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1427895), _1427899), _1427901)), _1427903) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427897, tc_HOL_Obool)), hAPP(_1427903, _1427899)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427895, tc_fun(_1427897, tc_HOL_Obool)), _1427901), _1427903)))], (4542 ^ _779203) ^ [_848192, _848194, _848196, _848198, _848200, _848202, _848204, _848206] : [-(c_Random__Sequence_ORandom(_848206, _848202, _848198, _848194) = c_Random__Sequence_ORandom(_848204, _848200, _848196, _848192)), _848206 = _848204, _848202 = _848200, _848198 = _848196, _848194 = _848192], (50795 ^ _779203) ^ [_1807890, _1807892, _1807894] : [class_Divides_Osemiring__div(_1807890), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807890), _1807892), _1807894)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807890), _1807892), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807890), _1807894), _1807892)) = _1807894)], (38122 ^ _779203) ^ [_1510219, _1510221, _1510223] : [class_Lattices_Odistrib__lattice(_1510219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510219), _1510221)), -(_1510221 = c_Orderings_Obot__class_Obot(tc_fun(_1510219, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1510219), _1510223), c_Big__Operators_Olattice__class_OSup__fin(_1510219, _1510221)) = c_Big__Operators_Olattice__class_OSup__fin(_1510219, hAPP(c_Set_OCollect(_1510219), hAPP(hAPP(c_COMBB(tc_fun(_1510219, tc_HOL_Obool), tc_HOL_Obool, _1510219), c_HOL_OEx(_1510219)), hAPP(hAPP(c_COMBC(_1510219, tc_fun(_1510219, tc_HOL_Obool), tc_fun(_1510219, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1510219, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1510219, tc_HOL_Obool), tc_fun(_1510219, tc_HOL_Obool)), _1510219), c_COMBS(_1510219, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1510219, tc_HOL_Obool), tc_fun(_1510219, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1510219), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510219), c_fconj)), hAPP(hAPP(c_COMBC(_1510219, tc_fun(_1510219, _1510219), tc_fun(_1510219, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1510219, tc_HOL_Obool), tc_fun(tc_fun(_1510219, _1510219), tc_fun(_1510219, tc_HOL_Obool)), _1510219), c_COMBB(_1510219, tc_HOL_Obool, _1510219)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1510219), _1510223))))), hAPP(hAPP(c_COMBC(_1510219, tc_fun(_1510219, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510219)), _1510221))))))], (39475 ^ _779203) ^ [_1547313, _1547315] : [-(c_Hilbert__Choice_OEps(_1547313, hAPP(c_fequal, _1547315)) = _1547315)], (28504 ^ _779203) ^ [_1283277, _1283279, _1283281, _1283283] : [class_Orderings_Olinorder(_1283277), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283277), _1283279), _1283281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283277), _1283281), _1283283)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283277, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1283277, _1283279, _1283281)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1283277, _1283281), _1283283)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1283277, _1283279, _1283283))], (12042 ^ _779203) ^ [_987309, _987311, _987313] : [class_Groups_Oordered__ab__group__add(_987309), 12045 ^ _779203 : [(12052 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987309), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_987309), _987311), _987313)), c_Groups_Ozero__class_Ozero(_987309))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987309), _987311), _987313)))], (12046 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987309), _987311), _987313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987309), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_987309), _987311), _987313)), c_Groups_Ozero__class_Ozero(_987309))))]]], (40191 ^ _779203) ^ [_1564031, _1564033, _1564035, _1564037] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564031, _1564031)), hAPP(hAPP(c_Product__Type_OPair(_1564031, _1564031), _1564033), _1564035)), _1564037)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564031, _1564031)), hAPP(hAPP(c_Product__Type_OPair(_1564031, _1564031), _1564033), _1564035)), c_Transitive__Closure_Otrancl(_1564031, _1564037))))], (19924 ^ _779203) ^ [_1130387, _1130389, _1130391] : [class_Groups_Oordered__ab__group__add(_1130387), 19927 ^ _779203 : [(19934 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130387), _1130391), _1130389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130387), hAPP(c_Groups_Ouminus__class_Ouminus(_1130387), _1130389)), hAPP(c_Groups_Ouminus__class_Ouminus(_1130387), _1130391))))], (19928 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130387), hAPP(c_Groups_Ouminus__class_Ouminus(_1130387), _1130389)), hAPP(c_Groups_Ouminus__class_Ouminus(_1130387), _1130391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130387), _1130391), _1130389)))]]], (41836 ^ _779203) ^ [_1609185, _1609187, _1609189, _1609191] : [-(_1609185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1609187), hAPP(hAPP(c_List_Olist_OCons(_1609187), _1609189), _1609191)), _1609185) = hAPP(hAPP(c_List_Onth(_1609187), _1609191), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1609185), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (9235 ^ _779203) ^ [_936741, _936743] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936741), hAPP(c_Nat_OSuc, _936743)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936741), _936743)))], (31075 ^ _779203) ^ [_1335054, _1335056, _1335058] : [class_Lattices_Olattice(_1335054), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335054), _1335056)), -(hBOOL(hAPP(hAPP(c_member(_1335054), _1335058), _1335056))), -(c_Big__Operators_Olattice__class_OInf__fin(_1335054, hAPP(hAPP(c_Set_Oinsert(_1335054), _1335058), _1335056)) = hAPP(hAPP(c_Finite__Set_Ofold(_1335054, _1335054, c_Lattices_Osemilattice__inf__class_Oinf(_1335054)), _1335058), _1335056))], (51403 ^ _779203) ^ [_1818413, _1818415] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818413), _1818415))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818413), _1818415)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818415), _1818413)))], (44921 ^ _779203) ^ [_1679824, _1679826, _1679828] : [44923 ^ _779203 : [(44926 ^ _779203) ^ [] : [hBOOL(hAPP(_1679826, 44922 ^ [_1679824, _1679826, _1679828]))], (44924 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1679824), 44922 ^ [_1679824, _1679826, _1679828]), hAPP(c_List_Oset(_1679824), _1679828))))]], -(hBOOL(hAPP(c_List_Olistsp(_1679824, _1679826), _1679828)))], (42214 ^ _779203) ^ [_1619997, _1619999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1619997), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1619999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1619999), _1619997)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619999))))], (23621 ^ _779203) ^ [_1195108, _1195110] : [_1195108 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1195108, _1195110) = _1195110)], (39732 ^ _779203) ^ [_1553137, _1553139, _1553141, _1553143, _1553145, _1553147] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1553137, tc_fun(_1553139, tc_HOL_Obool)), _1553141), hAPP(c_Fun_Ocomp(_1553143, tc_fun(_1553139, tc_HOL_Obool), _1553137, _1553145), _1553147)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1553143, tc_fun(_1553139, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1553137, _1553143, _1553147), _1553141)), _1553145))], (13611 ^ _779203) ^ [_1015723, _1015725, _1015727, _1015729] : [class_Rings_Odivision__ring(_1015723), -(_1015725 = c_Groups_Ozero__class_Ozero(_1015723)), _1015727 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015723), _1015729), _1015725), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015723), _1015727), _1015725) = _1015729)], (17436 ^ _779203) ^ [_1086685, _1086687, _1086689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086685), _1086687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086685), _1086689)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086687), _1086689))))], (38945 ^ _779203) ^ [_1533910, _1533912, _1533914, _1533916] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1533910, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1533910, _1533912), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1533910, _1533912), tc_HOL_Obool)), _1533914), _1533916))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1533910, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1533910, _1533912), _1533914)), hAPP(c_Relation_ODomain(_1533910, _1533912), _1533916)))))], (43680 ^ _779203) ^ [_1653291, _1653293, _1653295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653291), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653293)), _1653295))), -(hAPP(hAPP(c_List_Oappend(_1653293), hAPP(hAPP(c_List_Otake(_1653293), _1653291), _1653295)), hAPP(hAPP(c_List_Olist_OCons(_1653293), hAPP(c_List_Ohd(_1653293), hAPP(hAPP(c_List_Odrop(_1653293), _1653291), _1653295))), c_List_Olist_ONil(_1653293))) = hAPP(hAPP(c_List_Otake(_1653293), hAPP(c_Nat_OSuc, _1653291)), _1653295))], (32825 ^ _779203) ^ [_1380237, _1380239, _1380241, _1380243, _1380245, _1380247] : [hBOOL(hAPP(hAPP(_1380237, _1380239), _1380241)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1380243, tc_fun(_1380245, tc_HOL_Obool))), _1380247), _1380237), _1380239), _1380241)))], (14823 ^ _779203) ^ [_1037677, _1037679, _1037681] : [class_Lattices_Oab__semigroup__idem__mult(_1037677), hAPP(_1037679, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037677), 14828 ^ [_1037677, _1037679, _1037681]), 14829 ^ [_1037677, _1037679, _1037681])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1037677), hAPP(_1037679, 14828 ^ [_1037677, _1037679, _1037681])), hAPP(_1037679, 14829 ^ [_1037677, _1037679, _1037681])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1037677), _1037681)), -(_1037681 = c_Orderings_Obot__class_Obot(tc_fun(_1037677, tc_HOL_Obool))), -(hAPP(_1037679, hAPP(c_Finite__Set_Ofold1(_1037677, c_Groups_Otimes__class_Otimes(_1037677)), _1037681)) = hAPP(c_Finite__Set_Ofold1(_1037677, c_Groups_Otimes__class_Otimes(_1037677)), hAPP(c_Set_Oimage(_1037677, _1037677, _1037679), _1037681)))], (38172 ^ _779203) ^ [_1512302, _1512304, _1512306, _1512308, _1512310, _1512312, _1512314] : [class_Rings_Osemiring__0(_1512302), c_Fun_Oinj__on(tc_prod(_1512304, _1512306), _1512302, hAPP(c_Product__Type_Oprod_Oprod__case(_1512304, _1512306, _1512302), hAPP(hAPP(c_COMBC(_1512304, tc_fun(_1512306, _1512302), tc_fun(_1512306, _1512302)), hAPP(hAPP(c_COMBB(tc_fun(_1512302, _1512302), tc_fun(tc_fun(_1512306, _1512302), tc_fun(_1512306, _1512302)), _1512304), c_COMBB(_1512302, _1512302, _1512306)), hAPP(hAPP(c_COMBB(_1512302, tc_fun(_1512302, _1512302), _1512304), c_Groups_Otimes__class_Otimes(_1512302)), _1512308))), _1512310)), hAPP(hAPP(c_Product__Type_OSigma(_1512304, _1512306), _1512312), hAPP(c_COMBK(tc_fun(_1512306, tc_HOL_Obool), _1512304), _1512314))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1512302), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512304, _1512302), _1512308), _1512312)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512306, _1512302), _1512310), _1512314)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1512302, _1512302), c_Fun_Oid(_1512302)), hAPP(c_Set_OCollect(_1512302), hAPP(hAPP(c_COMBB(tc_fun(_1512304, tc_HOL_Obool), tc_HOL_Obool, _1512302), c_HOL_OEx(_1512304)), hAPP(hAPP(c_COMBB(tc_fun(_1512304, tc_fun(_1512306, tc_HOL_Obool)), tc_fun(_1512304, tc_HOL_Obool), _1512302), hAPP(c_COMBB(tc_fun(_1512306, tc_HOL_Obool), tc_HOL_Obool, _1512304), c_HOL_OEx(_1512306))), hAPP(hAPP(c_COMBC(_1512302, tc_fun(_1512304, tc_fun(_1512306, tc_HOL_Obool)), tc_fun(_1512304, tc_fun(_1512306, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512304, tc_fun(tc_fun(_1512306, tc_HOL_Obool), tc_fun(_1512306, tc_HOL_Obool))), tc_fun(tc_fun(_1512304, tc_fun(_1512306, tc_HOL_Obool)), tc_fun(_1512304, tc_fun(_1512306, tc_HOL_Obool))), _1512302), c_COMBS(_1512304, tc_fun(_1512306, tc_HOL_Obool), tc_fun(_1512306, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512304, tc_fun(_1512306, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1512304, tc_fun(tc_fun(_1512306, tc_HOL_Obool), tc_fun(_1512306, tc_HOL_Obool))), _1512302), hAPP(c_COMBB(tc_fun(_1512306, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1512306, tc_HOL_Obool), tc_fun(_1512306, tc_HOL_Obool)), _1512304), c_COMBS(_1512306, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1512304, tc_fun(_1512306, tc_HOL_Obool)), tc_fun(_1512304, tc_fun(_1512306, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1512302), hAPP(c_COMBB(tc_fun(_1512306, tc_HOL_Obool), tc_fun(_1512306, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1512304), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512306), c_fconj))), hAPP(hAPP(c_COMBC(_1512302, tc_fun(_1512304, tc_fun(_1512306, _1512302)), tc_fun(_1512304, tc_fun(_1512306, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1512306, _1512302), tc_fun(_1512306, tc_HOL_Obool)), tc_fun(tc_fun(_1512304, tc_fun(_1512306, _1512302)), tc_fun(_1512304, tc_fun(_1512306, tc_HOL_Obool))), _1512302), c_COMBB(tc_fun(_1512306, _1512302), tc_fun(_1512306, tc_HOL_Obool), _1512304)), hAPP(hAPP(c_COMBB(tc_fun(_1512302, tc_HOL_Obool), tc_fun(tc_fun(_1512306, _1512302), tc_fun(_1512306, tc_HOL_Obool)), _1512302), c_COMBB(_1512302, tc_HOL_Obool, _1512306)), c_fequal))), hAPP(hAPP(c_COMBC(_1512304, tc_fun(_1512306, _1512302), tc_fun(_1512306, _1512302)), hAPP(hAPP(c_COMBB(tc_fun(_1512302, _1512302), tc_fun(tc_fun(_1512306, _1512302), tc_fun(_1512306, _1512302)), _1512304), c_COMBB(_1512302, _1512302, _1512306)), hAPP(hAPP(c_COMBB(_1512302, tc_fun(_1512302, _1512302), _1512304), c_Groups_Otimes__class_Otimes(_1512302)), _1512308))), _1512310)))))), hAPP(hAPP(c_COMBC(_1512304, tc_fun(_1512306, tc_HOL_Obool), tc_fun(_1512306, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1512306, tc_HOL_Obool), tc_fun(_1512306, tc_HOL_Obool)), _1512304), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1512306)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1512304), c_fconj), hAPP(hAPP(c_COMBC(_1512304, tc_fun(_1512304, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512304)), _1512312)))), hAPP(hAPP(c_COMBC(_1512306, tc_fun(_1512306, tc_HOL_Obool), tc_HOL_Obool), c_member(_1512306)), _1512314))))))))], (28656 ^ _779203) ^ [_1286155, _1286157] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1286155, _1286157))))], (17900 ^ _779203) ^ [_1094760, _1094762, _1094764, _1094766, _1094768, _1094770] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1094760), _1094762)), _1094764) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1094766), _1094768)), _1094770), 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), _1094766), _1094768)), _1094770))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1094770), _1094766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1094764)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1094766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094766), _1094760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094762), _1094768)))], (31705 ^ _779203) ^ [_1348539, _1348541, _1348543, _1348545] : [-(hAPP(c_Finite__Set_Ofold__image(_1348539, _1348541, _1348543), _1348545) = c_Finite__Set_Ofold(_1348541, _1348539, hAPP(hAPP(c_COMBB(_1348539, tc_fun(_1348539, _1348539), _1348541), _1348543), _1348545)))], (52655 ^ _779203) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (6203 ^ _779203) ^ [_878712, _878714, _878716] : [hBOOL(hAPP(hAPP(c_member(_878712), _878714), hAPP(hAPP(c_Set_Oinsert(_878712), _878716), c_Orderings_Obot__class_Obot(tc_fun(_878712, tc_HOL_Obool))))), -(_878714 = _878716)], (24335 ^ _779203) ^ [_1208126, _1208128] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1208126)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1208126)), _1208128) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1208126)), _1208128)))], (25596 ^ _779203) ^ [_1230070] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1230070) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1230070))], (8308 ^ _779203) ^ [_917522, _917524, _917526, _917528] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_917522), _917524)), hBOOL(hAPP(hAPP(c_member(_917522), _917526), _917524)), hBOOL(hAPP(hAPP(c_member(_917522), _917528), _917524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_917522), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917522, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917522, tc_HOL_Obool)), _917524), hAPP(hAPP(c_Set_Oinsert(_917522), _917526), c_Orderings_Obot__class_Obot(tc_fun(_917522, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_917522), _917528), c_Orderings_Obot__class_Obot(tc_fun(_917522, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_917522), _917524))))], (44534 ^ _779203) ^ [_1671254, _1671256, _1671258, _1671260] : [class_Groups_Oab__group__add(_1671254), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1671254), hAPP(c_List_Omonoid__add__class_Olistsum(_1671254), hAPP(hAPP(c_List_Omap(_1671256, _1671254), _1671258), _1671260))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1671254), hAPP(hAPP(c_List_Omap(_1671256, _1671254), hAPP(c_Fun_Ocomp(_1671254, _1671254, _1671256, c_Groups_Ouminus__class_Ouminus(_1671254)), _1671258)), _1671260)))], (40400 ^ _779203) ^ [_1569898, _1569900] : [-(c_Transitive__Closure_Ortrancl(_1569898, c_Transitive__Closure_Ortrancl(_1569898, _1569900)) = c_Transitive__Closure_Ortrancl(_1569898, _1569900))], (42796 ^ _779203) ^ [_1632056, _1632058, _1632060] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632056), tc_List_Olist(_1632056))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632056), tc_List_Olist(_1632056)), c_List_Olist_ONil(_1632056)), _1632058)), c_List_Olistrel1(_1632056, _1632060)))], (33391 ^ _779203) ^ [_1390293, _1390295, _1390297, _1390299] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390293, _1390295), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1390297), _1390299))), -(_1390295 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390293, _1390295) = _1390299)], (2234 ^ _779203) ^ [_811796, _811798, _811800, _811802] : [-(c_Orderings_Oord_Omax(_811802, _811798) = c_Orderings_Oord_Omax(_811800, _811796)), _811802 = _811800, _811798 = _811796], (38228 ^ _779203) ^ [_1514825] : [-(hAPP(c_Set_Oimage(_1514825, _1514825, c_Fun_Oid(_1514825)), c_Orderings_Otop__class_Otop(tc_fun(_1514825, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1514825, tc_HOL_Obool)))], (19276 ^ _779203) ^ [_1118679, _1118681, _1118683] : [class_Groups_Oordered__ab__group__add__abs(_1118679), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118679), hAPP(c_Groups_Oabs__class_Oabs(_1118679), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118679), _1118681), _1118683))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1118679), hAPP(c_Groups_Oabs__class_Oabs(_1118679), _1118681)), hAPP(c_Groups_Oabs__class_Oabs(_1118679), _1118683)))))], (22782 ^ _779203) ^ [_1180609, _1180611, _1180613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180609), _1180611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180609), _1180613)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180611), _1180613))))], (37669 ^ _779203) ^ [_1494029, _1494031, _1494033, _1494035, _1494037, _1494039] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494029, _1494031)), hAPP(hAPP(c_Product__Type_OPair(_1494029, _1494031), _1494033), _1494035)), hAPP(hAPP(c_Product__Type_OSigma(_1494029, _1494031), _1494037), _1494039))), -(hBOOL(hAPP(hAPP(c_member(_1494031), _1494035), hAPP(_1494039, _1494033))))], (3006 ^ _779203) ^ [_823812, _823814, _823816, _823818] : [-(c_Nitpick_Ocard_H(_823818, _823814) = c_Nitpick_Ocard_H(_823816, _823812)), _823818 = _823816, _823814 = _823812], (31743 ^ _779203) ^ [_1349553, _1349555, _1349557, _1349559] : [class_Groups_Ocomm__monoid__add(_1349553), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349553), _1349555), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1349557)), hAPP(c_Nat_OSuc, _1349559))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1349553), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1349553, tc_Nat_Onat), _1349555), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1349557), _1349559)))], (21499 ^ _779203) ^ [_1157729, _1157731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1157729)), c_Int_OBit0(_1157731))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1157729), _1157731)))], (17778 ^ _779203) ^ [_1092553, _1092555, _1092557] : [class_Orderings_Olinorder(_1092553), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092553), _1092555)), 17785 ^ _779203 : [(17792 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1092553, tc_HOL_Obool)), _1092555), hAPP(hAPP(c_Set_Oinsert(_1092553), _1092557), c_Orderings_Obot__class_Obot(tc_fun(_1092553, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1092553, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1092553, c_Orderings_Oord__class_Omax(_1092553), hAPP(hAPP(c_Set_Oinsert(_1092553), _1092557), _1092555)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092553), _1092557), c_Big__Operators_Olattice_OSup__fin(_1092553, c_Orderings_Oord__class_Omax(_1092553), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1092553, tc_HOL_Obool)), _1092555), hAPP(hAPP(c_Set_Oinsert(_1092553), _1092557), c_Orderings_Obot__class_Obot(tc_fun(_1092553, tc_HOL_Obool)))))))], (17786 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1092553, tc_HOL_Obool)), _1092555), hAPP(hAPP(c_Set_Oinsert(_1092553), _1092557), c_Orderings_Obot__class_Obot(tc_fun(_1092553, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1092553, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1092553, c_Orderings_Oord__class_Omax(_1092553), hAPP(hAPP(c_Set_Oinsert(_1092553), _1092557), _1092555)) = _1092557)]]], (16080 ^ _779203) ^ [_1061727, _1061729] : [class_Int_Onumber__ring(_1061727), -(hBOOL(hAPP(hAPP(c_member(_1061727), hAPP(c_Int_Onumber__class_Onumber__of(_1061727), _1061729)), c_Int_Oring__1__class_OInts(_1061727))))], (33497 ^ _779203) ^ [_1392296, _1392298, _1392300, _1392302, _1392304, _1392306, _1392308] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1392296, _1392298), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1392300), _1392302))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1392304, _1392298), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1392306), _1392308))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1392298)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1392296), _1392304), _1392298), 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), _1392300), _1392306)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1392302), _1392308)), _1392298))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1392302), _1392308), _1392298)))))], (25794 ^ _779203) ^ [_1233035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233035)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1233035) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (39287 ^ _779203) ^ [_1542260, _1542262, _1542264, _1542266] : [c_Equiv__Relations_Ocongruent(_1542260, _1542262, _1542264, _1542266), 39290 ^ _779203 : [(39291 ^ _779203) ^ [_1542405] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542260, _1542260)), _1542405), _1542264)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1542260, _1542260, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1542260, tc_fun(_1542260, _1542262), tc_fun(_1542260, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542262, tc_HOL_Obool), tc_fun(tc_fun(_1542260, _1542262), tc_fun(_1542260, tc_HOL_Obool)), _1542260), c_COMBB(_1542262, tc_HOL_Obool, _1542260)), hAPP(hAPP(c_COMBB(_1542262, tc_fun(_1542262, tc_HOL_Obool), _1542260), c_fequal), _1542266))), _1542266)), _1542405)))]]], (25418 ^ _779203) ^ [] : [-(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))], (29324 ^ _779203) ^ [_1299172, _1299174, _1299176, _1299178, _1299180] : [class_Lattices_Olattice(_1299172), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299174, _1299172)), _1299176), _1299178), _1299180) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1299172), hAPP(_1299176, _1299180)), hAPP(_1299178, _1299180)))], (34414 ^ _779203) ^ [_1412970, _1412972, _1412974, _1412976, _1412978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412970, tc_HOL_Obool)), _1412972), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412974, tc_fun(_1412970, tc_HOL_Obool)), _1412976), _1412978))), 34417 ^ _779203 : [(34418 ^ _779203) ^ [_1413103] : [hBOOL(hAPP(hAPP(c_member(_1412974), _1413103), _1412976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1412970, tc_HOL_Obool)), _1412972), hAPP(_1412978, _1413103))))]]], (36636 ^ _779203) ^ [_1468806, _1468808, _1468810, _1468812, _1468814, _1468816] : [c_Fun_Oinj__on(_1468806, _1468808, _1468810, _1468812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468808, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468806, _1468808, _1468810), _1468812)), _1468814)), c_Fun_Oinj__on(_1468808, _1468806, _1468816, _1468814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1468806, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468808, _1468806, _1468816), _1468814)), _1468812)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468806), _1468812)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1468808), _1468814)), -(hAPP(c_Finite__Set_Ocard(_1468806), _1468812) = hAPP(c_Finite__Set_Ocard(_1468808), _1468814))], (42485 ^ _779203) ^ [_1626119, _1626121] : [42487 ^ _779203 : [(42491 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42489 ^ [_1626119, _1626121]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626119)), _1626121))))], (42493 ^ _779203) ^ [] : [42486 ^ [_1626119, _1626121] = 42489 ^ [_1626119, _1626121]], (42495 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1626119), _1626121), 42486 ^ [_1626119, _1626121]) = hAPP(hAPP(c_List_Onth(_1626119), _1626121), 42489 ^ [_1626119, _1626121]))], (42488 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42486 ^ [_1626119, _1626121]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626119)), _1626121))))]], -(hBOOL(hAPP(c_List_Odistinct(_1626119), _1626121)))], (9431 ^ _779203) ^ [_939941] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _939941), _939941))))], (21947 ^ _779203) ^ [_1166099, _1166101] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1166099, _1166101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1166099), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1166099), _1166101)), _1166101)))], (48198 ^ _779203) ^ [_1751369, _1751371, _1751373, _1751375] : [48206 ^ _779203 : [(48209 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1751375, 48205 ^ [_1751369, _1751371, _1751373, _1751375])))], (48207 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1751369), 48205 ^ [_1751369, _1751371, _1751373, _1751375]), hAPP(c_List_Oset(_1751369), c_List_Oreplicate(_1751369, _1751371, _1751373)))))]], hBOOL(hAPP(_1751375, _1751373)), -(_1751371 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33311 ^ _779203) ^ [_1389202, _1389204] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1389202, _1389204), c_Divides_Odivmod__nat(_1389202, _1389204))))], (14367 ^ _779203) ^ [_1029153, _1029155, _1029157] : [class_Fields_Olinordered__field(_1029153), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029153), _1029155), c_Groups_Ozero__class_Ozero(_1029153))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029153), c_Groups_Ozero__class_Ozero(_1029153)), _1029157)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1029153), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1029153), _1029155), _1029157)), c_Groups_Ozero__class_Ozero(_1029153))))], (2 ^ _779203) ^ [_779230] : [-(_779230 = _779230)], (23180 ^ _779203) ^ [_1186998, _1187000] : [-(hBOOL(hAPP(_1186998, hAPP(c_Int_Onat, _1187000)))), 23184 ^ _779203 : [(23187 ^ _779203) ^ [] : [hBOOL(hAPP(_1186998, 23183 ^ [_1186998, _1187000]))], (23185 ^ _779203) ^ [] : [-(_1187000 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23183 ^ [_1186998, _1187000]))]], 23188 ^ _779203 : [(23191 ^ _779203) ^ [] : [hBOOL(hAPP(_1186998, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23189 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1187000), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (18488 ^ _779203) ^ [_1105256, _1105258] : [18489 ^ _779203 : [(18490 ^ _779203) ^ [_1105312] : [_1105258 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105256), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1105312)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105256), _1105258)))], (2944 ^ _779203) ^ [_822795, _822797] : [_822797 = _822795, -(c_HOL_Obool_Obool__size(_822797) = c_HOL_Obool_Obool__size(_822795))], (47000 ^ _779203) ^ [_1724652, _1724654] : [-(c_List_OdropWhile(_1724652, _1724654, c_List_Olist_ONil(_1724652)) = c_List_Olist_ONil(_1724652))], (31761 ^ _779203) ^ [_1350049] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1350049) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1350049)))], (25728 ^ _779203) ^ [_1232029, _1232031] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232029), _1232031) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 25729 ^ _779203 : [(25736 ^ _779203) ^ [] : [_1232029 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1232031 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (25730 ^ _779203) ^ [] : [_1232029 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1232031 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (45789 ^ _779203) ^ [_1699551, _1699553, _1699555] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699551)), hAPP(c_List_Ofilter(_1699551, _1699553), _1699555)) = 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(_1699551)), _1699555)))), hAPP(hAPP(c_COMBB(_1699551, tc_HOL_Obool, tc_Nat_Onat), _1699553), hAPP(c_List_Onth(_1699551), _1699555))))))], (25754 ^ _779203) ^ [_1232357] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1232357)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1232357)))], (39179 ^ _779203) ^ [_1539392, _1539394] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539392, _1539392)), _1539394)), c_Wellfounded_Oacyclic(_1539392, _1539394), -(c_Wellfounded_Owf(_1539392, _1539394))], (23794 ^ _779203) ^ [_1197948, _1197950, _1197952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1197948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1197948), _1197950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1197952), _1197950)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1197952), _1197948))))], (19450 ^ _779203) ^ [_1122063, _1122065] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1122063) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1122065)), 19453 ^ _779203 : [(19456 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122065)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (19454 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122063))))]], 19457 ^ _779203 : [(19460 ^ _779203) ^ [] : [19461 ^ _779203 : [(19464 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122063) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (19462 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122065))))]], 19465 ^ _779203 : [(19468 ^ _779203) ^ [] : [_1122063 = _1122065], (19466 ^ _779203) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122065)))]]], (19458 ^ _779203) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122063)))]]], (18554 ^ _779203) ^ [_1106424, _1106426] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106424)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106426)))), 18557 ^ _779203 : [(18560 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1106426))], (18558 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106424), _1106426)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106424), _1106426))], (45059 ^ _779203) ^ [_1683110, _1683112, _1683114, _1683116, _1683118, _1683120, _1683122] : [c_List_Olist__all2(_1683110, _1683118, hAPP(hAPP(c_COMBC(_1683110, tc_fun(_1683118, _1683112), tc_fun(_1683118, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1683112, tc_HOL_Obool), tc_fun(tc_fun(_1683118, _1683112), tc_fun(_1683118, tc_HOL_Obool)), _1683110), c_COMBB(_1683112, tc_HOL_Obool, _1683118)), _1683114)), _1683120), _1683116, _1683122), -(c_List_Olist__all2(_1683110, _1683112, _1683114, _1683116, hAPP(hAPP(c_List_Omap(_1683118, _1683112), _1683120), _1683122)))], (16124 ^ _779203) ^ [_1062440, _1062442, _1062444, _1062446] : [class_Fields_Ofield__inverse__zero(_1062440), class_Int_Onumber(_1062440), 16131 ^ _779203 : [(16132 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1062440), _1062442) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1062440), _1062444), _1062446), 16135 ^ _779203 : [(16142 ^ _779203) ^ [] : [_1062446 = c_Groups_Ozero__class_Ozero(_1062440), -(hAPP(c_Int_Onumber__class_Onumber__of(_1062440), _1062442) = c_Groups_Ozero__class_Ozero(_1062440))], (16136 ^ _779203) ^ [] : [-(_1062446 = c_Groups_Ozero__class_Ozero(_1062440)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062440), hAPP(c_Int_Onumber__class_Onumber__of(_1062440), _1062442)), _1062446) = _1062444)]]], (16148 ^ _779203) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1062440), _1062442) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1062440), _1062444), _1062446)), 16151 ^ _779203 : [(16154 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062440), hAPP(c_Int_Onumber__class_Onumber__of(_1062440), _1062442)), _1062446) = _1062444], (16152 ^ _779203) ^ [] : [_1062446 = c_Groups_Ozero__class_Ozero(_1062440)]], 16155 ^ _779203 : [(16158 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1062440), _1062442) = c_Groups_Ozero__class_Ozero(_1062440)], (16156 ^ _779203) ^ [] : [-(_1062446 = c_Groups_Ozero__class_Ozero(_1062440))]]]]], (5821 ^ _779203) ^ [_871306, _871308] : [class_Finite__Set_Ofinite(_871306), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_871306), _871308)))], (20268 ^ _779203) ^ [_1136707, _1136709] : [class_Groups_Ogroup__add(_1136707), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136707), hAPP(c_Groups_Ouminus__class_Ouminus(_1136707), _1136709)), _1136709) = c_Groups_Ozero__class_Ozero(_1136707))], (39838 ^ _779203) ^ [_1555495, _1555497, _1555499, _1555501, _1555503, _1555505] : [c_Finite__Set_Ofolding(_1555495, _1555497, _1555499, _1555501), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555495), _1555503)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555495), _1555505)), -(hAPP(c_Fun_Ocomp(_1555497, _1555497, _1555497, hAPP(_1555501, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1555495, tc_HOL_Obool)), _1555503), _1555505))), hAPP(_1555501, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1555495, tc_HOL_Obool)), _1555503), _1555505))) = hAPP(c_Fun_Ocomp(_1555497, _1555497, _1555497, hAPP(_1555501, _1555503)), hAPP(_1555501, _1555505)))], (32219 ^ _779203) ^ [_1361679, _1361681, _1361683, _1361685, _1361687] : [class_Groups_Ocomm__monoid__add(_1361679), hBOOL(hAPP(c_Finite__Set_Ofinite(_1361681), _1361683)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361681, _1361679), _1361685), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1361681, tc_HOL_Obool)), _1361683), _1361687)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1361681, _1361679), hAPP(hAPP(c_COMBC(_1361681, _1361679, _1361679), hAPP(hAPP(c_COMBS(_1361681, _1361679, tc_fun(_1361679, _1361679)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1361679, tc_fun(_1361679, _1361679)), _1361681), c_If(_1361679)), hAPP(hAPP(c_COMBC(_1361681, tc_fun(_1361681, tc_HOL_Obool), tc_HOL_Obool), c_member(_1361681)), _1361687))), _1361685)), c_Groups_Ozero__class_Ozero(_1361679))), _1361683))], (22195 ^ _779203) ^ [_1171154, _1171156] : [class_Divides_Osemiring__div(_1171154), -(c_Divides_Odiv__class_Omod(_1171154, _1171156, c_Groups_Oone__class_Oone(_1171154)) = c_Groups_Ozero__class_Ozero(_1171154))], (43933 ^ _779203) ^ [_1658195, _1658197, _1658199] : [class_Orderings_Olinorder(_1658195), -(c_Big__Operators_Olinorder__class_OMin(_1658195, hAPP(c_List_Oset(_1658195), hAPP(hAPP(c_List_Olist_OCons(_1658195), _1658197), _1658199))) = hAPP(c_List_Ofoldl(_1658195, _1658195, c_Orderings_Oord__class_Omin(_1658195), _1658197), _1658199))], (40217 ^ _779203) ^ [_1564701, _1564703] : [-(hAPP(c_Relation_ODomain(_1564701, _1564701), c_Transitive__Closure_Otrancl(_1564701, _1564703)) = hAPP(c_Relation_ODomain(_1564701, _1564701), _1564703))], (9917 ^ _779203) ^ [_948458, _948460, _948462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _948458), _948462)), _948460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948458), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948460), _948462))))], (24718 ^ _779203) ^ [_1214567, _1214569, _1214571] : [class_Int_Onumber__ring(_1214567), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1214567), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214567), _1214569), _1214571)), 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(_1214567), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214567), hAPP(hAPP(c_Power_Opower__class_Opower(_1214567), _1214569), 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(_1214567), _1214571), 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(_1214567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214567), hAPP(c_Int_Onumber__class_Onumber__of(_1214567), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1214569)), _1214571)))], (27324 ^ _779203) ^ [_1260306, _1260308, _1260310] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260306, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260306, tc_HOL_Obool)), _1260308), _1260310)), _1260310) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260306, tc_HOL_Obool)), _1260308), _1260310))], (49590 ^ _779203) ^ [_1781324, _1781326, _1781328, _1781330] : [c_Fun_Oinj__on(_1781324, _1781326, _1781328, c_Orderings_Otop__class_Otop(tc_fun(_1781324, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781326, _1781324, c_Hilbert__Choice_Oinv__into(_1781324, _1781326, c_Orderings_Otop__class_Otop(tc_fun(_1781324, tc_HOL_Obool)), _1781328)), hAPP(c_Set_Oimage(_1781324, _1781326, _1781328), _1781330)) = _1781330)], (25544 ^ _779203) ^ [_1229256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1229256))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1229256)))], (50270 ^ _779203) ^ [_1795813, _1795815, _1795817, _1795819, _1795821] : [50272 ^ _779203 : [(50275 ^ _779203) ^ [] : [c_Relation_Orefl__on(_1795817, hAPP(_1795819, 50271 ^ [_1795813, _1795815, _1795817, _1795819, _1795821]), hAPP(_1795821, 50271 ^ [_1795813, _1795815, _1795817, _1795819, _1795821]))], (50273 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795813), 50271 ^ [_1795813, _1795815, _1795817, _1795819, _1795821]), _1795815)))]], -(c_Relation_Orefl__on(_1795817, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1795813, tc_fun(_1795817, tc_HOL_Obool)), _1795815), _1795819), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1795813, tc_fun(tc_prod(_1795817, _1795817), tc_HOL_Obool)), _1795815), _1795821)))], (13941 ^ _779203) ^ [_1021695, _1021697, _1021699] : [class_Fields_Olinordered__field__inverse__zero(_1021695), 13944 ^ _779203 : [(13959 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021695), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1021695), _1021697), _1021699)), c_Groups_Ozero__class_Ozero(_1021695)))), 13960 ^ _779203 : [(13967 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021695), _1021697), c_Groups_Ozero__class_Ozero(_1021695))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021695), c_Groups_Ozero__class_Ozero(_1021695)), _1021699))], (13961 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021695), c_Groups_Ozero__class_Ozero(_1021695)), _1021697)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021695), _1021699), c_Groups_Ozero__class_Ozero(_1021695)))]]], (13945 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021695), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1021695), _1021697), _1021699)), c_Groups_Ozero__class_Ozero(_1021695))), 13950 ^ _779203 : [(13953 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021695), _1021699), c_Groups_Ozero__class_Ozero(_1021695))))], (13951 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021695), c_Groups_Ozero__class_Ozero(_1021695)), _1021697)))]], 13954 ^ _779203 : [(13957 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021695), c_Groups_Ozero__class_Ozero(_1021695)), _1021699)))], (13955 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021695), _1021697), c_Groups_Ozero__class_Ozero(_1021695))))]]]]], (34512 ^ _779203) ^ [_1416254, _1416256, _1416258, _1416260, _1416262] : [-(hAPP(hAPP(c_Set_Oinsert(_1416254), _1416256), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416258, tc_fun(_1416254, tc_HOL_Obool)), _1416260), _1416262)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416258, tc_fun(_1416254, tc_HOL_Obool)), _1416260), hAPP(hAPP(c_COMBB(tc_fun(_1416254, tc_HOL_Obool), tc_fun(_1416254, tc_HOL_Obool), _1416258), hAPP(c_Set_Oinsert(_1416254), _1416256)), _1416262)))], (25568 ^ _779203) ^ [_1229648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1229648)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1229648), c_Int_OMin)))], (19162 ^ _779203) ^ [_1116688, _1116690, _1116692] : [class_Groups_Oordered__ab__group__add__abs(_1116688), -(hAPP(c_Groups_Oabs__class_Oabs(_1116688), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116688), hAPP(c_Groups_Oabs__class_Oabs(_1116688), _1116690)), hAPP(c_Groups_Oabs__class_Oabs(_1116688), _1116692))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1116688), hAPP(c_Groups_Oabs__class_Oabs(_1116688), _1116690)), hAPP(c_Groups_Oabs__class_Oabs(_1116688), _1116692)))], (37593 ^ _779203) ^ [_1491963, _1491965, _1491967] : [hBOOL(hAPP(_1491963, _1491965)), -(hAPP(c_Set_OCollect(_1491967), hAPP(hAPP(c_COMBS(_1491967, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1491967), c_fconj), hAPP(hAPP(c_COMBC(_1491967, _1491967, tc_HOL_Obool), c_fequal), _1491965))), _1491963)) = hAPP(hAPP(c_Set_Oinsert(_1491967), _1491965), c_Orderings_Obot__class_Obot(tc_fun(_1491967, tc_HOL_Obool))))], (50745 ^ _779203) ^ [_1806859, _1806861, _1806863] : [class_Rings_Ocomm__semiring__1(_1806859), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806859), _1806861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806859), _1806861), _1806863))))], (24351 ^ _779203) ^ [_1208359] : [24353 ^ _779203 : [(24356 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24352 ^ [_1208359]))], (24354 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 24352 ^ [_1208359]), _1208359)))]], -(c_Nat__Transfer_Onat__set(_1208359))], (25884 ^ _779203) ^ [_1234450] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1234450)], (37587 ^ _779203) ^ [_1491876, _1491878, _1491880] : [-(hBOOL(hAPP(_1491876, _1491878))), -(hAPP(c_Set_OCollect(_1491880), hAPP(hAPP(c_COMBS(_1491880, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1491880), c_fconj), hAPP(c_fequal, _1491878))), _1491876)) = c_Orderings_Obot__class_Obot(tc_fun(_1491880, tc_HOL_Obool)))], (11196 ^ _779203) ^ [_971857, _971859, _971861, _971863] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_971857, _971859)), c_Sum__Type_OPlus(_971857, _971859, _971861, _971863))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_971859), _971863)))], (27290 ^ _779203) ^ [_1259624, _1259626, _1259628, _1259630] : [hBOOL(hAPP(hAPP(c_member(_1259624), _1259626), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259624, tc_HOL_Obool)), _1259628), _1259630))), -(hBOOL(hAPP(hAPP(c_member(_1259624), _1259626), _1259628))), -(hBOOL(hAPP(hAPP(c_member(_1259624), _1259626), _1259630)))], (20060 ^ _779203) ^ [_1132909, _1132911, _1132913] : [hBOOL(hAPP(hAPP(c_member(_1132909), _1132911), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1132909, tc_HOL_Obool)), _1132913))), hBOOL(hAPP(hAPP(c_member(_1132909), _1132911), _1132913))], (386 ^ _779203) ^ [_784986, _784988, _784990, _784992, _784994, _784996, _784998, _785000] : [-(c_Finite__Set_Ofolding__idem(_784998, _784994, _784990, _784986)), c_Finite__Set_Ofolding__idem(_785000, _784996, _784992, _784988), _785000 = _784998, _784996 = _784994, _784992 = _784990, _784988 = _784986], (8919 ^ _779203) ^ [_929933, _929935, _929937, _929939, _929941] : [class_Groups_Oordered__cancel__ab__semigroup__add(_929933), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929933), _929935), _929937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929933), _929939), _929941)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929933), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929933), _929935), _929939)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929933), _929937), _929941))))], (52543 ^ _779203) ^ [_1835325] : [class_Enum_Oenum(_1835325), -(class_Enum_Oenum(tc_Option_Ooption(_1835325)))], (44528 ^ _779203) ^ [_1671113, _1671115] : [class_Groups_Oordered__ab__group__add__abs(_1671113), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1671113), hAPP(c_Groups_Oabs__class_Oabs(_1671113), hAPP(c_List_Omonoid__add__class_Olistsum(_1671113), _1671115))), hAPP(c_List_Omonoid__add__class_Olistsum(_1671113), hAPP(hAPP(c_List_Omap(_1671113, _1671113), c_Groups_Oabs__class_Oabs(_1671113)), _1671115)))))], (51737 ^ _779203) ^ [_1824179, _1824181, _1824183] : [class_Divides_Osemiring__div(_1824179), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1824179), _1824181), _1824183)), -(c_Divides_Odiv__class_Omod(_1824179, _1824183, _1824181) = c_Groups_Ozero__class_Ozero(_1824179))], (31294 ^ _779203) ^ [_1339845, _1339847, _1339849] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1339845, tc_HOL_Obool)), _1339847)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339845), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1339845, tc_HOL_Obool), _1339847))), 31304 ^ _779203 : [(31307 ^ _779203) ^ [] : [hAPP(c_Finite__Set_Ocard(_1339845), 31303 ^ [_1339845, _1339847, _1339849]) = _1339849], (31305 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1339845, tc_HOL_Obool)), 31303 ^ [_1339845, _1339847, _1339849]), _1339847)))]], 31311 ^ _779203 : [(31315 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1339845, tc_HOL_Obool)), 31313 ^ [_1339845, _1339847, _1339849]), _1339847)))], (31317 ^ _779203) ^ [] : [31310 ^ [_1339845, _1339847, _1339849] = 31313 ^ [_1339845, _1339847, _1339849]], (31319 ^ _779203) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339845, tc_HOL_Obool)), 31310 ^ [_1339845, _1339847, _1339849]), 31313 ^ [_1339845, _1339847, _1339849]) = c_Orderings_Obot__class_Obot(tc_fun(_1339845, tc_HOL_Obool))], (31312 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1339845, tc_HOL_Obool)), 31310 ^ [_1339845, _1339847, _1339849]), _1339847)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1339849), hAPP(c_Finite__Set_Ocard(tc_fun(_1339845, tc_HOL_Obool)), _1339847)) = hAPP(c_Finite__Set_Ocard(_1339845), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1339845, tc_HOL_Obool), _1339847)))], (49064 ^ _779203) ^ [_1771445, _1771447] : [c_Predicate_Oreflp(_1771445, _1771447), c_Predicate_Osymp(_1771445, _1771447), c_Predicate_Otransp(_1771445, _1771447), -(c_Equiv__Relations_Oequivp(_1771445, _1771447))], (20590 ^ _779203) ^ [_1142266] : [-(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, _1142266))))))], (22588 ^ _779203) ^ [] : [-(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))))], (45665 ^ _779203) ^ [_1696880, _1696882, _1696884, _1696886] : [-(hBOOL(hAPP(_1696880, _1696882))), -(c_List_Oremove1(_1696884, _1696882, hAPP(c_List_Ofilter(_1696884, _1696880), _1696886)) = hAPP(c_List_Ofilter(_1696884, _1696880), _1696886))], (52311 ^ _779203) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (9572 ^ _779203) ^ [_942662, _942664] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _942662), _942664) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 9575 ^ _779203 : [(9578 ^ _779203) ^ [] : [-(_942664 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9576 ^ _779203) ^ [] : [-(_942662 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (39542 ^ _779203) ^ [_1548799, _1548801] : [39543 ^ _779203 : [(39544 ^ _779203) ^ [_1548845] : [hBOOL(hAPP(_1548799, _1548845))]], -(hBOOL(hAPP(_1548799, c_Hilbert__Choice_OEps(_1548801, _1548799))))], (27642 ^ _779203) ^ [_1266329, _1266331, _1266333] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1266329), _1266331)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266329), _1266333)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1266329), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266329, tc_HOL_Obool)), _1266331), _1266333))))], (52075 ^ _779203) ^ [_1830262, _1830264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1830262)), 52078 ^ _779203 : [(52085 ^ _779203) ^ [] : [_1830264 = 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), _1830262), _1830264)), _1830262)))], (52079 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1830262), _1830264)), _1830262)), -(_1830264 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (6603 ^ _779203) ^ [_885681, _885683, _885685, _885687, _885689] : [c_Finite__Set_Ofolding__one__idem(_885681, _885683, _885685), hBOOL(hAPP(c_Finite__Set_Ofinite(_885681), _885687)), hBOOL(hAPP(hAPP(c_member(_885681), _885689), _885687)), -(hAPP(hAPP(_885683, _885689), hAPP(_885685, _885687)) = hAPP(_885685, _885687))], (43227 ^ _779203) ^ [_1641752, _1641754] : [-(hAPP(hAPP(c_List_Oappend(_1641752), _1641754), c_List_Olist_ONil(_1641752)) = _1641754)], (29224 ^ _779203) ^ [_1297048, _1297050] : [class_Lattices_Olattice(_1297048), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297048), _1297050), _1297050) = _1297050)], (48362 ^ _779203) ^ [_1754497, _1754499, _1754501] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1754497, _1754499), _1754501) = c_Lazy__Sequence_Oproduct(_1754497, _1754499, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1754497, _1754501), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1754499, _1754501))), class_Lazy__Sequence_Osmall__lazy(_1754497), class_Lazy__Sequence_Osmall__lazy(_1754499)], (5006 ^ _779203) ^ [_855544, _855546] : [_855546 = _855544, -(c_Orderings_Otop__class_Otop(_855546) = c_Orderings_Otop__class_Otop(_855544))], (26314 ^ _779203) ^ [_1242067, _1242069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1242067)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1242067, _1242069)))], (31612 ^ _779203) ^ [_1346471, _1346473, _1346475, _1346477, _1346479, _1346481, _1346483, _1346485] : [class_Groups_Ocomm__monoid__add(_1346471), class_Orderings_Oord(_1346473), _1346475 = _1346477, _1346479 = _1346481, 31630 ^ _779203 : [(31635 ^ _779203) ^ [] : [hAPP(_1346483, 31629 ^ [_1346471, _1346473, _1346475, _1346477, _1346479, _1346481, _1346483, _1346485]) = hAPP(_1346485, 31629 ^ [_1346471, _1346473, _1346475, _1346477, _1346479, _1346481, _1346483, _1346485])], (31633 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346473), 31629 ^ [_1346471, _1346473, _1346475, _1346477, _1346479, _1346481, _1346483, _1346485]), _1346481)))], (31631 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346473), _1346477), 31629 ^ [_1346471, _1346473, _1346475, _1346477, _1346479, _1346481, _1346483, _1346485])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346473, _1346471), _1346483), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346473, _1346475), _1346479)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1346473, _1346471), _1346485), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1346473, _1346477), _1346481)))], (30993 ^ _779203) ^ [_1333522, _1333524, _1333526] : [class_Lattices_Olattice(_1333522), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333522), _1333524)), -(hBOOL(hAPP(hAPP(c_member(_1333522), _1333526), _1333524))), -(_1333524 = c_Orderings_Obot__class_Obot(tc_fun(_1333522, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1333522, hAPP(hAPP(c_Set_Oinsert(_1333522), _1333526), _1333524)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1333522), _1333526), c_Big__Operators_Olattice__class_OInf__fin(_1333522, _1333524)))], (5494 ^ _779203) ^ [_863204, _863206] : [_863206 = _863204, -(tc_Option_Ooption(_863206) = tc_Option_Ooption(_863204))], (41168 ^ _779203) ^ [_1589103, _1589105, _1589107, _1589109, _1589111] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589103, _1589103)), hAPP(hAPP(c_Product__Type_OPair(_1589103, _1589103), _1589105), _1589107)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589103, _1589103), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1589109)), _1589111))), 41172 ^ _779203 : [(41175 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589103, _1589103)), hAPP(hAPP(c_Product__Type_OPair(_1589103, _1589103), 41171 ^ [_1589103, _1589105, _1589107, _1589109, _1589111]), _1589107)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589103, _1589103), tc_HOL_Obool), _1589109), _1589111))))], (41173 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589103, _1589103)), hAPP(hAPP(c_Product__Type_OPair(_1589103, _1589103), _1589105), 41171 ^ [_1589103, _1589105, _1589107, _1589109, _1589111])), _1589111)))]]], (40801 ^ _779203) ^ [_1579389, _1579391, _1579393, _1579395] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579389, _1579389)), hAPP(hAPP(c_Product__Type_OPair(_1579389, _1579389), _1579391), _1579393)), hAPP(c_Relation_Oconverse(_1579389, _1579389), c_Transitive__Closure_Otrancl(_1579389, _1579395)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579389, _1579389)), hAPP(hAPP(c_Product__Type_OPair(_1579389, _1579389), _1579391), _1579393)), c_Transitive__Closure_Otrancl(_1579389, hAPP(c_Relation_Oconverse(_1579389, _1579389), _1579395)))))], (19716 ^ _779203) ^ [_1127022, _1127024, _1127026] : [class_Groups_Ogroup__add(_1127022), 19719 ^ _779203 : [(19726 ^ _779203) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1127022), _1127026) = _1127024, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1127022), _1127024) = _1127026)], (19720 ^ _779203) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1127022), _1127024) = _1127026, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1127022), _1127026) = _1127024)]]], (28352 ^ _779203) ^ [_1280548, _1280550, _1280552] : [-(hAPP(c_Set_OPow(_1280548), hAPP(hAPP(c_Set_Oinsert(_1280548), _1280550), _1280552)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1280548, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1280548), _1280552)), hAPP(c_Set_Oimage(tc_fun(_1280548, tc_HOL_Obool), tc_fun(_1280548, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1280548), _1280550)), hAPP(c_Set_OPow(_1280548), _1280552))))], (5570 ^ _779203) ^ [_864348, _864350, _864352, _864354, _864356, _864358] : [-(c_COMBS(_864358, _864354, _864350) = c_COMBS(_864356, _864352, _864348)), _864358 = _864356, _864354 = _864352, _864350 = _864348], (15620 ^ _779203) ^ [_1053015, _1053017, _1053019, _1053021, _1053023] : [class_Orderings_Olinorder(_1053015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053015), _1053017), _1053019)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053015), _1053021), _1053023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053015), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1053015), _1053017), _1053021)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1053015), _1053019), _1053023))))], (44811 ^ _779203) ^ [_1677127, _1677129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1677127), _1677129)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677127)), hAPP(c_Code__Numeral_Onat__of, _1677129))))], (536 ^ _779203) ^ [_787211, _787213] : [-(class_Lattices_Oab__semigroup__idem__mult(_787211)), _787213 = _787211, class_Lattices_Oab__semigroup__idem__mult(_787213)], (43068 ^ _779203) ^ [_1638413, _1638415, _1638417, _1638419] : [-(hAPP(hAPP(c_List_Oappend(_1638413), hAPP(hAPP(c_List_Oappend(_1638413), _1638415), _1638417)), _1638419) = hAPP(hAPP(c_List_Oappend(_1638413), _1638415), hAPP(hAPP(c_List_Oappend(_1638413), _1638417), _1638419)))], (18718 ^ _779203) ^ [_1109108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1109108)), -(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), _1109108))))], (52483 ^ _779203) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (30612 ^ _779203) ^ [_1326043, _1326045, _1326047] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1326043, tc_HOL_Obool)), _1326045), _1326047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1326043, tc_HOL_Obool)), _1326045), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1326043, tc_HOL_Obool), _1326047))))], (20730 ^ _779203) ^ [_1145109, _1145111] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1145109, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1145109, tc_HOL_Obool)), _1145111)) = _1145111)], (14273 ^ _779203) ^ [_1027374, _1027376, _1027378] : [class_Fields_Olinordered__field(_1027374), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027374), c_Groups_Ozero__class_Ozero(_1027374)), _1027376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027374), c_Groups_Ozero__class_Ozero(_1027374)), _1027378)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027374), c_Groups_Ozero__class_Ozero(_1027374)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1027374), _1027376), _1027378))))], (11818 ^ _779203) ^ [_983134, _983136, _983138, _983140] : [class_Rings_Olinordered__ring__strict(_983134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983134), c_Groups_Ozero__class_Ozero(_983134)), _983136)), 11825 ^ _779203 : [(11832 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983134), _983138), _983140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983134), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983134), _983136), _983138)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983134), _983136), _983140))))], (11826 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983134), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983134), _983136), _983138)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983134), _983136), _983140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983134), _983138), _983140)))]]], (39530 ^ _779203) ^ [_1548541, _1548543, _1548545, _1548547] : [c_Finite__Set_Ofun__left__comm__idem(_1548541, _1548543, _1548545), -(hAPP(c_Fun_Ocomp(_1548543, _1548543, _1548543, hAPP(_1548545, _1548547)), hAPP(_1548545, _1548547)) = hAPP(_1548545, _1548547))], (45673 ^ _779203) ^ [_1696987, _1696989, _1696991, _1696993, _1696995, _1696997] : [class_Orderings_Olinorder(_1696987), -(hBOOL(hAPP(_1696989, _1696991))), -(hAPP(c_List_Ofilter(_1696993, _1696989), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696993, _1696987, _1696995), _1696991), _1696997)) = hAPP(c_List_Ofilter(_1696993, _1696989), _1696997))], (20426 ^ _779203) ^ [_1139385, _1139387, _1139389] : [class_Rings_Olinordered__idom(_1139385), 20429 ^ _779203 : [(20438 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139385), hAPP(c_Groups_Oabs__class_Oabs(_1139385), _1139387)), _1139389))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139385), _1139387), _1139389)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139385), hAPP(c_Groups_Ouminus__class_Ouminus(_1139385), _1139387)), _1139389))], (20430 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139385), hAPP(c_Groups_Oabs__class_Oabs(_1139385), _1139387)), _1139389)), 20433 ^ _779203 : [(20436 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139385), hAPP(c_Groups_Ouminus__class_Ouminus(_1139385), _1139387)), _1139389)))], (20434 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139385), _1139387), _1139389)))]]]]], (26829 ^ _779203) ^ [_1251830, _1251832, _1251834] : [26831 ^ _779203 : [(26836 ^ _779203) ^ [] : [hBOOL(hAPP(_1251832, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 26830 ^ [_1251830, _1251832, _1251834]), _1251830)))], (26834 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1251832, 26830 ^ [_1251830, _1251832, _1251834])))], (26832 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 26830 ^ [_1251830, _1251832, _1251834]), _1251830)))]], hBOOL(hAPP(_1251832, _1251834)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1251834), _1251830)), -(hBOOL(hAPP(_1251832, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (12775 ^ _779203) ^ [_999899, _999901, _999903, _999905] : [class_Rings_Olinordered__semiring__strict(_999899), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999899), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999899), _999901), _999903)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999899), _999901), _999905))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999899), c_Groups_Ozero__class_Ozero(_999899)), _999901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999899), _999903), _999905)))], (7541 ^ _779203) ^ [_903812, _903814, _903816, _903818] : [class_Orderings_Oord(_903812), 7544 ^ _779203 : [(7553 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_903814, _903812)), _903816), _903818))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903814, _903812)), _903816), _903818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903814, _903812)), _903818), _903816)))], (7545 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_903814, _903812)), _903816), _903818)), 7548 ^ _779203 : [(7551 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903814, _903812)), _903818), _903816))], (7549 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_903814, _903812)), _903816), _903818)))]]]]], (15982 ^ _779203) ^ [_1059693] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1059693) = _1059693)], (3946 ^ _779203) ^ [_838786, _838788] : [_838788 = _838786, -(c_New__DSequence_Opos__empty(_838788) = c_New__DSequence_Opos__empty(_838786))], (19206 ^ _779203) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (42614 ^ _779203) ^ [_1628918, _1628920, _1628922] : [_1628918 = c_List_Olist_ONil(_1628920), -(c_List_Obutlast(_1628920, hAPP(hAPP(c_List_Olist_OCons(_1628920), _1628922), _1628918)) = c_List_Olist_ONil(_1628920))], (34077 ^ _779203) ^ [_1404166, _1404168, _1404170] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1404166, tc_HOL_Obool), tc_fun(_1404166, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1404166, tc_HOL_Obool), tc_fun(_1404166, tc_HOL_Obool)), _1404168), _1404170)), c_Wellfounded_Ofinite__psubset(_1404166))), 34080 ^ _779203 : [(34083 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1404166), _1404170)))], (34081 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1404166, tc_HOL_Obool)), _1404168), _1404170)))]]], (17178 ^ _779203) ^ [_1081873, _1081875, _1081877] : [class_Orderings_Olinorder(_1081873), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081873), _1081875)), hBOOL(hAPP(hAPP(c_member(_1081873), _1081877), _1081875)), 17189 ^ _779203 : [(17196 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1081873, tc_HOL_Obool)), _1081875), hAPP(hAPP(c_Set_Oinsert(_1081873), _1081877), c_Orderings_Obot__class_Obot(tc_fun(_1081873, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1081873, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1081873, c_Orderings_Oord__class_Omax(_1081873), _1081875) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1081873), _1081877), c_Big__Operators_Olattice_OSup__fin(_1081873, c_Orderings_Oord__class_Omax(_1081873), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1081873, tc_HOL_Obool)), _1081875), hAPP(hAPP(c_Set_Oinsert(_1081873), _1081877), c_Orderings_Obot__class_Obot(tc_fun(_1081873, tc_HOL_Obool)))))))], (17190 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1081873, tc_HOL_Obool)), _1081875), hAPP(hAPP(c_Set_Oinsert(_1081873), _1081877), c_Orderings_Obot__class_Obot(tc_fun(_1081873, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1081873, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1081873, c_Orderings_Oord__class_Omax(_1081873), _1081875) = _1081877)]]], (21469 ^ _779203) ^ [] : [-(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))))], (40502 ^ _779203) ^ [_1572379, _1572381, _1572383, _1572385, _1572387] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572379, _1572379)), hAPP(hAPP(c_Product__Type_OPair(_1572379, _1572379), _1572381), _1572383)), _1572385)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1572379, _1572379)), hAPP(hAPP(c_Product__Type_OPair(_1572379, _1572379), _1572383), _1572387)), c_Transitive__Closure_Ortrancl(_1572379, _1572385))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572379, _1572379)), hAPP(hAPP(c_Product__Type_OPair(_1572379, _1572379), _1572381), _1572387)), c_Transitive__Closure_Otrancl(_1572379, _1572385))))], (45406 ^ _779203) ^ [_1690556, _1690558] : [_1690558 = c_List_Olist_ONil(_1690556), -(c_List_Oremdups(_1690556, _1690558) = c_List_Olist_ONil(_1690556))], (23116 ^ _779203) ^ [_1186003, _1186005] : [_1186003 = hAPP(c_Int_Onat, _1186005), 23119 ^ _779203 : [(23126 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186005))), -(_1186003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23120 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186005)), -(_1186005 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1186003))]]], (43945 ^ _779203) ^ [_1658453, _1658455, _1658457] : [class_Orderings_Olinorder(_1658453), -(c_Big__Operators_Olattice_OInf__fin(_1658453, c_Orderings_Oord__class_Omin(_1658453), hAPP(c_List_Oset(_1658453), hAPP(hAPP(c_List_Olist_OCons(_1658453), _1658455), _1658457))) = hAPP(c_List_Ofoldl(_1658453, _1658453, c_Orderings_Oord__class_Omin(_1658453), _1658455), _1658457))], (10975 ^ _779203) ^ [_968625] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _968625)], (24384 ^ _779203) ^ [_1208841, _1208843] : [class_Groups_Omonoid__mult(_1208841), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1208841), _1208843), 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(_1208841), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208841), _1208843), _1208843)), _1208843))], (26986 ^ _779203) ^ [_1254539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254539)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1254539) = 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, _1254539))))], (23810 ^ _779203) ^ [_1198260, _1198262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1198260)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198262), _1198260)), _1198260) = _1198262)], (5983 ^ _779203) ^ [_874102, _874104, _874106] : [-(hBOOL(hAPP(hAPP(c_member(_874102), _874104), hAPP(hAPP(c_Set_Oinsert(_874102), _874104), _874106))))], (14195 ^ _779203) ^ [_1026107, _1026109, _1026111, _1026113] : [class_Fields_Ofield__inverse__zero(_1026107), 14198 ^ _779203 : [(14199 ^ _779203) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026107), _1026109), _1026111) = _1026113, 14202 ^ _779203 : [(14209 ^ _779203) ^ [] : [_1026111 = c_Groups_Ozero__class_Ozero(_1026107), -(_1026113 = c_Groups_Ozero__class_Ozero(_1026107))], (14203 ^ _779203) ^ [] : [-(_1026111 = c_Groups_Ozero__class_Ozero(_1026107)), -(_1026109 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026107), _1026113), _1026111))]]], (14215 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026107), _1026109), _1026111) = _1026113), 14218 ^ _779203 : [(14221 ^ _779203) ^ [] : [_1026109 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026107), _1026113), _1026111)], (14219 ^ _779203) ^ [] : [_1026111 = c_Groups_Ozero__class_Ozero(_1026107)]], 14222 ^ _779203 : [(14225 ^ _779203) ^ [] : [_1026113 = c_Groups_Ozero__class_Ozero(_1026107)], (14223 ^ _779203) ^ [] : [-(_1026111 = c_Groups_Ozero__class_Ozero(_1026107))]]]]], (41038 ^ _779203) ^ [_1585557, _1585559, _1585561] : [41041 ^ _779203 : [(41047 ^ _779203) ^ [] : [41040 ^ [_1585557, _1585559, _1585561] = 41043 ^ [_1585557, _1585559, _1585561]], (41045 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585557, _1585559)), hAPP(hAPP(c_Product__Type_OPair(_1585557, _1585559), 41039 ^ [_1585557, _1585559, _1585561]), 41043 ^ [_1585557, _1585559, _1585561])), _1585561)))], (41042 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585557, _1585559)), hAPP(hAPP(c_Product__Type_OPair(_1585557, _1585559), 41039 ^ [_1585557, _1585559, _1585561]), 41040 ^ [_1585557, _1585559, _1585561])), _1585561)))]], -(c_Relation_Osingle__valued(_1585557, _1585559, _1585561))], (2796 ^ _779203) ^ [_820571, _820573, _820575, _820577] : [-(c_Relation_ODomain(_820577, _820573) = c_Relation_ODomain(_820575, _820571)), _820577 = _820575, _820573 = _820571], (7605 ^ _779203) ^ [_904740, _904742, _904744] : [class_Orderings_Oorder(_904740), 7608 ^ _779203 : [(7617 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904740), _904742), _904744))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904740), _904742), _904744)), -(_904742 = _904744)], (7609 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904740), _904742), _904744)), 7612 ^ _779203 : [(7615 ^ _779203) ^ [] : [_904742 = _904744], (7613 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904740), _904742), _904744)))]]]]], (22732 ^ _779203) ^ [_1179782, _1179784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179782), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 22735 ^ _779203 : [(22742 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179784), 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), _1179784), _1179782))))], (22736 ^ _779203) ^ [] : [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), _1179784), _1179782))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179784), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (52047 ^ _779203) ^ [_1829811, _1829813, _1829815] : [class_Rings_Ocomm__semiring__1(_1829811), 52052 ^ _779203 : [(52055 ^ _779203) ^ [] : [_1829815 = c_Groups_Oone__class_Oone(_1829811)], (52053 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829813))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829811), _1829815), hAPP(hAPP(c_Power_Opower__class_Opower(_1829811), _1829815), _1829813))))], (288 ^ _779203) ^ [_783611, _783613] : [-(c_Nat__Transfer_Ois__nat(_783611)), _783613 = _783611, c_Nat__Transfer_Ois__nat(_783613)], (27918 ^ _779203) ^ [_1271895, _1271897, _1271899] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271895, tc_HOL_Obool)), _1271897), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271895, tc_HOL_Obool)), _1271897), _1271899)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1271895, tc_HOL_Obool)), _1271897), _1271899))], (33453 ^ _779203) ^ [_1391270, _1391272, _1391274, _1391276] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1391270, _1391272), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1391274), _1391276))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1391270), _1391272), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1391276), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1391274)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1391274)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1391276), 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), _1391272), _1391276))))))], (24648 ^ _779203) ^ [_1213246, _1213248, _1213250] : [class_Rings_Olinordered__semidom(_1213246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213246), hAPP(hAPP(c_Power_Opower__class_Opower(_1213246), _1213248), 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(_1213246), _1213250), 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(_1213246), c_Groups_Ozero__class_Ozero(_1213246)), _1213250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1213246), _1213248), _1213250)))], (18373 ^ _779203) ^ [_1103347] : [class_Rings_Osemiring__1(_1103347), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103347), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1103347))], (43409 ^ _779203) ^ [_1646367, _1646369, _1646371, _1646373, _1646375, _1646377] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646367), tc_List_Olist(_1646367))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646367), tc_List_Olist(_1646367)), hAPP(hAPP(c_List_Oappend(_1646367), _1646369), hAPP(hAPP(c_List_Olist_OCons(_1646367), _1646371), c_List_Olist_ONil(_1646367)))), hAPP(hAPP(c_List_Oappend(_1646367), _1646373), hAPP(hAPP(c_List_Olist_OCons(_1646367), _1646375), c_List_Olist_ONil(_1646367))))), c_List_Olistrel1(_1646367, _1646377)))), 43410 ^ _779203 : [(43417 ^ _779203) ^ [] : [_1646369 = _1646373, hBOOL(hAPP(hAPP(c_member(tc_prod(_1646367, _1646367)), hAPP(hAPP(c_Product__Type_OPair(_1646367, _1646367), _1646371), _1646375)), _1646377))], (43411 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646367), tc_List_Olist(_1646367))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646367), tc_List_Olist(_1646367)), _1646369), _1646373)), c_List_Olistrel1(_1646367, _1646377))), _1646371 = _1646375]]], (43744 ^ _779203) ^ [_1654308, _1654310, _1654312] : [-(hAPP(c_List_Otl(_1654308), hAPP(hAPP(c_List_Olist_OCons(_1654308), _1654310), _1654312)) = _1654312)], (1240 ^ _779203) ^ [_797663, _797665] : [-(class_Rings_Olinordered__idom(_797663)), _797665 = _797663, class_Rings_Olinordered__idom(_797665)], (49967 ^ _779203) ^ [_1789831, _1789833, _1789835, _1789837, _1789839] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1789831, _1789833, tc_HOL_Obool, _1789835), _1789837), _1789839)), -(hBOOL(hAPP(_1789835, hAPP(hAPP(c_Product__Type_OPair(_1789831, _1789833), _1789837), _1789839))))], (23673 ^ _779203) ^ [_1195801, _1195803, _1195805] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195801), _1195803)), _1195805) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195801), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1195803), _1195805))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195801), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1195803, _1195805))), _1195805)))], (10329 ^ _779203) ^ [_956948, _956950, _956952] : [class_Rings_Ocomm__semiring__1(_956948), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956948), _956950), _956952)), _956952) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956948), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956948), _956950), c_Groups_Oone__class_Oone(_956948))), _956952))], (41280 ^ _779203) ^ [_1592330, _1592332, _1592334] : [c_Nitpick_Oless__frac(_1592330, _1592332, _1592334), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592330), c_Nitpick_Oplus__frac(_1592330, _1592332, c_Nitpick_Ouminus__frac(_1592330, _1592334)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28108 ^ _779203) ^ [_1275696, _1275698, _1275700, _1275702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1275696, tc_HOL_Obool)), _1275698), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275696, tc_HOL_Obool)), _1275700), _1275702))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1275696, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1275696, tc_HOL_Obool)), _1275698), _1275700)), _1275702)))], (18830 ^ _779203) ^ [_1110910, _1110912, _1110914, _1110916, _1110918] : [class_Groups_Oordered__ab__semigroup__add(_1110910), class_Rings_Osemiring__1(_1110910), 18840 ^ _779203 : [(18843 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110910), hAPP(_1110916, 18839 ^ [_1110910, _1110912, _1110914, _1110916, _1110918])), _1110918))], (18841 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1110912), 18839 ^ [_1110910, _1110912, _1110914, _1110916, _1110918]), _1110914)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1110910), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1110912, _1110910), _1110916), _1110914)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1110910), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1110910), hAPP(c_Finite__Set_Ocard(_1110912), _1110914))), _1110918))))], (38961 ^ _779203) ^ [_1534318, _1534320, _1534322] : [-(hAPP(c_Relation_ODomain(_1534318, _1534320), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1534318, _1534320), tc_HOL_Obool), _1534322)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1534318, _1534320), tc_HOL_Obool), tc_fun(_1534318, tc_HOL_Obool)), _1534322), c_Relation_ODomain(_1534318, _1534320)))], (40654 ^ _779203) ^ [_1575841, _1575843, _1575845, _1575847, _1575849] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575841, _1575841)), hAPP(hAPP(c_Product__Type_OPair(_1575841, _1575841), hAPP(_1575843, hAPP(c_Nat_OSuc, 40655 ^ [_1575841, _1575843, _1575845, _1575847, _1575849]))), hAPP(_1575843, 40655 ^ [_1575841, _1575843, _1575845, _1575847, _1575849]))), c_Transitive__Closure_Ortrancl(_1575841, _1575845))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1575841, _1575841)), hAPP(hAPP(c_Product__Type_OPair(_1575841, _1575841), hAPP(_1575843, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1575847), _1575849))), hAPP(_1575843, _1575847))), c_Transitive__Closure_Ortrancl(_1575841, _1575845))))], (44309 ^ _779203) ^ [_1665299, _1665301, _1665303, _1665305, _1665307, _1665309, _1665311] : [-(hAPP(c_List_Ofoldl(_1665299, _1665301, _1665303, _1665305), hAPP(hAPP(c_List_Omap(_1665307, _1665301), _1665309), _1665311)) = hAPP(c_List_Ofoldl(_1665299, _1665307, hAPP(hAPP(c_COMBC(_1665299, tc_fun(_1665307, _1665301), tc_fun(_1665307, _1665299)), hAPP(hAPP(c_COMBB(tc_fun(_1665301, _1665299), tc_fun(tc_fun(_1665307, _1665301), tc_fun(_1665307, _1665299)), _1665299), c_COMBB(_1665301, _1665299, _1665307)), _1665303)), _1665309), _1665305), _1665311))], (21745 ^ _779203) ^ [_1161981, _1161983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1161981), _1161983)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1161981)), c_Int_OBit0(_1161983))))], (49455 ^ _779203) ^ [_1778529, _1778531] : [c_Equiv__Relations_Opart__equivp(_1778529, _1778531), 49459 ^ _779203 : [(49472 ^ _779203) ^ [_1778871, _1778873] : [-(hBOOL(hAPP(hAPP(_1778531, _1778873), _1778871))), hBOOL(hAPP(hAPP(_1778531, _1778873), _1778873)), hBOOL(hAPP(hAPP(_1778531, _1778871), _1778871)), hAPP(_1778531, _1778873) = hAPP(_1778531, _1778871)], (49462 ^ _779203) ^ [_1778702, _1778704] : [hBOOL(hAPP(hAPP(_1778531, _1778704), _1778702)), 49465 ^ _779203 : [(49470 ^ _779203) ^ [] : [-(hAPP(_1778531, _1778704) = hAPP(_1778531, _1778702))], (49468 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1778531, _1778702), _1778702)))], (49466 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1778531, _1778704), _1778704)))]]], (49460 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1778531, 49458 ^ [_1778529, _1778531]), 49458 ^ [_1778529, _1778531])))]]], (37399 ^ _779203) ^ [_1486951, _1486953] : [-(hAPP(c_Set_OCollect(_1486951), hAPP(hAPP(c_COMBC(_1486951, tc_fun(_1486951, tc_HOL_Obool), tc_HOL_Obool), c_member(_1486951)), _1486953)) = _1486953)], (26102 ^ _779203) ^ [_1238120, _1238122] : [class_Rings_Oring__1(_1238120), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238122)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1238120), hAPP(c_Int_Onat, _1238122)) = hAPP(c_Int_Oring__1__class_Oof__int(_1238120), _1238122))], (5648 ^ _779203) ^ [_868286, _868288] : [hAPP(_868286, 5649 ^ [_868286, _868288]) = hAPP(_868288, 5649 ^ [_868286, _868288]), -(_868286 = _868288)], (29052 ^ _779203) ^ [_1293258, _1293260, _1293262] : [class_Lattices_Olattice(_1293258), hAPP(_1293260, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1293258), 29057 ^ [_1293258, _1293260, _1293262]), 29058 ^ [_1293258, _1293260, _1293262])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1293258), hAPP(_1293260, 29057 ^ [_1293258, _1293260, _1293262])), hAPP(_1293260, 29058 ^ [_1293258, _1293260, _1293262])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1293258), _1293262)), -(_1293262 = c_Orderings_Obot__class_Obot(tc_fun(_1293258, tc_HOL_Obool))), -(hAPP(_1293260, c_Big__Operators_Olattice__class_OSup__fin(_1293258, _1293262)) = c_Big__Operators_Olattice__class_OSup__fin(_1293258, hAPP(c_Set_Oimage(_1293258, _1293258, _1293260), _1293262)))], (43113 ^ _779203) ^ [_1639483, _1639485, _1639487, _1639489] : [hAPP(hAPP(c_List_Oappend(_1639483), _1639485), _1639487) = hAPP(hAPP(c_List_Oappend(_1639483), _1639489), _1639487), -(_1639485 = _1639489)], (31661 ^ _779203) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (41613 ^ _779203) ^ [_1602771, _1602773, _1602775, _1602777] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602771), tc_List_Olist(_1602771))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602771), tc_List_Olist(_1602771)), _1602773), _1602775)), c_List_Olistrel1(_1602771, _1602777))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602771), tc_List_Olist(_1602771))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602771), tc_List_Olist(_1602771)), _1602773), _1602775)), c_List_Olistrel(_1602771, c_Transitive__Closure_Ortrancl(_1602771, _1602777)))))], (52497 ^ _779203) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (30387 ^ _779203) ^ [_1321471, _1321473, _1321475] : [class_Orderings_Olinorder(_1321471), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321471), _1321473)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321471), _1321475)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321471, tc_HOL_Obool)), _1321473), _1321475) = c_Orderings_Obot__class_Obot(tc_fun(_1321471, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321471), c_Big__Operators_Olinorder__class_OMin(_1321471, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321471, tc_HOL_Obool)), _1321473), _1321475))), c_Big__Operators_Olinorder__class_OMin(_1321471, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321471, tc_HOL_Obool)), _1321473), _1321475))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321471), c_Big__Operators_Olinorder__class_OMin(_1321471, _1321473)), c_Big__Operators_Olinorder__class_OMin(_1321471, _1321475)))], (6907 ^ _779203) ^ [_892101, _892103] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892101, tc_HOL_Obool)), _892103), _892103) = c_Orderings_Obot__class_Obot(tc_fun(_892101, tc_HOL_Obool)))], (14009 ^ _779203) ^ [_1022875, _1022877, _1022879, _1022881] : [class_Fields_Olinordered__field(_1022875), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022875), _1022877), _1022879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022875), _1022881), c_Groups_Ozero__class_Ozero(_1022875))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1022875), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1022875), _1022879), _1022881)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1022875), _1022877), _1022881))))], (34266 ^ _779203) ^ [_1408445, _1408447, _1408449, _1408451, _1408453, _1408455, _1408457, _1408459] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408445, tc_fun(_1408447, tc_fun(_1408449, tc_HOL_Obool))), _1408451), _1408453), _1408455), _1408457)), -(hBOOL(hAPP(hAPP(hAPP(_1408453, _1408459), _1408455), _1408457))), hBOOL(hAPP(hAPP(c_member(_1408445), _1408459), _1408451))], (35588 ^ _779203) ^ [_1445473, _1445475, _1445477, _1445479] : [-(hAPP(c_Relation_OField(_1445473), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1445473, _1445473)), hAPP(hAPP(c_Product__Type_OPair(_1445473, _1445473), _1445475), _1445477)), _1445479)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1445473, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1445473), _1445475), hAPP(hAPP(c_Set_Oinsert(_1445473), _1445477), c_Orderings_Obot__class_Obot(tc_fun(_1445473, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1445473), _1445479)))], (39522 ^ _779203) ^ [_1548312, _1548314, _1548316, _1548318, _1548320, _1548322, _1548324, _1548326, _1548328, _1548330, _1548332] : [hAPP(_1548312, hAPP(_1548314, _1548316)) = hAPP(_1548318, hAPP(_1548320, _1548322)), -(hAPP(hAPP(c_Fun_Ocomp(_1548324, _1548326, _1548328, _1548312), _1548314), _1548316) = hAPP(hAPP(c_Fun_Ocomp(_1548330, _1548326, _1548332, _1548318), _1548320), _1548322))], (45518 ^ _779203) ^ [_1692676, _1692678] : [c_List_Olist_ONil(_1692676) = c_List_Oconcat(_1692676, _1692678), 45521 ^ _779203 : [(45522 ^ _779203) ^ [_1692767] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692676)), _1692767), hAPP(c_List_Oset(tc_List_Olist(_1692676)), _1692678))), -(_1692767 = c_List_Olist_ONil(_1692676))]]], (35667 ^ _779203) ^ [_1447589, _1447591, _1447593, _1447595] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1447589, _1447589)), hAPP(hAPP(c_Product__Type_OPair(_1447589, _1447589), _1447591), _1447593)), c_Relation_OId__on(_1447589, _1447595)))), _1447591 = _1447593, hBOOL(hAPP(hAPP(c_member(_1447589), _1447591), _1447595))], (45264 ^ _779203) ^ [_1687613, _1687615] : [hBOOL(hAPP(c_List_Odistinct(_1687613), _1687615)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1687613, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1687613), tc_fun(_1687613, tc_HOL_Obool)), c_List_Oset(_1687613)), c_Enum_Osublists(_1687613, _1687615)))))], (3844 ^ _779203) ^ [_836993, _836995, _836997, _836999, _837001, _837003, _837005, _837007] : [-(c_New__DSequence_Oneg__decr__bind(_837007, _837003, _836999, _836995) = c_New__DSequence_Oneg__decr__bind(_837005, _837001, _836997, _836993)), _837007 = _837005, _837003 = _837001, _836999 = _836997, _836995 = _836993], (25920 ^ _779203) ^ [_1234961] : [class_Rings_Oring__1(_1234961), -(hAPP(c_Int_Oring__1__class_Oof__int(_1234961), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1234961))], (52365 ^ _779203) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (21241 ^ _779203) ^ [_1153746, _1153748] : [class_Int_Onumber__ring(_1153746), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153746), hAPP(c_Int_Onumber__class_Onumber__of(_1153746), c_Int_OBit1(c_Int_OPls))), _1153748) = _1153748)], (37395 ^ _779203) ^ [_1486726, _1486728, _1486730, _1486732, _1486734] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1486726, _1486728), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486726, tc_HOL_Obool)), _1486730), _1486732)), hAPP(c_COMBK(tc_fun(_1486728, tc_HOL_Obool), _1486726), _1486734)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1486726, _1486728), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1486726, _1486728), _1486730), hAPP(c_COMBK(tc_fun(_1486728, tc_HOL_Obool), _1486726), _1486734))), hAPP(hAPP(c_Product__Type_OSigma(_1486726, _1486728), _1486732), hAPP(c_COMBK(tc_fun(_1486728, tc_HOL_Obool), _1486726), _1486734))))], (39610 ^ _779203) ^ [_1550343, _1550345, _1550347, _1550349] : [-(c_Hilbert__Choice_OEps(tc_prod(_1550343, _1550345), hAPP(c_Product__Type_Oprod_Oprod__case(_1550343, _1550345, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1550343, tc_fun(_1550345, tc_HOL_Obool), tc_fun(_1550345, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1550345, tc_HOL_Obool), tc_fun(_1550345, tc_HOL_Obool)), _1550343), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1550345)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1550343), c_fconj), hAPP(c_fequal, _1550347)))), hAPP(c_fequal, _1550349)))) = hAPP(hAPP(c_Product__Type_OPair(_1550343, _1550345), _1550347), _1550349))], (29660 ^ _779203) ^ [_1305531, _1305533, _1305535, _1305537] : [class_Lattices_Olattice(_1305531), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305531), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1305531), _1305533), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1305531), _1305535), _1305537))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1305531), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1305531), _1305533), _1305535)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1305531), _1305533), _1305537)))))], (18865 ^ _779203) ^ [_1111611, _1111613] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1111611)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1111613))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1111611), _1111613)))], (52643 ^ _779203) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (28730 ^ _779203) ^ [_1287299, _1287301, _1287303] : [_1287301 = _1287303, -(hBOOL(hAPP(hAPP(c_member(_1287299), _1287301), hAPP(c_fequal, _1287303))))], (10171 ^ _779203) ^ [_953769, _953771, _953773] : [class_Rings_Olinordered__semidom(_953769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953769), c_Groups_Oone__class_Oone(_953769)), _953771)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953769), c_Groups_Oone__class_Oone(_953769)), _953773)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953769), c_Groups_Oone__class_Oone(_953769)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_953769), _953771), _953773))))], (38086 ^ _779203) ^ [_1508634, _1508636, _1508638] : [class_Lattices_Odistrib__lattice(_1508634), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508634), _1508636)), -(_1508636 = c_Orderings_Obot__class_Obot(tc_fun(_1508634, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508634), _1508638)), -(_1508638 = c_Orderings_Obot__class_Obot(tc_fun(_1508634, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1508634), c_Big__Operators_Olattice__class_OInf__fin(_1508634, _1508636)), c_Big__Operators_Olattice__class_OInf__fin(_1508634, _1508638)) = c_Big__Operators_Olattice__class_OInf__fin(_1508634, hAPP(c_Set_OCollect(_1508634), hAPP(hAPP(c_COMBB(tc_fun(_1508634, tc_HOL_Obool), tc_HOL_Obool, _1508634), c_HOL_OEx(_1508634)), hAPP(hAPP(c_COMBB(tc_fun(_1508634, tc_fun(_1508634, tc_HOL_Obool)), tc_fun(_1508634, tc_HOL_Obool), _1508634), hAPP(c_COMBB(tc_fun(_1508634, tc_HOL_Obool), tc_HOL_Obool, _1508634), c_HOL_OEx(_1508634))), hAPP(hAPP(c_COMBC(_1508634, tc_fun(_1508634, tc_fun(_1508634, tc_HOL_Obool)), tc_fun(_1508634, tc_fun(_1508634, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1508634, tc_fun(tc_fun(_1508634, tc_HOL_Obool), tc_fun(_1508634, tc_HOL_Obool))), tc_fun(tc_fun(_1508634, tc_fun(_1508634, tc_HOL_Obool)), tc_fun(_1508634, tc_fun(_1508634, tc_HOL_Obool))), _1508634), c_COMBS(_1508634, tc_fun(_1508634, tc_HOL_Obool), tc_fun(_1508634, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1508634, tc_fun(_1508634, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1508634, tc_fun(tc_fun(_1508634, tc_HOL_Obool), tc_fun(_1508634, tc_HOL_Obool))), _1508634), hAPP(c_COMBB(tc_fun(_1508634, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1508634, tc_HOL_Obool), tc_fun(_1508634, tc_HOL_Obool)), _1508634), c_COMBS(_1508634, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1508634, tc_fun(_1508634, tc_HOL_Obool)), tc_fun(_1508634, tc_fun(_1508634, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1508634), hAPP(c_COMBB(tc_fun(_1508634, tc_HOL_Obool), tc_fun(_1508634, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1508634), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508634), c_fconj))), hAPP(hAPP(c_COMBC(_1508634, tc_fun(_1508634, tc_fun(_1508634, _1508634)), tc_fun(_1508634, tc_fun(_1508634, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1508634, _1508634), tc_fun(_1508634, tc_HOL_Obool)), tc_fun(tc_fun(_1508634, tc_fun(_1508634, _1508634)), tc_fun(_1508634, tc_fun(_1508634, tc_HOL_Obool))), _1508634), c_COMBB(tc_fun(_1508634, _1508634), tc_fun(_1508634, tc_HOL_Obool), _1508634)), hAPP(hAPP(c_COMBB(tc_fun(_1508634, tc_HOL_Obool), tc_fun(tc_fun(_1508634, _1508634), tc_fun(_1508634, tc_HOL_Obool)), _1508634), c_COMBB(_1508634, tc_HOL_Obool, _1508634)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1508634)))))), hAPP(hAPP(c_COMBC(_1508634, tc_fun(_1508634, tc_HOL_Obool), tc_fun(_1508634, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1508634, tc_HOL_Obool), tc_fun(_1508634, tc_HOL_Obool)), _1508634), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1508634)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508634), c_fconj), hAPP(hAPP(c_COMBC(_1508634, tc_fun(_1508634, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508634)), _1508636)))), hAPP(hAPP(c_COMBC(_1508634, tc_fun(_1508634, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508634)), _1508638))))))))], (31831 ^ _779203) ^ [_1351835, _1351837, _1351839, _1351841] : [class_Groups_Ouminus(_1351835), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1351837, _1351835)), _1351839), _1351841) = hAPP(c_Groups_Ouminus__class_Ouminus(_1351835), hAPP(_1351839, _1351841)))], (35341 ^ _779203) ^ [_1438084, _1438086, _1438088, _1438090] : [c_Wellfounded_Omax__extp(_1438084, hAPP(hAPP(c_COMBC(_1438084, tc_fun(tc_prod(_1438084, _1438084), tc_HOL_Obool), tc_fun(_1438084, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1438084, tc_fun(tc_fun(tc_prod(_1438084, _1438084), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1438084, _1438084), tc_HOL_Obool), tc_fun(_1438084, tc_HOL_Obool)), _1438084), c_COMBC(_1438084, tc_fun(tc_prod(_1438084, _1438084), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1438084, tc_prod(_1438084, _1438084)), tc_fun(_1438084, tc_fun(tc_fun(tc_prod(_1438084, _1438084), tc_HOL_Obool), tc_HOL_Obool)), _1438084), hAPP(c_COMBB(tc_prod(_1438084, _1438084), tc_fun(tc_fun(tc_prod(_1438084, _1438084), tc_HOL_Obool), tc_HOL_Obool), _1438084), c_member(tc_prod(_1438084, _1438084)))), c_Product__Type_OPair(_1438084, _1438084)))), _1438086), _1438088, _1438090), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1438084, tc_HOL_Obool), tc_fun(_1438084, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1438084, tc_HOL_Obool), tc_fun(_1438084, tc_HOL_Obool)), _1438088), _1438090)), c_Wellfounded_Omax__ext(_1438084, _1438086))))], (9580 ^ _779203) ^ [_942773, _942775] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _942773), _942775) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _942773 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _942775 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (34095 ^ _779203) ^ [_1404590, _1404592, _1404594, _1404596, _1404598] : [class_Groups_Oordered__ab__group__add(_1404590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404592), _1404594)), 34105 ^ _779203 : [(34108 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1404590), c_Groups_Ozero__class_Ozero(_1404590)), hAPP(_1404596, 34104 ^ [_1404590, _1404592, _1404594, _1404596, _1404598])))], (34106 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404592), 34104 ^ [_1404590, _1404592, _1404594, _1404596, _1404598]), _1404594)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1404592, _1404590), _1404596), _1404594) = c_Groups_Ozero__class_Ozero(_1404590), hBOOL(hAPP(hAPP(c_member(_1404592), _1404598), _1404594)), -(hAPP(_1404596, _1404598) = c_Groups_Ozero__class_Ozero(_1404590))], (46668 ^ _779203) ^ [_1717665, _1717667, _1717669] : [_1717667 = hAPP(c_List_Orev(_1717665), _1717669), -(hAPP(c_List_Orev(_1717665), _1717667) = _1717669)], (33719 ^ _779203) ^ [_1396575, _1396577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396575), 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)), _1396577)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396575, _1396577) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1396575, _1396577)))], (8741 ^ _779203) ^ [_926607, _926609, _926611, _926613] : [class_Groups_Oordered__ab__semigroup__add(_926607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926607), _926609), _926611)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926607), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926607), _926613), _926609)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926607), _926613), _926611))))], (23215 ^ _779203) ^ [_1187634, _1187636] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187634) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1187636), 23218 ^ _779203 : [(23221 ^ _779203) ^ [] : [-(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), _1187636))))], (23219 ^ _779203) ^ [] : [-(_1187634 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1187636)))]]], (41235 ^ _779203) ^ [_1591097, _1591099, _1591101, _1591103, _1591105, _1591107] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591097, _1591099)), _1591101), hAPP(hAPP(c_Relation_Orel__comp(_1591097, _1591103, _1591099), _1591105), _1591107))), 41241 ^ _779203 : [(41246 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591103, _1591099)), hAPP(hAPP(c_Product__Type_OPair(_1591103, _1591099), 41239 ^ [_1591097, _1591099, _1591101, _1591103, _1591105, _1591107]), 41240 ^ [_1591097, _1591099, _1591101, _1591103, _1591105, _1591107])), _1591107)))], (41244 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591097, _1591103)), hAPP(hAPP(c_Product__Type_OPair(_1591097, _1591103), 41238 ^ [_1591097, _1591099, _1591101, _1591103, _1591105, _1591107]), 41239 ^ [_1591097, _1591099, _1591101, _1591103, _1591105, _1591107])), _1591105)))], (41242 ^ _779203) ^ [] : [-(_1591101 = hAPP(hAPP(c_Product__Type_OPair(_1591097, _1591099), 41238 ^ [_1591097, _1591099, _1591101, _1591103, _1591105, _1591107]), 41240 ^ [_1591097, _1591099, _1591101, _1591103, _1591105, _1591107]))]]], (50198 ^ _779203) ^ [_1794284, _1794286, _1794288, _1794290] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1794284, _1794286, _1794288), c_Product__Type_Ocurry(_1794284, _1794286, _1794288, _1794290)) = _1794290)], (50965 ^ _779203) ^ [_1811119, _1811121] : [50966 ^ _779203 : [(50969 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811121), _1811119))], (50967 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811119), _1811121)))]], -(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)))), _1811119, _1811121))], (43460 ^ _779203) ^ [_1647897, _1647899, _1647901, _1647903] : [-(hAPP(hAPP(c_List_Odrop(_1647897), hAPP(c_Nat_OSuc, _1647899)), hAPP(hAPP(c_List_Olist_OCons(_1647897), _1647901), _1647903)) = hAPP(hAPP(c_List_Odrop(_1647897), _1647899), _1647903))], (52599 ^ _779203) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (14731 ^ _779203) ^ [_1035911, _1035913, _1035915] : [class_Fields_Olinordered__field(_1035911), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1035911), _1035913), _1035915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1035911), _1035913), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035911), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035911), _1035913), _1035915)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035911), c_Groups_Oone__class_Oone(_1035911)), c_Groups_Oone__class_Oone(_1035911))))))], (42802 ^ _779203) ^ [_1632263, _1632265, _1632267] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632263), tc_List_Olist(_1632263))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632263), tc_List_Olist(_1632263)), _1632265), c_List_Olist_ONil(_1632263))), c_List_Olex(_1632263, _1632267)))], (34480 ^ _779203) ^ [_1415179, _1415181, _1415183, _1415185, _1415187] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1415179, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415181, tc_fun(_1415179, tc_HOL_Obool)), _1415183), _1415185)), _1415187) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415181, tc_fun(_1415179, tc_HOL_Obool)), _1415183), hAPP(hAPP(c_COMBC(_1415181, tc_fun(_1415179, tc_HOL_Obool), tc_fun(_1415179, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1415179, tc_HOL_Obool), tc_fun(tc_fun(_1415179, tc_HOL_Obool), tc_fun(_1415179, tc_HOL_Obool)), _1415181), c_Groups_Ominus__class_Ominus(tc_fun(_1415179, tc_HOL_Obool))), _1415185)), _1415187)))], (1570 ^ _779203) ^ [_801788, _801790] : [-(class_Groups_Olinordered__ab__semigroup__add(_801788)), _801790 = _801788, class_Groups_Olinordered__ab__semigroup__add(_801790)], (33249 ^ _779203) ^ [_1388028, _1388030, _1388032, _1388034, _1388036] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1388028, _1388030), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1388032), _1388034))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1388030)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1388036), _1388028), _1388030), 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), _1388036), _1388032)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1388036), _1388034)), _1388030))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1388036), _1388034), _1388030)))))], (7161 ^ _779203) ^ [_897785, _897787, _897789, _897791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_897785, tc_HOL_Obool)), _897787), hAPP(hAPP(c_Set_Oinsert(_897785), _897789), _897791))), 7164 ^ _779203 : [(7171 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_897785), _897789), _897791))), 7174 ^ _779203 : [(7181 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_897785), _897789), _897787))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897785, tc_HOL_Obool)), _897787), _897791)))], (7175 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_897785), _897789), _897787)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_897785, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_897785, tc_HOL_Obool)), _897787), hAPP(hAPP(c_Set_Oinsert(_897785), _897789), c_Orderings_Obot__class_Obot(tc_fun(_897785, tc_HOL_Obool))))), _897791)))]]], (7165 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_897785), _897789), _897791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_897785, tc_HOL_Obool)), _897787), _897791)))]]], (18969 ^ _779203) ^ [_1113362, _1113364, _1113366] : [class_Rings_Osemiring__1(_1113362), hBOOL(hAPP(hAPP(c_member(_1113362), _1113364), c_Nat_Osemiring__1__class_ONats(_1113362))), hBOOL(hAPP(hAPP(c_member(_1113362), _1113366), c_Nat_Osemiring__1__class_ONats(_1113362))), -(hBOOL(hAPP(hAPP(c_member(_1113362), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1113362), _1113364), _1113366)), c_Nat_Osemiring__1__class_ONats(_1113362))))], (51619 ^ _779203) ^ [_1822048, _1822050, _1822052, _1822054] : [class_Rings_Ocomm__semiring__1(_1822048), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1822048), _1822050), _1822052)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1822048), hAPP(hAPP(c_Power_Opower__class_Opower(_1822048), _1822050), _1822054)), hAPP(hAPP(c_Power_Opower__class_Opower(_1822048), _1822052), _1822054))))], (30847 ^ _779203) ^ [_1331046, _1331048, _1331050] : [class_Lattices_Olattice(_1331046), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331046), _1331048)), hBOOL(hAPP(hAPP(c_member(_1331046), _1331050), _1331048)), 30858 ^ _779203 : [(30865 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331046, tc_HOL_Obool)), _1331048), hAPP(hAPP(c_Set_Oinsert(_1331046), _1331050), c_Orderings_Obot__class_Obot(tc_fun(_1331046, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1331046, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1331046, _1331048) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1331046), _1331050), c_Big__Operators_Olattice__class_OInf__fin(_1331046, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331046, tc_HOL_Obool)), _1331048), hAPP(hAPP(c_Set_Oinsert(_1331046), _1331050), c_Orderings_Obot__class_Obot(tc_fun(_1331046, tc_HOL_Obool)))))))], (30859 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1331046, tc_HOL_Obool)), _1331048), hAPP(hAPP(c_Set_Oinsert(_1331046), _1331050), c_Orderings_Obot__class_Obot(tc_fun(_1331046, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1331046, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1331046, _1331048) = _1331050)]]], (48965 ^ _779203) ^ [_1768385, _1768387, _1768389, _1768391] : [class_Complete__Lattice_Ocomplete__lattice(_1768385), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1768387, _1768385), _1768389), _1768391) = c_Complete__Lattice_OSup__class_OSup(_1768385, hAPP(c_Set_OCollect(_1768385), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768387, _1768385), tc_HOL_Obool), tc_HOL_Obool, _1768385), c_HOL_OEx(tc_fun(_1768387, _1768385))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768387, _1768385), tc_HOL_Obool), tc_fun(tc_fun(_1768387, _1768385), tc_HOL_Obool), _1768385), hAPP(c_COMBS(tc_fun(_1768387, _1768385), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1768387, _1768385)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1768387, _1768385), tc_fun(tc_fun(_1768387, _1768385), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1768387, _1768385))), _1768389)))), hAPP(hAPP(c_COMBC(_1768385, tc_fun(tc_fun(_1768387, _1768385), _1768385), tc_fun(tc_fun(_1768387, _1768385), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768385, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1768387, _1768385), _1768385), tc_fun(tc_fun(_1768387, _1768385), tc_HOL_Obool)), _1768385), c_COMBB(_1768385, tc_HOL_Obool, tc_fun(_1768387, _1768385))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1768387, _1768385), _1768387, _1768385), c_COMBI(tc_fun(_1768387, _1768385))), _1768391)))))))], (19348 ^ _779203) ^ [_1120094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120094), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1120094)))], (48450 ^ _779203) ^ [_1756126, _1756128] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1756126)), _1756128) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1756126, tc_Lazy__Sequence_Olazy__sequence(_1756126)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1756126, tc_Lazy__Sequence_Olazy__sequence(_1756126), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756126), tc_Nat_Onat), _1756126), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1756126), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1756126)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1756126)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1756126), _1756128)))], (21877 ^ _779203) ^ [_1164499, _1164501] : [class_Rings_Osemiring__1(_1164499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1164501)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1164499), 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)))), _1164501))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164499), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1164499), hAPP(c_Int_Onat, _1164501))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1164499), hAPP(c_Int_Onat, _1164501))))], (39516 ^ _779203) ^ [_1548158, _1548160, _1548162, _1548164, _1548166, _1548168, _1548170, _1548172] : [hAPP(c_Fun_Ocomp(_1548158, _1548160, _1548162, _1548164), _1548166) = hAPP(c_Fun_Ocomp(_1548168, _1548160, _1548162, _1548170), _1548172), 39519 ^ _779203 : [(39520 ^ _779203) ^ [_1548273] : [-(hAPP(_1548164, hAPP(_1548166, _1548273)) = hAPP(_1548170, hAPP(_1548172, _1548273)))]]], (22133 ^ _779203) ^ [_1169911, _1169913, _1169915] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1169911), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1169913, _1169915)), _1169915) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1169911), _1169913), _1169915))], (48553 ^ _779203) ^ [_1758600, _1758602, _1758604, _1758606] : [class_Groups_Ocomm__monoid__add(_1758600), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1758602, tc_HOL_Obool)), _1758604)), 48563 ^ _779203 : [(48566 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1758602), 48562 ^ [_1758600, _1758602, _1758604, _1758606]))], (48564 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758602, tc_HOL_Obool)), 48562 ^ [_1758600, _1758602, _1758604, _1758606]), _1758604)))]], 48570 ^ _779203 : [(48574 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758602, tc_HOL_Obool)), 48572 ^ [_1758600, _1758602, _1758604, _1758606]), _1758604)))], (48571 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1758602, tc_HOL_Obool)), 48569 ^ [_1758600, _1758602, _1758604, _1758606]), _1758604)))], (48583 ^ _779203) ^ [] : [hAPP(_1758606, 48577 ^ [_1758600, _1758602, _1758604, _1758606]) = c_Groups_Ozero__class_Ozero(_1758600)], (48579 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758602), 48577 ^ [_1758600, _1758602, _1758604, _1758606]), 48569 ^ [_1758600, _1758602, _1758604, _1758606])))], (48581 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758602), 48577 ^ [_1758600, _1758602, _1758604, _1758606]), 48572 ^ [_1758600, _1758602, _1758604, _1758606])))], (48576 ^ _779203) ^ [] : [48569 ^ [_1758600, _1758602, _1758604, _1758606] = 48572 ^ [_1758600, _1758602, _1758604, _1758606]]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1758602, _1758600), _1758606), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1758602, tc_HOL_Obool), _1758604)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1758602, tc_HOL_Obool), _1758600), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1758602, _1758600), _1758606)), _1758604))], (19336 ^ _779203) ^ [_1119911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1119911)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1119911))], (52537 ^ _779203) ^ [_1835250] : [class_Finite__Set_Ofinite(_1835250), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1835250)))], (766 ^ _779203) ^ [_790712, _790714, _790716, _790718] : [-(c_Wellfounded_Oacyclic(_790716, _790712)), c_Wellfounded_Oacyclic(_790718, _790714), _790718 = _790716, _790714 = _790712], (29928 ^ _779203) ^ [_1311784, _1311786, _1311788, _1311790] : [class_Orderings_Olinorder(_1311784), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311784, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1311784, _1311786, _1311788)), hAPP(c_SetInterval_Oord__class_OatMost(_1311784), _1311790)) = c_SetInterval_Oord__class_OatLeastAtMost(_1311784, _1311786, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311784), _1311788), _1311790)))], (40616 ^ _779203) ^ [_1574933, _1574935] : [-(c_Relation_Orefl__on(_1574933, c_Orderings_Otop__class_Otop(tc_fun(_1574933, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1574933, _1574933), tc_HOL_Obool)), _1574935), c_Relation_OId(_1574933))))], (9457 ^ _779203) ^ [_940452, _940454] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940452), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940454), _940452))))], (24620 ^ _779203) ^ [_1212804, _1212806, _1212808] : [class_Rings_Oring__1(_1212804), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1212804), hAPP(c_Groups_Ouminus__class_Ouminus(_1212804), _1212806)), 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)))), _1212808)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1212804), _1212806), 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)))), _1212808)))], (32501 ^ _779203) ^ [_1368592, _1368594] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368592)), hAPP(c_Nat_OSuc, _1368594)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1368592))), 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)), _1368594)))))], (112 ^ _779203) ^ [_780845, _780847] : [-(class_Fields_Olinordered__field__inverse__zero(_780845)), _780847 = _780845, class_Fields_Olinordered__field__inverse__zero(_780847)], (42814 ^ _779203) ^ [_1632611, _1632613] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1632611), _1632613))), -(c_List_Oupto(_1632611, _1632613) = c_List_Olist_ONil(tc_Int_Oint))], (24412 ^ _779203) ^ [_1209282, _1209284] : [24413 ^ _779203 : [(24416 ^ _779203) ^ [] : [_1209284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (24414 ^ _779203) ^ [] : [-(_1209282 = 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), _1209282)), _1209284))))], (17448 ^ _779203) ^ [_1086928, _1086930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086928), _1086930)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086928), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1086930), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (43574 ^ _779203) ^ [_1650481, _1650483, _1650485, _1650487] : [-(hAPP(hAPP(c_List_Odrop(_1650481), _1650483), hAPP(hAPP(c_List_Olist_OCons(_1650481), _1650485), _1650487)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1650481), hAPP(hAPP(c_List_Olist_OCons(_1650481), _1650485), _1650487), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1650481), tc_List_Olist(_1650481)), c_List_Odrop(_1650481)), _1650487), _1650483))], (4360 ^ _779203) ^ [_845331, _845333, _845335, _845337] : [-(c_Wellfounded_Oaccp(_845337, _845333) = c_Wellfounded_Oaccp(_845335, _845331)), _845337 = _845335, _845333 = _845331], (46244 ^ _779203) ^ [_1708977, _1708979, _1708981, _1708983, _1708985] : [class_Orderings_Olinorder(_1708977), c_List_Olinorder__class_Osorted(_1708977, hAPP(hAPP(c_List_Omap(_1708979, _1708977), _1708981), _1708983)), -(c_List_Olinorder__class_Osorted(_1708977, hAPP(hAPP(c_List_Omap(_1708979, _1708977), _1708981), c_List_Olinorder__class_Oinsort__insert__key(_1708979, _1708977, _1708981, _1708985, _1708983))))], (12645 ^ _779203) ^ [_997400, _997402, _997404, _997406, _997408] : [class_Rings_Olinordered__semiring__strict(_997400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997400), _997402), _997404)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997400), _997406), _997408)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997400), c_Groups_Ozero__class_Ozero(_997400)), _997404)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997400), c_Groups_Ozero__class_Ozero(_997400)), _997406)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997400), _997402), _997406)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997400), _997404), _997408))))], (19682 ^ _779203) ^ [_1126474, _1126476] : [class_Groups_Ogroup__add(_1126474), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1126474), hAPP(c_Groups_Ouminus__class_Ouminus(_1126474), _1126476)) = _1126476)], (948 ^ _779203) ^ [_793399, _793401, _793403, _793405] : [-(c_Equiv__Relations_Oequivp(_793403, _793399)), c_Equiv__Relations_Oequivp(_793405, _793401), _793405 = _793403, _793401 = _793399], (32407 ^ _779203) ^ [_1366185, _1366187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366185)), hAPP(c_Nat_OSuc, _1366187))), -(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(_1366185))), 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)), _1366187)))))], (20803 ^ _779203) ^ [_1146421, _1146423] : [class_Rings_Olinordered__idom(_1146421), 20806 ^ _779203 : [(20813 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146421), _1146423), c_Groups_Ozero__class_Ozero(_1146421))), -(c_Groups_Osgn__class_Osgn(_1146421, _1146423) = hAPP(c_Groups_Ouminus__class_Ouminus(_1146421), c_Groups_Oone__class_Oone(_1146421)))], (20807 ^ _779203) ^ [] : [c_Groups_Osgn__class_Osgn(_1146421, _1146423) = hAPP(c_Groups_Ouminus__class_Ouminus(_1146421), c_Groups_Oone__class_Oone(_1146421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146421), _1146423), c_Groups_Ozero__class_Ozero(_1146421))))]]], (48372 ^ _779203) ^ [_1754660, _1754662, _1754664, _1754666] : [-(hAPP(c_New__DSequence_Opos__union(_1754660, _1754662, _1754664), _1754666) = c_Lazy__Sequence_Oappend(_1754660, hAPP(_1754662, _1754666), hAPP(_1754664, _1754666)))], (22237 ^ _779203) ^ [_1171827, _1171829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171827)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1171829)), -(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), _1171827), _1171829))))], (30591 ^ _779203) ^ [_1325432, _1325434, _1325436] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325432, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1325432, tc_HOL_Obool), _1325434)), _1325436) = c_Orderings_Obot__class_Obot(tc_fun(_1325432, tc_HOL_Obool)), 30594 ^ _779203 : [(30595 ^ _779203) ^ [_1325567] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1325432, tc_HOL_Obool)), _1325567), _1325434)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325432, tc_HOL_Obool)), _1325567), _1325436) = c_Orderings_Obot__class_Obot(tc_fun(_1325432, tc_HOL_Obool)))]]], (44606 ^ _779203) ^ [_1672972, _1672974, _1672976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1672972), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672974)), _1672976))), -(hAPP(c_Random_Opick(_1672974, hAPP(hAPP(c_List_Omap(_1672974, tc_prod(tc_Code__Numeral_Ocode__numeral, _1672974)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1672974), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1672976)), hAPP(c_Code__Numeral_Oof__nat, _1672972)) = hAPP(hAPP(c_List_Onth(_1672974), _1672976), _1672972))], (10269 ^ _779203) ^ [_955701, _955703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955701), _955703)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955701), hAPP(c_Nat_OSuc, _955703))))], (42991 ^ _779203) ^ [_1636693, _1636695, _1636697, _1636699, _1636701] : [-(hAPP(hAPP(c_List_Olist_OCons(_1636693), _1636695), _1636697) = hAPP(hAPP(c_List_Oappend(_1636693), _1636699), _1636701)), 42992 ^ _779203 : [(42999 ^ _779203) ^ [_1636876] : [hAPP(hAPP(c_List_Olist_OCons(_1636693), _1636695), _1636876) = _1636699, _1636697 = hAPP(hAPP(c_List_Oappend(_1636693), _1636876), _1636701)], (42993 ^ _779203) ^ [] : [_1636699 = c_List_Olist_ONil(_1636693), hAPP(hAPP(c_List_Olist_OCons(_1636693), _1636695), _1636697) = _1636701]]], (25494 ^ _779203) ^ [_1228530, _1228532] : [c_Nat__Transfer_Ois__nat(_1228530), c_Nat__Transfer_Ois__nat(_1228532), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1228530), _1228532)))], (20911 ^ _779203) ^ [_1148066] : [class_Rings_Osemiring__1(_1148066), c_Int_Oiszero(_1148066, c_Groups_Oone__class_Oone(_1148066))], (33875 ^ _779203) ^ [_1399855, _1399857, _1399859, _1399861, _1399863] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1399855, _1399857, _1399859), _1399861), _1399863) = hAPP(hAPP(_1399861, hAPP(c_Product__Type_Ofst(_1399855, _1399857), _1399863)), hAPP(c_Product__Type_Osnd(_1399855, _1399857), _1399863)))], (38601 ^ _779203) ^ [_1526752, _1526754, _1526756, _1526758] : [c_Wellfounded_Owf(_1526752, _1526754), c_Wellfounded_Owf(_1526756, _1526758), -(c_Wellfounded_Owf(tc_prod(_1526752, _1526756), c_Wellfounded_Olex__prod(_1526752, _1526756, _1526754, _1526758)))], (4154 ^ _779203) ^ [_842076, _842078, _842080, _842082] : [-(c_List_Olast(_842082, _842078) = c_List_Olast(_842080, _842076)), _842082 = _842080, _842078 = _842076], (43698 ^ _779203) ^ [_1653744, _1653746, _1653748] : [_1653744 = c_List_Olist_ONil(_1653746), -(hAPP(c_List_Ohd(_1653746), hAPP(hAPP(c_List_Oappend(_1653746), _1653744), _1653748)) = hAPP(c_List_Ohd(_1653746), _1653748))], (35621 ^ _779203) ^ [_1446493, _1446495] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446493), c_Orderings_Obot__class_Obot(tc_fun(_1446493, tc_HOL_Obool))), _1446495) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446493, tc_HOL_Obool), tc_HOL_Obool)))], (42263 ^ _779203) ^ [_1621053, _1621055, _1621057] : [-(hAPP(hAPP(c_List_Olist__update(_1621053, _1621055), _1621057), hAPP(hAPP(c_List_Onth(_1621053), _1621055), _1621057)) = _1621055)], (34535 ^ _779203) ^ [_1416923, _1416925, _1416927, _1416929] : [c_Orderings_Otop__class_Otop(tc_fun(_1416923, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416925, tc_fun(_1416923, tc_HOL_Obool)), _1416927), _1416929), 34538 ^ _779203 : [(34539 ^ _779203) ^ [_1417039] : [hBOOL(hAPP(hAPP(c_member(_1416925), _1417039), _1416927)), -(hAPP(_1416929, _1417039) = c_Orderings_Otop__class_Otop(tc_fun(_1416923, tc_HOL_Obool)))]]], (44845 ^ _779203) ^ [_1677721] : [-(c_Code__Numeral_OSuc__code__numeral(_1677721) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1677721))))], (12012 ^ _779203) ^ [_986757, _986759, _986761, _986763] : [class_Rings_Olinordered__ring__strict(_986757), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986757), _986759), _986761)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986757), _986763), c_Groups_Ozero__class_Ozero(_986757))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986757), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986757), _986763), _986761)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986757), _986763), _986759))))], (27474 ^ _779203) ^ [_1263268, _1263270, _1263272] : [class_Lattices_Osemilattice__sup(_1263268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263268), _1263270), _1263272)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263268), _1263270), _1263272) = _1263272)], (43704 ^ _779203) ^ [_1653857, _1653859, _1653861] : [-(_1653857 = c_List_Olist_ONil(_1653859)), -(hAPP(c_List_Ohd(_1653859), hAPP(hAPP(c_List_Oappend(_1653859), _1653857), _1653861)) = hAPP(c_List_Ohd(_1653859), _1653857))], (34029 ^ _779203) ^ [_1402823, _1402825, _1402827, _1402829, _1402831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1402823, _1402825)), hAPP(_1402823, _1402827))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1402829, _1402829)), hAPP(hAPP(c_Product__Type_OPair(_1402829, _1402829), _1402825), _1402827)), c_Wellfounded_Omlex__prod(_1402829, _1402823, _1402831))))], (27026 ^ _779203) ^ [_1255192, _1255194, _1255196] : [class_Orderings_Olinorder(_1255192), 27029 ^ _779203 : [(27036 ^ _779203) ^ [] : [_1255194 = _1255196, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1255192), _1255194) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1255192), _1255196))], (27030 ^ _779203) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1255192), _1255194) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1255192), _1255196), -(_1255194 = _1255196)]]], (12939 ^ _779203) ^ [_1002938, _1002940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1002938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002938), hAPP(c_Nat_OSuc, _1002940))), _1002938)))], (37551 ^ _779203) ^ [_1490835, _1490837, _1490839, _1490841] : [hBOOL(hAPP(hAPP(c_member(_1490835), _1490837), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1490835, tc_HOL_Obool)), _1490839), hAPP(c_Set_OCollect(_1490835), _1490841)))), 37554 ^ _779203 : [(37557 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1490841, _1490837)))], (37555 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490835), _1490837), _1490839)))]]], (35470 ^ _779203) ^ [_1442226, _1442228, _1442230, _1442232, _1442234, _1442236] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1442226, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442228, _1442226, _1442230), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1442232, tc_fun(_1442228, tc_HOL_Obool)), _1442234), _1442236))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1442232, tc_fun(_1442226, tc_HOL_Obool)), _1442234), hAPP(hAPP(c_COMBB(tc_fun(_1442228, tc_HOL_Obool), tc_fun(_1442226, tc_HOL_Obool), _1442232), c_Relation_OImage(_1442228, _1442226, _1442230)), _1442236)))))], (46005 ^ _779203) ^ [_1704778, _1704780] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704778), hAPP(c_List_Onth(_1704778), _1704780)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704778)), _1704780))) = _1704780)], (49805 ^ _779203) ^ [_1786618] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786618), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1786618 = hAPP(c_Code__Numeral_Onat__of, 49808 ^ [_1786618]))], (45841 ^ _779203) ^ [_1701605, _1701607] : [class_Groups_Omonoid__add(_1701605), -(hAPP(c_List_Ofoldl(_1701605, _1701605, c_Groups_Oplus__class_Oplus(_1701605), c_Groups_Ozero__class_Ozero(_1701605)), _1701607) = c_List_Ofoldr(_1701605, _1701605, c_Groups_Oplus__class_Oplus(_1701605), _1701607, c_Groups_Ozero__class_Ozero(_1701605)))], (9255 ^ _779203) ^ [_937128, _937130, _937132] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _937128)), _937130) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _937128)), _937132), -(_937130 = _937132)], (20576 ^ _779203) ^ [_1142076, _1142078] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1142076)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1142078)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1142076), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1142078))))], (15974 ^ _779203) ^ [_1059529, _1059531, _1059533] : [class_Int_Onumber__ring(_1059529), -(hAPP(c_Int_Onumber__class_Onumber__of(_1059529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1059531), _1059533)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059529), hAPP(c_Int_Onumber__class_Onumber__of(_1059529), _1059531)), hAPP(c_Int_Onumber__class_Onumber__of(_1059529), _1059533)))], (9459 ^ _779203) ^ [_940488, _940490] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940488), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940488), _940490))))], (39439 ^ _779203) ^ [_1546471, _1546473, _1546475, _1546477, _1546479, _1546481] : [c_Fun_Oinj__on(_1546471, _1546473, _1546475, _1546477), 39442 ^ _779203 : [(39449 ^ _779203) ^ [] : [c_Fun_Oinj__on(_1546471, _1546479, hAPP(c_Fun_Ocomp(_1546473, _1546479, _1546471, _1546481), _1546475), _1546477), -(c_Fun_Oinj__on(_1546473, _1546479, _1546481, hAPP(c_Set_Oimage(_1546471, _1546473, _1546475), _1546477)))], (39443 ^ _779203) ^ [] : [c_Fun_Oinj__on(_1546473, _1546479, _1546481, hAPP(c_Set_Oimage(_1546471, _1546473, _1546475), _1546477)), -(c_Fun_Oinj__on(_1546471, _1546479, hAPP(c_Fun_Ocomp(_1546473, _1546479, _1546471, _1546481), _1546475), _1546477))]]], (25758 ^ _779203) ^ [_1232423, _1232425, _1232427, _1232429] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1232423, _1232425, _1232427), _1232429), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1232425)], (21313 ^ _779203) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (2478 ^ _779203) ^ [_815564, _815566, _815568, _815570] : [-(c_Nitpick_Onorm__frac(_815570, _815566) = c_Nitpick_Onorm__frac(_815568, _815564)), _815570 = _815568, _815566 = _815564], (28610 ^ _779203) ^ [_1285382, _1285384] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1285382, _1285384)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1285382, _1285384), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1285384), c_Orderings_Otop__class_Otop(tc_fun(_1285384, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1285382), c_Orderings_Otop__class_Otop(tc_fun(_1285382, tc_HOL_Obool)))))], (29522 ^ _779203) ^ [_1302990, _1302992, _1302994, _1302996] : [class_Lattices_Osemilattice__inf(_1302990), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302990), _1302992), _1302994)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302990), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1302990), _1302996), _1302992)), _1302994)))], (39940 ^ _779203) ^ [_1557907, _1557909, _1557911, _1557913, _1557915, _1557917] : [c_Finite__Set_Ofolding__idem(_1557907, _1557909, _1557911, _1557913), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557907), _1557915)), -(hAPP(_1557913, hAPP(hAPP(c_Set_Oinsert(_1557907), _1557917), _1557915)) = hAPP(c_Fun_Ocomp(_1557909, _1557909, _1557909, hAPP(_1557913, _1557915)), hAPP(_1557911, _1557917)))], (22608 ^ _779203) ^ [_1177878, _1177880] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1177878), _1177880) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1177880 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22617 ^ _779203 : [(22620 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177878), _1177880)))], (22618 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177878)))]], 22621 ^ _779203 : [(22624 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177880), _1177878)))], (22622 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177878), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (38554 ^ _779203) ^ [_1525631, _1525633, _1525635] : [c_Wellfounded_Owf(_1525631, _1525633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1525631, _1525631), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1525631, _1525631, _1525631), _1525633), _1525635)), _1525633)), -(c_FunDef_Oreduction__pair(_1525631, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1525631, _1525631), tc_HOL_Obool), tc_fun(tc_prod(_1525631, _1525631), tc_HOL_Obool)), _1525633), _1525635)))], (35553 ^ _779203) ^ [_1444602, _1444604, _1444606, _1444608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444602), _1444608)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444606), _1444604))), -(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), _1444602), _1444604)), 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), _1444606), _1444608)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (48452 ^ _779203) ^ [_1756222, _1756224, _1756226] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1756222, _1756224), _1756226) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1756222, tc_Lazy__Sequence_Olazy__sequence(_1756222)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1756222, tc_Lazy__Sequence_Olazy__sequence(_1756222), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1756222, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756222), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756222), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756222), tc_Nat_Onat)), _1756222), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1756222), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756222), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756222), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1756222), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1756222)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1756222, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756222), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756222), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756222), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1756222), tc_Nat_Onat)), _1756222), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1756222))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1756222), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1756224))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1756222, _1756224))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1756222), _1756226)))], (19512 ^ _779203) ^ [_1123189] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1123189) = 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(_1123189)))))], (21775 ^ _779203) ^ [_1162549, _1162551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1162549)), c_Int_OBit1(_1162551))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1162549), _1162551)))], (50675 ^ _779203) ^ [_1805600, _1805602, _1805604, _1805606] : [class_Rings_Ocomm__semiring__1(_1805600), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805600), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805600), _1805602), _1805604)), _1805606)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805600), _1805604), _1805606)))], (47799 ^ _779203) ^ [_1742558, _1742560, _1742562, _1742564] : [c_List_Olist__all(_1742558, _1742560, hAPP(hAPP(c_List_Oappend(_1742558), _1742562), _1742564)), 47802 ^ _779203 : [(47805 ^ _779203) ^ [] : [-(c_List_Olist__all(_1742558, _1742560, _1742564))], (47803 ^ _779203) ^ [] : [-(c_List_Olist__all(_1742558, _1742560, _1742562))]]], (12122 ^ _779203) ^ [_988687, _988689, _988691] : [class_Groups_Ocomm__monoid__add(_988687), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_988689, _988687), _988691), c_Orderings_Obot__class_Obot(tc_fun(_988689, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_988687))], (50547 ^ _779203) ^ [_1803404, _1803406, _1803408] : [-(c_Lazy__Sequence_Omap(_1803404, _1803406, _1803408, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1803404)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1803406))], (10911 ^ _779203) ^ [_967640, _967642] : [class_Groups_Ogroup__add(_967640), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967640), _967642), c_Groups_Ozero__class_Ozero(_967640)) = _967642)], (27956 ^ _779203) ^ [_1272657, _1272659, _1272661, _1272663] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272657, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1272657), _1272659), _1272661)), _1272663) = hAPP(hAPP(c_Set_Oinsert(_1272657), _1272659), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272657, tc_HOL_Obool)), _1272661), _1272663)))], (9273 ^ _779203) ^ [_937454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _937454), _937454))], (34757 ^ _779203) ^ [_1423467, _1423469, _1423471, _1423473] : [hBOOL(hAPP(hAPP(c_member(_1423469), _1423473), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423467, tc_fun(_1423469, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1423467, tc_HOL_Obool))), _1423471))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423467, tc_fun(_1423469, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1423467, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1423469, tc_HOL_Obool), tc_fun(_1423469, tc_HOL_Obool), _1423467), hAPP(c_COMBC(_1423469, tc_fun(_1423469, tc_HOL_Obool), tc_HOL_Obool), c_member(_1423469))), _1423471)), _1423473)))], (6326 ^ _779203) ^ [_881027, _881029, _881031, _881033] : [class_Orderings_Oord(_881027), 6329 ^ _779203 : [(6336 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881027), hAPP(_881031, 6337 ^ [_881027, _881029, _881031, _881033])), hAPP(_881033, 6337 ^ [_881027, _881029, _881031, _881033]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881029, _881027)), _881031), _881033)))], (6330 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881029, _881027)), _881031), _881033)), 6333 ^ _779203 : [(6334 ^ _779203) ^ [_881184] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881027), hAPP(_881031, _881184)), hAPP(_881033, _881184))))]]]]], (36420 ^ _779203) ^ [_1464382, _1464384, _1464386, _1464388] : [c_Fun_Oinj__on(_1464382, _1464384, _1464386, c_Orderings_Otop__class_Otop(tc_fun(_1464382, tc_HOL_Obool))), 36423 ^ _779203 : [(36437 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1464384), _1464388), hAPP(c_Set_Oimage(_1464382, _1464384, _1464386), c_Orderings_Otop__class_Otop(tc_fun(_1464382, tc_HOL_Obool)))))), 36438 ^ _779203 : [(36439 ^ _779203) ^ [_1464785] : [_1464388 = hAPP(_1464386, _1464785), 36443 ^ _779203 : [(36446 ^ _779203) ^ [] : [36442 ^ [_1464382, _1464384, _1464386, _1464388, _1464785] = _1464785], (36444 ^ _779203) ^ [] : [-(_1464388 = hAPP(_1464386, 36442 ^ [_1464382, _1464384, _1464386, _1464388, _1464785]))]]]]], (36424 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1464384), _1464388), hAPP(c_Set_Oimage(_1464382, _1464384, _1464386), c_Orderings_Otop__class_Otop(tc_fun(_1464382, tc_HOL_Obool))))), 36428 ^ _779203 : [(36431 ^ _779203) ^ [_1464647] : [_1464388 = hAPP(_1464386, _1464647), -(_1464647 = 36427 ^ [_1464382, _1464384, _1464386, _1464388])], (36429 ^ _779203) ^ [] : [-(_1464388 = hAPP(_1464386, 36427 ^ [_1464382, _1464384, _1464386, _1464388]))]]]]], (10955 ^ _779203) ^ [_968312] : [class_Rings_Ozero__neq__one(_968312), c_Groups_Oone__class_Oone(_968312) = c_Groups_Ozero__class_Ozero(_968312)], (1460 ^ _779203) ^ [_800413, _800415] : [-(class_Lattices_Oboolean__algebra(_800413)), _800415 = _800413, class_Lattices_Oboolean__algebra(_800415)], (27398 ^ _779203) ^ [_1261953, _1261955, _1261957] : [class_Lattices_Osemilattice__sup(_1261953), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261953), _1261955), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1261953), _1261955), _1261957))))], (23910 ^ _779203) ^ [_1200060, _1200062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200060)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1200060), _1200062)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1200060)), hAPP(c_Int_Onat, _1200062)))], (44275 ^ _779203) ^ [_1664688, _1664690, _1664692] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664688)), _1664690), c_List_Olists(_1664688, _1664692)))), 44276 ^ _779203 : [(44279 ^ _779203) ^ [_1664816, _1664818] : [_1664690 = hAPP(hAPP(c_List_Olist_OCons(_1664688), _1664818), _1664816), hBOOL(hAPP(hAPP(c_member(_1664688), _1664818), _1664692)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664688)), _1664816), c_List_Olists(_1664688, _1664692)))], (44277 ^ _779203) ^ [] : [_1664690 = c_List_Olist_ONil(_1664688)]]], (5340 ^ _779203) ^ [_860871, _860873, _860875, _860877, _860879, _860881] : [-(c_SetInterval_Oord_OatLeast(_860881, _860877, _860873) = c_SetInterval_Oord_OatLeast(_860879, _860875, _860871)), _860881 = _860879, _860877 = _860875, _860873 = _860871], (2902 ^ _779203) ^ [_822170, _822172, _822174, _822176, _822178, _822180] : [-(c_Nitpick_Oplus__frac(_822180, _822176, _822172) = c_Nitpick_Oplus__frac(_822178, _822174, _822170)), _822180 = _822178, _822176 = _822174, _822172 = _822170], (24748 ^ _779203) ^ [_1215336, _1215338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1215336)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1215338)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1215338), _1215336)), _1215338) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1215338), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1215336), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (9441 ^ _779203) ^ [_940138, _940140, _940142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940138), _940140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940142), _940138)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940142), _940140))))], (51303 ^ _779203) ^ [_1816798, _1816800, _1816802, _1816804] : [class_Rings_Ocomm__semiring__1(_1816798), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816798), _1816800), _1816802)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816798), _1816802), _1816804)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1816798), _1816800), _1816804)))], (22910 ^ _779203) ^ [_1182694, _1182696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1182694), hAPP(c_Int_Onat, _1182696))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1182694)), _1182696)))], (47687 ^ _779203) ^ [_1740118, _1740120, _1740122] : [c_List_Olist__ex(_1740118, _1740120, _1740122), 47691 ^ _779203 : [(47694 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1740120, 47690 ^ [_1740118, _1740120, _1740122])))], (47692 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740118), 47690 ^ [_1740118, _1740120, _1740122]), hAPP(c_List_Oset(_1740118), _1740122))))]]], (48170 ^ _779203) ^ [_1750895, _1750897, _1750899] : [-(_1750895 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1750897), c_List_Oreplicate(_1750897, _1750895, _1750899)) = _1750899)], (9229 ^ _779203) ^ [_936637] : [_936637 = hAPP(c_Nat_OSuc, _936637)], (37659 ^ _779203) ^ [_1493763, _1493765] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1493763, _1493765), c_Orderings_Otop__class_Otop(tc_fun(_1493763, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1493765, tc_HOL_Obool), _1493763), c_Orderings_Otop__class_Otop(tc_fun(_1493765, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1493763, _1493765), tc_HOL_Obool)))], (28844 ^ _779203) ^ [_1289449, _1289451, _1289453] : [class_Orderings_Olinorder(_1289449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289449), _1289451), _1289453)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289449, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1289449, _1289451, _1289453)), hAPP(hAPP(c_Set_Oinsert(_1289449), _1289453), c_Orderings_Obot__class_Obot(tc_fun(_1289449, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1289449, _1289451, _1289453))], (43686 ^ _779203) ^ [_1653493, _1653495, _1653497] : [-(_1653493 = c_List_Olist_ONil(_1653495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653497), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653495)), _1653493))), -(hAPP(c_List_Ohd(_1653495), hAPP(hAPP(c_List_Odrop(_1653495), _1653497), _1653493)) = hAPP(hAPP(c_List_Onth(_1653495), _1653493), _1653497))], (6819 ^ _779203) ^ [_890150, _890152, _890154, _890156] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890150, tc_HOL_Obool)), _890152), hAPP(hAPP(c_Set_Oinsert(_890150), _890154), _890156)))), 6822 ^ _779203 : [(6825 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890150, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890150, tc_HOL_Obool)), _890152), hAPP(hAPP(c_Set_Oinsert(_890150), _890154), c_Orderings_Obot__class_Obot(tc_fun(_890150, tc_HOL_Obool))))), _890156))], (6823 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_890150), _890154), _890152)))]], 6826 ^ _779203 : [(6829 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890150, tc_HOL_Obool)), _890152), _890156))], (6827 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_890150), _890154), _890152))]]], (39804 ^ _779203) ^ [_1554869, _1554871, _1554873, _1554875, _1554877, _1554879] : [c_Finite__Set_Ofolding(_1554869, _1554871, _1554873, _1554875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554869), _1554877)), -(hAPP(hAPP(_1554875, _1554877), _1554879) = hAPP(hAPP(c_Finite__Set_Ofold(_1554869, _1554871, _1554873), _1554879), _1554877))], (41933 ^ _779203) ^ [_1611786, _1611788, _1611790, _1611792] : [hBOOL(hAPP(hAPP(c_member(_1611786), _1611788), hAPP(c_List_Oset(_1611786), c_List_Osublist(_1611786, _1611790, _1611792)))), -(hBOOL(hAPP(hAPP(c_member(_1611786), _1611788), hAPP(c_List_Oset(_1611786), _1611790))))], (1700 ^ _779203) ^ [_803413, _803415] : [-(class_Rings_Oordered__semiring(_803413)), _803415 = _803413, class_Rings_Oordered__semiring(_803415)], (23986 ^ _779203) ^ [_1201534, _1201536] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201536)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1201534, _1201536)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1201534), hAPP(c_Int_Onat, _1201536)))], (50393 ^ _779203) ^ [_1798498, _1798500, _1798502, _1798504, _1798506, _1798508, _1798510] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798498, _1798500), tc_prod(_1798498, _1798500))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798498, _1798500), tc_prod(_1798498, _1798500)), hAPP(hAPP(c_Product__Type_OPair(_1798498, _1798500), _1798502), _1798504)), hAPP(hAPP(c_Product__Type_OPair(_1798498, _1798500), _1798506), _1798508))), c_Transitive__Closure_Ortrancl(tc_prod(_1798498, _1798500), _1798510))), -(hAPP(hAPP(c_Product__Type_OPair(_1798498, _1798500), _1798502), _1798504) = hAPP(hAPP(c_Product__Type_OPair(_1798498, _1798500), _1798506), _1798508)), 50402 ^ _779203 : [(50405 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798498, _1798500), tc_prod(_1798498, _1798500))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798498, _1798500), tc_prod(_1798498, _1798500)), hAPP(hAPP(c_Product__Type_OPair(_1798498, _1798500), 50400 ^ [_1798498, _1798500, _1798502, _1798504, _1798506, _1798508, _1798510]), 50401 ^ [_1798498, _1798500, _1798502, _1798504, _1798506, _1798508, _1798510])), hAPP(hAPP(c_Product__Type_OPair(_1798498, _1798500), _1798506), _1798508))), c_Transitive__Closure_Ortrancl(tc_prod(_1798498, _1798500), _1798510))))], (50403 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1798498, _1798500), tc_prod(_1798498, _1798500))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1798498, _1798500), tc_prod(_1798498, _1798500)), hAPP(hAPP(c_Product__Type_OPair(_1798498, _1798500), _1798502), _1798504)), hAPP(hAPP(c_Product__Type_OPair(_1798498, _1798500), 50400 ^ [_1798498, _1798500, _1798502, _1798504, _1798506, _1798508, _1798510]), 50401 ^ [_1798498, _1798500, _1798502, _1798504, _1798506, _1798508, _1798510]))), _1798510)))]]], (43179 ^ _779203) ^ [_1640913, _1640915, _1640917] : [_1640917 = c_List_Olist_ONil(_1640913), -(hAPP(hAPP(c_List_Oappend(_1640913), _1640915), _1640917) = _1640915)], (4288 ^ _779203) ^ [_844157, _844159, _844161, _844163, _844165, _844167, _844169, _844171, _844173, _844175, _844177, _844179] : [-(c_New__Random__Sequence_Opos__union(_844179, _844175, _844171, _844167, _844163, _844159) = c_New__Random__Sequence_Opos__union(_844177, _844173, _844169, _844165, _844161, _844157)), _844179 = _844177, _844175 = _844173, _844171 = _844169, _844167 = _844165, _844163 = _844161, _844159 = _844157], (21063 ^ _779203) ^ [_1150454, _1150456] : [class_Int_Onumber__ring(_1150454), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1150454), c_Groups_Oone__class_Oone(_1150454)), hAPP(c_Int_Onumber__class_Onumber__of(_1150454), _1150456)) = hAPP(c_Int_Onumber__class_Onumber__of(_1150454), 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), _1150456))))], (31464 ^ _779203) ^ [_1343453, _1343455] : [class_Complete__Lattice_Ocomplete__lattice(_1343453), -(c_Complete__Lattice_OInf__class_OInf(_1343453, hAPP(hAPP(c_Set_Oinsert(_1343453), _1343455), c_Orderings_Obot__class_Obot(tc_fun(_1343453, tc_HOL_Obool)))) = _1343455)], (21209 ^ _779203) ^ [_1153212] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1153212)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1153212))))], (22121 ^ _779203) ^ [_1169716] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1169716) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (52431 ^ _779203) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (32685 ^ _779203) ^ [_1376331, _1376333, _1376335, _1376337, _1376339, _1376341] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376331, tc_fun(_1376333, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1376331, tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_fun(_1376333, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376333, tc_fun(tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_fun(_1376333, tc_HOL_Obool)), _1376331), c_COMBC(_1376333, tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376333, tc_prod(_1376331, _1376333)), tc_fun(_1376333, tc_fun(tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_HOL_Obool)), _1376331), hAPP(c_COMBB(tc_prod(_1376331, _1376333), tc_fun(tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_HOL_Obool), _1376333), c_member(tc_prod(_1376331, _1376333)))), c_Product__Type_OPair(_1376331, _1376333)))), _1376335)), hAPP(hAPP(c_COMBC(_1376331, tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_fun(_1376333, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376333, tc_fun(tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_fun(_1376333, tc_HOL_Obool)), _1376331), c_COMBC(_1376333, tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376333, tc_prod(_1376331, _1376333)), tc_fun(_1376333, tc_fun(tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_HOL_Obool)), _1376331), hAPP(c_COMBB(tc_prod(_1376331, _1376333), tc_fun(tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool), tc_HOL_Obool), _1376333), c_member(tc_prod(_1376331, _1376333)))), c_Product__Type_OPair(_1376331, _1376333)))), _1376337)), _1376339), _1376341)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1376331, _1376333)), hAPP(hAPP(c_Product__Type_OPair(_1376331, _1376333), _1376339), _1376341)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1376331, _1376333), tc_HOL_Obool)), _1376335), _1376337))))], (37922 ^ _779203) ^ [_1502350, _1502352, _1502354, _1502356, _1502358, _1502360] : [class_Groups_Ocomm__monoid__mult(_1502350), hBOOL(hAPP(c_Finite__Set_Ofinite(_1502352), _1502354)), 37932 ^ _779203 : [(37935 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1502356), hAPP(_1502358, 37931 ^ [_1502350, _1502352, _1502354, _1502356, _1502358, _1502360])))], (37933 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502352), 37931 ^ [_1502350, _1502352, _1502354, _1502356, _1502358, _1502360]), _1502354)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1502352, _1502350), hAPP(hAPP(c_COMBS(_1502352, tc_fun(_1502356, tc_HOL_Obool), _1502350), hAPP(hAPP(c_COMBB(tc_fun(_1502356, _1502350), tc_fun(tc_fun(_1502356, tc_HOL_Obool), _1502350), _1502352), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1502356, _1502350)), _1502360)), _1502358)), _1502354) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1502352, _1502356), _1502350), hAPP(c_Product__Type_Oprod_Oprod__case(_1502352, _1502356, _1502350), _1502360)), hAPP(hAPP(c_Product__Type_OSigma(_1502352, _1502356), _1502354), _1502358)))], (47854 ^ _779203) ^ [_1743503, _1743505, _1743507] : [c_FunDef_Ois__measure(_1743503, _1743505), -(c_FunDef_Ois__measure(tc_prod(_1743507, _1743503), hAPP(hAPP(c_COMBB(_1743503, tc_Nat_Onat, tc_prod(_1743507, _1743503)), _1743505), c_Product__Type_Osnd(_1743507, _1743503))))], (25598 ^ _779203) ^ [_1230099, _1230101] : [c_Nat__Transfer_Ois__nat(_1230099), c_Nat__Transfer_Ois__nat(_1230101), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1230099, _1230101)))], (32009 ^ _779203) ^ [_1356486, _1356488, _1356490, _1356492, _1356494] : [class_Groups_Ocomm__monoid__add(_1356486), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1356486), _1356488), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1356490), _1356492)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1356494), _1356492))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1356486), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1356486, tc_Nat_Onat), _1356488), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1356492))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1356490), _1356494)))], (37681 ^ _779203) ^ [_1494372, _1494374, _1494376, _1494378, _1494380, _1494382] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494372, _1494374)), hAPP(hAPP(c_Product__Type_OPair(_1494372, _1494374), _1494376), _1494378)), hAPP(hAPP(c_Product__Type_OSigma(_1494372, _1494374), _1494380), _1494382))), 37684 ^ _779203 : [(37687 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494374), _1494378), hAPP(_1494382, _1494376))))], (37685 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494372), _1494376), _1494380)))]]], (23369 ^ _779203) ^ [_1190420, _1190422, _1190424] : [-(hBOOL(hAPP(_1190420, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1190422), _1190424)))), 23372 ^ _779203 : [(23375 ^ _779203) ^ [] : [hBOOL(hAPP(_1190420, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23373 ^ _779203) ^ [] : [-(_1190424 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 23378 ^ _779203 : [(23379 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190424)))], (23385 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 23381 ^ [_1190420, _1190422, _1190424]), _1190424)))], (23389 ^ _779203) ^ [] : [hBOOL(hAPP(_1190420, 23380 ^ [_1190420, _1190422, _1190424]))], (23387 ^ _779203) ^ [] : [-(_1190422 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1190424), 23380 ^ [_1190420, _1190422, _1190424])), 23381 ^ [_1190420, _1190422, _1190424]))], (23383 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23381 ^ [_1190420, _1190422, _1190424])))]], 23390 ^ _779203 : [(23391 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190424), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23397 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 23393 ^ [_1190420, _1190422, _1190424]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23401 ^ _779203) ^ [] : [hBOOL(hAPP(_1190420, 23392 ^ [_1190420, _1190422, _1190424]))], (23399 ^ _779203) ^ [] : [-(_1190422 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1190424), 23392 ^ [_1190420, _1190422, _1190424])), 23393 ^ [_1190420, _1190422, _1190424]))], (23395 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190424), 23393 ^ [_1190420, _1190422, _1190424])))]]], (3700 ^ _779203) ^ [_834629, _834631, _834633, _834635, _834637, _834639, _834641, _834643] : [-(c_List_Ofoldl(_834643, _834639, _834635, _834631) = c_List_Ofoldl(_834641, _834637, _834633, _834629)), _834643 = _834641, _834639 = _834637, _834635 = _834633, _834631 = _834629], (52435 ^ _779203) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (11670 ^ _779203) ^ [_980483, _980485, _980487, _980489] : [class_Rings_Olinordered__semidom(_980483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980483), c_Groups_Ozero__class_Ozero(_980483)), _980485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980483), _980487), _980489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980483), _980487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980483), _980485), _980489))))], (27508 ^ _779203) ^ [_1263839, _1263841, _1263843, _1263845] : [class_Lattices_Osemilattice__sup(_1263839), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263839), _1263841), _1263843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263839), _1263845), _1263843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263839), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263839), _1263841), _1263845)), _1263843)))], (5032 ^ _779203) ^ [_855935, _855937, _855939, _855941] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855941, _855937) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_855939, _855935)), _855941 = _855939, _855937 = _855935], (9618 ^ _779203) ^ [_943521, _943523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943521), _943523)), -(_943523 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943521), 9621 ^ [_943521, _943523])))], (19694 ^ _779203) ^ [_1126664, _1126666, _1126668, _1126670] : [class_Groups_Ouminus(_1126664), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1126666, _1126664)), _1126668), _1126670) = hAPP(c_Groups_Ouminus__class_Ouminus(_1126664), hAPP(_1126668, _1126670)))], (45254 ^ _779203) ^ [_1687259, _1687261, _1687263, _1687265] : [-(hAPP(c_List_Oset(tc_prod(_1687259, _1687261)), c_Enum_Oproduct(_1687259, _1687261, _1687263, _1687265)) = hAPP(hAPP(c_Product__Type_OSigma(_1687259, _1687261), hAPP(c_List_Oset(_1687259), _1687263)), hAPP(c_COMBK(tc_fun(_1687261, tc_HOL_Obool), _1687259), hAPP(c_List_Oset(_1687261), _1687265))))], (48038 ^ _779203) ^ [_1747239, _1747241, _1747243, _1747245, _1747247, _1747249, _1747251] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1747239, _1747241, _1747243, _1747245), _1747247), _1747249), _1747251) = c_New__DSequence_Oneg__bind(_1747239, _1747241, hAPP(hAPP(hAPP(_1747243, _1747247), _1747249), _1747251), hAPP(hAPP(c_COMBC(_1747239, 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(_1747241)))), hAPP(hAPP(c_COMBC(_1747239, 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(_1747241))))), hAPP(hAPP(c_COMBC(_1747239, 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(_1747241)))))), _1747245), _1747247)), _1747249)), _1747251)))], (5388 ^ _779203) ^ [_861619, _861621, _861623, _861625, _861627, _861629, _861631, _861633] : [-(c_SetInterval_Oord_OatLeastAtMost(_861633, _861629, _861625, _861621) = c_SetInterval_Oord_OatLeastAtMost(_861631, _861627, _861623, _861619)), _861633 = _861631, _861629 = _861627, _861625 = _861623, _861621 = _861619], (35015 ^ _779203) ^ [_1429967, _1429969, _1429971, _1429973, _1429975] : [_1429967 = c_Orderings_Obot__class_Obot(tc_fun(_1429969, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1429971, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429969, tc_fun(_1429971, tc_HOL_Obool)), _1429967), _1429973)), _1429975) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1429971, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1429971, tc_HOL_Obool))), _1429975))], (26274 ^ _779203) ^ [_1241286, _1241288, _1241290, _1241292] : [class_Orderings_Oorder(_1241286), 26277 ^ _779203 : [(26286 ^ _779203) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1241286, _1241288, _1241290) = hAPP(hAPP(c_Set_Oinsert(_1241286), _1241292), c_Orderings_Obot__class_Obot(tc_fun(_1241286, tc_HOL_Obool)))), _1241288 = _1241290, _1241290 = _1241292], (26278 ^ _779203) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1241286, _1241288, _1241290) = hAPP(hAPP(c_Set_Oinsert(_1241286), _1241292), c_Orderings_Obot__class_Obot(tc_fun(_1241286, tc_HOL_Obool))), 26281 ^ _779203 : [(26284 ^ _779203) ^ [] : [-(_1241290 = _1241292)], (26282 ^ _779203) ^ [] : [-(_1241288 = _1241290)]]]]], (26138 ^ _779203) ^ [_1238814, _1238816] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1238814, tc_HOL_Obool)), _1238816), hAPP(c_Set_OPow(_1238814), _1238816))))], (26596 ^ _779203) ^ [_1247279, _1247281, _1247283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247279)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1247281), _1247283)), 26603 ^ _779203 : [(26604 ^ _779203) ^ [_1247475] : [26606 ^ _779203 : [(26612 ^ _779203) ^ [] : [-(_1247475 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26608 ^ [_1247279, _1247281, _1247283, _1247475]), 26605 ^ [_1247279, _1247281, _1247283, _1247475]))], (26610 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26608 ^ [_1247279, _1247281, _1247283, _1247475]), _1247283)))], (26607 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26605 ^ [_1247279, _1247281, _1247283, _1247475]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1247279))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247281), _1247475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247281), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1247475), _1247279))))]]], (22990 ^ _779203) ^ [_1183997, _1183999] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183997, _1183999) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 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^ _779203 : [(16370 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), hAPP(c_Int_Onumber__class_Onumber__of(_1066584), _1066586)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066584), _1066588), _1066590))), 16373 ^ _779203 : [(16380 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), c_Groups_Ozero__class_Ozero(_1066584)), _1066590))), 16383 ^ _779203 : [(16390 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), _1066590), c_Groups_Ozero__class_Ozero(_1066584)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), hAPP(c_Int_Onumber__class_Onumber__of(_1066584), _1066586)), c_Groups_Ozero__class_Ozero(_1066584))))], (16384 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), _1066590), c_Groups_Ozero__class_Ozero(_1066584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), _1066588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066584), hAPP(c_Int_Onumber__class_Onumber__of(_1066584), _1066586)), _1066590))))]]], (16374 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), c_Groups_Ozero__class_Ozero(_1066584)), _1066590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066584), hAPP(c_Int_Onumber__class_Onumber__of(_1066584), _1066586)), _1066590)), _1066588)))]]], (16396 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), hAPP(c_Int_Onumber__class_Onumber__of(_1066584), _1066586)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1066584), _1066588), _1066590)))), 16399 ^ _779203 : [(16402 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066584), hAPP(c_Int_Onumber__class_Onumber__of(_1066584), _1066586)), _1066590)), _1066588))], (16400 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), c_Groups_Ozero__class_Ozero(_1066584)), _1066590)))]], 16403 ^ _779203 : [(16406 ^ _779203) ^ [] : [16407 ^ _779203 : [(16410 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), _1066588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066584), hAPP(c_Int_Onumber__class_Onumber__of(_1066584), _1066586)), _1066590)))], (16408 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), _1066590), c_Groups_Ozero__class_Ozero(_1066584))))]], 16411 ^ _779203 : [(16414 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), hAPP(c_Int_Onumber__class_Onumber__of(_1066584), _1066586)), c_Groups_Ozero__class_Ozero(_1066584)))], (16412 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), _1066590), c_Groups_Ozero__class_Ozero(_1066584)))]]], (16404 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1066584), c_Groups_Ozero__class_Ozero(_1066584)), _1066590))]]]]], (564 ^ _779203) ^ [_787605, _787607, _787609, _787611, _787613, _787615, _787617, _787619, _787621, _787623] : [-(c_Typedef_Otype__definition(_787621, _787617, _787613, _787609, _787605)), c_Typedef_Otype__definition(_787623, _787619, _787615, _787611, _787607), _787623 = _787621, _787619 = _787617, _787615 = _787613, _787611 = _787609, _787607 = _787605], (744 ^ _779203) ^ [_790359, _790361, _790363, _790365, _790367, _790369, _790371, _790373] : [-(c_Wellfounded_Omax__extp(_790371, _790367, _790363, _790359)), c_Wellfounded_Omax__extp(_790373, _790369, _790365, _790361), _790373 = _790371, _790369 = _790367, _790365 = _790363, _790361 = _790359], (40273 ^ _779203) ^ [_1566084, _1566086, _1566088, _1566090] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566084, _1566084)), _1566086), c_Transitive__Closure_Otrancl(_1566084, _1566088))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566084, _1566084), tc_HOL_Obool)), _1566088), _1566090)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566084, _1566084)), _1566086), c_Transitive__Closure_Otrancl(_1566084, _1566090))))], (28272 ^ _779203) ^ [_1279046] : [class_Lattices_Oboolean__algebra(_1279046), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1279046), c_Orderings_Obot__class_Obot(_1279046)) = c_Orderings_Otop__class_Otop(_1279046))], (44 ^ _779203) ^ [_779781, _779783, _779785, _779787, _779789, _779791, _779793, _779795, _779797, _779799, _779801, _779803] : [-(c_Nitpick_Ofold__graph_H(_779801, _779797, _779793, _779789, _779785, _779781)), c_Nitpick_Ofold__graph_H(_779803, _779799, _779795, _779791, _779787, _779783), _779803 = _779801, _779799 = _779797, _779795 = _779793, _779791 = _779789, _779787 = _779785, _779783 = _779781], (29330 ^ _779203) ^ [_1299309] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1299309) = c_Orderings_Oord__class_Omin(_1299309)), class_Lattices_Osemilattice__inf(_1299309), class_Orderings_Olinorder(_1299309)], (19618 ^ _779203) ^ [_1125289, _1125291] : [class_Groups_Olinordered__ab__group__add(_1125289), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125289), _1125291)), 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_1203770] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1203768))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203768), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203770)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52323 ^ _779203) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (27924 ^ _779203) ^ [_1272040, _1272042] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272040, tc_HOL_Obool)), _1272042), c_Orderings_Otop__class_Otop(tc_fun(_1272040, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1272040, tc_HOL_Obool)))], (13239 ^ _779203) ^ [_1008243, _1008245, _1008247] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1008243), _1008245)), 13242 ^ _779203 : [(13262 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1008243, tc_Nat_Onat), _1008247), _1008245) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 13263 ^ _779203 : [(13264 ^ _779203) ^ [_1008724] : [hBOOL(hAPP(hAPP(c_member(_1008243), _1008724), _1008245)), hAPP(_1008247, _1008724) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 13272 ^ _779203 : [(13277 ^ _779203) ^ [] : [hAPP(_1008247, 13271 ^ [_1008243, _1008245, _1008247, _1008724]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13275 ^ _779203) ^ [] : [_1008724 = 13271 ^ [_1008243, _1008245, _1008247, _1008724]], (13273 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008243), 13271 ^ [_1008243, _1008245, _1008247, _1008724]), _1008245)))]]]]], (13243 ^ _779203) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1008243, tc_Nat_Onat), _1008247), _1008245) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 13247 ^ _779203 : [(13252 ^ _779203) ^ [_1008563] : [hBOOL(hAPP(hAPP(c_member(_1008243), _1008563), _1008245)), -(13246 ^ [_1008243, _1008245, _1008247] = _1008563), -(hAPP(_1008247, _1008563) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13250 ^ _779203) ^ [] : [-(hAPP(_1008247, 13246 ^ [_1008243, _1008245, _1008247]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (13248 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008243), 13246 ^ [_1008243, _1008245, _1008247]), _1008245)))]]]]], (4334 ^ _779203) ^ [_844948, _844950] : [_844950 = _844948, -(c_Lazy__Sequence_Osingle(_844950) = c_Lazy__Sequence_Osingle(_844948))], (49156 ^ _779203) ^ [_1773083, _1773085] : [c_Relation_Oantisym(_1773083, hAPP(c_Relation_Oconverse(_1773083, _1773083), _1773085)), -(c_Relation_Oantisym(_1773083, _1773085))], (37161 ^ _779203) ^ [_1480762, _1480764, _1480766, _1480768, _1480770, _1480772] : [hAPP(_1480762, _1480764) = _1480766, hBOOL(hAPP(hAPP(c_member(_1480768), _1480766), _1480770)), -(hBOOL(hAPP(hAPP(c_member(_1480772), _1480764), hAPP(c_Set_Ovimage(_1480772, _1480768, _1480762), _1480770))))], (5042 ^ _779203) ^ [_856084, _856086, _856088, _856090] : [-(c_Quotient_ORespects(_856090, _856086) = c_Quotient_ORespects(_856088, _856084)), _856090 = _856088, _856086 = _856084], (2380 ^ _779203) ^ [_813999, _814001, _814003, _814005] : [-(c_Divides_OposDivAlg(_814005, _814001) = c_Divides_OposDivAlg(_814003, _813999)), _814005 = _814003, _814001 = _813999], (51827 ^ _779203) ^ [_1825829, _1825831, _1825833] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825829), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1825831), _1825833))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825829), _1825831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1825833), _1825831)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825829), _1825833)))], (40949 ^ _779203) ^ [_1583161, _1583163, _1583165, _1583167] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1583161, _1583163), tc_fun(_1583161, _1583163)), _1583165), c_Fun_Ocomp(_1583163, _1583163, _1583161, _1583167)) = c_Fun_Ocomp(_1583163, _1583163, _1583161, hAPP(hAPP(c_Nat_Ocompow(_1583163, _1583163), _1583165), _1583167)))], (41339 ^ _779203) ^ [_1594094, _1594096, _1594098] : [-(hAPP(c_List_Olexn(_1594094, _1594096), hAPP(c_Nat_OSuc, _1594098)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1594094), tc_List_Olist(_1594094)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1594094, tc_List_Olist(_1594094)), tc_prod(_1594094, tc_List_Olist(_1594094))), tc_prod(tc_List_Olist(_1594094), tc_List_Olist(_1594094)), c_Product__Type_Omap__pair(tc_prod(_1594094, tc_List_Olist(_1594094)), tc_List_Olist(_1594094), tc_prod(_1594094, tc_List_Olist(_1594094)), tc_List_Olist(_1594094), hAPP(c_Product__Type_Oprod_Oprod__case(_1594094, tc_List_Olist(_1594094), tc_List_Olist(_1594094)), c_List_Olist_OCons(_1594094)), hAPP(c_Product__Type_Oprod_Oprod__case(_1594094, tc_List_Olist(_1594094), tc_List_Olist(_1594094)), c_List_Olist_OCons(_1594094)))), c_Wellfounded_Olex__prod(_1594094, tc_List_Olist(_1594094), _1594096, hAPP(c_List_Olexn(_1594094, _1594096), _1594098)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1594094), tc_List_Olist(_1594094))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1594094), tc_List_Olist(_1594094), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1594094), tc_fun(tc_List_Olist(_1594094), tc_HOL_Obool), tc_fun(tc_List_Olist(_1594094), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1594094), tc_HOL_Obool), tc_fun(tc_List_Olist(_1594094), tc_HOL_Obool)), tc_List_Olist(_1594094)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1594094))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1594094)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1594094), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1594094)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1594094)))), hAPP(c_Nat_OSuc, _1594098))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1594094), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1594094)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1594094)))), hAPP(c_Nat_OSuc, _1594098)))))))], (18282 ^ _779203) ^ [_1101676, _1101678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101676)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101678))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1101676), _1101678)))], (43850 ^ _779203) ^ [_1656484, _1656486, _1656488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656484), _1656486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656484), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656486), _1656488))))], (34152 ^ _779203) ^ [_1405841, _1405843, _1405845, _1405847, _1405849, _1405851, _1405853] : [-(hAPP(c_Product__Type_Oapfst(_1405841, _1405843, _1405845, _1405847), hAPP(c_Product__Type_Oapsnd(_1405849, _1405845, _1405841, _1405851), _1405853)) = hAPP(hAPP(c_Product__Type_OPair(_1405843, _1405845), hAPP(_1405847, hAPP(c_Product__Type_Ofst(_1405841, _1405849), _1405853))), hAPP(_1405851, hAPP(c_Product__Type_Osnd(_1405841, _1405849), _1405853))))], (42638 ^ _779203) ^ [_1629280, _1629282, _1629284] : [hAPP(hAPP(c_List_Olist_OCons(_1629280), _1629282), _1629284) = c_List_Olist_ONil(_1629280)], (19198 ^ _779203) ^ [_1117438, _1117440, _1117442] : [class_Fields_Olinordered__field__inverse__zero(_1117438), -(hAPP(c_Groups_Oabs__class_Oabs(_1117438), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117438), _1117440), _1117442)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1117438), hAPP(c_Groups_Oabs__class_Oabs(_1117438), _1117440)), hAPP(c_Groups_Oabs__class_Oabs(_1117438), _1117442)))], (26394 ^ _779203) ^ [_1243310, _1243312, _1243314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243310)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1243312), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1243314)), 26401 ^ _779203 : [(26402 ^ _779203) ^ [_1243518] : [26404 ^ _779203 : [(26410 ^ _779203) ^ [] : [-(_1243518 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26406 ^ [_1243310, _1243312, _1243314, _1243518]), 26403 ^ [_1243310, _1243312, _1243314, _1243518]))], (26408 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26406 ^ [_1243310, _1243312, _1243314, _1243518]), _1243314)))], (26405 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26403 ^ [_1243310, _1243312, _1243314, _1243518]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1243310))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1243312), _1243518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1243312), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1243518), _1243310))))]]], (27794 ^ _779203) ^ [_1269324, _1269326, _1269328] : [class_Lattices_Olattice(_1269324), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269324), _1269326), _1269328) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269324), _1269328), _1269326))], (46849 ^ _779203) ^ [_1721541, _1721543, _1721545, _1721547, _1721549] : [-(hAPP(hAPP(c_List_Ozip(_1721541, _1721543), c_List_OtakeWhile(_1721541, _1721545, _1721547)), _1721549) = c_List_OtakeWhile(tc_prod(_1721541, _1721543), hAPP(c_Fun_Ocomp(_1721541, tc_HOL_Obool, tc_prod(_1721541, _1721543), _1721545), c_Product__Type_Ofst(_1721541, _1721543)), hAPP(hAPP(c_List_Ozip(_1721541, _1721543), _1721547), _1721549)))], (51061 ^ _779203) ^ [_1812752, _1812754, _1812756] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812752), _1812754)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812752), _1812756)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1812752), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1812754), _1812756))))], (49776 ^ _779203) ^ [_1785658, _1785660, _1785662, _1785664, _1785666, _1785668] : [class_Groups_Ocomm__monoid__mult(_1785658), hBOOL(hAPP(c_Finite__Set_Ofinite(_1785660), _1785662)), 49786 ^ _779203 : [(49789 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1785664), hAPP(_1785666, 49785 ^ [_1785658, _1785660, _1785662, _1785664, _1785666, _1785668])))], (49787 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785660), 49785 ^ [_1785658, _1785660, _1785662, _1785664, _1785666, _1785668]), _1785662)))]], 49793 ^ _779203 : [(49797 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785660), 49795 ^ [_1785658, _1785660, _1785662, _1785664, _1785666, _1785668]), _1785662)))], (49799 ^ _779203) ^ [] : [49792 ^ [_1785658, _1785660, _1785662, _1785664, _1785666, _1785668] = 49795 ^ [_1785658, _1785660, _1785662, _1785664, _1785666, _1785668]], (49801 ^ _779203) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1785664, tc_HOL_Obool)), hAPP(_1785666, 49792 ^ [_1785658, _1785660, _1785662, _1785664, _1785666, _1785668])), hAPP(_1785666, 49795 ^ [_1785658, _1785660, _1785662, _1785664, _1785666, _1785668])) = c_Orderings_Obot__class_Obot(tc_fun(_1785664, tc_HOL_Obool))], (49794 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785660), 49792 ^ [_1785658, _1785660, _1785662, _1785664, _1785666, _1785668]), _1785662)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785658, _1785664, c_Groups_Otimes__class_Otimes(_1785658)), _1785668), c_Groups_Oone__class_Oone(_1785658)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1785660, tc_fun(_1785664, tc_HOL_Obool)), _1785662), _1785666)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1785658, _1785660, c_Groups_Otimes__class_Otimes(_1785658)), hAPP(hAPP(c_COMBB(tc_fun(_1785664, tc_HOL_Obool), _1785658, _1785660), hAPP(hAPP(c_Finite__Set_Ofold__image(_1785658, _1785664, c_Groups_Otimes__class_Otimes(_1785658)), _1785668), c_Groups_Oone__class_Oone(_1785658))), _1785666)), c_Groups_Oone__class_Oone(_1785658)), _1785662))], (10323 ^ _779203) ^ [_956803, _956805, _956807] : [class_Rings_Ocomm__semiring__1(_956803), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956803), _956805), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956803), _956807), _956805)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956803), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956803), _956807), c_Groups_Oone__class_Oone(_956803))), _956805))], (38589 ^ _779203) ^ [_1526536, _1526538, _1526540] : [-(hAPP(c_Relation_ODomain(_1526536, _1526538), hAPP(c_Set_OCollect(tc_prod(_1526536, _1526538)), hAPP(c_Product__Type_Oprod_Oprod__case(_1526536, _1526538, tc_HOL_Obool), _1526540))) = hAPP(c_Set_OCollect(_1526536), hAPP(hAPP(c_COMBB(tc_fun(_1526538, tc_HOL_Obool), tc_HOL_Obool, _1526536), c_HOL_OEx(_1526538)), _1526540)))], (44488 ^ _779203) ^ [_1670292, _1670294, _1670296, _1670298, _1670300] : [hAPP(hAPP(c_List_Omap(_1670292, _1670294), _1670296), _1670298) = hAPP(hAPP(c_List_Omap(_1670292, _1670294), _1670296), _1670300), c_Fun_Oinj__on(_1670292, _1670294, _1670296, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1670292, tc_HOL_Obool)), hAPP(c_List_Oset(_1670292), _1670298)), hAPP(c_List_Oset(_1670292), _1670300))), -(_1670298 = _1670300)], (364 ^ _779203) ^ [_784633, _784635, _784637, _784639, _784641, _784643, _784645, _784647] : [-(c_Finite__Set_Ofolding(_784645, _784641, _784637, _784633)), c_Finite__Set_Ofolding(_784647, _784643, _784639, _784635), _784647 = _784645, _784643 = _784641, _784639 = _784637, _784635 = _784633], (52621 ^ _779203) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (37605 ^ _779203) ^ [_1492218, _1492220, _1492222] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1492218, tc_HOL_Obool)), _1492220), _1492222) = hAPP(c_Set_OCollect(_1492218), hAPP(hAPP(c_COMBS(_1492218, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1492218), c_fconj), hAPP(hAPP(c_COMBC(_1492218, tc_fun(_1492218, tc_HOL_Obool), tc_HOL_Obool), c_member(_1492218)), _1492220))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1492218), c_fNot), hAPP(hAPP(c_COMBC(_1492218, tc_fun(_1492218, tc_HOL_Obool), tc_HOL_Obool), c_member(_1492218)), _1492222)))))], (2520 ^ _779203) ^ [_816251, _816253, _816255, _816257] : [-(c_Divides_Odivmod__nat(_816257, _816253) = c_Divides_Odivmod__nat(_816255, _816251)), _816257 = _816255, _816253 = _816251], (1380 ^ _779203) ^ [_799413, _799415] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799413)), _799415 = _799413, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_799415)], (35329 ^ _779203) ^ [_1437652, _1437654, _1437656, _1437658, _1437660, _1437662] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1437652, tc_HOL_Obool), tc_fun(_1437652, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1437652, tc_HOL_Obool), tc_fun(_1437652, tc_HOL_Obool)), _1437654), _1437656)), c_Wellfounded_Omax__ext(_1437652, _1437658))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1437652, tc_HOL_Obool), tc_fun(_1437652, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1437652, tc_HOL_Obool), tc_fun(_1437652, tc_HOL_Obool)), _1437660), _1437662)), c_Wellfounded_Omax__ext(_1437652, _1437658))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1437652, tc_HOL_Obool), tc_fun(_1437652, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1437652, tc_HOL_Obool), tc_fun(_1437652, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437652, tc_HOL_Obool)), _1437654), _1437660)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1437652, tc_HOL_Obool)), _1437656), _1437662))), c_Wellfounded_Omax__ext(_1437652, _1437658))))], (41687 ^ _779203) ^ [_1605292, _1605294, _1605296, _1605298, _1605300, _1605302] : [hBOOL(hAPP(hAPP(_1605292, _1605294), _1605296)), c_List_Olistrelp(_1605298, _1605292, _1605300, _1605302), -(c_List_Olistrelp(_1605298, _1605292, hAPP(hAPP(c_List_Olist_OCons(_1605298), _1605294), _1605300), hAPP(hAPP(c_List_Olist_OCons(_1605298), _1605296), _1605302)))], (21081 ^ _779203) ^ [_1150831, _1150833, _1150835, _1150837] : [class_Rings_Olinordered__semidom(_1150831), 21087 ^ _779203 : [(21090 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150831), c_Groups_Ozero__class_Ozero(_1150831)), hAPP(_1150837, 21086 ^ [_1150831, _1150833, _1150835, _1150837])))], (21088 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1150833), 21086 ^ [_1150831, _1150833, _1150835, _1150837]), _1150835)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1150831), c_Groups_Ozero__class_Ozero(_1150831)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1150833, _1150831), _1150837), _1150835))))], (8332 ^ _779203) ^ [_918109, _918111, _918113, _918115, _918117, _918119, _918121] : [-(hBOOL(hAPP(hAPP(c_member(_918109), _918111), _918113))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_918109, _918115, _918117, _918119, _918113), _918121)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_918109, _918115, _918117, _918119, hAPP(hAPP(c_Set_Oinsert(_918109), _918111), _918113)), hAPP(hAPP(_918117, _918111), _918121))))], (15906 ^ _779203) ^ [_1057978, _1057980, _1057982] : [class_Int_Onumber__ring(_1057978), class_Rings_Olinordered__idom(_1057978), 15913 ^ _779203 : [(15920 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1057980), _1057982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057978), hAPP(c_Int_Onumber__class_Onumber__of(_1057978), _1057980)), hAPP(c_Int_Onumber__class_Onumber__of(_1057978), _1057982))))], (15914 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057978), hAPP(c_Int_Onumber__class_Onumber__of(_1057978), _1057980)), hAPP(c_Int_Onumber__class_Onumber__of(_1057978), _1057982))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1057980), _1057982)))]]], (52325 ^ _779203) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (41824 ^ _779203) ^ [_1608909, _1608911, _1608913, _1608915] : [-(hAPP(hAPP(c_List_Onth(_1608909), hAPP(hAPP(c_List_Olist_OCons(_1608909), _1608911), _1608913)), hAPP(c_Nat_OSuc, _1608915)) = hAPP(hAPP(c_List_Onth(_1608909), _1608913), _1608915))], (34402 ^ _779203) ^ [_1412705, _1412707, _1412709, _1412711, _1412713] : [_1412705 = c_Orderings_Obot__class_Obot(tc_fun(_1412707, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1412709, tc_HOL_Obool)), _1412711), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412707, tc_fun(_1412709, tc_HOL_Obool)), _1412705), _1412713)) = _1412711)], (20116 ^ _779203) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (31522 ^ _779203) ^ [_1344519, _1344521, _1344523, _1344525] : [class_Groups_Ocomm__monoid__mult(_1344519), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344521), _1344523)), 31532 ^ _779203 : [(31535 ^ _779203) ^ [] : [hAPP(_1344525, 31531 ^ [_1344519, _1344521, _1344523, _1344525]) = c_Groups_Oone__class_Oone(_1344519)], (31533 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344521), 31531 ^ [_1344519, _1344521, _1344523, _1344525]), _1344523)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1344519, _1344521, c_Groups_Otimes__class_Otimes(_1344519)), _1344525), c_Groups_Oone__class_Oone(_1344519)), _1344523) = c_Groups_Oone__class_Oone(_1344519))], (46925 ^ _779203) ^ [_1723080] : [c_List_Onat__list(_1723080), -(c_List_Oembed__list(c_List_Oreturn__list(_1723080)) = _1723080)], (1860 ^ _779203) ^ [_805413, _805415] : [-(class_Orderings_Oorder(_805413)), _805415 = _805413, class_Orderings_Oorder(_805415)], (10746 ^ _779203) ^ [_965066, _965068, _965070] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_965066), _965068)), 10749 ^ _779203 : [(10750 ^ _779203) ^ [] : [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(_965066, tc_Nat_Onat), _965070), _965068))), 10753 ^ _779203 : [(10754 ^ _779203) ^ [_965234] : [hBOOL(hAPP(hAPP(c_member(_965066), _965234), _965068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_965070, _965234))))]]], (10760 ^ _779203) ^ [] : [10762 ^ _779203 : [(10765 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_965070, 10761 ^ [_965066, _965068, _965070])))], (10763 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_965066), 10761 ^ [_965066, _965068, _965070]), _965068)))]], -(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(_965066, tc_Nat_Onat), _965070), _965068))))]]], (31476 ^ _779203) ^ [_1343653] : [class_Complete__Lattice_Ocomplete__lattice(_1343653), -(c_Complete__Lattice_OInf__class_OInf(_1343653, c_Orderings_Otop__class_Otop(tc_fun(_1343653, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1343653))], (13012 ^ _779203) ^ [_1004220, _1004222, _1004224] : [hBOOL(hAPP(_1004220, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004222), _1004224))), 13015 ^ _779203 : [(13022 ^ _779203) ^ [_1004411] : [_1004222 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1004224), _1004411), -(hBOOL(hAPP(_1004220, _1004411)))], (13016 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004222), _1004224)), -(hBOOL(hAPP(_1004220, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (50631 ^ _779203) ^ [_1804884, _1804886, _1804888, _1804890] : [class_Rings_Oidom(_1804884), 50634 ^ _779203 : [(50635 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804884), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804884), _1804886), _1804888)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804884), _1804886), _1804890))), -(_1804886 = c_Groups_Ozero__class_Ozero(_1804884)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804884), _1804888), _1804890)))], (50645 ^ _779203) ^ [] : [50646 ^ _779203 : [(50649 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804884), _1804888), _1804890))], (50647 ^ _779203) ^ [] : [_1804886 = c_Groups_Ozero__class_Ozero(_1804884)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804884), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804884), _1804886), _1804888)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804884), _1804886), _1804890))))]]], (26886 ^ _779203) ^ [_1252762] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1252762)) = _1252762)], (15414 ^ _779203) ^ [_1049481, _1049483] : [class_Orderings_Olinorder(_1049481), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1049481), _1049483), _1049483) = _1049483)], (12144 ^ _779203) ^ [_989029, _989031, _989033, _989035] : [class_Groups_Ocomm__monoid__add(_989029), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_989031), _989033))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_989031, _989029), _989035), _989033) = c_Groups_Ozero__class_Ozero(_989029))], (37607 ^ _779203) ^ [_1492321, _1492323] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492321), hAPP(c_Set_OCollect(_1492321), _1492323))), 37610 ^ _779203 : [(37617 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492321), c_Orderings_Otop__class_Otop(tc_fun(_1492321, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1492321), hAPP(c_Set_OCollect(_1492321), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1492321), c_fNot), _1492323)))))], (37611 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492321), hAPP(c_Set_OCollect(_1492321), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1492321), c_fNot), _1492323)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1492321), c_Orderings_Otop__class_Otop(tc_fun(_1492321, tc_HOL_Obool)))))]]], (34712 ^ _779203) ^ [_1422357, _1422359, _1422361, _1422363, _1422365] : [class_Complete__Lattice_Ocomplete__lattice(_1422357), class_Orderings_Olinorder(_1422357), 34719 ^ _779203 : [(34729 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422357), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1422359, _1422357), _1422361), _1422363)), _1422365))), 34730 ^ _779203 : [(34731 ^ _779203) ^ [_1422705] : [hBOOL(hAPP(hAPP(c_member(_1422359), _1422705), _1422361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422357), hAPP(_1422363, _1422705)), _1422365))]]], (34720 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422357), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1422359, _1422357), _1422361), _1422363)), _1422365)), 34724 ^ _779203 : [(34727 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422357), hAPP(_1422363, 34723 ^ [_1422357, _1422359, _1422361, _1422363, _1422365])), _1422365)))], (34725 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1422359), 34723 ^ [_1422357, _1422359, _1422361, _1422363, _1422365]), _1422361)))]]]]], (18443 ^ _779203) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (17362 ^ _779203) ^ [_1085251, _1085253, _1085255] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085251), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085253), _1085255)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085253), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085251), _1085255)))], (4068 ^ _779203) ^ [_840759, _840761, _840763, _840765, _840767, _840769, _840771, _840773] : [-(c_New__Random__Sequence_Opos__bind(_840773, _840769, _840765, _840761) = c_New__Random__Sequence_Opos__bind(_840771, _840767, _840763, _840759)), _840773 = _840771, _840769 = _840767, _840765 = _840763, _840761 = _840759], (18859 ^ _779203) ^ [_1111506, _1111508] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1111506), _1111508)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1111506)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1111508))))], (33915 ^ _779203) ^ [_1400601, _1400603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400601), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400603), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1400601), _1400603) = 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), _1400601), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1400603)))))], (14395 ^ _779203) ^ [_1029663, _1029665, _1029667, _1029669] : [class_Fields_Olinordered__field__inverse__zero(_1029663), 14398 ^ _779203 : [(14399 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), _1029665), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1029663), _1029667), _1029669))), 14402 ^ _779203 : [(14409 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), c_Groups_Ozero__class_Ozero(_1029663)), _1029669))), 14412 ^ _779203 : [(14419 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), _1029669), c_Groups_Ozero__class_Ozero(_1029663)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), _1029665), c_Groups_Ozero__class_Ozero(_1029663))))], (14413 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), _1029669), c_Groups_Ozero__class_Ozero(_1029663))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), _1029667), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029663), _1029665), _1029669))))]]], (14403 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), c_Groups_Ozero__class_Ozero(_1029663)), _1029669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029663), _1029665), _1029669)), _1029667)))]]], (14425 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), _1029665), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1029663), _1029667), _1029669)))), 14428 ^ _779203 : [(14431 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029663), _1029665), _1029669)), _1029667))], (14429 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), c_Groups_Ozero__class_Ozero(_1029663)), _1029669)))]], 14432 ^ _779203 : [(14435 ^ _779203) ^ [] : [14436 ^ _779203 : [(14439 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), _1029667), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1029663), _1029665), _1029669)))], (14437 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), _1029669), c_Groups_Ozero__class_Ozero(_1029663))))]], 14440 ^ _779203 : [(14443 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), _1029665), c_Groups_Ozero__class_Ozero(_1029663)))], (14441 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), _1029669), c_Groups_Ozero__class_Ozero(_1029663)))]]], (14433 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1029663), c_Groups_Ozero__class_Ozero(_1029663)), _1029669))]]]]], (49690 ^ _779203) ^ [_1783497, _1783499, _1783501] : [hAPP(c_Set_Oimage(_1783497, _1783499, _1783501), c_Orderings_Otop__class_Otop(tc_fun(_1783497, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1783499, tc_HOL_Obool)), 49693 ^ _779203 : [(49694 ^ _779203) ^ [_1783608] : [-(hAPP(_1783501, hAPP(c_Hilbert__Choice_Oinv__into(_1783497, _1783499, c_Orderings_Otop__class_Otop(tc_fun(_1783497, tc_HOL_Obool)), _1783501), _1783608)) = _1783608)]]], (29532 ^ _779203) ^ [_1303169, _1303171, _1303173, _1303175] : [class_Lattices_Osemilattice__inf(_1303169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303169), _1303171), _1303173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303169), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1303169), _1303171), _1303175)), _1303173)))], (46072 ^ _779203) ^ [_1706365, _1706367] : [class_Orderings_Olinorder(_1706365), -(c_List_Olinorder__class_Osorted(_1706365, c_List_Olinorder__class_Osort__key(_1706365, _1706365, c_COMBI(_1706365), _1706367)))], (22217 ^ _779203) ^ [_1171517, _1171519] : [-(_1171517 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22220 ^ _779203 : [(22227 ^ _779203) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1171519, _1171517) = 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), _1171519)), _1171517) = 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), _1171519), _1171517))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22221 ^ _779203) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1171519, _1171517) = 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), _1171519)), _1171517) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1171519), _1171517)))]]], (41897 ^ _779203) ^ [_1610927, _1610929, _1610931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610927)), _1610929)), _1610931)), -(hAPP(hAPP(c_List_Otake(_1610927), _1610931), _1610929) = _1610929)], (34959 ^ _779203) ^ [_1428532, _1428534, _1428536, _1428538, _1428540] : [class_Complete__Lattice_Ocomplete__lattice(_1428532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428534, tc_HOL_Obool)), _1428536), _1428538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428532), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428534, _1428532), _1428538), _1428540)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428534, _1428532), _1428536), _1428540))))], (52657 ^ _779203) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (52141 ^ _779203) ^ [_1831219, _1831221] : [class_Lattices_Olattice(_1831219), -(class_Lattices_Osemilattice__inf(tc_fun(_1831221, _1831219)))], (18343 ^ _779203) ^ [_1102833] : [class_Int_Onumber__ring(_1102833), -(hAPP(c_Int_Onumber__class_Onumber__of(_1102833), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1102833))], (7691 ^ _779203) ^ [_905971, _905973, _905975] : [class_Orderings_Olinorder(_905971), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905971), _905973), _905975))), 7698 ^ _779203 : [(7705 ^ _779203) ^ [] : [_905973 = _905975, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905971), _905973), _905975)))], (7699 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905971), _905973), _905975)), -(_905973 = _905975)]]], (24267 ^ _779203) ^ [_1206818, _1206820, _1206822] : [class_Rings_Ocomm__semiring__1(_1206818), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1206818), _1206820), hAPP(c_Nat_OSuc, _1206822)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206818), _1206820), hAPP(hAPP(c_Power_Opower__class_Opower(_1206818), _1206820), _1206822)))], (7393 ^ _779203) ^ [_901463, _901465, _901467] : [class_Orderings_Oorder(_901463), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901463), _901465), _901467)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901463), _901467), _901465))], (47052 ^ _779203) ^ [_1725788, _1725790, _1725792, _1725794, _1725796] : [class_Groups_Omonoid__add(_1725788), 47058 ^ _779203 : [(47063 ^ _779203) ^ [] : [hAPP(_1725796, 47057 ^ [_1725788, _1725790, _1725792, _1725794, _1725796]) = c_Groups_Ozero__class_Ozero(_1725788)], (47061 ^ _779203) ^ [] : [hBOOL(hAPP(_1725794, 47057 ^ [_1725788, _1725790, _1725792, _1725794, _1725796]))], (47059 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1725790), 47057 ^ [_1725788, _1725790, _1725792, _1725794, _1725796]), hAPP(c_List_Oset(_1725790), _1725792))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1725788), hAPP(hAPP(c_List_Omap(_1725790, _1725788), _1725796), hAPP(c_List_Ofilter(_1725790, _1725794), _1725792))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1725788), hAPP(hAPP(c_List_Omap(_1725790, _1725788), _1725796), _1725792)))], (48060 ^ _779203) ^ [_1747960, _1747962] : [-(c_List_Osplice(_1747960, c_List_Olist_ONil(_1747960), _1747962) = _1747962)], (52263 ^ _779203) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (50739 ^ _779203) ^ [_1806752, _1806754, _1806756] : [class_Rings_Ocomm__semiring__1(_1806752), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806752), _1806754), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806752), _1806756), _1806754))))], (30369 ^ _779203) ^ [_1321123, _1321125, _1321127] : [class_Lattices_Olattice(_1321123), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321123), _1321125)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321123), _1321127)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321123, tc_HOL_Obool)), _1321125), _1321127) = c_Orderings_Obot__class_Obot(tc_fun(_1321123, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321123), c_Big__Operators_Olattice__class_OSup__fin(_1321123, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321123, tc_HOL_Obool)), _1321125), _1321127))), c_Big__Operators_Olattice__class_OSup__fin(_1321123, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321123, tc_HOL_Obool)), _1321125), _1321127))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1321123), c_Big__Operators_Olattice__class_OSup__fin(_1321123, _1321125)), c_Big__Operators_Olattice__class_OSup__fin(_1321123, _1321127)))], (49628 ^ _779203) ^ [_1782176, _1782178, _1782180, _1782182, _1782184] : [c_Fun_Oinj__on(_1782176, _1782178, _1782180, _1782182), hBOOL(hAPP(hAPP(c_member(_1782176), _1782184), _1782182)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1782176, _1782178, _1782182, _1782180), hAPP(_1782180, _1782184)) = _1782184)], (4148 ^ _779203) ^ [_841991, _841993] : [_841993 = _841991, -(c_List_Ohd(_841993) = c_List_Ohd(_841991))], (52281 ^ _779203) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (23832 ^ _779203) ^ [_1198629, _1198631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1198629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1198631, _1198629)), _1198629)))], (41765 ^ _779203) ^ [_1607218, _1607220, _1607222, _1607224] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607218), tc_List_Olist(_1607218))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607218), tc_List_Olist(_1607218)), _1607220), _1607222)), c_List_Olistrel(_1607218, _1607224))), 41768 ^ _779203 : [(41771 ^ _779203) ^ [_1607447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1607447), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607218)), _1607220))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607218, _1607218)), hAPP(hAPP(c_Product__Type_OPair(_1607218, _1607218), hAPP(hAPP(c_List_Onth(_1607218), _1607220), _1607447)), hAPP(hAPP(c_List_Onth(_1607218), _1607222), _1607447))), _1607224)))], (41769 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607218)), _1607220) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607218)), _1607222))]]], (38294 ^ _779203) ^ [_1516384, _1516386] : [-(c_Product__Type_Omap__pair(_1516384, _1516384, _1516386, _1516386, c_Fun_Oid(_1516384), c_Fun_Oid(_1516386)) = c_Fun_Oid(tc_prod(_1516384, _1516386)))], (52243 ^ _779203) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (21593 ^ _779203) ^ [_1159313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1159313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1159313))))], (42303 ^ _779203) ^ [_1621975, _1621977, _1621979] : [hBOOL(hAPP(hAPP(c_member(_1621975), _1621977), hAPP(c_List_Oset(_1621975), c_List_Obutlast(_1621975, _1621979)))), -(hBOOL(hAPP(hAPP(c_member(_1621975), _1621977), hAPP(c_List_Oset(_1621975), _1621979))))], (42179 ^ _779203) ^ [_1619329, _1619331] : [class_Groups_Ocomm__monoid__add(_1619329), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1619329), _1619331) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1619329), hAPP(c_List_Onth(_1619329), _1619331)), 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(_1619329)), _1619331))))], (35476 ^ _779203) ^ [_1442471, _1442473, _1442475] : [-(hAPP(c_Relation_OImage(_1442471, _1442473, _1442475), c_Orderings_Obot__class_Obot(tc_fun(_1442471, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1442473, tc_HOL_Obool)))], (258 ^ _779203) ^ [_783236, _783238] : [-(class_Fields_Olinordered__field(_783236)), _783238 = _783236, class_Fields_Olinordered__field(_783238)], (2932 ^ _779203) ^ [_822625, _822627] : [_822627 = _822625, -(c_Nitpick_Odenom(_822627) = c_Nitpick_Odenom(_822625))], (45428 ^ _779203) ^ [_1690968, _1690970, _1690972] : [hBOOL(hAPP(c_List_Odistinct(_1690968), _1690970)), -(c_List_Oremove1(_1690968, _1690972, c_List_Oremdups(_1690968, _1690970)) = c_List_Oremdups(_1690968, c_List_Oremove1(_1690968, _1690972, _1690970)))], (20420 ^ _779203) ^ [_1139276, _1139278] : [class_Groups_Oordered__ab__group__add__abs(_1139276), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1139276), hAPP(c_Groups_Ouminus__class_Ouminus(_1139276), _1139278)), hAPP(c_Groups_Oabs__class_Oabs(_1139276), _1139278))))], (2926 ^ _779203) ^ [_822540, _822542] : [_822542 = _822540, -(c_Nitpick_Onum(_822542) = c_Nitpick_Onum(_822540))], (28298 ^ _779203) ^ [_1279497, _1279499, _1279501] : [class_Orderings_Olinorder(_1279497), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279497), _1279499), _1279501)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279497, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1279497), _1279499)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1279497, _1279499), _1279501)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1279497), _1279501))], (27382 ^ _779203) ^ [_1261647, _1261649, _1261651] : [class_Orderings_Olinorder(_1261647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261647), _1261649), _1261651)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261647, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1261647, _1261649), _1261651)), hAPP(c_SetInterval_Oord__class_OatLeast(_1261647), _1261651)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1261647), _1261649))], (31895 ^ _779203) ^ [_1353137, _1353139, _1353141, _1353143, _1353145] : [class_Fields_Ofield(_1353137), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353137), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353139, _1353137), _1353141), _1353143)), _1353145) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353139, _1353137), hAPP(hAPP(c_COMBC(_1353139, _1353137, _1353137), hAPP(hAPP(c_COMBB(_1353137, tc_fun(_1353137, _1353137), _1353139), c_Rings_Oinverse__class_Odivide(_1353137)), _1353141)), _1353145)), _1353143))], (4598 ^ _779203) ^ [_849100, _849102] : [_849102 = _849100, -(c_DSequence_Oempty(_849102) = c_DSequence_Oempty(_849100))], (52327 ^ _779203) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (14127 ^ _779203) ^ [_1025023, _1025025, _1025027] : [class_Fields_Olinordered__field__inverse__zero(_1025023), 14130 ^ _779203 : [(14145 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025023), c_Groups_Ozero__class_Ozero(_1025023)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025023), _1025025), _1025027)))), 14146 ^ _779203 : [(14153 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025023), _1025025), c_Groups_Ozero__class_Ozero(_1025023))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025023), _1025027), c_Groups_Ozero__class_Ozero(_1025023)))], (14147 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025023), c_Groups_Ozero__class_Ozero(_1025023)), _1025025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025023), c_Groups_Ozero__class_Ozero(_1025023)), _1025027))]]], (14131 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025023), c_Groups_Ozero__class_Ozero(_1025023)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1025023), _1025025), _1025027))), 14136 ^ _779203 : [(14139 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025023), c_Groups_Ozero__class_Ozero(_1025023)), _1025027)))], (14137 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025023), c_Groups_Ozero__class_Ozero(_1025023)), _1025025)))]], 14140 ^ _779203 : [(14143 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025023), _1025027), c_Groups_Ozero__class_Ozero(_1025023))))], (14141 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1025023), _1025025), c_Groups_Ozero__class_Ozero(_1025023))))]]]]], (8094 ^ _779203) ^ [_913359, _913361, _913363, _913365, _913367] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_913359), _913361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913359, tc_HOL_Obool)), _913361), hAPP(c_Set_Oimage(_913363, _913359, _913365), _913367))), 8102 ^ _779203 : [(8107 ^ _779203) ^ [] : [-(_913361 = hAPP(c_Set_Oimage(_913363, _913359, _913365), 8101 ^ [_913359, _913361, _913363, _913365, _913367]))], (8105 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_913363), 8101 ^ [_913359, _913361, _913363, _913365, _913367])))], (8103 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913363, tc_HOL_Obool)), 8101 ^ [_913359, _913361, _913363, _913365, _913367]), _913367)))]]], (45931 ^ _779203) ^ [_1703409, _1703411] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1703409), _1703411)) = c_List_Oupt(_1703409, _1703411))], (32777 ^ _779203) ^ [_1379132, _1379134, _1379136, _1379138, _1379140, _1379142] : [hBOOL(hAPP(hAPP(_1379132, _1379134), _1379136)), hBOOL(hAPP(hAPP(_1379138, _1379134), _1379136)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1379140, tc_fun(_1379142, tc_HOL_Obool))), _1379132), _1379138), _1379134), _1379136)))], (50208 ^ _779203) ^ [_1794579, _1794581, _1794583, _1794585, _1794587] : [c_Fun_Obij__betw(_1794579, _1794581, _1794583, c_Orderings_Otop__class_Otop(tc_fun(_1794579, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794581, tc_HOL_Obool))), 50211 ^ _779203 : [(50218 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794581, tc_HOL_Obool)), _1794585), hAPP(c_Set_Oimage(_1794579, _1794581, _1794583), _1794587))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794579, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1794579, _1794581, _1794583), _1794585)), _1794587)))], (50212 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794579, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1794579, _1794581, _1794583), _1794585)), _1794587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1794581, tc_HOL_Obool)), _1794585), hAPP(c_Set_Oimage(_1794579, _1794581, _1794583), _1794587))))]]], (46875 ^ _779203) ^ [_1722027, _1722029, _1722031] : [hBOOL(hAPP(c_List_Odistinct(_1722027), _1722029)), -(hBOOL(hAPP(c_List_Odistinct(_1722027), c_List_OtakeWhile(_1722027, _1722031, _1722029))))], (46430 ^ _779203) ^ [_1712528, _1712530, _1712532] : [class_Orderings_Olinorder(_1712528), hBOOL(hAPP(hAPP(c_member(_1712528), _1712530), hAPP(c_List_Oset(_1712528), _1712532))), c_List_Olinorder__class_Osorted(_1712528, _1712532), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1712528, _1712528, c_COMBI(_1712528)), _1712530), c_List_Oremove1(_1712528, _1712530, _1712532)) = _1712532)], (26144 ^ _779203) ^ [_1238949] : [-(hAPP(c_Set_OPow(_1238949), c_Orderings_Obot__class_Obot(tc_fun(_1238949, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1238949, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1238949, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1238949, tc_HOL_Obool), tc_HOL_Obool))))], (43554 ^ _779203) ^ [_1649984, _1649986, _1649988, _1649990] : [-(hAPP(hAPP(c_List_Odrop(_1649984), _1649986), hAPP(hAPP(c_List_Oappend(_1649984), _1649988), _1649990)) = hAPP(hAPP(c_List_Oappend(_1649984), hAPP(hAPP(c_List_Odrop(_1649984), _1649986), _1649988)), hAPP(hAPP(c_List_Odrop(_1649984), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1649986), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649984)), _1649988))), _1649990)))], (4192 ^ _779203) ^ [_842629, _842631, _842633, _842635] : [-(c_List_Ofilter(_842635, _842631) = c_List_Ofilter(_842633, _842629)), _842635 = _842633, _842631 = _842629], (27236 ^ _779203) ^ [_1258735, _1258737, _1258739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1258735), _1258737)), -(c_Random_Ominus__shift(_1258739, _1258735, _1258737) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1258739), _1258735)), _1258737))], (29850 ^ _779203) ^ [_1309943, _1309945, _1309947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309943, tc_HOL_Obool)), _1309945), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1309943, tc_HOL_Obool)), _1309947))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309943, tc_HOL_Obool)), _1309945), _1309947) = c_Orderings_Obot__class_Obot(tc_fun(_1309943, tc_HOL_Obool)))], (16086 ^ _779203) ^ [_1061830, _1061832, _1061834, _1061836] : [class_Fields_Ofield__inverse__zero(_1061830), class_Int_Onumber(_1061830), 16093 ^ _779203 : [(16094 ^ _779203) ^ [] : [_1061832 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1061830), _1061834), hAPP(c_Int_Onumber__class_Onumber__of(_1061830), _1061836)), 16097 ^ _779203 : [(16104 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1061830), _1061836) = c_Groups_Ozero__class_Ozero(_1061830), -(_1061832 = c_Groups_Ozero__class_Ozero(_1061830))], (16098 ^ _779203) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1061830), _1061836) = c_Groups_Ozero__class_Ozero(_1061830)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061830), _1061832), hAPP(c_Int_Onumber__class_Onumber__of(_1061830), _1061836)) = _1061834)]]], (16110 ^ _779203) ^ [] : [-(_1061832 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1061830), _1061834), hAPP(c_Int_Onumber__class_Onumber__of(_1061830), _1061836))), 16113 ^ _779203 : [(16116 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061830), _1061832), hAPP(c_Int_Onumber__class_Onumber__of(_1061830), _1061836)) = _1061834], (16114 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1061830), _1061836) = c_Groups_Ozero__class_Ozero(_1061830)]], 16117 ^ _779203 : [(16120 ^ _779203) ^ [] : [_1061832 = c_Groups_Ozero__class_Ozero(_1061830)], (16118 ^ _779203) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1061830), _1061836) = c_Groups_Ozero__class_Ozero(_1061830))]]]]], (25690 ^ _779203) ^ [_1231455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1231455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1231455))))], (44644 ^ _779203) ^ [_1673667, _1673669] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1673667), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1673669), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 44651 ^ _779203 : [(44658 ^ _779203) ^ [] : [_1673667 = _1673669, -(hAPP(c_Code__Numeral_Oof__nat, _1673667) = hAPP(c_Code__Numeral_Oof__nat, _1673669))], (44652 ^ _779203) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1673667) = hAPP(c_Code__Numeral_Oof__nat, _1673669), -(_1673667 = _1673669)]]], (2370 ^ _779203) ^ [_813850, _813852, _813854, _813856] : [-(c_Divides_OnegDivAlg(_813856, _813852) = c_Divides_OnegDivAlg(_813854, _813850)), _813856 = _813854, _813852 = _813850], (26716 ^ _779203) ^ [_1249641, _1249643, _1249645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249641)), 26719 ^ _779203 : [(26720 ^ _779203) ^ [_1249775] : [26722 ^ _779203 : [(26728 ^ _779203) ^ [] : [-(_1249775 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26724 ^ [_1249641, _1249643, _1249645, _1249775]), 26721 ^ [_1249641, _1249643, _1249645, _1249775]))], (26726 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26724 ^ [_1249641, _1249643, _1249645, _1249775]), _1249643)))], (26723 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26721 ^ [_1249641, _1249643, _1249645, _1249775]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1249641))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249645), _1249775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249645), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1249775), _1249641))))]]], (27690 ^ _779203) ^ [_1267253, _1267255] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267253, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1267253, tc_HOL_Obool))), _1267255) = _1267255)], (26114 ^ _779203) ^ [_1238320, _1238322] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1238320), _1238322)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1238320, tc_HOL_Obool)), hAPP(c_Set_OPow(_1238320), _1238322)) = 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(_1238320), _1238322)))], (31973 ^ _779203) ^ [_1355471, _1355473, _1355475, _1355477, _1355479] : [class_Lattices_Olattice(_1355471), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1355473, _1355471)), _1355475), _1355477), _1355479) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1355471), hAPP(_1355475, _1355479)), hAPP(_1355477, _1355479)))], (19544 ^ _779203) ^ [_1123823] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1123823)), 19548 ^ _779203 : [(19549 ^ _779203) ^ [_1123903] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1123903), _1123823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1123903), 19547 ^ [_1123823])))]]], (39103 ^ _779203) ^ [_1537787, _1537789, _1537791] : [c_Wellfounded_OwfP(_1537787, _1537789), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1537787, _1537789), _1537791)))], (27934 ^ _779203) ^ [_1272223, _1272225] : [class_Lattices_Oboolean__algebra(_1272223), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272223), hAPP(c_Groups_Ouminus__class_Ouminus(_1272223), _1272225)), _1272225) = c_Orderings_Otop__class_Otop(_1272223))], (13913 ^ _779203) ^ [_1021157, _1021159, _1021161, _1021163] : [class_Fields_Olinordered__field__inverse__zero(_1021157), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021157), _1021159), _1021161)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021157), _1021163), c_Groups_Ozero__class_Ozero(_1021157))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021157), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1021157), _1021161), _1021163)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1021157), _1021159), _1021163))))], (38308 ^ _779203) ^ [_1516741, _1516743, _1516745, _1516747] : [-(c_Product__Type_Oapsnd(_1516741, _1516743, _1516745, _1516747) = c_Product__Type_Omap__pair(_1516745, _1516745, _1516741, _1516743, c_Fun_Oid(_1516745), _1516747))], (52307 ^ _779203) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (5472 ^ _779203) ^ [_862885, _862887] : [_862887 = _862885, -(c_Orderings_Oord__class_Oless(_862887) = c_Orderings_Oord__class_Oless(_862885))], (52461 ^ _779203) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (25114 ^ _779203) ^ [_1221823, _1221825, _1221827, _1221829] : [class_Groups_Omonoid__mult(_1221823), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1221823), _1221825), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1221827), _1221829)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1221823), hAPP(hAPP(c_Power_Opower__class_Opower(_1221823), _1221825), _1221827)), hAPP(hAPP(c_Power_Opower__class_Opower(_1221823), _1221825), _1221829)))], (52553 ^ _779203) ^ [_1835451, _1835453] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1835451, _1835453))), class_Lazy__Sequence_Osmall__lazy(_1835451), class_Lazy__Sequence_Osmall__lazy(_1835453)], (16296 ^ _779203) ^ [_1065313, _1065315] : [class_Orderings_Olinorder(_1065313), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065313), _1065315)), -(c_Big__Operators_Olinorder__class_OMin(_1065313, _1065315) = hAPP(c_Finite__Set_Ofold1(_1065313, c_Orderings_Oord__class_Omin(_1065313)), _1065315))], (9297 ^ _779203) ^ [_937792, _937794, _937796] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937792), _937794)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937792), _937796))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _937794), _937796)))], (7487 ^ _779203) ^ [_902965, _902967, _902969] : [class_Orderings_Opreorder(_902965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902965), _902967), _902969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902965), _902969), _902967))], (40813 ^ _779203) ^ [_1579799, _1579801, _1579803, _1579805, _1579807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579799, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579801, _1579799, _1579803), _1579805)), _1579807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579801, tc_HOL_Obool)), _1579805), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579801, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579799, _1579801, hAPP(c_Relation_Oconverse(_1579801, _1579799), _1579803)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579799, tc_HOL_Obool)), _1579807))))))], (49260 ^ _779203) ^ [_1775365, _1775367] : [49263 ^ _779203 : [(49266 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775365, _1775365)), hAPP(hAPP(c_Product__Type_OPair(_1775365, _1775365), 49262 ^ [_1775365, _1775367]), 49261 ^ [_1775365, _1775367])), _1775367))], (49264 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775365, _1775365)), hAPP(hAPP(c_Product__Type_OPair(_1775365, _1775365), 49261 ^ [_1775365, _1775367]), 49262 ^ [_1775365, _1775367])), _1775367)))]], -(c_Relation_Osym(_1775365, _1775367))], (24946 ^ _779203) ^ [_1218823, _1218825] : [class_Groups_Omonoid__mult(_1218823), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1218823), c_Groups_Oone__class_Oone(_1218823)), _1218825) = c_Groups_Oone__class_Oone(_1218823))], (46859 ^ _779203) ^ [_1721759, _1721761, _1721763, _1721765] : [hBOOL(hAPP(_1721759, _1721761)), -(c_List_OtakeWhile(_1721763, _1721759, hAPP(hAPP(c_List_Olist_OCons(_1721763), _1721761), _1721765)) = hAPP(hAPP(c_List_Olist_OCons(_1721763), _1721761), c_List_OtakeWhile(_1721763, _1721759, _1721765)))], (7511 ^ _779203) ^ [_903260, _903262, _903264, _903266, _903268] : [c_Finite__Set_Ofun__left__comm__idem(_903260, _903262, _903264), -(hAPP(hAPP(_903264, _903266), hAPP(hAPP(_903264, _903266), _903268)) = hAPP(hAPP(_903264, _903266), _903268))], (52747 ^ _779203) ^ [_1837693, _1837695] : [hBOOL(_1837693), -(hBOOL(hAPP(hAPP(c_fdisj, _1837695), _1837693)))], (22139 ^ _779203) ^ [_1170064, _1170066, _1170068] : [-(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, _1170064, _1170066)), _1170068), _1170066) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1170064), _1170068), _1170066))], (46212 ^ _779203) ^ [_1708487, _1708489, _1708491] : [class_Orderings_Olinorder(_1708487), c_List_Olinorder__class_Osorted(_1708487, _1708489), hBOOL(hAPP(c_List_Odistinct(_1708487), _1708489)), c_List_Olinorder__class_Osorted(_1708487, _1708491), hBOOL(hAPP(c_List_Odistinct(_1708487), _1708491)), hAPP(c_List_Oset(_1708487), _1708489) = hAPP(c_List_Oset(_1708487), _1708491), -(_1708489 = _1708491)], (35699 ^ _779203) ^ [_1448369, _1448371, _1448373, _1448375, _1448377] : [c_Equiv__Relations_Oequiv(_1448369, _1448371, _1448373), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1448369, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1448369, _1448369, _1448373), hAPP(hAPP(c_Set_Oinsert(_1448369), _1448375), c_Orderings_Obot__class_Obot(tc_fun(_1448369, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1448369, _1448369, _1448373), hAPP(hAPP(c_Set_Oinsert(_1448369), _1448377), c_Orderings_Obot__class_Obot(tc_fun(_1448369, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1448369), _1448375), _1448371)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1448369, _1448369)), hAPP(hAPP(c_Product__Type_OPair(_1448369, _1448369), _1448377), _1448375)), _1448373)))], (37096 ^ _779203) ^ [_1479144, _1479146] : [-(c_Set_Othe__elem(_1479144, _1479146) = c_HOL_OThe(_1479144, hAPP(hAPP(c_COMBB(tc_fun(_1479144, tc_HOL_Obool), tc_HOL_Obool, _1479144), hAPP(c_fequal, _1479146)), hAPP(hAPP(c_COMBC(_1479144, tc_fun(_1479144, tc_HOL_Obool), tc_fun(_1479144, tc_HOL_Obool)), c_Set_Oinsert(_1479144)), c_Orderings_Obot__class_Obot(tc_fun(_1479144, tc_HOL_Obool))))))], (38858 ^ _779203) ^ [_1531808, _1531810, _1531812, _1531814] : [hBOOL(hAPP(hAPP(c_member(_1531808), _1531810), hAPP(c_Relation_ODomain(_1531808, _1531812), _1531814))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531808, _1531812)), hAPP(hAPP(c_Product__Type_OPair(_1531808, _1531812), _1531810), 38861 ^ [_1531808, _1531810, _1531812, _1531814])), _1531814)))], (25130 ^ _779203) ^ [_1222156, _1222158, _1222160] : [class_Fields_Ofield__inverse__zero(_1222156), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222156), c_Groups_Oone__class_Oone(_1222156)), hAPP(hAPP(c_Power_Opower__class_Opower(_1222156), _1222158), _1222160)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1222156), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1222156), c_Groups_Oone__class_Oone(_1222156)), _1222158)), _1222160))], (45230 ^ _779203) ^ [_1686783, _1686785, _1686787, _1686789, _1686791, _1686793, _1686795, _1686797] : [c_List_Olist__all2(_1686783, _1686785, _1686787, _1686789, _1686791), hBOOL(hAPP(hAPP(_1686787, _1686793), _1686795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686797), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686785)), _1686791))), -(c_List_Olist__all2(_1686783, _1686785, _1686787, hAPP(hAPP(c_List_Olist__update(_1686783, _1686789), _1686797), _1686793), hAPP(hAPP(c_List_Olist__update(_1686785, _1686791), _1686797), _1686795)))], (42431 ^ _779203) ^ [_1624906, _1624908, _1624910, _1624912] : [hBOOL(hAPP(c_List_Odistinct(_1624906), _1624908)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1624906, _1624910)), hAPP(hAPP(c_List_Ozip(_1624906, _1624910), _1624908), _1624912))))], (43193 ^ _779203) ^ [_1641161, _1641163, _1641165] : [-(hAPP(hAPP(c_List_Oappend(_1641161), _1641163), _1641165) = c_List_Olist_ONil(_1641161)), _1641163 = c_List_Olist_ONil(_1641161), _1641165 = c_List_Olist_ONil(_1641161)], (11568 ^ _779203) ^ [_978684, _978686, _978688] : [class_Rings_Oordered__cancel__semiring(_978684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978684), c_Groups_Ozero__class_Ozero(_978684)), _978686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978684), _978688), c_Groups_Ozero__class_Ozero(_978684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978684), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978684), _978686), _978688)), c_Groups_Ozero__class_Ozero(_978684))))], (1730 ^ _779203) ^ [_803788, _803790] : [-(class_Rings_Ocomm__semiring__1(_803788)), _803790 = _803788, class_Rings_Ocomm__semiring__1(_803790)], (21581 ^ _779203) ^ [_1159117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1159117), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1159117)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (39334 ^ _779203) ^ [_1543874, _1543876, _1543878, _1543880] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1543874), _1543876)), 39340 ^ _779203 : [(39343 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1543878), hAPP(_1543880, 39339 ^ [_1543874, _1543876, _1543878, _1543880])))], (39341 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543874), 39339 ^ [_1543874, _1543876, _1543878, _1543880]), _1543876)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1543878), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1543874, tc_fun(_1543878, tc_HOL_Obool)), _1543876), _1543880))))], (40986 ^ _779203) ^ [_1584130, _1584132, _1584134, _1584136, _1584138, _1584140] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584130, _1584130)), hAPP(hAPP(c_Product__Type_OPair(_1584130, _1584130), _1584132), _1584134)), _1584136)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584130, _1584130)), hAPP(hAPP(c_Product__Type_OPair(_1584130, _1584130), _1584134), _1584138)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584130, _1584130), tc_HOL_Obool), _1584140), _1584136))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584130, _1584130)), hAPP(hAPP(c_Product__Type_OPair(_1584130, _1584130), _1584132), _1584138)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584130, _1584130), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1584140)), _1584136))))], (52341 ^ _779203) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (35892 ^ _779203) ^ [_1452525, _1452527, _1452529, _1452531, _1452533] : [c_Equiv__Relations_Oequiv(_1452525, _1452527, _1452529), hBOOL(hAPP(hAPP(c_member(tc_prod(_1452525, _1452525)), hAPP(hAPP(c_Product__Type_OPair(_1452525, _1452525), _1452531), _1452533)), _1452529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1452525, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1452525, _1452525, _1452529), hAPP(hAPP(c_Set_Oinsert(_1452525), _1452531), c_Orderings_Obot__class_Obot(tc_fun(_1452525, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1452525, _1452525, _1452529), hAPP(hAPP(c_Set_Oinsert(_1452525), _1452533), c_Orderings_Obot__class_Obot(tc_fun(_1452525, tc_HOL_Obool)))))))], (34937 ^ _779203) ^ [_1427972, _1427974, _1427976, _1427978] : [-(hAPP(c_Set_Oimage(_1427972, _1427974, _1427976), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1427972, tc_HOL_Obool), _1427978)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1427972, tc_HOL_Obool), tc_fun(_1427974, tc_HOL_Obool)), _1427978), c_Set_Oimage(_1427972, _1427974, _1427976)))], (35125 ^ _779203) ^ [_1432621, _1432623, _1432625, _1432627, _1432629, _1432631] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432621, tc_fun(_1432623, tc_HOL_Obool)), _1432625), hAPP(hAPP(c_COMBC(_1432621, tc_fun(_1432627, tc_fun(_1432623, tc_HOL_Obool)), tc_fun(_1432623, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432627, tc_HOL_Obool), tc_fun(tc_fun(_1432627, tc_fun(_1432623, tc_HOL_Obool)), tc_fun(_1432623, tc_HOL_Obool)), _1432621), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432627, tc_fun(_1432623, tc_HOL_Obool))), _1432629)), _1432631)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432627, tc_fun(_1432623, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432621, tc_fun(_1432627, tc_HOL_Obool)), _1432625), _1432629)), _1432631))], (49088 ^ _779203) ^ [_1771783, _1771785] : [c_Equiv__Relations_Oequivp(_1771783, _1771785), 49091 ^ _779203 : [(49096 ^ _779203) ^ [] : [-(c_Predicate_Otransp(_1771783, _1771785))], (49094 ^ _779203) ^ [] : [-(c_Predicate_Osymp(_1771783, _1771785))], (49092 ^ _779203) ^ [] : [-(c_Predicate_Oreflp(_1771783, _1771785))]]], (22369 ^ _779203) ^ [_1173923] : [-(_1173923 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1173923), _1173923) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (42642 ^ _779203) ^ [_1629369, _1629371] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1629369), _1629371)), -(c_List_Oupto(_1629371, _1629369) = c_List_Olist_ONil(tc_Int_Oint))], (48458 ^ _779203) ^ [_1756510, _1756512, _1756514, _1756516, _1756518, _1756520] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1756510, _1756512, _1756514, _1756516, c_Lazy__Sequence_Olazy__sequence_OInsert(_1756512, _1756518, _1756520)) = hAPP(hAPP(_1756516, _1756518), _1756520))], (25714 ^ _779203) ^ [_1231845, _1231847] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231845), _1231847) = c_Groups_Oone__class_Oone(tc_Int_Oint), 25719 ^ _779203 : [(25722 ^ _779203) ^ [] : [-(_1231847 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25720 ^ _779203) ^ [] : [-(_1231845 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 25723 ^ _779203 : [(25726 ^ _779203) ^ [] : [-(_1231847 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (25724 ^ _779203) ^ [] : [-(_1231845 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (30501 ^ _779203) ^ [_1323616, _1323618, _1323620] : [class_Orderings_Olinorder(_1323616), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323616), _1323618)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323616), _1323620)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323616, tc_HOL_Obool)), _1323618), _1323620) = c_Orderings_Obot__class_Obot(tc_fun(_1323616, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1323616), c_Big__Operators_Olattice_OInf__fin(_1323616, c_Orderings_Oord__class_Omin(_1323616), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1323616, tc_HOL_Obool)), _1323618), _1323620))), c_Big__Operators_Olattice_OInf__fin(_1323616, c_Orderings_Oord__class_Omin(_1323616), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323616, tc_HOL_Obool)), _1323618), _1323620))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1323616), c_Big__Operators_Olattice_OInf__fin(_1323616, c_Orderings_Oord__class_Omin(_1323616), _1323618)), c_Big__Operators_Olattice_OInf__fin(_1323616, c_Orderings_Oord__class_Omin(_1323616), _1323620)))], (3328 ^ _779203) ^ [_828797, _828799, _828801, _828803] : [-(c_Enum_Oenum__the(_828803, _828799) = c_Enum_Oenum__the(_828801, _828797)), _828803 = _828801, _828799 = _828797], (29136 ^ _779203) ^ [_1294978, _1294980, _1294982, _1294984] : [class_Lattices_Odistrib__lattice(_1294978), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1294978), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294978), _1294980), _1294982)), _1294984) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1294978), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1294978), _1294980), _1294984)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1294978), _1294982), _1294984)))], (52713 ^ _779203) ^ [_1837258] : [-(hBOOL(_1837258)), -(hBOOL(hAPP(c_fNot, _1837258)))], (44909 ^ _779203) ^ [_1679576, _1679578] : [-(hBOOL(hAPP(c_List_Olistsp(_1679576, _1679578), c_List_Olist_ONil(_1679576))))], (52235 ^ _779203) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (18915 ^ _779203) ^ [_1112430, _1112432] : [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)), _1112430)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1112432))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1112430), _1112432)))], (18058 ^ _779203) ^ [_1097835, _1097837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097835), _1097837)), -(c_Nat__Transfer_Otsub(_1097837, _1097835) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1097837), _1097835))], (48697 ^ _779203) ^ [_1761806, _1761808, _1761810, _1761812] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761806, _1761808, _1761810, c_Code__Numeral_OSuc__code__numeral(_1761812)) = hAPP(hAPP(_1761810, _1761812), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1761806, _1761808, _1761810, _1761812)))], (44464 ^ _779203) ^ [_1669734, _1669736, _1669738, _1669740, _1669742] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1669734), tc_List_Olist(_1669736), tc_List_Olist(_1669738), hAPP(c_List_Omap(_1669734, _1669736), _1669740)), hAPP(c_List_Omap(_1669738, _1669734), _1669742)) = hAPP(c_List_Omap(_1669738, _1669736), hAPP(c_Fun_Ocomp(_1669734, _1669736, _1669738, _1669740), _1669742)))], (41024 ^ _779203) ^ [_1585183, _1585185, _1585187] : [c_Relation_Osingle__valued(_1585183, _1585185, _1585187), 41027 ^ _779203 : [(41028 ^ _779203) ^ [_1585304, _1585306] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585183, _1585185)), hAPP(hAPP(c_Product__Type_OPair(_1585183, _1585185), _1585306), _1585304)), _1585187)), 41031 ^ _779203 : [(41032 ^ _779203) ^ [_1585430] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585183, _1585185)), hAPP(hAPP(c_Product__Type_OPair(_1585183, _1585185), _1585306), _1585430)), _1585187)), -(_1585304 = _1585430)]]]]], (37515 ^ _779203) ^ [_1489709, _1489711, _1489713, _1489715] : [hAPP(hAPP(c_Product__Type_OSigma(_1489709, _1489711), _1489713), hAPP(c_COMBK(tc_fun(_1489711, tc_HOL_Obool), _1489709), _1489715)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489709, _1489711), tc_HOL_Obool)), -(_1489713 = c_Orderings_Obot__class_Obot(tc_fun(_1489709, tc_HOL_Obool))), -(_1489715 = c_Orderings_Obot__class_Obot(tc_fun(_1489711, tc_HOL_Obool)))], (19374 ^ _779203) ^ [_1120604, _1120606, _1120608] : [class_Rings_Olinordered__idom(_1120604), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120604), c_Groups_Ozero__class_Ozero(_1120604)), _1120606)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120604), hAPP(c_Groups_Oabs__class_Oabs(_1120604), _1120608)), _1120606) = hAPP(c_Groups_Oabs__class_Oabs(_1120604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120604), _1120608), _1120606)))], (31639 ^ _779203) ^ [_1347100, _1347102, _1347104] : [hBOOL(hAPP(hAPP(c_member(_1347100), _1347102), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1347100, tc_HOL_Obool), _1347104))), 31643 ^ _779203 : [(31646 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1347100, tc_HOL_Obool)), 31642 ^ [_1347100, _1347102, _1347104]), _1347104)))], (31644 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1347100), _1347102), 31642 ^ [_1347100, _1347102, _1347104])))]]], (22129 ^ _779203) ^ [_1169825, _1169827] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1169825), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1169827)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1169825)), _1169827))], (17004 ^ _779203) ^ [_1078643, _1078645, _1078647] : [class_Orderings_Olinorder(_1078643), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078643), _1078645)), -(hBOOL(hAPP(hAPP(c_member(_1078643), _1078647), _1078645))), -(_1078645 = c_Orderings_Obot__class_Obot(tc_fun(_1078643, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1078643, hAPP(hAPP(c_Set_Oinsert(_1078643), _1078647), _1078645)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1078643), _1078647), c_Big__Operators_Olinorder__class_OMax(_1078643, _1078645)))], (9275 ^ _779203) ^ [_937494, _937496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937494), _937496)), _937494))], (18494 ^ _779203) ^ [_1105382] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1105382)) = 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), _1105382)))], (24315 ^ _779203) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (43752 ^ _779203) ^ [_1654469, _1654471, _1654473] : [hBOOL(hAPP(c_List_Odistinct(_1654469), _1654473)), -(hBOOL(hAPP(c_List_Odistinct(_1654469), hAPP(c_List_Orotate(_1654469, _1654471), _1654473))))], (26392 ^ _779203) ^ [_1243261, _1243263] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1243261), _1243263) = 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), _1243261)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1243263)))))], (9243 ^ _779203) ^ [_936934, _936936] : [hAPP(c_Nat_OSuc, _936934) = hAPP(c_Nat_OSuc, _936936), -(_936934 = _936936)], (33313 ^ _779203) ^ [_1389235, _1389237, _1389239, _1389241, _1389243, _1389245] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389235, _1389237), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1389239), _1389241))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389235, _1389237), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1389243), _1389245))), -(_1389237 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1389241 = _1389245)], (48909 ^ _779203) ^ [_1766945, _1766947, _1766949, _1766951] : [c_Relation_Otrans(_1766945, _1766947), -(c_Relation_Otrans(_1766949, hAPP(hAPP(c_Relation_Oinv__image(_1766945, _1766949), _1766947), _1766951)))], (28082 ^ _779203) ^ [_1275098, _1275100, _1275102] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1275098), _1275100)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275098, tc_HOL_Obool)), _1275100), _1275102) = hAPP(hAPP(c_Finite__Set_Ofold(_1275098, tc_fun(_1275098, tc_HOL_Obool), c_Set_Oinsert(_1275098)), _1275102), _1275100))], (9177 ^ _779203) ^ [_935726, _935728, _935730] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935726), _935728) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935730), _935728), -(_935726 = _935730)], (30680 ^ _779203) ^ [_1327369] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1327369, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1327369, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1327369, tc_HOL_Obool)))], (48485 ^ _779203) ^ [_1757171, _1757173, _1757175, _1757177] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757171), hAPP(hAPP(c_List_Olist_OCons(_1757171), _1757173), _1757175)), _1757177)), -(_1757173 = _1757177), -(hBOOL(hAPP(hAPP(c_List_Omember(_1757171), _1757175), _1757177)))], (38897 ^ _779203) ^ [_1532928, _1532930, _1532932, _1532934] : [c_Relation_Orefl__on(_1532928, _1532930, _1532932), hBOOL(hAPP(hAPP(c_member(_1532928), _1532934), _1532930)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532928, _1532928)), hAPP(hAPP(c_Product__Type_OPair(_1532928, _1532928), _1532934), _1532934)), _1532932)))], (31919 ^ _779203) ^ [_1354015, _1354017, _1354019, _1354021, _1354023] : [class_Rings_Osemiring__0(_1354015), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354015), _1354017), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354019, _1354015), _1354021), _1354023)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354019, _1354015), hAPP(hAPP(c_COMBB(_1354015, _1354015, _1354019), hAPP(c_Groups_Otimes__class_Otimes(_1354015), _1354017)), _1354021)), _1354023))], (29804 ^ _779203) ^ [_1309052, _1309054] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1309052), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1309052, tc_HOL_Obool), _1309054))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1309052, tc_HOL_Obool)), _1309054)))], (7285 ^ _779203) ^ [_900020, _900022, _900024] : [class_Orderings_Olinorder(_900020), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900020), _900022), _900024))), -(_900022 = _900024), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900020), _900024), _900022)))], (46040 ^ _779203) ^ [_1705786, _1705788, _1705790, _1705792, _1705794] : [class_Orderings_Olinorder(_1705786), hBOOL(hAPP(hAPP(c_member(_1705788), _1705790), hAPP(c_List_Oset(_1705788), _1705792))), c_List_Olinorder__class_Osorted(_1705786, hAPP(hAPP(c_List_Omap(_1705788, _1705786), _1705794), _1705792)), hAPP(c_List_Ohd(_1705788), hAPP(c_List_Ofilter(_1705788, hAPP(hAPP(c_COMBB(_1705786, tc_HOL_Obool, _1705788), hAPP(c_fequal, hAPP(_1705794, _1705790))), _1705794)), _1705792)) = _1705790, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1705788, _1705786, _1705794), _1705790), c_List_Oremove1(_1705788, _1705790, _1705792)) = _1705792)], (6929 ^ _779203) ^ [_892507, _892509, _892511, _892513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892507, tc_HOL_Obool)), _892509), _892511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_892507, tc_HOL_Obool)), _892511), _892513)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892507, tc_HOL_Obool)), _892511), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892507, tc_HOL_Obool)), _892513), _892509)) = _892509)], (3352 ^ _779203) ^ [_829167, _829169, _829171, _829173, _829175, _829177] : [-(c_Enum_On__lists(_829177, _829173, _829169) = c_Enum_On__lists(_829175, _829171, _829167)), _829177 = _829175, _829173 = _829171, _829169 = _829167], (7431 ^ _779203) ^ [_902061, _902063, _902065, _902067] : [class_Orderings_Oord(_902061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902061), _902063), _902065)), _902065 = _902067, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902061), _902063), _902067)))], (21155 ^ _779203) ^ [_1152290, _1152292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1152290)), c_Int_OBit1(_1152292))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152290), _1152292)))], (49270 ^ _779203) ^ [_1775630, _1775632, _1775634, _1775636] : [c_Relation_Osym(_1775630, _1775632), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775630, _1775630)), hAPP(hAPP(c_Product__Type_OPair(_1775630, _1775630), _1775634), _1775636)), _1775632)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775630, _1775630)), hAPP(hAPP(c_Product__Type_OPair(_1775630, _1775630), _1775636), _1775634)), _1775632)))], (31715 ^ _779203) ^ [_1348800, _1348802, _1348804] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1348800), _1348802), _1348804) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1348800), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1348800, tc_Int_Oint), _1348802), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1348804))), class_Groups_Ocomm__monoid__add(_1348800), class_Groups_Ocomm__monoid__mult(_1348800)], (34296 ^ _779203) ^ [_1409118, _1409120, _1409122, _1409124] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1409122), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409118, tc_fun(_1409122, tc_HOL_Obool)), _1409120), _1409124)))), 34297 ^ _779203 : [(34298 ^ _779203) ^ [_1409192] : [hBOOL(hAPP(hAPP(c_member(_1409118), _1409192), _1409120)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1409122), hAPP(_1409124, _1409192)))]]], (12563 ^ _779203) ^ [_995875, _995877, _995879, _995881] : [class_Groups_Oordered__comm__monoid__add(_995875), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995875), c_Groups_Ozero__class_Ozero(_995875)), _995877)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995875), _995879), _995881)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995875), _995879), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995875), _995877), _995881))))], (42612 ^ _779203) ^ [_1628876] : [-(c_List_Obutlast(_1628876, c_List_Olist_ONil(_1628876)) = c_List_Olist_ONil(_1628876))], (30193 ^ _779203) ^ [_1317548, _1317550, _1317552, _1317554, _1317556, _1317558, _1317560, _1317562] : [c_Finite__Set_Ofolding__image__simple(_1317548, _1317550, _1317552, _1317554, _1317556, _1317558), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317550), _1317560)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317550), _1317562)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1317550, tc_HOL_Obool)), _1317560), _1317562) = c_Orderings_Obot__class_Obot(tc_fun(_1317550, tc_HOL_Obool)), -(hAPP(_1317558, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317550, tc_HOL_Obool)), _1317560), _1317562)) = hAPP(hAPP(_1317552, hAPP(_1317558, _1317560)), hAPP(_1317558, _1317562)))], (20626 ^ _779203) ^ [_1142999] : [-(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, _1142999)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (41854 ^ _779203) ^ [_1609493, _1609495, _1609497, _1609499] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1609493), tc_List_Olist(_1609493))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1609493), tc_List_Olist(_1609493)), _1609495), _1609497)), c_List_Olexord(_1609493, _1609499))), 41859 ^ _779203 : [(41862 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1609493), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609493)), _1609495)), _1609497) = _1609495)], (41860 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609493)), _1609495)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609493)), _1609497))))]], 41864 ^ _779203 : [(41869 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609493, _1609493)), hAPP(hAPP(c_Product__Type_OPair(_1609493, _1609493), hAPP(hAPP(c_List_Onth(_1609493), _1609495), 41863 ^ [_1609493, _1609495, _1609497, _1609499])), hAPP(hAPP(c_List_Onth(_1609493), _1609497), 41863 ^ [_1609493, _1609495, _1609497, _1609499]))), _1609499)))], (41867 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1609493), 41863 ^ [_1609493, _1609495, _1609497, _1609499]), _1609495) = hAPP(hAPP(c_List_Otake(_1609493), 41863 ^ [_1609493, _1609495, _1609497, _1609499]), _1609497))], (41865 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41863 ^ [_1609493, _1609495, _1609497, _1609499]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609493)), _1609495)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1609493)), _1609497)))))]]], (43548 ^ _779203) ^ [_1649859, _1649861, _1649863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649859)), _1649863)), _1649861)), -(hAPP(hAPP(c_List_Odrop(_1649859), _1649861), _1649863) = c_List_Olist_ONil(_1649859))], (644 ^ _779203) ^ [_788889, _788891, _788893, _788895] : [-(c_List_Olinorder__class_Osorted(_788893, _788889)), c_List_Olinorder__class_Osorted(_788895, _788891), _788895 = _788893, _788891 = _788889], (40715 ^ _779203) ^ [_1577445, _1577447, _1577449, _1577451, _1577453] : [-(hAPP(c_Relation_Oconverse(_1577445, _1577447), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577449, tc_fun(tc_prod(_1577445, _1577447), tc_HOL_Obool)), _1577451), _1577453)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1577449, tc_fun(tc_prod(_1577447, _1577445), tc_HOL_Obool)), _1577451), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1577445, _1577447), tc_HOL_Obool), tc_fun(tc_prod(_1577447, _1577445), tc_HOL_Obool), _1577449), c_Relation_Oconverse(_1577445, _1577447)), _1577453)))], (24500 ^ _779203) ^ [_1210775, _1210777] : [class_Rings_Olinordered__idom(_1210775), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210775), c_Groups_Ozero__class_Ozero(_1210775)), hAPP(hAPP(c_Power_Opower__class_Opower(_1210775), _1210777), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (52331 ^ _779203) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (5707 ^ _779203) ^ [_869311, _869313, _869315, _869317] : [5708 ^ _779203 : [(5711 ^ _779203) ^ [] : [_869313 = _869317], (5709 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_869311), _869313), _869315))]], -(hBOOL(hAPP(hAPP(c_member(_869311), _869313), hAPP(hAPP(c_Set_Oinsert(_869311), _869317), _869315))))], (43504 ^ _779203) ^ [_1648901, _1648903, _1648905] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648901)), hAPP(hAPP(c_List_Odrop(_1648901), _1648903), _1648905)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648901)), _1648905)), _1648903))], (4228 ^ _779203) ^ [_843161, _843163, _843165, _843167, _843169, _843171] : [-(c_List_Oreplicate(_843171, _843167, _843163) = c_List_Oreplicate(_843169, _843165, _843161)), _843171 = _843169, _843167 = _843165, _843163 = _843161], (40697 ^ _779203) ^ [_1577083, _1577085, _1577087, _1577089, _1577091] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1577083, _1577085)), hAPP(hAPP(c_Product__Type_OPair(_1577083, _1577085), _1577087), _1577089)), hAPP(c_Relation_Oconverse(_1577085, _1577083), _1577091))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577085, _1577083)), hAPP(hAPP(c_Product__Type_OPair(_1577085, _1577083), _1577089), _1577087)), _1577091)))], (23778 ^ _779203) ^ [_1197610, _1197612, _1197614] : [-(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), _1197610), _1197612)), _1197614), _1197612) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197614, _1197612))], (48080 ^ _779203) ^ [_1748450, _1748452, _1748454, _1748456] : [-(c_Predicate_Oconversep(_1748450, _1748452, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1748450, tc_fun(_1748452, tc_HOL_Obool))), _1748454), _1748456)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1748452, tc_fun(_1748450, tc_HOL_Obool))), c_Predicate_Oconversep(_1748450, _1748452, _1748454)), c_Predicate_Oconversep(_1748450, _1748452, _1748456)))], (10595 ^ _779203) ^ [_962578, _962580, _962582, _962584] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_962578), _962580)), hBOOL(hAPP(c_Finite__Set_Ofinite(_962582), _962584)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_962578, _962582)), c_Sum__Type_OPlus(_962578, _962582, _962580, _962584)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_962578), _962580)), hAPP(c_Finite__Set_Ocard(_962582), _962584)))], (42100 ^ _779203) ^ [_1617153, _1617155, _1617157, _1617159] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1617153, _1617155))), hAPP(hAPP(c_List_Ozip(_1617153, _1617155), _1617157), _1617159)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617153)), _1617157)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617155)), _1617159)))], (25610 ^ _779203) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (46684 ^ _779203) ^ [_1717950, _1717952, _1717954, _1717956, _1717958] : [-(hAPP(c_List_Ofoldl(_1717950, _1717952, _1717954, _1717956), _1717958) = c_List_Ofoldr(_1717952, _1717950, hAPP(c_COMBC(_1717950, _1717952, _1717950), _1717954), hAPP(c_List_Orev(_1717952), _1717958), _1717956))], (49965 ^ _779203) ^ [_1789775, _1789777, _1789779, _1789781, _1789783, _1789785] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1789775, _1789777, _1789779, _1789781), _1789783), _1789785) = hAPP(_1789781, hAPP(hAPP(c_Product__Type_OPair(_1789775, _1789777), _1789783), _1789785)))], (2622 ^ _779203) ^ [_817832, _817834] : [_817834 = _817832, -(c_Int_Oint__ge__less__than2(_817834) = c_Int_Oint__ge__less__than2(_817832))], (3680 ^ _779203) ^ [_834331, _834333, _834335, _834337] : [-(c_List_Olex(_834337, _834333) = c_List_Olex(_834335, _834331)), _834337 = _834335, _834333 = _834331], (29608 ^ _779203) ^ [_1304569, _1304571, _1304573, _1304575] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304569, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304569, tc_HOL_Obool)), _1304571), _1304573)), _1304575) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304569, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304569, tc_HOL_Obool)), _1304571), _1304575)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304569, tc_HOL_Obool)), _1304573), _1304575)))], (39131 ^ _779203) ^ [_1538444, _1538446] : [c_Wellfounded_Owf(_1538444, _1538446), -(c_Wellfounded_OwfP(_1538444, hAPP(hAPP(c_COMBC(_1538444, tc_fun(tc_prod(_1538444, _1538444), tc_HOL_Obool), tc_fun(_1538444, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538444, tc_fun(tc_fun(tc_prod(_1538444, _1538444), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1538444, _1538444), tc_HOL_Obool), tc_fun(_1538444, tc_HOL_Obool)), _1538444), c_COMBC(_1538444, tc_fun(tc_prod(_1538444, _1538444), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538444, tc_prod(_1538444, _1538444)), tc_fun(_1538444, tc_fun(tc_fun(tc_prod(_1538444, _1538444), tc_HOL_Obool), tc_HOL_Obool)), _1538444), hAPP(c_COMBB(tc_prod(_1538444, _1538444), tc_fun(tc_fun(tc_prod(_1538444, _1538444), tc_HOL_Obool), tc_HOL_Obool), _1538444), c_member(tc_prod(_1538444, _1538444)))), c_Product__Type_OPair(_1538444, _1538444)))), _1538446)))], (38108 ^ _779203) ^ [_1509733, _1509735, _1509737] : [class_Lattices_Odistrib__lattice(_1509733), hBOOL(hAPP(c_Finite__Set_Ofinite(_1509733), _1509735)), -(_1509735 = c_Orderings_Obot__class_Obot(tc_fun(_1509733, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1509733), _1509737), c_Big__Operators_Olattice__class_OInf__fin(_1509733, _1509735)) = c_Big__Operators_Olattice__class_OInf__fin(_1509733, hAPP(c_Set_OCollect(_1509733), hAPP(hAPP(c_COMBB(tc_fun(_1509733, tc_HOL_Obool), tc_HOL_Obool, _1509733), c_HOL_OEx(_1509733)), hAPP(hAPP(c_COMBC(_1509733, tc_fun(_1509733, tc_HOL_Obool), tc_fun(_1509733, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509733, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1509733, tc_HOL_Obool), tc_fun(_1509733, tc_HOL_Obool)), _1509733), c_COMBS(_1509733, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509733, tc_HOL_Obool), tc_fun(_1509733, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1509733), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1509733), c_fconj)), hAPP(hAPP(c_COMBC(_1509733, tc_fun(_1509733, _1509733), tc_fun(_1509733, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1509733, tc_HOL_Obool), tc_fun(tc_fun(_1509733, _1509733), tc_fun(_1509733, tc_HOL_Obool)), _1509733), c_COMBB(_1509733, tc_HOL_Obool, _1509733)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1509733), _1509737))))), hAPP(hAPP(c_COMBC(_1509733, tc_fun(_1509733, tc_HOL_Obool), tc_HOL_Obool), c_member(_1509733)), _1509735))))))], (38050 ^ _779203) ^ [_1507021, _1507023, _1507025, _1507027] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1507021), hAPP(c_Set_OCollect(_1507021), _1507023))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1507025), hAPP(c_Set_OCollect(_1507025), hAPP(hAPP(c_COMBB(tc_fun(_1507021, tc_HOL_Obool), tc_HOL_Obool, _1507025), c_HOL_OEx(_1507021)), hAPP(hAPP(c_COMBC(_1507025, tc_fun(_1507021, tc_HOL_Obool), tc_fun(_1507021, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507021, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1507021, tc_HOL_Obool), tc_fun(_1507021, tc_HOL_Obool)), _1507025), c_COMBS(_1507021, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507021, tc_HOL_Obool), tc_fun(_1507021, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1507025), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1507021), c_fconj)), hAPP(hAPP(c_COMBC(_1507025, tc_fun(_1507021, _1507025), tc_fun(_1507021, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1507025, tc_HOL_Obool), tc_fun(tc_fun(_1507021, _1507025), tc_fun(_1507021, tc_HOL_Obool)), _1507025), c_COMBB(_1507025, tc_HOL_Obool, _1507021)), c_fequal)), _1507027)))), _1507023))))))], (6316 ^ _779203) ^ [_880842, _880844, _880846, _880848, _880850] : [class_Orderings_Oord(_880842), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880844, _880842)), _880846), _880848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880842), hAPP(_880846, _880850)), hAPP(_880848, _880850))))], (7951 ^ _779203) ^ [_910133] : [-(c_Finite__Set_Ofun__left__comm__idem(_910133, tc_fun(_910133, tc_HOL_Obool), c_Set_Oinsert(_910133)))], (20618 ^ _779203) ^ [_1142827, _1142829] : [class_Int_Onumber__ring(_1142827), -(hAPP(c_Int_Onumber__class_Onumber__of(_1142827), c_Int_Opred(_1142829)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142827), hAPP(c_Groups_Ouminus__class_Ouminus(_1142827), c_Groups_Oone__class_Oone(_1142827))), hAPP(c_Int_Onumber__class_Onumber__of(_1142827), _1142829)))], (10419 ^ _779203) ^ [_958859, _958861, _958863, _958865, _958867] : [class_Rings_Ocomm__semiring__1(_958859), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958859), _958861), _958863)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958859), _958865), _958867)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958859), _958865), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958859), _958861), _958863)), _958867)))], (46967 ^ _779203) ^ [_1724002, _1724004, _1724006] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724002)), c_List_OdropWhile(_1724002, _1724004, _1724006))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724002)), _1724006))))], (45418 ^ _779203) ^ [_1690779, _1690781, _1690783, _1690785] : [-(_1690779 = _1690781), -(hAPP(c_List_OremoveAll(_1690783, _1690779), hAPP(hAPP(c_List_Olist_OCons(_1690783), _1690781), _1690785)) = hAPP(hAPP(c_List_Olist_OCons(_1690783), _1690781), hAPP(c_List_OremoveAll(_1690783, _1690779), _1690785)))], (45857 ^ _779203) ^ [_1702167, _1702169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702167), _1702169)), -(c_List_Oupt(_1702167, hAPP(c_Nat_OSuc, _1702169)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1702167, _1702169)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702169), c_List_Olist_ONil(tc_Nat_Onat))))], (21031 ^ _779203) ^ [_1149936, _1149938] : [class_Int_Onumber__ring(_1149936), 21034 ^ _779203 : [(21041 ^ _779203) ^ [] : [c_Int_Oiszero(_1149936, hAPP(c_Int_Onumber__class_Onumber__of(_1149936), 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), _1149938)))), -(c_Groups_Oone__class_Oone(_1149936) = hAPP(c_Int_Onumber__class_Onumber__of(_1149936), _1149938))], (21035 ^ _779203) ^ [] : [c_Groups_Oone__class_Oone(_1149936) = hAPP(c_Int_Onumber__class_Onumber__of(_1149936), _1149938), -(c_Int_Oiszero(_1149936, hAPP(c_Int_Onumber__class_Onumber__of(_1149936), 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), _1149938)))))]]], (39076 ^ _779203) ^ [_1537312, _1537314] : [c_Wellfounded_OwfP(_1537312, _1537314), -(c_Wellfounded_Owf(_1537312, hAPP(c_Set_OCollect(tc_prod(_1537312, _1537312)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537312, _1537312, tc_HOL_Obool), _1537314))))], (28518 ^ _779203) ^ [_1283546] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1283546), c_Orderings_Otop__class_Otop(tc_fun(_1283546, 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(_1283546), c_Orderings_Otop__class_Otop(tc_fun(_1283546, tc_HOL_Obool))))))], (21641 ^ _779203) ^ [_1160151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1160151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1160151))))], (9785 ^ _779203) ^ [_946249, _946251] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946249), _946251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _946249)), hAPP(c_Nat_OSuc, _946251))))], (44861 ^ _779203) ^ [_1678028] : [-(_1678028 = 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, _1678028)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1678028))))], (37122 ^ _779203) ^ [_1479785, _1479787, _1479789, _1479791, _1479793] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1479785, _1479787, _1479789), _1479791), _1479793) = c_HOL_OThe(_1479787, c_Finite__Set_Ofold__graph(_1479785, _1479787, _1479789, _1479791, _1479793)))], (45103 ^ _779203) ^ [_1684093, _1684095, _1684097, _1684099, _1684101, _1684103, _1684105] : [c_List_Olist__all2(_1684093, _1684095, _1684097, hAPP(hAPP(c_List_Olist_OCons(_1684093), _1684099), _1684101), hAPP(hAPP(c_List_Olist_OCons(_1684095), _1684103), _1684105)), 45106 ^ _779203 : [(45109 ^ _779203) ^ [] : [-(c_List_Olist__all2(_1684093, _1684095, _1684097, _1684101, _1684105))], (45107 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1684097, _1684099), _1684103)))]]], (14323 ^ _779203) ^ [_1028307, _1028309, _1028311, _1028313, _1028315] : [class_Fields_Olinordered__field(_1028307), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028307), c_Groups_Ozero__class_Ozero(_1028307)), _1028309)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028307), _1028309), _1028311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028307), c_Groups_Ozero__class_Ozero(_1028307)), _1028313)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1028307), _1028313), _1028315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1028307), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1028307), _1028309), _1028315)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1028307), _1028311), _1028313))))], (8388 ^ _779203) ^ [_919345, _919347, _919349, _919351, _919353, _919355, _919357] : [c_Finite__Set_Ofun__left__comm(_919345, _919347, _919349), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_919345, _919347, _919349, _919351, _919353), _919355)), hBOOL(hAPP(hAPP(c_member(_919345), _919357), _919353)), 8400 ^ _779203 : [(8403 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_919345, _919347, _919349, _919351, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919345, tc_HOL_Obool)), _919353), hAPP(hAPP(c_Set_Oinsert(_919345), _919357), c_Orderings_Obot__class_Obot(tc_fun(_919345, tc_HOL_Obool))))), 8399 ^ [_919345, _919347, _919349, _919351, _919353, _919355, _919357])))], (8401 ^ _779203) ^ [] : [-(_919355 = hAPP(hAPP(_919349, _919357), 8399 ^ [_919345, _919347, _919349, _919351, _919353, _919355, _919357]))]]], (35468 ^ _779203) ^ [_1442142, _1442144, _1442146, _1442148, _1442150] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1442142, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442144, _1442142, _1442146), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442144, tc_HOL_Obool)), _1442148), _1442150))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442142, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442144, _1442142, _1442146), _1442148)), hAPP(c_Relation_OImage(_1442144, _1442142, _1442146), _1442150)))))], (31931 ^ _779203) ^ [_1354451, _1354453, _1354455, _1354457] : [class_Groups_Oab__group__add(_1354451), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354453, _1354451), hAPP(hAPP(c_COMBB(_1354451, _1354451, _1354453), c_Groups_Ouminus__class_Ouminus(_1354451)), _1354455)), _1354457) = hAPP(c_Groups_Ouminus__class_Ouminus(_1354451), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354453, _1354451), _1354455), _1354457)))], (43872 ^ _779203) ^ [_1657015] : [class_Groups_Omonoid__add(_1657015), -(c_List_Omonoid__add__class_Olistsum(_1657015) = c_List_Ofoldl(_1657015, _1657015, c_Groups_Oplus__class_Oplus(_1657015), c_Groups_Ozero__class_Ozero(_1657015)))], (37501 ^ _779203) ^ [_1489194, _1489196, _1489198, _1489200] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1489194, _1489196), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1489194, tc_HOL_Obool), _1489198)), _1489200) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1489194, tc_HOL_Obool), tc_fun(tc_prod(_1489194, _1489196), tc_HOL_Obool)), _1489198), hAPP(hAPP(c_COMBC(tc_fun(_1489194, tc_HOL_Obool), tc_fun(_1489194, tc_fun(_1489196, tc_HOL_Obool)), tc_fun(tc_prod(_1489194, _1489196), tc_HOL_Obool)), c_Product__Type_OSigma(_1489194, _1489196)), _1489200)))], (9655 ^ _779203) ^ [_944144, _944146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944144), _944146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _944144)), hAPP(c_Nat_OSuc, _944146))))], (48098 ^ _779203) ^ [_1748833, _1748835, _1748837, _1748839, _1748841] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748833, _1748835, _1748837), _1748839), _1748841)), -(hBOOL(hAPP(hAPP(_1748837, _1748841), _1748839)))], (39226 ^ _779203) ^ [_1540329, _1540331, _1540333] : [c_Relation_Orefl__on(_1540329, _1540331, _1540333), 39229 ^ _779203 : [(39236 ^ _779203) ^ [_1540813] : [hBOOL(hAPP(hAPP(c_member(_1540329), _1540813), _1540331)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540329, _1540329)), hAPP(hAPP(c_Product__Type_OPair(_1540329, _1540329), _1540813), _1540813)), _1540333)))], (39230 ^ _779203) ^ [_1540540] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540329, _1540329)), _1540540), _1540333)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1540329, _1540329, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1540329, tc_fun(_1540329, tc_HOL_Obool), tc_fun(_1540329, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1540329, tc_HOL_Obool), tc_fun(_1540329, tc_HOL_Obool)), _1540329), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1540329)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540329), c_fconj), hAPP(hAPP(c_COMBC(_1540329, tc_fun(_1540329, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540329)), _1540331)))), hAPP(hAPP(c_COMBC(_1540329, tc_fun(_1540329, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540329)), _1540331))), _1540540)))]]], (22407 ^ _779203) ^ [_1174500] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1174500)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1174500))], (10317 ^ _779203) ^ [_956672, _956674] : [class_Rings_Ocomm__semiring__1(_956672), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956672), _956674), _956674) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_956672), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_956672), c_Groups_Oone__class_Oone(_956672)), c_Groups_Oone__class_Oone(_956672))), _956674))], (36668 ^ _779203) ^ [_1469502, _1469504, _1469506, _1469508, _1469510] : [c_Fun_Oinj__on(_1469502, _1469504, _1469506, hAPP(hAPP(c_Set_Oinsert(_1469502), _1469508), _1469510)), 36671 ^ _779203 : [(36674 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1469504), hAPP(_1469506, _1469508)), hAPP(c_Set_Oimage(_1469502, _1469504, _1469506), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469502, tc_HOL_Obool)), _1469510), hAPP(hAPP(c_Set_Oinsert(_1469502), _1469508), c_Orderings_Obot__class_Obot(tc_fun(_1469502, tc_HOL_Obool)))))))], (36672 ^ _779203) ^ [] : [-(c_Fun_Oinj__on(_1469502, _1469504, _1469506, _1469510))]]], (39347 ^ _779203) ^ [_1544161, _1544163] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1544161, tc_HOL_Obool), _1544163) = hAPP(c_Set_OCollect(_1544161), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1544161, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1544161), c_HOL_OAll(tc_fun(_1544161, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1544161, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1544161, tc_HOL_Obool), tc_HOL_Obool), _1544161), hAPP(c_COMBS(tc_fun(_1544161, 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(_1544161, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1544161, tc_HOL_Obool), tc_fun(tc_fun(_1544161, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1544161, tc_HOL_Obool))), _1544163)))), c_member(_1544161)))))], (34391 ^ _779203) ^ [_1412362, _1412364, _1412366, _1412368] : [34393 ^ _779203 : [(34396 ^ _779203) ^ [] : [hAPP(_1412368, 34392 ^ [_1412362, _1412364, _1412366, _1412368]) = c_Orderings_Obot__class_Obot(tc_fun(_1412364, tc_HOL_Obool))], (34394 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1412362), 34392 ^ [_1412362, _1412364, _1412366, _1412368]), _1412366)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412362, tc_fun(_1412364, tc_HOL_Obool)), _1412366), _1412368) = c_Orderings_Obot__class_Obot(tc_fun(_1412364, tc_HOL_Obool)))], (35211 ^ _779203) ^ [_1435179, _1435181, _1435183, _1435185, _1435187] : [35213 ^ _779203 : [(35216 ^ _779203) ^ [] : [hBOOL(hAPP(_1435187, 35212 ^ [_1435179, _1435181, _1435183, _1435185, _1435187]))], (35214 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1435179), 35212 ^ [_1435179, _1435181, _1435183, _1435185, _1435187]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1435181, tc_fun(_1435179, tc_HOL_Obool)), _1435183), _1435185))))]], 35217 ^ _779203 : [(35218 ^ _779203) ^ [_1435401] : [hBOOL(hAPP(hAPP(c_member(_1435181), _1435401), _1435183)), 35221 ^ _779203 : [(35222 ^ _779203) ^ [_1435498] : [hBOOL(hAPP(hAPP(c_member(_1435179), _1435498), hAPP(_1435185, _1435401))), -(hBOOL(hAPP(_1435187, _1435498)))]]]]], (4868 ^ _779203) ^ [_853321, _853323, _853325, _853327] : [-(c_Quickcheck_Obeyond(_853327, _853323) = c_Quickcheck_Obeyond(_853325, _853321)), _853327 = _853325, _853323 = _853321], (17332 ^ _779203) ^ [_1084775, _1084777, _1084779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084775), _1084777)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084777), _1084779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084775), _1084779)))], (40819 ^ _779203) ^ [_1579990, _1579992, _1579994, _1579996, _1579998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579992, tc_HOL_Obool)), _1579996), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579992, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579990, _1579992, hAPP(c_Relation_Oconverse(_1579992, _1579990), _1579994)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1579990, tc_HOL_Obool)), _1579998))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1579990, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1579992, _1579990, _1579994), _1579996)), _1579998)))], (49282 ^ _779203) ^ [_1775888, _1775890] : [c_Relation_Osym(_1775888, _1775890), -(c_Relation_Osym(_1775888, c_Transitive__Closure_Ortrancl(_1775888, _1775890)))], (50879 ^ _779203) ^ [_1809724, _1809726] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809726, _1809724) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809724), _1809726)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809726), _1809724)))], (5913 ^ _779203) ^ [_872971, _872973] : [-(_872973 = c_Orderings_Obot__class_Obot(tc_fun(_872971, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_872971), 5916 ^ [_872971, _872973]), _872973)))], (46905 ^ _779203) ^ [_1722636, _1722638] : [-(_1722636 = c_List_Olist_ONil(_1722638)), hBOOL(hAPP(c_List_Odistinct(_1722638), _1722636)), -(c_List_OtakeWhile(_1722638, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1722638), c_fNot), hAPP(hAPP(c_COMBC(_1722638, _1722638, tc_HOL_Obool), c_fequal), c_List_Olast(_1722638, _1722636))), _1722636) = c_List_Obutlast(_1722638, _1722636))], (5442 ^ _779203) ^ [_862460, _862462] : [_862462 = _862460, -(c_Power_Opower__class_Opower(_862462) = c_Power_Opower__class_Opower(_862460))], (546 ^ _779203) ^ [_787336, _787338, _787340, _787342, _787344, _787346] : [-(c_Finite__Set_Ofun__left__comm__idem(_787344, _787340, _787336)), c_Finite__Set_Ofun__left__comm__idem(_787346, _787342, _787338), _787346 = _787344, _787342 = _787340, _787338 = _787336], (6300 ^ _779203) ^ [_880560, _880562, _880564] : [class_Orderings_Obot(_880560), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_880562, _880560)), _880564) = c_Orderings_Obot__class_Obot(_880560))], (50045 ^ _779203) ^ [_1791513, _1791515, _1791517, _1791519, _1791521] : [c_Fun_Obij__betw(_1791513, _1791515, _1791517, _1791519, _1791521), 50048 ^ _779203 : [(50051 ^ _779203) ^ [] : [-(hAPP(c_Set_Oimage(_1791513, _1791515, _1791517), _1791519) = _1791521)], (50049 ^ _779203) ^ [] : [-(c_Fun_Oinj__on(_1791513, _1791515, _1791517, _1791519))]]], (6445 ^ _779203) ^ [_883233, _883235, _883237] : [class_Orderings_Opreorder(_883233), _883235 = _883237, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883233), _883235), _883237)))], (10301 ^ _779203) ^ [_956336, _956338, _956340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956336), _956338)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956340), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956338), _956336))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _956340), _956336)), hAPP(c_Nat_OSuc, _956338)))], (5268 ^ _779203) ^ [_859705, _859707, _859709, _859711, _859713, _859715, _859717, _859719] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_859719, _859715, _859711, _859707) = c_SetInterval_Oord_OgreaterThanLessThan(_859717, _859713, _859709, _859705)), _859719 = _859717, _859715 = _859713, _859711 = _859709, _859707 = _859705], (45762 ^ _779203) ^ [_1698889, _1698891, _1698893] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1698889, tc_HOL_Obool)), hAPP(c_List_Oset(_1698889), _1698891)), hAPP(hAPP(c_Set_Oinsert(_1698889), _1698893), c_Orderings_Obot__class_Obot(tc_fun(_1698889, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1698889), hAPP(c_List_Ofilter(_1698889, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1698889), c_fNot), hAPP(hAPP(c_COMBC(_1698889, _1698889, tc_HOL_Obool), c_fequal), _1698893))), _1698891)))], (15009 ^ _779203) ^ [_1041502] : [class_Rings_Oring__1(_1041502), -(hBOOL(hAPP(hAPP(c_member(_1041502), c_Groups_Oone__class_Oone(_1041502)), c_Int_Oring__1__class_OInts(_1041502))))], (8637 ^ _779203) ^ [_924767, _924769, _924771, _924773] : [class_Groups_Ocancel__semigroup__add(_924767), 8640 ^ _779203 : [(8647 ^ _779203) ^ [] : [_924771 = _924773, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924767), _924769), _924771) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924767), _924769), _924773))], (8641 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924767), _924769), _924771) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924767), _924769), _924773), -(_924771 = _924773)]]], (52459 ^ _779203) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (20118 ^ _779203) ^ [_1134149, _1134151] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1134149), _1134151)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1134149)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1134151)))], (36181 ^ _779203) ^ [] : [-(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))], (24810 ^ _779203) ^ [_1216437, _1216439, _1216441] : [class_Rings_Olinordered__semidom(_1216437), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216437), c_Groups_Oone__class_Oone(_1216437)), _1216439)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1216441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1216437), c_Groups_Oone__class_Oone(_1216437)), hAPP(hAPP(c_Power_Opower__class_Opower(_1216437), _1216439), _1216441))))], (29512 ^ _779203) ^ [_1302829, _1302831, _1302833] : [class_Lattices_Osemilattice__inf(_1302829), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302829), _1302831), _1302833)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1302829), _1302831), _1302833) = _1302831)], (12204 ^ _779203) ^ [_989968, _989970] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _989968), _989970), 12209 ^ _779203 : [(12212 ^ _779203) ^ [] : [-(_989970 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12210 ^ _779203) ^ [] : [-(_989968 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 12213 ^ _779203 : [(12216 ^ _779203) ^ [] : [-(_989970 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12214 ^ _779203) ^ [] : [-(_989968 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (40951 ^ _779203) ^ [_1583224, _1583226, _1583228, _1583230] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583224, _1583224)), _1583226), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583224, _1583224), tc_HOL_Obool), _1583228), _1583230))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583224, _1583224)), _1583226), c_Transitive__Closure_Ortrancl(_1583224, _1583230))))], (25156 ^ _779203) ^ [_1222713, _1222715, _1222717, _1222719] : [class_Rings_Olinordered__semidom(_1222713), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222713), hAPP(hAPP(c_Power_Opower__class_Opower(_1222713), _1222715), hAPP(c_Nat_OSuc, _1222717))), hAPP(hAPP(c_Power_Opower__class_Opower(_1222713), _1222719), hAPP(c_Nat_OSuc, _1222717)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222713), c_Groups_Ozero__class_Ozero(_1222713)), _1222719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222713), _1222715), _1222719)))], (22856 ^ _779203) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23269 ^ _779203) ^ [] : [-(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)))))], (52443 ^ _779203) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (29188 ^ _779203) ^ [_1296050, _1296052, _1296054] : [class_Lattices_Olattice(_1296050), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1296050), _1296052), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1296050), _1296052), _1296054)) = _1296052)], (45145 ^ _779203) ^ [_1684914, _1684916, _1684918, _1684920] : [c_List_Olist__all2(_1684914, _1684916, _1684918, _1684920, c_List_Olist_ONil(_1684916)), -(_1684920 = c_List_Olist_ONil(_1684914))], (48166 ^ _779203) ^ [_1750808, _1750810, _1750812] : [-(hAPP(c_List_Orev(_1750808), c_List_Oreplicate(_1750808, _1750810, _1750812)) = c_List_Oreplicate(_1750808, _1750810, _1750812))], (6136 ^ _779203) ^ [_877234, _877236, _877238, _877240] : [_877240 = c_Orderings_Obot__class_Obot(tc_fun(_877236, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_877234, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_877236, _877234, _877238), _877240))], (10239 ^ _779203) ^ [_955162, _955164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955162), _955164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _955162)), _955164)))], (42780 ^ _779203) ^ [_1631771, _1631773] : [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(_1631771)), _1631773))), _1631773 = c_List_Olist_ONil(_1631771)], (9371 ^ _779203) ^ [_939015, _939017, _939019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _939015), _939017)), _939019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _939015), _939019)))], (18355 ^ _779203) ^ [_1103007, _1103009] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1103007)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1103009)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1103007), _1103009)))], (52313 ^ _779203) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (27940 ^ _779203) ^ [_1272328, _1272330] : [class_Lattices_Oboolean__algebra(_1272328), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1272328), _1272330), hAPP(c_Groups_Ouminus__class_Ouminus(_1272328), _1272330)) = c_Orderings_Otop__class_Otop(_1272328))], (24402 ^ _779203) ^ [_1209133, _1209135] : [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), _1209133)), _1209135))), _1209133 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1209135 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18746 ^ _779203) ^ [_1109593, _1109595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1109595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1109593, _1109595))))], (27090 ^ _779203) ^ [_1256221, _1256223, _1256225, _1256227, _1256229] : [class_Orderings_Olinorder(_1256221), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256221, _1256223), _1256225) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256221, _1256227), _1256229), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256221), _1256223), _1256225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256221), _1256227), _1256229)), -(_1256225 = _1256229)], (10905 ^ _779203) ^ [_967541, _967543] : [class_Rings_Ocomm__semiring__1(_967541), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967541), _967543), c_Groups_Ozero__class_Ozero(_967541)) = c_Groups_Ozero__class_Ozero(_967541))], (25804 ^ _779203) ^ [_1233156, _1233158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1233156), _1233158)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1233156), _1233158) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (2462 ^ _779203) ^ [_815330, _815332] : [_815332 = _815330, -(c_Nitpick_Oone__frac(_815332) = c_Nitpick_Oone__frac(_815330))], (18112 ^ _779203) ^ [_1098766, _1098768, _1098770] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098766), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098766)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098768)), _1098770)) = 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), _1098766), _1098768))), _1098770))], (15796 ^ _779203) ^ [_1056043, _1056045, _1056047, _1056049] : [class_Orderings_Olinorder(_1056043), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056043), _1056045), _1056047)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056043), _1056045), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1056043), _1056047), _1056049))))], (48891 ^ _779203) ^ [_1766633, _1766635, _1766637] : [c_Relation_Otrans(_1766633, _1766635), c_Relation_Otrans(_1766633, _1766637), -(c_Relation_Otrans(_1766633, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1766633, _1766633), tc_HOL_Obool)), _1766635), _1766637)))], (29690 ^ _779203) ^ [_1306206, _1306208, _1306210] : [class_Lattices_Oboolean__algebra(_1306206), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1306206), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1306206), _1306208), _1306210)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1306206), hAPP(c_Groups_Ouminus__class_Ouminus(_1306206), _1306208)), hAPP(c_Groups_Ouminus__class_Ouminus(_1306206), _1306210)))], (20030 ^ _779203) ^ [_1132329, _1132331, _1132333] : [class_Rings_Oring(_1132329), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1132329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132329), _1132331), _1132333)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132329), hAPP(c_Groups_Ouminus__class_Ouminus(_1132329), _1132331)), _1132333))], (45476 ^ _779203) ^ [_1691905, _1691907, _1691909] : [class_Orderings_Olinorder(_1691905), -(c_List_Olinorder__class_Osort__key(_1691907, _1691905, _1691909, c_List_Olist_ONil(_1691907)) = c_List_Olist_ONil(_1691907))], (50585 ^ _779203) ^ [_1804069, _1804071, _1804073] : [class_Rings_Odvd(_1804069), class_Rings_Osemiring__0(_1804069), 50592 ^ _779203 : [(50602 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1804071, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804069), _1804073), 50609 ^ [_1804069, _1804071, _1804073])))), 50603 ^ _779203 : [(50604 ^ _779203) ^ [_1804398] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804069), _1804073), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1804069), _1804398), c_Groups_Ozero__class_Ozero(_1804069)))), hBOOL(hAPP(_1804071, _1804398))]]], (50593 ^ _779203) ^ [] : [50594 ^ _779203 : [(50595 ^ _779203) ^ [_1804261] : [hBOOL(hAPP(_1804071, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1804069), _1804073), _1804261)))]], 50597 ^ _779203 : [(50600 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1804071, 50596 ^ [_1804069, _1804071, _1804073])))], (50598 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1804069), _1804073), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1804069), 50596 ^ [_1804069, _1804071, _1804073]), c_Groups_Ozero__class_Ozero(_1804069)))))]]]]], (39279 ^ _779203) ^ [_1541998, _1542000, _1542002] : [hBOOL(hAPP(hAPP(c_member(_1542000), _1541998), c_Orderings_Obot__class_Obot(tc_fun(_1542000, tc_HOL_Obool)))), -(hBOOL(hAPP(_1542002, _1541998)))], (2322 ^ _779203) ^ [_813148, _813150, _813152, _813154] : [-(c_Divides_Odivmod__int__rel(_813154, _813150) = c_Divides_Odivmod__int__rel(_813152, _813148)), _813154 = _813152, _813150 = _813148], (9560 ^ _779203) ^ [_942475, _942477] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _942475), _942477)), _942475 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _942477 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (9761 ^ _779203) ^ [_945862, _945864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945862), hAPP(c_Nat_OSuc, _945864))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945862), _945864))), -(_945862 = hAPP(c_Nat_OSuc, _945864))], (44968 ^ _779203) ^ [_1680830, _1680832, _1680834, _1680836] : [-(hBOOL(hAPP(c_List_Olistsp(_1680830, _1680832), hAPP(hAPP(c_List_Olist_OCons(_1680830), _1680834), _1680836)))), hBOOL(hAPP(_1680832, _1680834)), hBOOL(hAPP(c_List_Olistsp(_1680830, _1680832), _1680836))], (35296 ^ _779203) ^ [_1436963, _1436965] : [hAPP(c_Int_ORep__Integ, _1436963) = hAPP(c_Int_ORep__Integ, _1436965), -(_1436963 = _1436965)], (33057 ^ _779203) ^ [_1384816, _1384818] : [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), _1384816))), 33060 ^ _779203 : [(33067 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384818)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384816)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384818), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384816)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384816)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384818), 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), _1384816)))))], (33061 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384818)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384816))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384818), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384816)) = 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), _1384818)))]]], (34939 ^ _779203) ^ [_1428033, _1428035, _1428037] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428033, tc_HOL_Obool)), _1428035), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1428033, tc_HOL_Obool), _1428037)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1428033, tc_HOL_Obool), tc_fun(_1428033, tc_HOL_Obool)), _1428037), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428033, tc_HOL_Obool)), _1428035)))], (40470 ^ _779203) ^ [_1571577, _1571579, _1571581, _1571583, _1571585] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571577, _1571577)), hAPP(hAPP(c_Product__Type_OPair(_1571577, _1571577), _1571579), _1571581)), c_Transitive__Closure_Otrancl(_1571577, _1571583))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1571577, _1571577)), hAPP(hAPP(c_Product__Type_OPair(_1571577, _1571577), _1571581), _1571585)), c_Transitive__Closure_Ortrancl(_1571577, _1571583))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571577, _1571577)), hAPP(hAPP(c_Product__Type_OPair(_1571577, _1571577), _1571579), _1571585)), c_Transitive__Closure_Otrancl(_1571577, _1571583))))], (31689 ^ _779203) ^ [_1348100, _1348102, _1348104, _1348106, _1348108, _1348110] : [-(c_Nitpick_Opair__box_Opair__box__case(_1348100, _1348102, _1348104, _1348106, c_Nitpick_Opair__box_OPairBox(_1348100, _1348102, _1348108, _1348110)) = hAPP(hAPP(_1348106, _1348108), _1348110))], (9183 ^ _779203) ^ [_935825, _935827, _935829] : [_935825 = _935829, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935825), _935827) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935829), _935827))], (52283 ^ _779203) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (39764 ^ _779203) ^ [_1554017, _1554019, _1554021, _1554023, _1554025, _1554027] : [c_Finite__Set_Ofolding(_1554017, _1554019, _1554021, _1554023), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554017), _1554025)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554017), _1554027)), -(hAPP(c_Fun_Ocomp(_1554019, _1554019, _1554019, hAPP(_1554023, _1554027)), hAPP(_1554023, _1554025)) = hAPP(c_Fun_Ocomp(_1554019, _1554019, _1554019, hAPP(_1554023, _1554025)), hAPP(_1554023, _1554027)))], (4470 ^ _779203) ^ [_847034, _847036] : [_847036 = _847034, -(c_Nat_Osize__class_Osize(_847036) = c_Nat_Osize__class_Osize(_847034))], (4476 ^ _779203) ^ [_847119, _847121, _847123, _847125] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_847125, _847121) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_847123, _847119)), _847125 = _847123, _847121 = _847119], (22748 ^ _779203) ^ [_1180038, _1180040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180038), 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)), _1180040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180038), _1180040)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22698 ^ _779203) ^ [_1179223, _1179225, _1179227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179223)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1179225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179225), _1179227)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179223), _1179227)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1179223), _1179225))))], (40731 ^ _779203) ^ [_1577886, _1577888, _1577890] : [c_Relation_Ototal__on(_1577886, _1577888, _1577890), -(c_Relation_Ototal__on(_1577886, _1577888, hAPP(c_Relation_Oconverse(_1577886, _1577886), _1577890)))], (52425 ^ _779203) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (10489 ^ _779203) ^ [_960465, _960467, _960469, _960471] : [class_Rings_Ocomm__semiring__1(_960465), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960465), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960465), _960467), _960469)), _960471) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960465), _960467), _960471)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960465), _960469), _960471)))], (44630 ^ _779203) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (18724 ^ _779203) ^ [_1109208, _1109210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109208), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109208)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109210)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109210))], (32970 ^ _779203) ^ [_1383121, _1383123] : [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), _1383121))), 32973 ^ _779203 : [(32980 ^ _779203) ^ [] : [-(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), _1383123)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1383121))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1383123), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1383121)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1383121)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1383123), 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), _1383121)))))], (32974 ^ _779203) ^ [] : [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), _1383123)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1383121)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1383123), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1383121)) = 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), _1383123)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1383121))))]]], (44179 ^ _779203) ^ [_1663152, _1663154, _1663156] : [_1663152 = c_List_Olist_ONil(_1663154), -(c_List_Olast(_1663154, hAPP(hAPP(c_List_Olist_OCons(_1663154), _1663156), _1663152)) = _1663156)], (5827 ^ _779203) ^ [_871410, _871412, _871414, _871416] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_871410), _871412), _871414), _871416)), -(_871412 = _871416), -(hBOOL(hAPP(_871414, _871416)))], (41074 ^ _779203) ^ [_1586500, _1586502, _1586504, _1586506, _1586508] : [c_Relation_Osingle__valued(_1586500, _1586500, _1586502), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586500, _1586500)), hAPP(hAPP(c_Product__Type_OPair(_1586500, _1586500), _1586504), _1586506)), c_Transitive__Closure_Ortrancl(_1586500, _1586502))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586500, _1586500)), hAPP(hAPP(c_Product__Type_OPair(_1586500, _1586500), _1586504), _1586508)), c_Transitive__Closure_Ortrancl(_1586500, _1586502))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586500, _1586500)), hAPP(hAPP(c_Product__Type_OPair(_1586500, _1586500), _1586506), _1586508)), c_Transitive__Closure_Ortrancl(_1586500, _1586502)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586500, _1586500)), hAPP(hAPP(c_Product__Type_OPair(_1586500, _1586500), _1586508), _1586506)), c_Transitive__Closure_Ortrancl(_1586500, _1586502))))], (44855 ^ _779203) ^ [_1677898, _1677900] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1677898), _1677900) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677898)), hAPP(c_Code__Numeral_Onat__of, _1677900))))], (32499 ^ _779203) ^ [_1368529, _1368531] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1368529)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368531)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1368531))), 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), _1368529)), c_Int_Onat)))))], (40913 ^ _779203) ^ [_1582496, _1582498, _1582500] : [c_Relation_Osingle__valued(_1582496, _1582496, _1582498), -(c_Relation_Osingle__valued(_1582496, _1582496, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582496, _1582496), tc_HOL_Obool), _1582500), _1582498)))], (43261 ^ _779203) ^ [_1642313, _1642315, _1642317, _1642319] : [-(hAPP(hAPP(c_List_Onth(_1642313), hAPP(hAPP(c_List_Oappend(_1642313), _1642315), hAPP(hAPP(c_List_Olist_OCons(_1642313), _1642317), _1642319))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642313)), _1642315)) = _1642317)], (14499 ^ _779203) ^ [_1031569, _1031571, _1031573, _1031575] : [class_Fields_Olinordered__field(_1031569), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031569), c_Groups_Ozero__class_Ozero(_1031569)), _1031571)), 14506 ^ _779203 : [(14513 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031569), _1031573), _1031571)), _1031575)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031569), _1031573), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1031569), _1031575), _1031571))))], (14507 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031569), _1031573), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1031569), _1031575), _1031571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031569), _1031573), _1031571)), _1031575)))]]], (24464 ^ _779203) ^ [_1210111] : [class_Rings_Osemiring__1(_1210111), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1210111), c_Groups_Oone__class_Oone(_1210111)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1210111))], (22375 ^ _779203) ^ [_1173963, _1173965] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173965)), -(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, _1173963, _1173965))))], (10257 ^ _779203) ^ [_955482, _955484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955482), _955484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _955482)), _955484)))], (4486 ^ _779203) ^ [_847268, _847270, _847272, _847274, _847276, _847278, _847280, _847282, _847284, _847286] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_847286, _847282, _847278, _847274, _847270) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_847284, _847280, _847276, _847272, _847268)), _847286 = _847284, _847282 = _847280, _847278 = _847276, _847274 = _847272, _847270 = _847268], (29212 ^ _779203) ^ [_1296656, _1296658, _1296660, _1296662] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296656, tc_HOL_Obool)), _1296658), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296656, tc_HOL_Obool)), _1296660), _1296662)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296656, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296656, tc_HOL_Obool)), _1296658), _1296660)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296656, tc_HOL_Obool)), _1296658), _1296662)))], (30792 ^ _779203) ^ [_1329797, _1329799, _1329801, _1329803, _1329805] : [class_Groups_Ocomm__monoid__add(_1329797), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329799), _1329801)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329799), _1329803)), 30806 ^ _779203 : [(30809 ^ _779203) ^ [] : [hAPP(_1329805, 30805 ^ [_1329797, _1329799, _1329801, _1329803, _1329805]) = c_Groups_Ozero__class_Ozero(_1329797)], (30807 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329799), 30805 ^ [_1329797, _1329799, _1329801, _1329803, _1329805]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329799, tc_HOL_Obool)), _1329801), _1329803))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329799, _1329797), _1329805), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329799, tc_HOL_Obool)), _1329801), _1329803)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1329797), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329799, _1329797), _1329805), _1329801)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329799, _1329797), _1329805), _1329803)))], (23790 ^ _779203) ^ [_1197864, _1197866] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197864, _1197866)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197864), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197866)))], (1230 ^ _779203) ^ [_797538, _797540] : [-(class_Rings_Olinordered__ring(_797538)), _797540 = _797538, class_Rings_Olinordered__ring(_797540)], (44938 ^ _779203) ^ [_1680208, _1680210, _1680212, _1680214] : [-(hBOOL(hAPP(c_List_Olistsp(_1680208, hAPP(hAPP(c_COMBS(_1680208, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1680208), c_fconj), _1680210)), _1680212)), _1680214))), hBOOL(hAPP(c_List_Olistsp(_1680208, _1680210), _1680214)), hBOOL(hAPP(c_List_Olistsp(_1680208, _1680212), _1680214))], (52587 ^ _779203) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (18164 ^ _779203) ^ [_1099750, _1099752] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1099750), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1099752)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1099750), _1099752)))], (34615 ^ _779203) ^ [_1418880, _1418882, _1418884, _1418886, _1418888, _1418890] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1418880, tc_fun(_1418882, tc_fun(_1418884, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1418880, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1418882, _1418884), tc_HOL_Obool), tc_fun(_1418882, tc_fun(_1418884, tc_HOL_Obool)), _1418880), hAPP(c_COMBC(_1418882, tc_fun(tc_prod(_1418882, _1418884), tc_HOL_Obool), tc_fun(_1418884, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1418884, tc_fun(tc_fun(tc_prod(_1418882, _1418884), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1418882, _1418884), tc_HOL_Obool), tc_fun(_1418884, tc_HOL_Obool)), _1418882), c_COMBC(_1418884, tc_fun(tc_prod(_1418882, _1418884), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1418884, tc_prod(_1418882, _1418884)), tc_fun(_1418884, tc_fun(tc_fun(tc_prod(_1418882, _1418884), tc_HOL_Obool), tc_HOL_Obool)), _1418882), hAPP(c_COMBB(tc_prod(_1418882, _1418884), tc_fun(tc_fun(tc_prod(_1418882, _1418884), tc_HOL_Obool), tc_HOL_Obool), _1418884), c_member(tc_prod(_1418882, _1418884)))), c_Product__Type_OPair(_1418882, _1418884))))), _1418886)), _1418888), _1418890)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1418882, _1418884)), hAPP(hAPP(c_Product__Type_OPair(_1418882, _1418884), _1418888), _1418890)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1418880, tc_fun(tc_prod(_1418882, _1418884), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1418880, tc_HOL_Obool))), _1418886))))], (37199 ^ _779203) ^ [_1481645, _1481647, _1481649, _1481651, _1481653] : [-(hAPP(c_Set_Ovimage(_1481645, _1481647, _1481649), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481647, tc_HOL_Obool)), _1481651), _1481653)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1481645, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1481645, _1481647, _1481649), _1481651)), hAPP(c_Set_Ovimage(_1481645, _1481647, _1481649), _1481653)))], (15360 ^ _779203) ^ [_1048426, _1048428, _1048430] : [class_Orderings_Olinorder(_1048426), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048426), _1048428), _1048430) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048426), _1048430), _1048428))], (39056 ^ _779203) ^ [_1536676, _1536678] : [-(hAPP(c_List_Olexn(_1536676, _1536678), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1536676), tc_List_Olist(_1536676)), tc_HOL_Obool)))], (12951 ^ _779203) ^ [_1003144, _1003146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1003144)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1003146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003144), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1003146), _1003144))))], (23259 ^ _779203) ^ [_1188409, _1188411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188409)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1188409), _1188411)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1188411), _1188409)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1188411)), hAPP(c_Int_Onat, _1188409)))], (38715 ^ _779203) ^ [_1528743] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1528743)))], (28156 ^ _779203) ^ [_1276746, _1276748] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276746), _1276748)), 28159 ^ _779203 : [(28166 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276746), c_Orderings_Otop__class_Otop(tc_fun(_1276746, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1276746), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276746, tc_HOL_Obool)), _1276748))))], (28160 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276746), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276746, tc_HOL_Obool)), _1276748))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1276746), c_Orderings_Otop__class_Otop(tc_fun(_1276746, tc_HOL_Obool)))))]]], (29264 ^ _779203) ^ [_1297830, _1297832, _1297834] : [class_Lattices_Osemilattice__inf(_1297830), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297830), _1297832), _1297834) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297830), _1297834), _1297832))], (17536 ^ _779203) ^ [_1088367, _1088369] : [class_Orderings_Olinorder(_1088367), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088367), _1088369)), -(_1088369 = c_Orderings_Obot__class_Obot(tc_fun(_1088367, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1088367), c_Big__Operators_Olattice_OInf__fin(_1088367, c_Orderings_Oord__class_Omin(_1088367), _1088369)), c_Big__Operators_Olattice_OSup__fin(_1088367, c_Orderings_Oord__class_Omax(_1088367), _1088369))))], (52453 ^ _779203) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (27108 ^ _779203) ^ [_1256528, _1256530, _1256532] : [class_Orderings_Oorder(_1256528), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1256528), _1256530), _1256532)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256528, _1256532), _1256530) = c_Orderings_Obot__class_Obot(tc_fun(_1256528, tc_HOL_Obool)))], (40921 ^ _779203) ^ [_1582662, _1582664, _1582666, _1582668] : [-(hAPP(hAPP(c_Nat_Ocompow(_1582662, _1582662), _1582664), hAPP(hAPP(c_Nat_Ocompow(_1582662, _1582662), _1582666), _1582668)) = hAPP(hAPP(c_Nat_Ocompow(_1582662, _1582662), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1582666), _1582664)), _1582668))], (29714 ^ _779203) ^ [_1306758, _1306760, _1306762, _1306764] : [hBOOL(hAPP(hAPP(c_member(_1306758), _1306760), _1306762)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306758, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1306758), _1306760), _1306764)), _1306762) = hAPP(hAPP(c_Set_Oinsert(_1306758), _1306760), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306758, tc_HOL_Obool)), _1306764), _1306762)))], (41385 ^ _779203) ^ [_1595437, _1595439, _1595441, _1595443, _1595445, _1595447] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595437), tc_List_Olist(_1595437))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595437), tc_List_Olist(_1595437)), hAPP(hAPP(c_List_Olist_OCons(_1595437), _1595439), _1595441)), hAPP(hAPP(c_List_Olist_OCons(_1595437), _1595443), _1595445))), c_List_Olex(_1595437, _1595447)))), 41386 ^ _779203 : [(41393 ^ _779203) ^ [] : [_1595439 = _1595443, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595437), tc_List_Olist(_1595437))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595437), tc_List_Olist(_1595437)), _1595441), _1595445)), c_List_Olex(_1595437, _1595447)))], (41387 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595437, _1595437)), hAPP(hAPP(c_Product__Type_OPair(_1595437, _1595437), _1595439), _1595443)), _1595447)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595437)), _1595441) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595437)), _1595445)]]], (7187 ^ _779203) ^ [_898312, _898314, _898316, _898318] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898312, tc_HOL_Obool)), _898314), hAPP(hAPP(c_Set_Oinsert(_898312), _898316), _898318)))), 7190 ^ _779203 : [(7193 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898312, tc_HOL_Obool)), _898314), _898318))], (7191 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898312), _898316), _898318)))]], 7194 ^ _779203 : [(7197 ^ _779203) ^ [] : [7198 ^ _779203 : [(7201 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_898312, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898312, tc_HOL_Obool)), _898314), hAPP(hAPP(c_Set_Oinsert(_898312), _898316), c_Orderings_Obot__class_Obot(tc_fun(_898312, tc_HOL_Obool))))), _898318))], (7199 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898312), _898316), _898314)))]], 7202 ^ _779203 : [(7205 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898312, tc_HOL_Obool)), _898314), _898318))], (7203 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898312), _898316), _898314))]]], (7195 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898312), _898316), _898318))]]], (32191 ^ _779203) ^ [_1361070, _1361072] : [-(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)), _1361070)), 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), _1361072), _1361070))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1361070), _1361072))], (34662 ^ _779203) ^ [_1421345, _1421347, _1421349, _1421351, _1421353] : [class_Complete__Lattice_Ocomplete__lattice(_1421345), 34665 ^ _779203 : [(34666 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421345), _1421347), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1421349, _1421345), _1421351), _1421353))), 34669 ^ _779203 : [(34670 ^ _779203) ^ [_1421526] : [hBOOL(hAPP(hAPP(c_member(_1421349), _1421526), _1421351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421345), _1421347), hAPP(_1421353, _1421526))))]]], (34676 ^ _779203) ^ [] : [34678 ^ _779203 : [(34681 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421345), _1421347), hAPP(_1421353, 34677 ^ [_1421345, _1421347, _1421349, _1421351, _1421353])))], (34679 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1421349), 34677 ^ [_1421345, _1421347, _1421349, _1421351, _1421353]), _1421351)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421345), _1421347), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1421349, _1421345), _1421351), _1421353))))]]], (26308 ^ _779203) ^ [_1241870, _1241872, _1241874, _1241876, _1241878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1241870, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1241872, _1241870, _1241874), _1241876)), _1241878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1241870, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1241872, tc_HOL_Obool), tc_fun(_1241870, tc_HOL_Obool), c_Set_Oimage(_1241872, _1241870, _1241874)), hAPP(c_Set_OPow(_1241872), _1241876))), hAPP(c_Set_OPow(_1241870), _1241878))))], (22970 ^ _779203) ^ [_1183702] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183702))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36632 ^ _779203) ^ [_1468719] : [-(c_Fun_Oinj__on(_1468719, tc_fun(_1468719, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1468719, tc_fun(_1468719, tc_HOL_Obool), tc_fun(_1468719, tc_HOL_Obool)), c_Set_Oinsert(_1468719)), c_Orderings_Obot__class_Obot(tc_fun(_1468719, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1468719, tc_HOL_Obool))))], (30573 ^ _779203) ^ [_1325052, _1325054, _1325056] : [class_Complete__Lattice_Ocomplete__lattice(_1325052), -(c_Complete__Lattice_OSup__class_OSup(_1325052, hAPP(hAPP(c_Set_Oinsert(_1325052), _1325054), hAPP(hAPP(c_Set_Oinsert(_1325052), _1325056), c_Orderings_Obot__class_Obot(tc_fun(_1325052, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1325052), _1325054), _1325056))], (48678 ^ _779203) ^ [_1761449, _1761451, _1761453] : [c_List_Oall__interval__int(_1761449, _1761451, _1761453), 48681 ^ _779203 : [(48682 ^ _779203) ^ [_1761527] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1761527), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1761451, _1761453))), -(hBOOL(hAPP(_1761449, _1761527)))]]], (31817 ^ _779203) ^ [_1351531, _1351533, _1351535] : [class_Orderings_Obot(_1351531), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1351533, _1351531)), _1351535) = c_Orderings_Obot__class_Obot(_1351531))], (2456 ^ _779203) ^ [_815245, _815247] : [_815247 = _815245, -(c_Nitpick_Ozero__frac(_815247) = c_Nitpick_Ozero__frac(_815245))], (16286 ^ _779203) ^ [_1065156, _1065158] : [class_Orderings_Olinorder(_1065156), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065156), _1065158)), -(c_Big__Operators_Olinorder__class_OMax(_1065156, _1065158) = hAPP(c_Finite__Set_Ofold1(_1065156, c_Orderings_Oord__class_Omax(_1065156)), _1065158))], (37655 ^ _779203) ^ [_1493662, _1493664] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1493662, _1493662), tc_HOL_Obool)), c_Relation_OId__on(_1493662, _1493664)), hAPP(hAPP(c_Product__Type_OSigma(_1493662, _1493662), _1493664), hAPP(c_COMBK(tc_fun(_1493662, tc_HOL_Obool), _1493662), _1493664)))))], (42746 ^ _779203) ^ [_1631170, _1631172] : [-(c_List_Olist_Olist__size(_1631170, _1631172, c_List_Olist_ONil(_1631170)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35377 ^ _779203) ^ [_1439522, _1439524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1439522), _1439524)), -(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), _1439522), _1439524)), c_Wellfounded_Oless__than)))], (52199 ^ _779203) ^ [_1831980, _1831982] : [class_Orderings_Obot(_1831980), -(class_Orderings_Obot(tc_fun(_1831982, _1831980)))], (15252 ^ _779203) ^ [_1045928, _1045930, _1045932, _1045934] : [class_Orderings_Olinorder(_1045928), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045928), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1045928), _1045930), _1045932)), _1045934) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1045928), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045928), _1045930), _1045934)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045928), _1045932), _1045934)))], (17506 ^ _779203) ^ [_1087876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1087876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1087876)))], (33691 ^ _779203) ^ [_1395926, _1395928, _1395930, _1395932] : [-(hAPP(c_Product__Type_Osnd(_1395926, _1395928), hAPP(hAPP(c_Product__Type_OPair(_1395926, _1395928), _1395930), _1395932)) = _1395932)], (34815 ^ _779203) ^ [_1424758, _1424760, _1424762, _1424764, _1424766] : [-(_1424758 = c_Orderings_Obot__class_Obot(tc_fun(_1424760, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424762, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424760, tc_fun(_1424762, tc_HOL_Obool)), _1424758), _1424764)), _1424766) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424760, tc_fun(_1424762, tc_HOL_Obool)), _1424758), hAPP(hAPP(c_COMBC(_1424760, tc_fun(_1424762, tc_HOL_Obool), tc_fun(_1424762, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1424762, tc_HOL_Obool), tc_fun(tc_fun(_1424762, tc_HOL_Obool), tc_fun(_1424762, tc_HOL_Obool)), _1424760), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424762, tc_HOL_Obool))), _1424764)), _1424766)))], (21699 ^ _779203) ^ [_1161206] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1161206))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1161206)))))], (24305 ^ _779203) ^ [_1207615, _1207617, _1207619] : [class_Rings_Oring__1(_1207615), hBOOL(hAPP(hAPP(c_member(_1207615), _1207617), c_Int_Oring__1__class_OInts(_1207615))), -(hBOOL(hAPP(hAPP(c_member(_1207615), hAPP(hAPP(c_Power_Opower__class_Opower(_1207615), _1207617), _1207619)), c_Int_Oring__1__class_OInts(_1207615))))], (51201 ^ _779203) ^ [_1815203, _1815205] : [51208 ^ _779203 : [(51211 ^ _779203) ^ [] : [_1815203 = _1815205], (51209 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815203), _1815205)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815203), _1815205)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815205), _1815203)))], (45081 ^ _779203) ^ [_1683641, _1683643, _1683645, _1683647, _1683649, _1683651, _1683653] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683641)), _1683643) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683645)), _1683647), 45084 ^ _779203 : [(45093 ^ _779203) ^ [] : [-(c_List_Olist__all2(_1683641, _1683645, _1683649, hAPP(hAPP(c_List_Oappend(_1683641), _1683643), _1683651), hAPP(hAPP(c_List_Oappend(_1683645), _1683647), _1683653))), c_List_Olist__all2(_1683641, _1683645, _1683649, _1683643, _1683647), c_List_Olist__all2(_1683641, _1683645, _1683649, _1683651, _1683653)], (45085 ^ _779203) ^ [] : [c_List_Olist__all2(_1683641, _1683645, _1683649, hAPP(hAPP(c_List_Oappend(_1683641), _1683643), _1683651), hAPP(hAPP(c_List_Oappend(_1683645), _1683647), _1683653)), 45088 ^ _779203 : [(45091 ^ _779203) ^ [] : [-(c_List_Olist__all2(_1683641, _1683645, _1683649, _1683651, _1683653))], (45089 ^ _779203) ^ [] : [-(c_List_Olist__all2(_1683641, _1683645, _1683649, _1683643, _1683647))]]]]], (35135 ^ _779203) ^ [_1433240, _1433242, _1433244, _1433246, _1433248] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1433240, tc_fun(_1433242, tc_HOL_Obool)), _1433244), _1433246), _1433248)), 35138 ^ _779203 : [(35139 ^ _779203) ^ [_1433349] : [hBOOL(hAPP(hAPP(c_member(_1433240), _1433349), _1433244)), -(hBOOL(hAPP(hAPP(_1433246, _1433349), _1433248)))]]], (52495 ^ _779203) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (37136 ^ _779203) ^ [_1480129, _1480131, _1480133] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480129, tc_HOL_Obool)), _1480131), hAPP(hAPP(c_Set_Oinsert(_1480129), _1480133), c_Orderings_Obot__class_Obot(tc_fun(_1480129, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1480129, _1480133, _1480131) = c_HOL_OThe(_1480129, hAPP(hAPP(c_COMBC(_1480129, tc_fun(_1480129, tc_HOL_Obool), tc_HOL_Obool), c_member(_1480129)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1480129, tc_HOL_Obool)), _1480131), hAPP(hAPP(c_Set_Oinsert(_1480129), _1480133), c_Orderings_Obot__class_Obot(tc_fun(_1480129, tc_HOL_Obool)))))))], (42425 ^ _779203) ^ [_1624785, _1624787, _1624789, _1624791] : [hBOOL(hAPP(c_List_Odistinct(_1624785), _1624787)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1624789, _1624785)), hAPP(hAPP(c_List_Ozip(_1624789, _1624785), _1624791), _1624787))))], (38963 ^ _779203) ^ [_1534396, _1534398] : [c_Predicate_Oreflp(_1534396, _1534398), -(c_Relation_Orefl__on(_1534396, c_Orderings_Otop__class_Otop(tc_fun(_1534396, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1534396, _1534396)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534396, _1534396, tc_HOL_Obool), _1534398))))], (25942 ^ _779203) ^ [_1235325, _1235327, _1235329] : [class_Rings_Olinordered__idom(_1235325), 25945 ^ _779203 : [(25952 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235327), _1235329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235325), hAPP(c_Int_Oring__1__class_Oof__int(_1235325), _1235327)), hAPP(c_Int_Oring__1__class_Oof__int(_1235325), _1235329))))], (25946 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1235325), hAPP(c_Int_Oring__1__class_Oof__int(_1235325), _1235327)), hAPP(c_Int_Oring__1__class_Oof__int(_1235325), _1235329))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235327), _1235329)))]]], (43985 ^ _779203) ^ [_1659431, _1659433, _1659435] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659431), tc_List_Olist(_1659431))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659431), tc_List_Olist(_1659431)), c_List_Olist_ONil(_1659431)), _1659433)), c_List_Olexord(_1659431, _1659435))), -(_1659433 = hAPP(hAPP(c_List_Olist_OCons(_1659431), 43988 ^ [_1659431, _1659433, _1659435]), 43989 ^ [_1659431, _1659433, _1659435]))], (33771 ^ _779203) ^ [_1397548, _1397550, _1397552, _1397554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1397554, _1397550)), hAPP(_1397554, _1397552))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1397548, _1397548)), hAPP(hAPP(c_Product__Type_OPair(_1397548, _1397548), _1397550), _1397552)), hAPP(c_Wellfounded_Omeasure(_1397548), _1397554))))], (27922 ^ _779203) ^ [_1272004, _1272006] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272004, tc_HOL_Obool)), _1272006), _1272006) = _1272006)], (3338 ^ _779203) ^ [_828946, _828948, _828950, _828952, _828954, _828956] : [-(c_Finite__Set_Ofold(_828956, _828952, _828948) = c_Finite__Set_Ofold(_828954, _828950, _828946)), _828956 = _828954, _828952 = _828950, _828948 = _828946], (21887 ^ _779203) ^ [_1164698] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1164698), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (26850 ^ _779203) ^ [_1252220] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1252220))))], (34951 ^ _779203) ^ [_1428421, _1428423, _1428425, _1428427] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1428421, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428423, tc_fun(_1428421, tc_HOL_Obool), _1428425), _1428427)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428423, tc_fun(_1428421, tc_HOL_Obool)), _1428427), _1428425))], (1470 ^ _779203) ^ [_800538, _800540] : [-(class_Lattices_Olattice(_800538)), _800540 = _800538, class_Lattices_Olattice(_800540)], (2018 ^ _779203) ^ [_808284, _808286, _808288, _808290] : [-(c_SMT_Oz3mod(_808290, _808286) = c_SMT_Oz3mod(_808288, _808284)), _808290 = _808288, _808286 = _808284], (28542 ^ _779203) ^ [_1283990, _1283992, _1283994] : [class_Orderings_Olinorder(_1283990), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283990), _1283992), _1283994)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283990, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1283990), _1283992)), c_SetInterval_Oord__class_OatLeastAtMost(_1283990, _1283992, _1283994)) = hAPP(c_SetInterval_Oord__class_OatMost(_1283990), _1283994))], (38494 ^ _779203) ^ [_1523361, _1523363, _1523365, _1523367, _1523369, _1523371, _1523373] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1523361, _1523363, _1523365, hAPP(hAPP(c_COMBC(_1523361, tc_fun(tc_prod(_1523361, _1523363), tc_HOL_Obool), tc_fun(_1523363, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523363, tc_fun(tc_fun(tc_prod(_1523361, _1523363), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1523361, _1523363), tc_HOL_Obool), tc_fun(_1523363, tc_HOL_Obool)), _1523361), c_COMBC(_1523363, tc_fun(tc_prod(_1523361, _1523363), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523363, tc_prod(_1523361, _1523363)), tc_fun(_1523363, tc_fun(tc_fun(tc_prod(_1523361, _1523363), tc_HOL_Obool), tc_HOL_Obool)), _1523361), hAPP(c_COMBB(tc_prod(_1523361, _1523363), tc_fun(tc_fun(tc_prod(_1523361, _1523363), tc_HOL_Obool), tc_HOL_Obool), _1523363), c_member(tc_prod(_1523361, _1523363)))), c_Product__Type_OPair(_1523361, _1523363)))), _1523367), hAPP(hAPP(c_COMBC(_1523363, tc_fun(tc_prod(_1523363, _1523365), tc_HOL_Obool), tc_fun(_1523365, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523365, tc_fun(tc_fun(tc_prod(_1523363, _1523365), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1523363, _1523365), tc_HOL_Obool), tc_fun(_1523365, tc_HOL_Obool)), _1523363), c_COMBC(_1523365, tc_fun(tc_prod(_1523363, _1523365), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523365, tc_prod(_1523363, _1523365)), tc_fun(_1523365, tc_fun(tc_fun(tc_prod(_1523363, _1523365), tc_HOL_Obool), tc_HOL_Obool)), _1523363), hAPP(c_COMBB(tc_prod(_1523363, _1523365), tc_fun(tc_fun(tc_prod(_1523363, _1523365), tc_HOL_Obool), tc_HOL_Obool), _1523365), c_member(tc_prod(_1523363, _1523365)))), c_Product__Type_OPair(_1523363, _1523365)))), _1523369)), _1523371), _1523373)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523361, _1523365)), hAPP(hAPP(c_Product__Type_OPair(_1523361, _1523365), _1523371), _1523373)), hAPP(hAPP(c_Relation_Orel__comp(_1523361, _1523363, _1523365), _1523367), _1523369))))], (34510 ^ _779203) ^ [_1416172, _1416174, _1416176, _1416178] : [-(hAPP(c_Set_OPow(_1416172), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416174, tc_fun(_1416172, tc_HOL_Obool)), _1416176), _1416178)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416174, tc_fun(tc_fun(_1416172, tc_HOL_Obool), tc_HOL_Obool)), _1416176), hAPP(hAPP(c_COMBB(tc_fun(_1416172, tc_HOL_Obool), tc_fun(tc_fun(_1416172, tc_HOL_Obool), tc_HOL_Obool), _1416174), c_Set_OPow(_1416172)), _1416178)))], (39950 ^ _779203) ^ [_1558114, _1558116, _1558118, _1558120, _1558122, _1558124, _1558126, _1558128] : [class_Groups_Ocomm__monoid__mult(_1558114), c_Fun_Oinj__on(_1558116, _1558118, _1558120, _1558122), _1558124 = hAPP(c_Set_Oimage(_1558116, _1558118, _1558120), _1558122), 39964 ^ _779203 : [(39967 ^ _779203) ^ [] : [hAPP(_1558126, 39963 ^ [_1558114, _1558116, _1558118, _1558120, _1558122, _1558124, _1558126, _1558128]) = hAPP(hAPP(c_Fun_Ocomp(_1558118, _1558114, _1558116, _1558128), _1558120), 39963 ^ [_1558114, _1558116, _1558118, _1558120, _1558122, _1558124, _1558126, _1558128])], (39965 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558116), 39963 ^ [_1558114, _1558116, _1558118, _1558120, _1558122, _1558124, _1558126, _1558128]), _1558122)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1558118, _1558114), _1558128), _1558124) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1558116, _1558114), _1558126), _1558122))], (42568 ^ _779203) ^ [_1628049, _1628051, _1628053, _1628055] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628049) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1628051), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628049)), hAPP(hAPP(c_List_Olist_OCons(_1628051), _1628053), _1628055)) = c_List_Olist_ONil(_1628051))], (35647 ^ _779203) ^ [_1447055, _1447057] : [-(c_Relation_OId__on(_1447055, _1447057) = hAPP(c_Product__Type_Oprod_Oprod__case(_1447055, _1447055, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1447055, tc_HOL_Obool, tc_fun(_1447055, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447055, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1447055, tc_HOL_Obool)), _1447055), c_COMBC(_1447055, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1447055, tc_HOL_Obool), tc_fun(_1447055, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1447055), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1447055), c_fconj)), c_fequal))), _1447057)))], (38469 ^ _779203) ^ [_1522066, _1522068, _1522070] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1522066, _1522066), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1522066, _1522066, _1522066), _1522068), _1522070)), _1522068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1522066, tc_HOL_Obool), tc_fun(_1522066, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1522066, tc_HOL_Obool), tc_fun(_1522066, tc_HOL_Obool), tc_fun(_1522066, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1522066, _1522068)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1522066, tc_HOL_Obool), tc_fun(_1522066, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1522066, _1522070)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1522066, tc_HOL_Obool), tc_fun(_1522066, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1522066, tc_HOL_Obool), tc_fun(_1522066, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1522066, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1522066, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1522066, tc_HOL_Obool), tc_fun(_1522066, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1522066, _1522068))))], (23603 ^ _779203) ^ [_1194769, _1194771] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1194769)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1194771))) = 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), _1194769), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194771))))], (32493 ^ _779203) ^ [_1368206, _1368208, _1368210, _1368212] : [class_Rings_Ocomm__semiring__1(_1368206), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1368206), c_Groups_Oone__class_Oone(_1368206)), c_Groups_Oone__class_Oone(_1368206))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1368206), hAPP(hAPP(c_COMBB(_1368206, _1368206, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1368206), _1368208)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1368206, _1368206), hAPP(hAPP(c_COMBB(_1368206, tc_fun(_1368206, _1368206), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1368206)), c_Nat_Osemiring__1__class_Oof__nat(_1368206))), _1368210))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1368212))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368206), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368206), _1368212)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1368206), _1368208), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1368206), _1368208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368206), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1368206), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1368212), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1368210)))))], (33187 ^ _779203) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (11498 ^ _779203) ^ [_977381, _977383, _977385, _977387] : [class_Rings_Oordered__semiring(_977381), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977381), _977383), _977385)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977381), c_Groups_Ozero__class_Ozero(_977381)), _977387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977381), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977381), _977387), _977383)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977381), _977387), _977385))))], (21473 ^ _779203) ^ [] : [-(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))], (38877 ^ _779203) ^ [_1532232, _1532234, _1532236, _1532238, _1532240] : [-(hAPP(c_Relation_ODomain(_1532232, _1532234), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1532232, _1532234)), hAPP(hAPP(c_Product__Type_OPair(_1532232, _1532234), _1532236), _1532238)), _1532240)) = hAPP(hAPP(c_Set_Oinsert(_1532232), _1532236), hAPP(c_Relation_ODomain(_1532232, _1532234), _1532240)))], (45707 ^ _779203) ^ [_1697651, _1697653, _1697655, _1697657] : [-(hAPP(c_List_Ofilter(_1697651, _1697653), hAPP(hAPP(c_List_Oappend(_1697651), _1697655), _1697657)) = hAPP(hAPP(c_List_Oappend(_1697651), hAPP(c_List_Ofilter(_1697651, _1697653), _1697655)), hAPP(c_List_Ofilter(_1697651, _1697653), _1697657)))], (18254 ^ _779203) ^ [_1101131] : [-(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), _1101131))))], (9447 ^ _779203) ^ [_940261, _940263, _940265, _940267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940261), _940263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940265), _940267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940261), _940265)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940263), _940267))))], (24796 ^ _779203) ^ [_1216153, _1216155, _1216157, _1216159] : [class_Fields_Ofield(_1216153), -(_1216155 = c_Groups_Ozero__class_Ozero(_1216153)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1216157), _1216159)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1216153), _1216155), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216159), _1216157)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1216153), hAPP(hAPP(c_Power_Opower__class_Opower(_1216153), _1216155), _1216159)), hAPP(hAPP(c_Power_Opower__class_Opower(_1216153), _1216155), _1216157)))], (26930 ^ _779203) ^ [_1253486, _1253488, _1253490] : [class_Orderings_Olinorder(_1253486), 26933 ^ _779203 : [(26940 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253486), _1253488), _1253490)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1253486, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1253486), _1253488)), hAPP(c_SetInterval_Oord__class_OlessThan(_1253486), _1253490))))], (26934 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1253486, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1253486), _1253488)), hAPP(c_SetInterval_Oord__class_OlessThan(_1253486), _1253490))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253486), _1253488), _1253490)))]]], (42083 ^ _779203) ^ [_1616114, _1616116, _1616118, _1616120] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1616114), tc_List_Olist(_1616114))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616114), tc_List_Olist(_1616114)), _1616116), _1616118)), c_List_Olistrel(_1616114, _1616120)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616114)), _1616116) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616114)), _1616118), 42089 ^ _779203 : [(42092 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1616114, _1616114, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1616114, tc_fun(tc_prod(_1616114, _1616114), tc_HOL_Obool), tc_fun(_1616114, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616114, tc_fun(tc_fun(tc_prod(_1616114, _1616114), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1616114, _1616114), tc_HOL_Obool), tc_fun(_1616114, tc_HOL_Obool)), _1616114), c_COMBC(_1616114, tc_fun(tc_prod(_1616114, _1616114), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1616114, tc_prod(_1616114, _1616114)), tc_fun(_1616114, tc_fun(tc_fun(tc_prod(_1616114, _1616114), tc_HOL_Obool), tc_HOL_Obool)), _1616114), hAPP(c_COMBB(tc_prod(_1616114, _1616114), tc_fun(tc_fun(tc_prod(_1616114, _1616114), tc_HOL_Obool), tc_HOL_Obool), _1616114), c_member(tc_prod(_1616114, _1616114)))), c_Product__Type_OPair(_1616114, _1616114)))), _1616120)), 42088 ^ [_1616114, _1616116, _1616118, _1616120]))], (42090 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1616114, _1616114)), 42088 ^ [_1616114, _1616116, _1616118, _1616120]), hAPP(c_List_Oset(tc_prod(_1616114, _1616114)), hAPP(hAPP(c_List_Ozip(_1616114, _1616114), _1616116), _1616118)))))]]], (5933 ^ _779203) ^ [_873204, _873206, _873208] : [hBOOL(hAPP(hAPP(c_member(_873204), _873206), _873208)), -(hAPP(hAPP(c_Set_Oinsert(_873204), _873206), _873208) = _873208)], (31855 ^ _779203) ^ [_1352400, _1352402, _1352404, _1352406, _1352408, _1352410] : [_1352400 = _1352402, -(hAPP(c_Fun_Ofun__upd(_1352404, _1352406, _1352408, _1352402, _1352410), _1352400) = _1352410)], (25612 ^ _779203) ^ [_1230264] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1230264) = c_Int_Opred(_1230264))], (32303 ^ _779203) ^ [_1363763, _1363765] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1363763) = hAPP(c_Nat_OSuc, _1363765), -(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(_1363763))), 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)), _1363765))))))], (10449 ^ _779203) ^ [_959642, _959644, _959646, _959648] : [class_Rings_Ocomm__semiring__1(_959642), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959642), _959644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959642), _959646), _959648)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959642), _959646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959642), _959644), _959648)))], (43672 ^ _779203) ^ [_1652995, _1652997, _1652999, _1653001, _1653003] : [-(hAPP(hAPP(c_List_Ozip(_1652995, _1652997), hAPP(hAPP(c_List_Oappend(_1652995), _1652999), _1653001)), _1653003) = hAPP(hAPP(c_List_Oappend(tc_prod(_1652995, _1652997)), hAPP(hAPP(c_List_Ozip(_1652995, _1652997), _1652999), hAPP(hAPP(c_List_Otake(_1652997), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652995)), _1652999)), _1653003))), hAPP(hAPP(c_List_Ozip(_1652995, _1652997), _1653001), hAPP(hAPP(c_List_Odrop(_1652997), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652995)), _1652999)), _1653003))))], (9911 ^ _779203) ^ [_948339, _948341, _948343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948339), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948341), _948343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _948339), _948343)), _948341)))], (37479 ^ _779203) ^ [_1488669, _1488671] : [-(hAPP(c_Set_OCollect(_1488669), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1488669), c_fNot), _1488671)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1488669, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1488669), _1488671)))], (52309 ^ _779203) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (50613 ^ _779203) ^ [_1804589, _1804591, _1804593] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1804589), _1804591)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1804589), _1804593))), -(_1804589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1804591), _1804593)))], (15608 ^ _779203) ^ [_1052792, _1052794, _1052796, _1052798] : [class_Orderings_Olinorder(_1052792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052792), _1052794), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1052792), _1052796), _1052798))), 15615 ^ _779203 : [(15618 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052792), _1052794), _1052798)))], (15616 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052792), _1052794), _1052796)))]]], (24329 ^ _779203) ^ [_1208021, _1208023] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1208021))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1208021)), _1208023) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1208023))], (22053 ^ _779203) ^ [_1168294, _1168296, _1168298, _1168300] : [class_Divides_Osemiring__div(_1168294), -(c_Divides_Odiv__class_Omod(_1168294, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168294), c_Divides_Odiv__class_Omod(_1168294, _1168296, _1168298)), _1168300), _1168298) = c_Divides_Odiv__class_Omod(_1168294, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168294), _1168296), _1168300), _1168298))], (1620 ^ _779203) ^ [_802413, _802415] : [-(class_Rings_Oordered__cancel__semiring(_802413)), _802415 = _802413, class_Rings_Oordered__cancel__semiring(_802415)], (19424 ^ _779203) ^ [_1121678, _1121680] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1121678) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1121680), 19427 ^ _779203 : [(19434 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1121678)))), 19437 ^ _779203 : [(19444 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1121680)))), -(_1121678 = _1121680)], (19438 ^ _779203) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1121680))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1121678) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (19428 ^ _779203) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1121678))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1121680)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (29772 ^ _779203) ^ [_1308158, _1308160, _1308162, _1308164] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308158, tc_HOL_Obool)), _1308160), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308158, tc_HOL_Obool)), _1308162), _1308164)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308158, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308158, tc_HOL_Obool)), _1308160), _1308162)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308158, tc_HOL_Obool)), _1308160), _1308164)))], (2806 ^ _779203) ^ [_820720, _820722] : [_820722 = _820720, -(c_Nat_Ofunpow(_820722) = c_Nat_Ofunpow(_820720))], (30221 ^ _779203) ^ [_1318122, _1318124] : [class_Complete__Lattice_Ocomplete__lattice(_1318122), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318122), _1318124)), -(_1318124 = c_Orderings_Obot__class_Obot(tc_fun(_1318122, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1318122, _1318124) = c_Complete__Lattice_OSup__class_OSup(_1318122, _1318124))], (31450 ^ _779203) ^ [_1343176] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1343176, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1343176, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1343176, tc_HOL_Obool)))], (47491 ^ _779203) ^ [_1736058, _1736060, _1736062, _1736064, _1736066] : [hAPP(hAPP(c_List_Olist_OCons(_1736058), _1736060), _1736062) = hAPP(c_List_Ofilter(_1736058, _1736064), _1736066), 47496 ^ _779203 : [(47505 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1736064, _1736060)))], (47507 ^ _779203) ^ [] : [-(_1736062 = hAPP(c_List_Ofilter(_1736058, _1736064), 47495 ^ [_1736058, _1736060, _1736062, _1736064, _1736066]))], (47499 ^ _779203) ^ [_1736372] : [hBOOL(hAPP(hAPP(c_member(_1736058), _1736372), hAPP(c_List_Oset(_1736058), 47494 ^ [_1736058, _1736060, _1736062, _1736064, _1736066]))), hBOOL(hAPP(_1736064, _1736372))], (47497 ^ _779203) ^ [] : [-(_1736066 = hAPP(hAPP(c_List_Oappend(_1736058), 47494 ^ [_1736058, _1736060, _1736062, _1736064, _1736066]), hAPP(hAPP(c_List_Olist_OCons(_1736058), _1736060), 47495 ^ [_1736058, _1736060, _1736062, _1736064, _1736066])))]]], (21107 ^ _779203) ^ [_1151438, _1151440] : [c_Int_OBit1(_1151438) = c_Int_OBit1(_1151440), -(_1151438 = _1151440)], (52347 ^ _779203) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (36008 ^ _779203) ^ [_1455572, _1455574, _1455576] : [c_Equiv__Relations_Oequivp(_1455572, _1455574), -(hBOOL(hAPP(hAPP(_1455574, _1455576), _1455576)))], (39325 ^ _779203) ^ [_1543705, _1543707] : [39327 ^ _779203 : [(39330 ^ _779203) ^ [] : [hBOOL(hAPP(_1543705, hAPP(c_Int_OAbs__Integ, 39326 ^ [_1543705, _1543707])))], (39328 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39326 ^ [_1543705, _1543707]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1543705, _1543707)))], (20492 ^ _779203) ^ [_1140625, _1140627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1140625)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1140627))))], (12488 ^ _779203) ^ [_994527, _994529, _994531] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_994527), _994529)), 12491 ^ _779203 : [(12492 ^ _779203) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_994527, tc_Nat_Onat), _994531), _994529) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 12495 ^ _779203 : [(12496 ^ _779203) ^ [_994689] : [hBOOL(hAPP(hAPP(c_member(_994527), _994689), _994529)), -(hAPP(_994531, _994689) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (12502 ^ _779203) ^ [] : [12504 ^ _779203 : [(12507 ^ _779203) ^ [] : [hAPP(_994531, 12503 ^ [_994527, _994529, _994531]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12505 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_994527), 12503 ^ [_994527, _994529, _994531]), _994529)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_994527, tc_Nat_Onat), _994531), _994529) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (45695 ^ _779203) ^ [_1697452, _1697454, _1697456, _1697458] : [hBOOL(hAPP(_1697452, _1697454)), -(hAPP(c_List_Ofilter(_1697456, _1697452), hAPP(hAPP(c_List_Olist_OCons(_1697456), _1697454), _1697458)) = hAPP(hAPP(c_List_Olist_OCons(_1697456), _1697454), hAPP(c_List_Ofilter(_1697456, _1697452), _1697458)))], (6168 ^ _779203) ^ [_877842, _877844, _877846, _877848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877842, tc_HOL_Obool)), _877844), _877846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877842, tc_HOL_Obool)), _877844), hAPP(hAPP(c_Set_Oinsert(_877842), _877848), _877846))))], (30044 ^ _779203) ^ [_1314178, _1314180, _1314182] : [class_Lattices_Osemilattice__inf(_1314178), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314178), _1314180)), -(_1314180 = c_Orderings_Obot__class_Obot(tc_fun(_1314178, tc_HOL_Obool))), 30055 ^ _779203 : [(30056 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314178), _1314182), hAPP(c_Finite__Set_Ofold1(_1314178, c_Lattices_Osemilattice__inf__class_Oinf(_1314178)), _1314180))), 30059 ^ _779203 : [(30060 ^ _779203) ^ [_1314471] : [hBOOL(hAPP(hAPP(c_member(_1314178), _1314471), _1314180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314178), _1314182), _1314471)))]]], (30066 ^ _779203) ^ [] : [30068 ^ _779203 : [(30071 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314178), _1314182), 30067 ^ [_1314178, _1314180, _1314182]))], (30069 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1314178), 30067 ^ [_1314178, _1314180, _1314182]), _1314180)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314178), _1314182), hAPP(c_Finite__Set_Ofold1(_1314178, c_Lattices_Osemilattice__inf__class_Oinf(_1314178)), _1314180))))]]], (14803 ^ _779203) ^ [_1037294, _1037296] : [class_Rings_Olinordered__idom(_1037294), hBOOL(hAPP(hAPP(c_member(_1037294), _1037296), c_Int_Oring__1__class_OInts(_1037294))), 14810 ^ _779203 : [(14817 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037294), _1037296), c_Groups_Ozero__class_Ozero(_1037294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037294), c_Groups_Oone__class_Oone(_1037294)), _1037296)), _1037296)), c_Groups_Ozero__class_Ozero(_1037294))))], (14811 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1037294), c_Groups_Oone__class_Oone(_1037294)), _1037296)), _1037296)), c_Groups_Ozero__class_Ozero(_1037294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1037294), _1037296), c_Groups_Ozero__class_Ozero(_1037294))))]]], (47109 ^ _779203) ^ [_1727075, _1727077, _1727079, _1727081] : [47111 ^ _779203 : [(47114 ^ _779203) ^ [] : [hBOOL(hAPP(_1727077, hAPP(hAPP(c_List_Onth(_1727079), _1727081), 47110 ^ [_1727075, _1727077, _1727079, _1727081])))], (47112 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47110 ^ [_1727075, _1727077, _1727079, _1727081]), _1727075)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1727075), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727079)), _1727081))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1727075), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1727079)), c_List_OtakeWhile(_1727079, _1727077, _1727081)))))], (19844 ^ _779203) ^ [_1129201, _1129203, _1129205] : [class_Lattices_Oboolean__algebra(_1129201), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129201), _1129203), _1129205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129201), hAPP(c_Groups_Ouminus__class_Ouminus(_1129201), _1129205)), hAPP(c_Groups_Ouminus__class_Ouminus(_1129201), _1129203))))], (6072 ^ _779203) ^ [_875898, _875900, _875902, _875904, _875906] : [-(hAPP(hAPP(c_Set_Oinsert(_875898), _875900), hAPP(hAPP(c_Set_Oinsert(_875898), _875902), c_Orderings_Obot__class_Obot(tc_fun(_875898, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_875898), _875904), hAPP(hAPP(c_Set_Oinsert(_875898), _875906), c_Orderings_Obot__class_Obot(tc_fun(_875898, tc_HOL_Obool))))), 6073 ^ _779203 : [(6080 ^ _779203) ^ [] : [_875900 = _875906, _875902 = _875904], (6074 ^ _779203) ^ [] : [_875900 = _875904, _875902 = _875906]]], (39926 ^ _779203) ^ [_1557642, _1557644, _1557646, _1557648, _1557650, _1557652] : [c_Finite__Set_Ofolding__idem(_1557642, _1557644, _1557646, _1557648), hBOOL(hAPP(c_Finite__Set_Ofinite(_1557642), _1557650)), hBOOL(hAPP(hAPP(c_member(_1557642), _1557652), _1557650)), -(hAPP(c_Fun_Ocomp(_1557644, _1557644, _1557644, hAPP(_1557648, _1557650)), hAPP(_1557646, _1557652)) = hAPP(_1557648, _1557650))], (21853 ^ _779203) ^ [_1163957, _1163959] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1163957), 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)))), _1163959)), 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)))), _1163957)) = 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), _1163959), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1163957))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (5837 ^ _779203) ^ [_871524, _871526, _871528, _871530] : [5838 ^ _779203 : [(5841 ^ _779203) ^ [] : [hBOOL(hAPP(_871528, _871530))], (5839 ^ _779203) ^ [] : [_871526 = _871530]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_871524), _871526), _871528), _871530)))], (21635 ^ _779203) ^ [_1160068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1160068))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1160068)))], (32735 ^ _779203) ^ [_1378328] : [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), _1378328))), 32738 ^ _779203 : [(32745 ^ _779203) ^ [] : [-(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), _1378328))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1378328)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1378328)), 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), _1378328)))))], (32739 ^ _779203) ^ [] : [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), _1378328)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1378328)) = 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), _1378328))))]]], (11153 ^ _779203) ^ [_971189, _971191, _971193, _971195] : [class_Groups_Ocomm__monoid__mult(_971189), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_971191), _971193))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_971191, _971189), _971195), _971193) = c_Groups_Oone__class_Oone(_971189))], (38374 ^ _779203) ^ [_1519126, _1519128, _1519130, _1519132, _1519134, _1519136, _1519138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519126, _1519128), tc_HOL_Obool)), _1519130), _1519132)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519128, _1519134), tc_HOL_Obool)), _1519136), _1519138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1519126, _1519134), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1519126, _1519128, _1519134), _1519130), _1519136)), hAPP(hAPP(c_Relation_Orel__comp(_1519126, _1519128, _1519134), _1519132), _1519138))))], (3366 ^ _779203) ^ [_829388, _829390, _829392, _829394, _829396, _829398] : [-(c_List_Opartition(_829398, _829394, _829390) = c_List_Opartition(_829396, _829392, _829388)), _829398 = _829396, _829394 = _829392, _829390 = _829388], (13835 ^ _779203) ^ [_1019646, _1019648, _1019650, _1019652] : [class_Fields_Olinordered__field(_1019646), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1019646), c_Groups_Ozero__class_Ozero(_1019646)), _1019648)), 13842 ^ _779203 : [(13849 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019646), _1019650), _1019648)), _1019652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019646), _1019650), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1019646), _1019652), _1019648))))], (13843 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019646), _1019650), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1019646), _1019652), _1019648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019646), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1019646), _1019650), _1019648)), _1019652)))]]], (27770 ^ _779203) ^ [_1268840, _1268842, _1268844] : [class_Lattices_Osemilattice__sup(_1268840), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268840), _1268842), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268840), _1268842), _1268844)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268840), _1268842), _1268844))], (38424 ^ _779203) ^ [_1520532, _1520534, _1520536, _1520538, _1520540, _1520542, _1520544, _1520546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520532, _1520534), tc_HOL_Obool)), _1520536), hAPP(hAPP(c_Product__Type_OSigma(_1520532, _1520534), _1520538), hAPP(c_COMBK(tc_fun(_1520534, tc_HOL_Obool), _1520532), _1520540)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520534, _1520542), tc_HOL_Obool)), _1520544), hAPP(hAPP(c_Product__Type_OSigma(_1520534, _1520542), _1520540), hAPP(c_COMBK(tc_fun(_1520542, tc_HOL_Obool), _1520534), _1520546)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1520532, _1520542), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1520532, _1520534, _1520542), _1520536), _1520544)), hAPP(hAPP(c_Product__Type_OSigma(_1520532, _1520542), _1520538), hAPP(c_COMBK(tc_fun(_1520542, tc_HOL_Obool), _1520532), _1520546)))))], (25426 ^ _779203) ^ [] : [c_Int_OMin = c_Int_OPls], (28962 ^ _779203) ^ [_1291573, _1291575, _1291577] : [class_Lattices_Olattice(_1291573), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291573), _1291575)), -(_1291575 = c_Orderings_Obot__class_Obot(tc_fun(_1291573, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291573), _1291577)), -(_1291577 = c_Orderings_Obot__class_Obot(tc_fun(_1291573, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1291573, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1291573, tc_HOL_Obool)), _1291575), _1291577)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291573), c_Big__Operators_Olattice__class_OSup__fin(_1291573, _1291575)), c_Big__Operators_Olattice__class_OSup__fin(_1291573, _1291577)))], (8220 ^ _779203) ^ [_915739, _915741, _915743] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_915739), _915741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_915739, tc_HOL_Obool)), _915743), _915741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_915739), _915743)), hAPP(c_Finite__Set_Ocard(_915739), _915741))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_915739, tc_HOL_Obool)), _915743), _915741)))], (51917 ^ _779203) ^ [_1827506, _1827508, _1827510, _1827512, _1827514] : [class_Divides_Osemiring__div(_1827506), -(_1827508 = c_Groups_Ozero__class_Ozero(_1827506)), -(_1827510 = c_Groups_Ozero__class_Ozero(_1827506)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827506), _1827508), _1827512)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1827506), _1827510), _1827514)), 51936 ^ _779203 : [(51943 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827506), _1827512), _1827510) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827506), _1827508), _1827514), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827506), _1827512), _1827508) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827506), _1827514), _1827510))], (51937 ^ _779203) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827506), _1827512), _1827508) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1827506), _1827514), _1827510), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827506), _1827512), _1827510) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1827506), _1827508), _1827514))]]], (25460 ^ _779203) ^ [_1228086, _1228088] : [c_Nat__Transfer_Ois__nat(_1228086), c_Nat__Transfer_Ois__nat(_1228088), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1228086), _1228088)))], (31941 ^ _779203) ^ [_1354722, _1354724] : [-(hAPP(c_Set_Oimage(_1354722, _1354722, c_COMBI(_1354722)), _1354724) = _1354724)], (32551 ^ _779203) ^ [_1369938, _1369940, _1369942, _1369944] : [-(c_Nat_Onat_Onat__case(_1369938, _1369940, _1369942, hAPP(c_Nat_OSuc, _1369944)) = hAPP(_1369942, _1369944))], (18214 ^ _779203) ^ [_1100452] : [18216 ^ _779203 : [(18219 ^ _779203) ^ [] : [hBOOL(hAPP(_1100452, 18215 ^ [_1100452]))], (18217 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 18215 ^ [_1100452])))]], 18220 ^ _779203 : [(18221 ^ _779203) ^ [_1100579] : [-(hBOOL(hAPP(_1100452, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1100579))))]]], (21315 ^ _779203) ^ [_1154870] : [class_Int_Onumber__ring(_1154870), c_Int_Oiszero(_1154870, hAPP(c_Int_Onumber__class_Onumber__of(_1154870), c_Int_OBit1(c_Int_OPls)))], (15702 ^ _779203) ^ [_1054464, _1054466, _1054468, _1054470] : [class_Orderings_Olinorder(_1054464), 15705 ^ _779203 : [(15714 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054464), _1054466), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1054464), _1054468), _1054470)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054464), _1054466), _1054468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054464), _1054466), _1054470))], (15706 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054464), _1054466), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1054464), _1054468), _1054470))), 15709 ^ _779203 : [(15712 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054464), _1054466), _1054470)))], (15710 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054464), _1054466), _1054468)))]]]]], (49338 ^ _779203) ^ [_1776737, _1776739, _1776741] : [c_Relation_Osym(_1776737, _1776739), c_Relation_Osym(_1776737, _1776741), -(c_Relation_Osym(_1776737, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1776737, _1776737), tc_HOL_Obool)), _1776739), _1776741)))], (15106 ^ _779203) ^ [_1043367, _1043369, _1043371, _1043373] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1043367, tc_Nat_Onat), _1043369), _1043371) = hAPP(c_Nat_OSuc, _1043373), 15110 ^ _779203 : [(15113 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1043369, 15109 ^ [_1043367, _1043369, _1043371, _1043373]))))], (15111 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1043367), 15109 ^ [_1043367, _1043369, _1043371, _1043373]), _1043371)))]]], (30682 ^ _779203) ^ [_1327411, _1327413, _1327415] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1327411, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1327411, tc_HOL_Obool), tc_HOL_Obool)), _1327413), _1327415)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327411, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1327411, tc_HOL_Obool), _1327413)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1327411, tc_HOL_Obool), _1327415)))], (35507 ^ _779203) ^ [_1443246, _1443248, _1443250, _1443252] : [-(hAPP(c_Relation_OImage(_1443246, _1443248, _1443250), _1443252) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1443246, tc_fun(_1443248, tc_HOL_Obool)), _1443252), hAPP(hAPP(c_COMBB(tc_fun(_1443246, tc_HOL_Obool), tc_fun(_1443248, tc_HOL_Obool), _1443246), c_Relation_OImage(_1443246, _1443248, _1443250)), hAPP(hAPP(c_COMBC(_1443246, tc_fun(_1443246, tc_HOL_Obool), tc_fun(_1443246, tc_HOL_Obool)), c_Set_Oinsert(_1443246)), c_Orderings_Obot__class_Obot(tc_fun(_1443246, tc_HOL_Obool))))))], (40448 ^ _779203) ^ [_1571064, _1571066, _1571068] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571064, _1571064)), hAPP(hAPP(c_Product__Type_OPair(_1571064, _1571064), _1571066), _1571068)), c_Relation_OId(_1571064))), -(_1571066 = _1571068)], (41521 ^ _779203) ^ [_1600017, _1600019, _1600021, _1600023] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600017), tc_List_Olist(_1600017))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600017), tc_List_Olist(_1600017)), _1600019), _1600021)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1600017), tc_List_Olist(_1600017)), c_List_Olistrel1(_1600017, _1600023)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600017), tc_List_Olist(_1600017))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600017), tc_List_Olist(_1600017)), _1600019), _1600021)), c_List_Olistrel1(_1600017, hAPP(c_Relation_Oconverse(_1600017, _1600017), _1600023)))))], (38195 ^ _779203) ^ [_1513866, _1513868, _1513870, _1513872, _1513874, _1513876] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513866), _1513868)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1513870), _1513872)), 38205 ^ _779203 : [(38208 ^ _779203) ^ [] : [hAPP(c_Finite__Set_Ocard(_1513866), hAPP(c_Set_OCollect(_1513866), hAPP(hAPP(c_COMBS(_1513866, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513866), c_fconj), hAPP(hAPP(c_COMBC(_1513866, tc_fun(_1513866, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513866)), _1513868))), hAPP(hAPP(c_COMBC(_1513866, _1513870, tc_HOL_Obool), _1513874), 38204 ^ [_1513866, _1513868, _1513870, _1513872, _1513874, _1513876])))) = hAPP(_1513876, 38204 ^ [_1513866, _1513868, _1513870, _1513872, _1513874, _1513876])], (38206 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513870), 38204 ^ [_1513866, _1513868, _1513870, _1513872, _1513874, _1513876]), _1513872)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513866, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1513870, tc_HOL_Obool), tc_Nat_Onat, _1513866), c_Finite__Set_Ocard(_1513870)), hAPP(hAPP(c_COMBB(tc_fun(_1513870, tc_HOL_Obool), tc_fun(_1513870, tc_HOL_Obool), _1513866), c_Set_OCollect(_1513870)), hAPP(hAPP(c_COMBB(tc_fun(_1513870, tc_HOL_Obool), tc_fun(_1513870, tc_HOL_Obool), _1513866), hAPP(c_COMBS(_1513870, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1513870), c_fconj), hAPP(hAPP(c_COMBC(_1513870, tc_fun(_1513870, tc_HOL_Obool), tc_HOL_Obool), c_member(_1513870)), _1513872)))), _1513874)))), _1513868) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1513870, tc_Nat_Onat), _1513876), _1513872))], (9351 ^ _779203) ^ [_938643, _938645, _938647, _938649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938643), _938645)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938647), _938649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938643), _938647)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938645), _938649))))], (33305 ^ _779203) ^ [_1389107, _1389109, _1389111] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1389107, _1389109), _1389111)), -(c_Divides_Odivmod__nat(_1389107, _1389109) = _1389111)], (41921 ^ _779203) ^ [_1611517, _1611519, _1611521, _1611523] : [-(hBOOL(hAPP(hAPP(c_member(_1611517), _1611519), hAPP(c_List_Oset(_1611517), _1611521)))), hBOOL(hAPP(hAPP(c_member(_1611517), _1611519), hAPP(c_List_Oset(_1611517), c_List_Osublist(_1611517, _1611521, _1611523))))], (9606 ^ _779203) ^ [_943355, _943357] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943355), _943357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943357), hAPP(c_Nat_OSuc, _943355))))], (47203 ^ _779203) ^ [_1728884, _1728886, _1728888, _1728890] : [-(c_List_Omaps(_1728884, _1728886, _1728888, _1728890) = c_List_Oconcat(_1728886, hAPP(hAPP(c_List_Omap(_1728884, tc_List_Olist(_1728886)), _1728888), _1728890)))], (34 ^ _779203) ^ [_779656, _779658] : [-(v_wt(_779656)), _779658 = _779656, v_wt(_779658)], (6617 ^ _779203) ^ [_885928, _885930, _885932, _885934, _885936] : [c_Finite__Set_Ofolding__one__idem(_885928, _885930, _885932), hBOOL(hAPP(c_Finite__Set_Ofinite(_885928), _885934)), -(_885934 = c_Orderings_Obot__class_Obot(tc_fun(_885928, tc_HOL_Obool))), -(hAPP(_885932, hAPP(hAPP(c_Set_Oinsert(_885928), _885936), _885934)) = hAPP(hAPP(_885930, _885936), hAPP(_885932, _885934)))], (50093 ^ _779203) ^ [_1792342, _1792344, _1792346, _1792348] : [c_Fun_Obij__betw(_1792342, _1792344, _1792346, c_Orderings_Obot__class_Obot(tc_fun(_1792342, tc_HOL_Obool)), _1792348), -(_1792348 = c_Orderings_Obot__class_Obot(tc_fun(_1792344, tc_HOL_Obool)))], (48396 ^ _779203) ^ [_1755106, _1755108, _1755110, _1755112, _1755114, _1755116] : [-(c_New__Random__Sequence_Opos__union(_1755106, _1755108, _1755110, _1755112, _1755114, _1755116) = c_New__DSequence_Opos__union(_1755106, hAPP(hAPP(hAPP(_1755108, _1755112), _1755114), _1755116), hAPP(hAPP(hAPP(_1755110, _1755112), _1755114), _1755116)))], (28796 ^ _779203) ^ [] : [-(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))))], (1330 ^ _779203) ^ [_798788, _798790] : [-(class_Groups_Osgn__if(_798788)), _798790 = _798788, class_Groups_Osgn__if(_798790)], (44948 ^ _779203) ^ [_1680417, _1680419, _1680421, _1680423] : [hBOOL(hAPP(c_List_Olistsp(_1680417, _1680419), _1680421)), hBOOL(hAPP(c_List_Olistsp(_1680417, _1680423), _1680421)), -(hBOOL(hAPP(c_List_Olistsp(_1680417, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680417, tc_HOL_Obool)), _1680419), _1680423)), _1680421)))], (17758 ^ _779203) ^ [_1092065, _1092067, _1092069] : [class_Orderings_Olinorder(_1092065), hBOOL(hAPP(c_Finite__Set_Ofinite(_1092065), _1092067)), 17765 ^ _779203 : [(17772 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1092065, tc_HOL_Obool)), _1092067), hAPP(hAPP(c_Set_Oinsert(_1092065), _1092069), c_Orderings_Obot__class_Obot(tc_fun(_1092065, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1092065, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1092065, c_Orderings_Oord__class_Omin(_1092065), hAPP(hAPP(c_Set_Oinsert(_1092065), _1092069), _1092067)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1092065), _1092069), c_Big__Operators_Olattice_OInf__fin(_1092065, c_Orderings_Oord__class_Omin(_1092065), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1092065, tc_HOL_Obool)), _1092067), hAPP(hAPP(c_Set_Oinsert(_1092065), _1092069), c_Orderings_Obot__class_Obot(tc_fun(_1092065, tc_HOL_Obool)))))))], (17766 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1092065, tc_HOL_Obool)), _1092067), hAPP(hAPP(c_Set_Oinsert(_1092065), _1092069), c_Orderings_Obot__class_Obot(tc_fun(_1092065, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1092065, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1092065, c_Orderings_Oord__class_Omin(_1092065), hAPP(hAPP(c_Set_Oinsert(_1092065), _1092069), _1092067)) = _1092069)]]], (17158 ^ _779203) ^ [_1081429, _1081431] : [class_Orderings_Olinorder(_1081429), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081429), _1081431)), -(_1081431 = c_Orderings_Obot__class_Obot(tc_fun(_1081429, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1081429), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1081429), 17171 ^ [_1081429, _1081431]), 17172 ^ [_1081429, _1081431])), hAPP(hAPP(c_Set_Oinsert(_1081429), 17171 ^ [_1081429, _1081431]), hAPP(hAPP(c_Set_Oinsert(_1081429), 17172 ^ [_1081429, _1081431]), c_Orderings_Obot__class_Obot(tc_fun(_1081429, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1081429), c_Big__Operators_Olinorder__class_OMin(_1081429, _1081431)), _1081431)))], (45466 ^ _779203) ^ [_1691661, _1691663, _1691665] : [-(hAPP(c_List_Oset(_1691661), hAPP(c_List_OremoveAll(_1691661, _1691663), _1691665)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1691661, tc_HOL_Obool)), hAPP(c_List_Oset(_1691661), _1691665)), hAPP(hAPP(c_Set_Oinsert(_1691661), _1691663), c_Orderings_Obot__class_Obot(tc_fun(_1691661, tc_HOL_Obool)))))], (10347 ^ _779203) ^ [_957315, _957317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957315), _957317)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957315), _957317)))], (14301 ^ _779203) ^ [_1027884, _1027886, _1027888, _1027890, _1027892] : [class_Fields_Olinordered__field(_1027884), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027884), c_Groups_Ozero__class_Ozero(_1027884)), _1027886)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027884), _1027886), _1027888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027884), c_Groups_Ozero__class_Ozero(_1027884)), _1027890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027884), _1027890), _1027892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027884), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1027884), _1027886), _1027892)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1027884), _1027888), _1027890))))], (42660 ^ _779203) ^ [_1629629, _1629631, _1629633] : [42661 ^ _779203 : [(42664 ^ _779203) ^ [] : [_1629633 = c_List_Olist_ONil(_1629629)], (42662 ^ _779203) ^ [] : [_1629631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1629629), _1629631), _1629633) = c_List_Olist_ONil(_1629629))], (51809 ^ _779203) ^ [_1825512, _1825514] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1825512), 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)))), _1825514))), 51812 ^ _779203 : [(51815 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825512), _1825514))], (51813 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825514), _1825512)))]]], (28722 ^ _779203) ^ [_1287148, _1287150] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1287148, _1287150)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1287150), _1287148))], (10821 ^ _779203) ^ [_966313, _966315, _966317] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_966313), 10824 ^ _779203 : [(10831 ^ _779203) ^ [] : [_966317 = c_Groups_Ozero__class_Ozero(_966313), -(_966315 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966313), _966315), _966317))], (10825 ^ _779203) ^ [] : [_966315 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966313), _966315), _966317), -(_966317 = c_Groups_Ozero__class_Ozero(_966313))]]], (23205 ^ _779203) ^ [_1187440, _1187442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187442)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1187440)), hAPP(c_Int_Onat, _1187442)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1187440), _1187442)))], (31925 ^ _779203) ^ [_1354178, _1354180, _1354182, _1354184, _1354186, _1354188] : [class_Groups_Ocomm__monoid__add(_1354178), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354180, _1354178), hAPP(hAPP(c_COMBC(_1354180, tc_fun(_1354182, tc_HOL_Obool), _1354178), hAPP(hAPP(c_COMBB(tc_fun(_1354182, _1354178), tc_fun(tc_fun(_1354182, tc_HOL_Obool), _1354178), _1354180), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354182, _1354178)), _1354184)), _1354186)), _1354188) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354182, _1354178), hAPP(hAPP(c_COMBC(_1354182, tc_fun(_1354180, tc_HOL_Obool), _1354178), hAPP(hAPP(c_COMBB(tc_fun(_1354180, _1354178), tc_fun(tc_fun(_1354180, tc_HOL_Obool), _1354178), _1354182), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354180, _1354178)), hAPP(c_COMBC(_1354180, _1354182, _1354178), _1354184))), _1354188)), _1354186))], (32377 ^ _779203) ^ [_1365415, _1365417] : [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(_1365415))), 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)), _1365417)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365415)), hAPP(c_Nat_OSuc, _1365417))))], (41441 ^ _779203) ^ [_1597475, _1597477, _1597479, _1597481] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597475), tc_List_Olist(_1597475))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597475), tc_List_Olist(_1597475)), _1597477), _1597479)), c_List_Olex(_1597475, _1597481))), 41444 ^ _779203 : [(41447 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597475)), _1597477) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597475)), _1597479))], (41445 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597475), tc_List_Olist(_1597475))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597475), tc_List_Olist(_1597475)), _1597477), _1597479)), c_List_Olexord(_1597475, _1597481))))]]], (38516 ^ _779203) ^ [_1524832, _1524834, _1524836, _1524838, _1524840] : [hBOOL(hAPP(hAPP(_1524832, _1524834), _1524836)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1524838, _1524840, _1524832), _1524836)))], (41635 ^ _779203) ^ [_1603406, _1603408, _1603410, _1603412, _1603414, _1603416] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603406, _1603406)), hAPP(hAPP(c_Product__Type_OPair(_1603406, _1603406), _1603408), _1603410)), _1603412)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603406), tc_List_Olist(_1603406))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603406), tc_List_Olist(_1603406)), _1603414), _1603416)), c_List_Olistrel(_1603406, _1603412))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603406), tc_List_Olist(_1603406))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603406), tc_List_Olist(_1603406)), hAPP(hAPP(c_List_Olist_OCons(_1603406), _1603408), _1603414)), hAPP(hAPP(c_List_Olist_OCons(_1603406), _1603410), _1603416))), c_List_Olistrel(_1603406, _1603412))))], (13625 ^ _779203) ^ [_1015953, _1015955, _1015957, _1015959] : [class_Rings_Odivision__ring(_1015953), -(_1015955 = c_Groups_Ozero__class_Ozero(_1015953)), 13632 ^ _779203 : [(13639 ^ _779203) ^ [] : [_1015957 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015953), _1015959), _1015955), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015953), _1015957), _1015955) = _1015959)], (13633 ^ _779203) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015953), _1015957), _1015955) = _1015959, -(_1015957 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015953), _1015959), _1015955))]]], (6401 ^ _779203) ^ [_882600] : [hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _882600), v_U)), -(v_wt(c_Option_Othe(tc_Com_Ocom, c_Com_Obody(_882600))))], (28202 ^ _779203) ^ [_1277617, _1277619, _1277621] : [class_Orderings_Oord(_1277617), 28205 ^ _779203 : [(28212 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277617), _1277621), _1277619)), -(hBOOL(hAPP(hAPP(c_member(_1277617), _1277619), hAPP(c_SetInterval_Oord__class_OatLeast(_1277617), _1277621))))], (28206 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1277617), _1277619), hAPP(c_SetInterval_Oord__class_OatLeast(_1277617), _1277621))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277617), _1277621), _1277619)))]]], (18190 ^ _779203) ^ [_1100123] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1100123) = _1100123)], (4006 ^ _779203) ^ [_839774, _839776] : [_839776 = _839774, -(c_New__Random__Sequence_Oneg__single(_839776) = c_New__Random__Sequence_Oneg__single(_839774))], (6110 ^ _779203) ^ [_876690, _876692] : [_876692 = c_Orderings_Obot__class_Obot(tc_fun(_876690, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876690, tc_HOL_Obool)), _876692), c_Orderings_Obot__class_Obot(tc_fun(_876690, tc_HOL_Obool)))))], (52447 ^ _779203) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (34873 ^ _779203) ^ [_1426367, _1426369, _1426371, _1426373, _1426375] : [_1426367 = c_Orderings_Obot__class_Obot(tc_fun(_1426369, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_1426371), _1426373), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426369, tc_fun(_1426371, tc_HOL_Obool)), _1426367), _1426375)) = hAPP(hAPP(c_Set_Oinsert(_1426371), _1426373), c_Orderings_Obot__class_Obot(tc_fun(_1426371, tc_HOL_Obool))))], (34172 ^ _779203) ^ [_1406417, _1406419, _1406421, _1406423, _1406425, _1406427, _1406429] : [-(hAPP(c_Product__Type_Oapsnd(_1406417, _1406419, _1406421, _1406423), hAPP(c_Product__Type_Oapfst(_1406425, _1406421, _1406417, _1406427), _1406429)) = hAPP(c_Product__Type_Oapfst(_1406425, _1406421, _1406419, _1406427), hAPP(c_Product__Type_Oapsnd(_1406417, _1406419, _1406425, _1406423), _1406429)))], (10101 ^ _779203) ^ [_952084, _952086, _952088, _952090, _952092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952084), _952086)), -(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), _952086), _952088)), _952090)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952084), _952088)), _952092)) = 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), _952086), _952084)), _952088)), _952090)), _952092))], (41619 ^ _779203) ^ [_1602978, _1602980, _1602982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602978, _1602978), tc_HOL_Obool)), _1602980), _1602982)), c_Relation_Orefl__on(_1602978, c_Orderings_Otop__class_Otop(tc_fun(_1602978, tc_HOL_Obool)), _1602982), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1602978), tc_List_Olist(_1602978)), tc_HOL_Obool)), c_List_Olistrel1(_1602978, _1602980)), c_List_Olistrel(_1602978, _1602982))))], (41759 ^ _779203) ^ [_1607054, _1607056, _1607058] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607054)), _1607056), c_List_Olists(_1607054, c_Wellfounded_Oacc(_1607054, _1607058)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1607054)), _1607056), c_Wellfounded_Oacc(tc_List_Olist(_1607054), c_List_Olistrel1(_1607054, _1607058)))))], (49612 ^ _779203) ^ [_1781862, _1781864, _1781866, _1781868] : [c_Fun_Oinj__on(_1781862, _1781864, _1781866, c_Orderings_Otop__class_Otop(tc_fun(_1781862, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1781862, _1781864, c_Orderings_Otop__class_Otop(tc_fun(_1781862, tc_HOL_Obool)), _1781866), hAPP(_1781866, _1781868)) = _1781868)], (13458 ^ _779203) ^ [_1012573, _1012575, _1012577] : [hAPP(c_Finite__Set_Ocard(_1012573), _1012575) = hAPP(c_Nat_OSuc, _1012577), 13463 ^ _779203 : [(13466 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1012573), 13461 ^ [_1012573, _1012575, _1012577]), 13462 ^ [_1012573, _1012575, _1012577]))], (13468 ^ _779203) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1012573), 13462 ^ [_1012573, _1012575, _1012577]) = _1012577)], (13470 ^ _779203) ^ [] : [_1012577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(13462 ^ [_1012573, _1012575, _1012577] = c_Orderings_Obot__class_Obot(tc_fun(_1012573, tc_HOL_Obool)))], (13464 ^ _779203) ^ [] : [-(_1012575 = hAPP(hAPP(c_Set_Oinsert(_1012573), 13461 ^ [_1012573, _1012575, _1012577]), 13462 ^ [_1012573, _1012575, _1012577]))]]], (17408 ^ _779203) ^ [_1086212, _1086214, _1086216, _1086218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086212), _1086214)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086216), _1086218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086212), _1086216)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1086214), _1086218))))], (50785 ^ _779203) ^ [_1807677, _1807679, _1807681, _1807683] : [class_Divides_Osemiring__div(_1807677), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1807677), _1807679), _1807681)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807677), _1807683), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807677), _1807681), _1807679)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1807677), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1807677), _1807683), _1807681)), _1807679))], (43790 ^ _779203) ^ [_1655205, _1655207] : [-(c_List_Orotate(_1655205, _1655207) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1655205), tc_List_Olist(_1655205)), _1655207), c_List_Orotate1(_1655205)))], (10781 ^ _779203) ^ [_965692, _965694] : [class_Groups_Olinordered__ab__group__add(_965692), 10784 ^ _779203 : [(10791 ^ _779203) ^ [] : [_965694 = c_Groups_Ozero__class_Ozero(_965692), -(c_Groups_Ozero__class_Ozero(_965692) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965692), _965694), _965694))], (10785 ^ _779203) ^ [] : [c_Groups_Ozero__class_Ozero(_965692) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965692), _965694), _965694), -(_965694 = c_Groups_Ozero__class_Ozero(_965692))]]], (48044 ^ _779203) ^ [_1747488, _1747490, _1747492, _1747494, _1747496] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1747488), _1747490), _1747492), _1747494), _1747496) = c_New__DSequence_Oneg__single(_1747488, _1747490))], (45537 ^ _779203) ^ [_1693088, _1693090] : [c_List_Oconcat(_1693088, _1693090) = c_List_Olist_ONil(_1693088), 45540 ^ _779203 : [(45541 ^ _779203) ^ [_1693179] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1693088)), _1693179), hAPP(c_List_Oset(tc_List_Olist(_1693088)), _1693090))), -(_1693179 = c_List_Olist_ONil(_1693088))]]], (29344 ^ _779203) ^ [_1299548, _1299550, _1299552] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299548, tc_HOL_Obool)), _1299550), _1299552) = c_Orderings_Obot__class_Obot(tc_fun(_1299548, tc_HOL_Obool)), 29347 ^ _779203 : [(29348 ^ _779203) ^ [_1299672] : [hBOOL(hAPP(hAPP(c_member(_1299548), _1299672), _1299550)), 29351 ^ _779203 : [(29352 ^ _779203) ^ [_1299762] : [hBOOL(hAPP(hAPP(c_member(_1299548), _1299762), _1299552)), _1299672 = _1299762]]]]], (43107 ^ _779203) ^ [_1639347, _1639349, _1639351, _1639353] : [_1639351 = _1639353, -(hAPP(hAPP(c_List_Oappend(_1639347), _1639349), _1639351) = hAPP(hAPP(c_List_Oappend(_1639347), _1639349), _1639353))], (52649 ^ _779203) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (21561 ^ _779203) ^ [_1158749, _1158751] : [c_Int_OBit0(_1158749) = c_Int_OBit1(_1158751)], (46696 ^ _779203) ^ [_1718297, _1718299, _1718301, _1718303] : [_1718299 = hAPP(hAPP(c_List_Oappend(_1718297), hAPP(c_List_Orev(_1718297), _1718303)), hAPP(hAPP(c_List_Olist_OCons(_1718297), _1718301), c_List_Olist_ONil(_1718297))), -(hAPP(c_List_Orev(_1718297), _1718299) = hAPP(hAPP(c_List_Olist_OCons(_1718297), _1718301), _1718303))], (48184 ^ _779203) ^ [_1751034, _1751036, _1751038, _1751040, _1751042, _1751044] : [-(hAPP(hAPP(c_List_Ozip(_1751034, _1751036), c_List_Oreplicate(_1751034, _1751038, _1751040)), c_List_Oreplicate(_1751036, _1751042, _1751044)) = c_List_Oreplicate(tc_prod(_1751034, _1751036), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1751038), _1751042), hAPP(hAPP(c_Product__Type_OPair(_1751034, _1751036), _1751040), _1751044)))], (45452 ^ _779203) ^ [_1691379, _1691381, _1691383] : [-(hBOOL(hAPP(hAPP(c_member(_1691379), _1691381), hAPP(c_List_Oset(_1691379), _1691383)))), -(c_List_Oremdups(_1691379, hAPP(hAPP(c_List_Olist_OCons(_1691379), _1691381), _1691383)) = hAPP(hAPP(c_List_Olist_OCons(_1691379), _1691381), c_List_Oremdups(_1691379, _1691383)))], (15348 ^ _779203) ^ [_1048208, _1048210, _1048212] : [class_Orderings_Olinorder(_1048208), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048208), _1048210), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1048208), _1048210), _1048212)) = _1048210)], (13028 ^ _779203) ^ [_1004512, _1004514, _1004516] : [-(hBOOL(hAPP(_1004512, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1004514), _1004516)))), 13031 ^ _779203 : [(13034 ^ _779203) ^ [] : [hBOOL(hAPP(_1004512, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13032 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1004514), _1004516)))]], 13036 ^ _779203 : [(13039 ^ _779203) ^ [] : [hBOOL(hAPP(_1004512, 13035 ^ [_1004512, _1004514, _1004516]))], (13037 ^ _779203) ^ [] : [-(_1004514 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1004516), 13035 ^ [_1004512, _1004514, _1004516]))]]], (13428 ^ _779203) ^ [_1011916, _1011918, _1011920, _1011922] : [-(c_Sum__Type_OPlus(_1011916, _1011918, _1011920, _1011922) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1011916, _1011918), tc_HOL_Obool))), _1011920 = c_Orderings_Obot__class_Obot(tc_fun(_1011916, tc_HOL_Obool)), _1011922 = c_Orderings_Obot__class_Obot(tc_fun(_1011918, tc_HOL_Obool))], (32813 ^ _779203) ^ [_1379953, _1379955, _1379957, _1379959, _1379961, _1379963, _1379965] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1379953, _1379955, tc_fun(_1379957, tc_HOL_Obool)), _1379959), hAPP(hAPP(c_Product__Type_OPair(_1379953, _1379955), _1379961), _1379963)), _1379965)), -(hBOOL(hAPP(hAPP(hAPP(_1379959, _1379961), _1379963), _1379965)))], (37699 ^ _779203) ^ [_1494806, _1494808, _1494810, _1494812] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1494806, _1494808)), hAPP(hAPP(c_Product__Type_OSigma(_1494806, _1494808), hAPP(hAPP(c_Set_Oinsert(_1494806), _1494810), c_Orderings_Obot__class_Obot(tc_fun(_1494806, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1494808, tc_HOL_Obool), _1494806), _1494812))) = hAPP(c_Finite__Set_Ocard(_1494808), _1494812))], (9771 ^ _779203) ^ [_945980, _945982] : [9772 ^ _779203 : [(9775 ^ _779203) ^ [] : [_945980 = hAPP(c_Nat_OSuc, _945982)], (9773 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945980), _945982))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945980), hAPP(c_Nat_OSuc, _945982))))], (17126 ^ _779203) ^ [_1080811] : [class_Orderings_Oord(_1080811), -(c_Orderings_Oord__class_Omax(_1080811) = c_Orderings_Oord_Omax(_1080811, c_Orderings_Oord__class_Oless__eq(_1080811)))], (5012 ^ _779203) ^ [_855629, _855631, _855633, _855635, _855637, _855639] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_855639, _855635, _855631) = c_SetInterval_Oord__class_OatLeastAtMost(_855637, _855633, _855629)), _855639 = _855637, _855635 = _855633, _855631 = _855629], (19802 ^ _779203) ^ [_1128456, _1128458, _1128460] : [class_Groups_Oordered__ab__group__add(_1128456), 19805 ^ _779203 : [(19812 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128456), _1128460), _1128458)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128456), hAPP(c_Groups_Ouminus__class_Ouminus(_1128456), _1128458)), hAPP(c_Groups_Ouminus__class_Ouminus(_1128456), _1128460))))], (19806 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128456), hAPP(c_Groups_Ouminus__class_Ouminus(_1128456), _1128458)), hAPP(c_Groups_Ouminus__class_Ouminus(_1128456), _1128460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128456), _1128460), _1128458)))]]], (10263 ^ _779203) ^ [_955602, _955604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955602), hAPP(c_Nat_OSuc, _955604))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _955602), _955604)))], (45811 ^ _779203) ^ [_1700744] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1700744)), c_List_Otranspose__rel(_1700744)), c_List_Olist_ONil(tc_List_Olist(_1700744)))), -(c_List_Otranspose(_1700744, c_List_Olist_ONil(tc_List_Olist(_1700744))) = c_List_Olist_ONil(tc_List_Olist(_1700744)))], (5815 ^ _779203) ^ [_871223, _871225] : [class_Finite__Set_Ofinite(_871223), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_871223), _871225)))], (19314 ^ _779203) ^ [_1119612, _1119614, _1119616] : [class_Fields_Olinordered__field(_1119612), -(_1119614 = c_Groups_Ozero__class_Ozero(_1119612)), -(hAPP(c_Groups_Oabs__class_Oabs(_1119612), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119612), _1119616), _1119614)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1119612), hAPP(c_Groups_Oabs__class_Oabs(_1119612), _1119616)), hAPP(c_Groups_Oabs__class_Oabs(_1119612), _1119614)))], (44558 ^ _779203) ^ [_1671846, _1671848, _1671850] : [c_Fun_Oinj__on(tc_List_Olist(_1671846), tc_List_Olist(_1671848), hAPP(c_List_Omap(_1671846, _1671848), _1671850), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671846), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1671846, _1671848, _1671850, c_Orderings_Otop__class_Otop(tc_fun(_1671846, tc_HOL_Obool))))], (34408 ^ _779203) ^ [_1412838, _1412840, _1412842, _1412844, _1412846] : [-(_1412838 = c_Orderings_Obot__class_Obot(tc_fun(_1412840, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1412842, tc_HOL_Obool)), _1412844), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412840, tc_fun(_1412842, tc_HOL_Obool)), _1412838), _1412846)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1412840, tc_fun(_1412842, tc_HOL_Obool)), _1412838), hAPP(hAPP(c_COMBB(tc_fun(_1412842, tc_HOL_Obool), tc_fun(_1412842, tc_HOL_Obool), _1412840), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1412842, tc_HOL_Obool)), _1412844)), _1412846)))], (3718 ^ _779203) ^ [_834930, _834932] : [_834932 = _834930, -(c_Enum_Oenum__class_Oenum__ex(_834932) = c_Enum_Oenum__class_Oenum__ex(_834930))], (25628 ^ _779203) ^ [_1230486] : [c_Nat__Transfer_Ois__nat(_1230486), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230486)))], (43488 ^ _779203) ^ [_1648457, _1648459, _1648461] : [-(hAPP(hAPP(c_List_Odrop(_1648457), _1648459), c_List_Obutlast(_1648457, _1648461)) = c_List_Obutlast(_1648457, hAPP(hAPP(c_List_Odrop(_1648457), _1648459), _1648461)))], (46988 ^ _779203) ^ [_1724477, _1724479, _1724481, _1724483] : [hBOOL(hAPP(_1724477, _1724479)), -(c_List_OdropWhile(_1724481, _1724477, hAPP(hAPP(c_List_Olist_OCons(_1724481), _1724479), _1724483)) = c_List_OdropWhile(_1724481, _1724477, _1724483))], (7925 ^ _779203) ^ [_909620, _909622, _909624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_909620, tc_HOL_Obool)), _909622), _909624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909620, tc_HOL_Obool)), _909622), _909624)))], (27432 ^ _779203) ^ [_1262530, _1262532, _1262534, _1262536] : [class_Lattices_Osemilattice__sup(_1262530), 27435 ^ _779203 : [(27444 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262530), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262530), _1262532), _1262534)), _1262536))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262530), _1262532), _1262536)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262530), _1262534), _1262536))], (27436 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262530), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262530), _1262532), _1262534)), _1262536)), 27439 ^ _779203 : [(27442 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262530), _1262534), _1262536)))], (27440 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262530), _1262532), _1262536)))]]]]], (7749 ^ _779203) ^ [_906866, _906868, _906870] : [class_Orderings_Opreorder(_906866), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906866), _906868), _906870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906866), _906868), _906870)))], (4314 ^ _779203) ^ [_844642, _844644, _844646, _844648, _844650, _844652] : [-(c_New__DSequence_Opos__union(_844652, _844648, _844644) = c_New__DSequence_Opos__union(_844650, _844646, _844642)), _844652 = _844650, _844648 = _844646, _844644 = _844642], (46806 ^ _779203) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (9474 ^ _779203) ^ [_940778, _940780, _940782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940778), _940780)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940778), _940782))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940780), _940782)))], (44253 ^ _779203) ^ [_1664325, _1664327] : [-(_1664325 = c_List_Olist_ONil(_1664327)), -(hAPP(hAPP(c_List_Oappend(_1664327), c_List_Obutlast(_1664327, _1664325)), hAPP(hAPP(c_List_Olist_OCons(_1664327), c_List_Olast(_1664327, _1664325)), c_List_Olist_ONil(_1664327))) = _1664325)], (4340 ^ _779203) ^ [_845033, _845035, _845037, _845039] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_845039, _845035) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_845037, _845033)), _845039 = _845037, _845035 = _845033], (37195 ^ _779203) ^ [_1481527, _1481529] : [-(hAPP(c_Set_Ovimage(_1481527, _1481527, c_COMBI(_1481527)), _1481529) = _1481529)], (3308 ^ _779203) ^ [_828499, _828501, _828503, _828505] : [-(c_HOL_OLet(_828505, _828501) = c_HOL_OLet(_828503, _828499)), _828505 = _828503, _828501 = _828499], (3232 ^ _779203) ^ [_827347, _827349, _827351, _827353] : [-(c_Code__Numeral_Onat__of__aux(_827353, _827349) = c_Code__Numeral_Onat__of__aux(_827351, _827347)), _827353 = _827351, _827349 = _827347], (47008 ^ _779203) ^ [_1724787, _1724789, _1724791] : [-(c_List_OdropWhile(_1724787, _1724789, _1724791) = c_List_Olist_ONil(_1724787)), hBOOL(hAPP(_1724789, hAPP(c_List_Ohd(_1724787), c_List_OdropWhile(_1724787, _1724789, _1724791))))], (45616 ^ _779203) ^ [_1695363, _1695365, _1695367, _1695369] : [-(c_List_Oconcat(_1695363, hAPP(hAPP(c_List_Omap(_1695365, tc_List_Olist(_1695363)), hAPP(hAPP(c_COMBC(_1695365, tc_List_Olist(_1695363), tc_List_Olist(_1695363)), hAPP(hAPP(c_COMBB(_1695363, tc_fun(tc_List_Olist(_1695363), tc_List_Olist(_1695363)), _1695365), c_List_Olist_OCons(_1695363)), _1695367)), c_List_Olist_ONil(_1695363))), _1695369)) = hAPP(hAPP(c_List_Omap(_1695365, _1695363), _1695367), _1695369))], (29358 ^ _779203) ^ [_1299862, _1299864, _1299866] : [29360 ^ _779203 : [(29366 ^ _779203) ^ [] : [-(29359 ^ [_1299862, _1299864, _1299866] = 29362 ^ [_1299862, _1299864, _1299866])], (29364 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1299862), 29362 ^ [_1299862, _1299864, _1299866]), _1299866)))], (29361 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1299862), 29359 ^ [_1299862, _1299864, _1299866]), _1299864)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1299862, tc_HOL_Obool)), _1299864), _1299866) = c_Orderings_Obot__class_Obot(tc_fun(_1299862, tc_HOL_Obool)))], (50202 ^ _779203) ^ [_1794366, _1794368, _1794370, _1794372, _1794374, _1794376] : [c_Fun_Obij__betw(_1794366, _1794368, _1794370, c_Orderings_Otop__class_Otop(tc_fun(_1794366, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1794368, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1794366, _1794368, _1794370), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1794372, tc_fun(_1794366, tc_HOL_Obool)), _1794374), _1794376)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1794372, tc_fun(_1794368, tc_HOL_Obool)), _1794374), hAPP(hAPP(c_COMBB(tc_fun(_1794366, tc_HOL_Obool), tc_fun(_1794368, tc_HOL_Obool), _1794372), c_Set_Oimage(_1794366, _1794368, _1794370)), _1794376)))], (41611 ^ _779203) ^ [_1602732, _1602734] : [-(c_List_Olistrel(_1602732, c_Transitive__Closure_Ortrancl(_1602732, _1602734)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1602732), c_List_Olistrel1(_1602732, _1602734)))], (48503 ^ _779203) ^ [_1757488, _1757490, _1757492] : [hBOOL(hAPP(hAPP(c_member(_1757488), _1757490), hAPP(c_List_Oset(_1757488), _1757492))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1757488), _1757492), _1757490)))], (52253 ^ _779203) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (38844 ^ _779203) ^ [_1531526, _1531528, _1531530] : [c_Wellfounded_Owf(_1531526, _1531528), c_Wellfounded_Owf(_1531526, _1531530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531526, _1531526), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531526, _1531526, _1531526), _1531528), _1531530)), _1531528)), -(c_Wellfounded_Owf(_1531526, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1531526, _1531526), tc_HOL_Obool)), _1531528), _1531530)))], (40964 ^ _779203) ^ [_1583552, _1583554, _1583556] : [40965 ^ _779203 : [(40966 ^ _779203) ^ [_1583628] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583552, _1583552)), _1583554), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583552, _1583552), tc_HOL_Obool), _1583628), _1583556)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583552, _1583552)), _1583554), c_Transitive__Closure_Ortrancl(_1583552, _1583556))))], (49584 ^ _779203) ^ [_1781177, _1781179, _1781181] : [c_Fun_Oinj__on(_1781177, _1781179, _1781181, c_Orderings_Otop__class_Otop(tc_fun(_1781177, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781179, _1781177, c_Hilbert__Choice_Oinv__into(_1781177, _1781179, c_Orderings_Otop__class_Otop(tc_fun(_1781177, tc_HOL_Obool)), _1781181)), c_Orderings_Otop__class_Otop(tc_fun(_1781179, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1781177, tc_HOL_Obool)))], (36466 ^ _779203) ^ [_1465323, _1465325, _1465327, _1465329] : [-(_1465323 = c_Orderings_Obot__class_Obot(tc_fun(_1465325, tc_HOL_Obool))), 36469 ^ _779203 : [(36470 ^ _779203) ^ [] : [-(hAPP(c_Set_Oimage(_1465327, _1465325, 36477 ^ [_1465323, _1465325, _1465327, _1465329]), _1465329) = _1465323), 36471 ^ _779203 : [(36472 ^ _779203) ^ [_1465464] : [c_Fun_Oinj__on(_1465325, _1465327, _1465464, _1465323), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465327, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1465325, _1465327, _1465464), _1465323)), _1465329))]]], (36481 ^ _779203) ^ [] : [36482 ^ _779203 : [(36483 ^ _779203) ^ [_1465656] : [hAPP(c_Set_Oimage(_1465327, _1465325, _1465656), _1465329) = _1465323]], 36485 ^ _779203 : [(36488 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465327, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1465325, _1465327, 36484 ^ [_1465323, _1465325, _1465327, _1465329]), _1465323)), _1465329)))], (36486 ^ _779203) ^ [] : [-(c_Fun_Oinj__on(_1465325, _1465327, 36484 ^ [_1465323, _1465325, _1465327, _1465329], _1465323))]]]]], (48613 ^ _779203) ^ [_1760128, _1760130, _1760132, _1760134, _1760136, _1760138, _1760140] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1760128, tc_fun(_1760130, tc_fun(_1760132, tc_HOL_Obool))), _1760134), _1760136), _1760138), _1760140)), 48617 ^ _779203 : [(48620 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1760136, 48616 ^ [_1760128, _1760130, _1760132, _1760134, _1760136, _1760138, _1760140]), _1760138), _1760140)))], (48618 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760128), 48616 ^ [_1760128, _1760130, _1760132, _1760134, _1760136, _1760138, _1760140]), _1760134)))]]], (50407 ^ _779203) ^ [_1799079, _1799081, _1799083, _1799085, _1799087, _1799089, _1799091, _1799093] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799079, _1799081), tc_prod(_1799079, _1799081))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799079, _1799081), tc_prod(_1799079, _1799081)), hAPP(hAPP(c_Product__Type_OPair(_1799079, _1799081), _1799083), _1799085)), hAPP(hAPP(c_Product__Type_OPair(_1799079, _1799081), _1799087), _1799089))), c_Transitive__Closure_Ortrancl(tc_prod(_1799079, _1799081), _1799091))), hBOOL(hAPP(hAPP(_1799093, _1799083), _1799085)), 50418 ^ _779203 : [(50423 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799079, _1799081), tc_prod(_1799079, _1799081))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799079, _1799081), tc_prod(_1799079, _1799081)), hAPP(hAPP(c_Product__Type_OPair(_1799079, _1799081), 50416 ^ [_1799079, _1799081, _1799083, _1799085, _1799087, _1799089, _1799091, _1799093]), 50417 ^ [_1799079, _1799081, _1799083, _1799085, _1799087, _1799089, _1799091, _1799093])), hAPP(hAPP(c_Product__Type_OPair(_1799079, _1799081), 50420 ^ [_1799079, _1799081, _1799083, _1799085, _1799087, _1799089, _1799091, _1799093]), 50421 ^ [_1799079, _1799081, _1799083, _1799085, _1799087, _1799089, _1799091, _1799093]))), _1799091)))], (50425 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1799093, 50416 ^ [_1799079, _1799081, _1799083, _1799085, _1799087, _1799089, _1799091, _1799093]), 50417 ^ [_1799079, _1799081, _1799083, _1799085, _1799087, _1799089, _1799091, _1799093])))], (50427 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1799093, 50420 ^ [_1799079, _1799081, _1799083, _1799085, _1799087, _1799089, _1799091, _1799093]), 50421 ^ [_1799079, _1799081, _1799083, _1799085, _1799087, _1799089, _1799091, _1799093]))], (50419 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1799079, _1799081), tc_prod(_1799079, _1799081))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1799079, _1799081), tc_prod(_1799079, _1799081)), hAPP(hAPP(c_Product__Type_OPair(_1799079, _1799081), _1799083), _1799085)), hAPP(hAPP(c_Product__Type_OPair(_1799079, _1799081), 50416 ^ [_1799079, _1799081, _1799083, _1799085, _1799087, _1799089, _1799091, _1799093]), 50417 ^ [_1799079, _1799081, _1799083, _1799085, _1799087, _1799089, _1799091, _1799093]))), c_Transitive__Closure_Ortrancl(tc_prod(_1799079, _1799081), _1799091))))]], -(hBOOL(hAPP(hAPP(_1799093, _1799087), _1799089)))], (46238 ^ _779203) ^ [_1708870, _1708872, _1708874, _1708876] : [class_Orderings_Olinorder(_1708870), -(c_List_Olinorder__class_Osorted(_1708870, hAPP(hAPP(c_List_Omap(_1708872, _1708870), _1708874), c_List_Olinorder__class_Osort__key(_1708872, _1708870, _1708874, _1708876))))], (26194 ^ _779203) ^ [_1240017, _1240019, _1240021] : [class_Orderings_Oorder(_1240017), 26197 ^ _779203 : [(26204 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240017), _1240019), _1240021))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1240017, _1240019, _1240021) = c_Orderings_Obot__class_Obot(tc_fun(_1240017, tc_HOL_Obool)))], (26198 ^ _779203) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1240017, _1240019, _1240021) = c_Orderings_Obot__class_Obot(tc_fun(_1240017, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240017), _1240019), _1240021))]]], (4218 ^ _779203) ^ [_843012, _843014, _843016, _843018] : [-(c_List_Omap(_843018, _843014) = c_List_Omap(_843016, _843012)), _843018 = _843016, _843014 = _843012], (29210 ^ _779203) ^ [_1296572, _1296574, _1296576, _1296578] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296572, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296572, tc_HOL_Obool)), _1296574), _1296576)), _1296578) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296572, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296572, tc_HOL_Obool)), _1296574), _1296578)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296572, tc_HOL_Obool)), _1296576), _1296578)))], (5697 ^ _779203) ^ [_869171, _869173, _869175, _869177] : [hBOOL(hAPP(hAPP(c_member(_869171), _869173), hAPP(hAPP(c_Set_Oinsert(_869171), _869175), _869177))), -(_869173 = _869175), -(hBOOL(hAPP(hAPP(c_member(_869171), _869173), _869177)))], (10461 ^ _779203) ^ [_959894, _959896, _959898, _959900, _959902] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_959894), 10464 ^ _779203 : [(10465 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959894), _959896), _959898)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959894), _959900), _959902)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959894), _959896), _959902)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959894), _959900), _959898)), -(_959896 = _959900), -(_959898 = _959902)], (10475 ^ _779203) ^ [] : [10476 ^ _779203 : [(10479 ^ _779203) ^ [] : [_959898 = _959902], (10477 ^ _779203) ^ [] : [_959896 = _959900]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959894), _959896), _959898)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959894), _959900), _959902)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_959894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959894), _959896), _959902)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959894), _959900), _959898)))]]], (17970 ^ _779203) ^ [_1096119] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1096119) = _1096119)], (11664 ^ _779203) ^ [_980374, _980376] : [class_Rings_Olinordered__ring(_980374), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980374), c_Groups_Ozero__class_Ozero(_980374)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_980374), _980376), _980376))))], (26980 ^ _779203) ^ [_1254380, _1254382] : [class_Orderings_Oorder(_1254380), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1254380, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1254380), _1254382), c_Orderings_Obot__class_Obot(tc_fun(_1254380, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1254380), _1254382)) = hAPP(hAPP(c_Set_Oinsert(_1254380), _1254382), c_Orderings_Obot__class_Obot(tc_fun(_1254380, tc_HOL_Obool))))], (27788 ^ _779203) ^ [_1269215, _1269217, _1269219] : [class_Lattices_Osemilattice__sup(_1269215), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269215), _1269217), _1269219) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269215), _1269219), _1269217))], (2752 ^ _779203) ^ [_819887, _819889, _819891, _819893] : [-(c_Wellfounded_Omax__ext(_819893, _819889) = c_Wellfounded_Omax__ext(_819891, _819887)), _819893 = _819891, _819889 = _819887], (6909 ^ _779203) ^ [_892142, _892144] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892142, tc_HOL_Obool)), _892144), c_Orderings_Obot__class_Obot(tc_fun(_892142, tc_HOL_Obool))) = _892144)], (39510 ^ _779203) ^ [_1548011, _1548013, _1548015, _1548017, _1548019, _1548021, _1548023, _1548025, _1548027] : [hAPP(c_Fun_Ocomp(_1548011, _1548013, _1548015, _1548017), _1548019) = hAPP(c_Fun_Ocomp(_1548021, _1548013, _1548015, _1548023), _1548025), -(hAPP(_1548017, hAPP(_1548019, _1548027)) = hAPP(_1548023, hAPP(_1548025, _1548027)))], (47827 ^ _779203) ^ [_1742971, _1742973] : [-(c_FunDef_Ois__measure(_1742971, _1742973))], (4030 ^ _779203) ^ [_840160, _840162, _840164, _840166] : [-(c_New__DSequence_Oneg__single(_840166, _840162) = c_New__DSequence_Oneg__single(_840164, _840160)), _840166 = _840164, _840162 = _840160], (48096 ^ _779203) ^ [_1748774, _1748776, _1748778] : [-(c_Predicate_Oconversep(_1748774, _1748776, c_Predicate_Oconversep(_1748776, _1748774, _1748778)) = _1748778)], (3408 ^ _779203) ^ [_830059, _830061, _830063, _830065] : [-(c_Random_Oselect__weight(_830065, _830061) = c_Random_Oselect__weight(_830063, _830059)), _830065 = _830063, _830061 = _830059], (43806 ^ _779203) ^ [_1655514, _1655516, _1655518] : [-(hAPP(c_List_Otl(_1655514), hAPP(hAPP(c_List_Oappend(_1655514), _1655516), _1655518)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1655514), _1655514, hAPP(c_List_Otl(_1655514), _1655518), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1655514), tc_List_Olist(_1655514)), _1655514), hAPP(hAPP(c_COMBC(tc_List_Olist(_1655514), tc_List_Olist(_1655514), tc_List_Olist(_1655514)), c_List_Oappend(_1655514)), _1655518))), _1655516))], (52501 ^ _779203) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (2688 ^ _779203) ^ [_818843, _818845, _818847, _818849, _818851, _818853] : [-(c_Predicate_ODomainP(_818853, _818849, _818845) = c_Predicate_ODomainP(_818851, _818847, _818843)), _818853 = _818851, _818849 = _818847, _818845 = _818843], (44468 ^ _779203) ^ [_1669876, _1669878, _1669880, _1669882, _1669884] : [-(c_List_Olist_Olist__size(_1669876, _1669878, hAPP(hAPP(c_List_Omap(_1669880, _1669876), _1669882), _1669884)) = c_List_Olist_Olist__size(_1669880, hAPP(c_Fun_Ocomp(_1669876, tc_Nat_Onat, _1669880, _1669878), _1669882), _1669884))], (50431 ^ _779203) ^ [_1800209, _1800211, _1800213, _1800215, _1800217, _1800219, _1800221, _1800223] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1800209, _1800211), tc_prod(_1800209, _1800211))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1800209, _1800211), tc_prod(_1800209, _1800211)), hAPP(hAPP(c_Product__Type_OPair(_1800209, _1800211), _1800213), _1800215)), hAPP(hAPP(c_Product__Type_OPair(_1800209, _1800211), _1800217), _1800219))), c_Transitive__Closure_Ortrancl(tc_prod(_1800209, _1800211), _1800221))), hBOOL(hAPP(hAPP(_1800223, _1800217), _1800219)), 50444 ^ _779203 : [(50447 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1800209, _1800211), tc_prod(_1800209, _1800211))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1800209, _1800211), tc_prod(_1800209, _1800211)), hAPP(hAPP(c_Product__Type_OPair(_1800209, _1800211), 50442 ^ [_1800209, _1800211, _1800213, _1800215, _1800217, _1800219, _1800221, _1800223]), 50443 ^ [_1800209, _1800211, _1800213, _1800215, _1800217, _1800219, _1800221, _1800223])), hAPP(hAPP(c_Product__Type_OPair(_1800209, _1800211), _1800217), _1800219))), c_Transitive__Closure_Ortrancl(tc_prod(_1800209, _1800211), _1800221))))], (50449 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1800223, 50442 ^ [_1800209, _1800211, _1800213, _1800215, _1800217, _1800219, _1800221, _1800223]), 50443 ^ [_1800209, _1800211, _1800213, _1800215, _1800217, _1800219, _1800221, _1800223])))], (50451 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1800223, 50440 ^ [_1800209, _1800211, _1800213, _1800215, _1800217, _1800219, _1800221, _1800223]), 50441 ^ [_1800209, _1800211, _1800213, _1800215, _1800217, _1800219, _1800221, _1800223]))], (50445 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1800209, _1800211), tc_prod(_1800209, _1800211))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1800209, _1800211), tc_prod(_1800209, _1800211)), hAPP(hAPP(c_Product__Type_OPair(_1800209, _1800211), 50440 ^ [_1800209, _1800211, _1800213, _1800215, _1800217, _1800219, _1800221, _1800223]), 50441 ^ [_1800209, _1800211, _1800213, _1800215, _1800217, _1800219, _1800221, _1800223])), hAPP(hAPP(c_Product__Type_OPair(_1800209, _1800211), 50442 ^ [_1800209, _1800211, _1800213, _1800215, _1800217, _1800219, _1800221, _1800223]), 50443 ^ [_1800209, _1800211, _1800213, _1800215, _1800217, _1800219, _1800221, _1800223]))), _1800221)))]], -(hBOOL(hAPP(hAPP(_1800223, _1800213), _1800215)))], (44827 ^ _779203) ^ [] : [-(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))], (42367 ^ _779203) ^ [_1623325, _1623327, _1623329, _1623331] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623325), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623327)), _1623329))), -(hBOOL(hAPP(hAPP(c_member(_1623327), _1623331), hAPP(c_List_Oset(_1623327), hAPP(hAPP(c_List_Olist__update(_1623327, _1623329), _1623325), _1623331)))))], (36761 ^ _779203) ^ [_1471872, _1471874, _1471876, _1471878, _1471880, _1471882, _1471884, _1471886] : [c_Fun_Oinj__on(_1471872, _1471874, _1471876, _1471878), 36767 ^ _779203 : [(36770 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471872, tc_HOL_Obool)), hAPP(_1471884, 36766 ^ [_1471872, _1471874, _1471876, _1471878, _1471880, _1471882, _1471884, _1471886])), _1471878))], (36768 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1471880), 36766 ^ [_1471872, _1471874, _1471876, _1471878, _1471880, _1471882, _1471884, _1471886]), _1471882)))]], hBOOL(hAPP(hAPP(c_member(_1471880), _1471886), _1471882)), -(hAPP(c_Set_Oimage(_1471872, _1471874, _1471876), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1471880, tc_fun(_1471872, tc_HOL_Obool)), _1471882), _1471884)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1471880, tc_fun(_1471874, tc_HOL_Obool)), _1471882), hAPP(hAPP(c_COMBB(tc_fun(_1471872, tc_HOL_Obool), tc_fun(_1471874, tc_HOL_Obool), _1471880), c_Set_Oimage(_1471872, _1471874, _1471876)), _1471884)))], (14023 ^ _779203) ^ [_1023144, _1023146, _1023148, _1023150] : [class_Fields_Olinordered__field(_1023144), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023144), _1023146), _1023148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023144), c_Groups_Ozero__class_Ozero(_1023144)), _1023150)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023144), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1023144), _1023146), _1023150)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1023144), _1023148), _1023150))))], (26664 ^ _779203) ^ [_1248646, _1248648] : [26666 ^ _779203 : [(26669 ^ _779203) ^ [] : [hBOOL(hAPP(_1248648, 26665 ^ [_1248646, _1248648]))], (26667 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 26665 ^ [_1248646, _1248648]), _1248646)))]], 26670 ^ _779203 : [(26671 ^ _779203) ^ [_1248797] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1248797), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1248646))), -(hBOOL(hAPP(_1248648, _1248797)))]]], (18616 ^ _779203) ^ [_1107520, _1107522] : [class_Int_Onumber__ring(_1107520), class_Rings_Olinordered__idom(_1107520), 18623 ^ _779203 : [(18630 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107522), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107520), hAPP(c_Int_Onumber__class_Onumber__of(_1107520), _1107522)), c_Groups_Ozero__class_Ozero(_1107520))))], (18624 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107520), hAPP(c_Int_Onumber__class_Onumber__of(_1107520), _1107522)), c_Groups_Ozero__class_Ozero(_1107520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1107522), c_Int_OPls)))]]], (52671 ^ _779203) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (47653 ^ _779203) ^ [_1739465, _1739467, _1739469] : [hBOOL(hAPP(hAPP(c_member(_1739465), _1739467), hAPP(c_List_Oset(_1739465), _1739469))), -(_1739469 = hAPP(hAPP(c_List_Oappend(_1739465), 47656 ^ [_1739465, _1739467, _1739469]), hAPP(hAPP(c_List_Olist_OCons(_1739465), _1739467), 47657 ^ [_1739465, _1739467, _1739469])))], (23008 ^ _779203) ^ [_1184289, _1184291, _1184293, _1184295] : [class_Divides_Osemiring__div(_1184289), -(_1184291 = c_Groups_Ozero__class_Ozero(_1184289)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1184289), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184289), _1184293), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184289), _1184295), _1184291))), _1184291) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184289), _1184295), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1184289), _1184293), _1184291)))], (20496 ^ _779203) ^ [_1140704, _1140706] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140704), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1140706)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1140704), _1140706))], (48515 ^ _779203) ^ [_1757738, _1757740, _1757742] : [c_List_Olist__ex1(_1757738, _1757740, _1757742), 48519 ^ _779203 : [(48524 ^ _779203) ^ [_1757984] : [-(_1757984 = 48518 ^ [_1757738, _1757740, _1757742]), hBOOL(hAPP(hAPP(c_member(_1757738), _1757984), hAPP(c_List_Oset(_1757738), _1757742))), hBOOL(hAPP(_1757740, _1757984))], (48522 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1757740, 48518 ^ [_1757738, _1757740, _1757742])))], (48520 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757738), 48518 ^ [_1757738, _1757740, _1757742]), hAPP(c_List_Oset(_1757738), _1757742))))]]], (52245 ^ _779203) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (9631 ^ _779203) ^ [_943769, _943771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943769), hAPP(c_Nat_OSuc, _943771))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943769), _943771))), -(_943769 = _943771)], (45626 ^ _779203) ^ [_1695994, _1695996, _1695998, _1696000, _1696002] : [class_Orderings_Olinorder(_1695994), -(hAPP(c_List_Ofilter(_1695996, _1695998), c_List_Olinorder__class_Osort__key(_1695996, _1695994, _1696000, _1696002)) = c_List_Olinorder__class_Osort__key(_1695996, _1695994, _1696000, hAPP(c_List_Ofilter(_1695996, _1695998), _1696002)))], (20120 ^ _779203) ^ [_1134195] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1134195)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1134195)))], (43927 ^ _779203) ^ [_1658066, _1658068, _1658070] : [class_Lattices_Olattice(_1658066), -(c_Big__Operators_Olattice__class_OInf__fin(_1658066, hAPP(c_List_Oset(_1658066), hAPP(hAPP(c_List_Olist_OCons(_1658066), _1658068), _1658070))) = hAPP(c_List_Ofoldl(_1658066, _1658066, c_Lattices_Osemilattice__inf__class_Oinf(_1658066), _1658068), _1658070))], (44027 ^ _779203) ^ [_1660440, _1660442, _1660444, _1660446, _1660448] : [class_Orderings_Olinorder(_1660440), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660442)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660442, _1660440, _1660444), _1660446), _1660448)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660442)), _1660448)))], (47246 ^ _779203) ^ [_1730061, _1730063, _1730065] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1730061, _1730061)), hAPP(hAPP(c_Product__Type_OPair(_1730061, _1730061), _1730063), _1730065)), c_List_Omeasures(_1730061, c_List_Olist_ONil(tc_fun(_1730061, tc_Nat_Onat)))))], (5727 ^ _779203) ^ [_869716, _869718, _869720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_869716, tc_HOL_Obool)), _869718), hAPP(hAPP(c_Set_Oinsert(_869716), _869720), c_Orderings_Obot__class_Obot(tc_fun(_869716, tc_HOL_Obool))))), -(_869718 = c_Orderings_Obot__class_Obot(tc_fun(_869716, tc_HOL_Obool))), -(_869718 = hAPP(hAPP(c_Set_Oinsert(_869716), _869720), c_Orderings_Obot__class_Obot(tc_fun(_869716, tc_HOL_Obool))))], (49828 ^ _779203) ^ [_1786966, _1786968] : [49830 ^ _779203 : [(49833 ^ _779203) ^ [] : [hBOOL(hAPP(_1786966, hAPP(c_Code__Numeral_Oof__nat, 49829 ^ [_1786966, _1786968])))], (49831 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49829 ^ [_1786966, _1786968]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))]], -(hBOOL(hAPP(_1786966, _1786968)))], (7877 ^ _779203) ^ [_908733, _908735, _908737, _908739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_908733, tc_HOL_Obool)), _908735), _908737)), hBOOL(hAPP(hAPP(c_member(_908733), _908739), _908735)), -(hBOOL(hAPP(hAPP(c_member(_908733), _908739), _908737)))], (23804 ^ _779203) ^ [_1198129, _1198131, _1198133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1198129)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198129), _1198131)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1198129), _1198133)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1198131), _1198133))], (52241 ^ _779203) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (34506 ^ _779203) ^ [_1416008, _1416010, _1416012, _1416014] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1416008, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416010, tc_fun(_1416008, tc_HOL_Obool)), _1416012), _1416014)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416010, tc_fun(_1416008, tc_HOL_Obool)), _1416012), hAPP(hAPP(c_COMBB(tc_fun(_1416008, tc_HOL_Obool), tc_fun(_1416008, tc_HOL_Obool), _1416010), c_Groups_Ouminus__class_Ouminus(tc_fun(_1416008, tc_HOL_Obool))), _1416014)))], (28674 ^ _779203) ^ [_1286409, _1286411, _1286413] : [class_Orderings_Oorder(_1286409), 28677 ^ _779203 : [(28684 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286409), _1286411), _1286413))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1286409, _1286411, _1286413) = c_Orderings_Obot__class_Obot(tc_fun(_1286409, tc_HOL_Obool)))], (28678 ^ _779203) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1286409, _1286411, _1286413) = c_Orderings_Obot__class_Obot(tc_fun(_1286409, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286409), _1286411), _1286413))]]], (46994 ^ _779203) ^ [_1724588, _1724590, _1724592, _1724594] : [-(hBOOL(hAPP(_1724588, _1724590))), -(c_List_OdropWhile(_1724592, _1724588, hAPP(hAPP(c_List_Olist_OCons(_1724592), _1724590), _1724594)) = hAPP(hAPP(c_List_Olist_OCons(_1724592), _1724590), _1724594))], (52687 ^ _779203) ^ [_1836855, _1836857, _1836859, _1836861, _1836863, _1836865] : [-(hAPP(hAPP(hAPP(c_COMBC(_1836855, _1836857, _1836859), _1836861), _1836863), _1836865) = hAPP(hAPP(_1836861, _1836865), _1836863))], (326 ^ _779203) ^ [_784122, _784124, _784126, _784128] : [-(c_Nitpick_Owf_H(_784126, _784122)), c_Nitpick_Owf_H(_784128, _784124), _784128 = _784126, _784124 = _784122], (27636 ^ _779203) ^ [_1266234, _1266236] : [class_Lattices_Obounded__lattice__bot(_1266234), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266234), c_Orderings_Obot__class_Obot(_1266234)), _1266236) = _1266236)], (18778 ^ _779203) ^ [_1110152, _1110154, _1110156] : [-(hBOOL(hAPP(_1110152, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110154), _1110156))))), 18781 ^ _779203 : [(18784 ^ _779203) ^ [] : [hBOOL(hAPP(_1110152, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1110154)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1110156))))], (18782 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110156), _1110154)))]], 18785 ^ _779203 : [(18788 ^ _779203) ^ [] : [hBOOL(hAPP(_1110152, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (18786 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110154), _1110156)))]]], (34955 ^ _779203) ^ [] : [-(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)))], (22409 ^ _779203) ^ [_1174547, _1174549] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1174547, _1174549) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1174547 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1174549), 22412 ^ [_1174547, _1174549]))], (9590 ^ _779203) ^ [_942916, _942918, _942920, _942922] : [class_Rings_Ocomm__semiring(_942916), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942916), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942916), _942918), _942920)), _942922) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_942916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942916), _942918), _942922)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_942916), _942920), _942922)))], (39536 ^ _779203) ^ [_1548658, _1548660, _1548662, _1548664, _1548666] : [c_Finite__Set_Ofun__left__comm(_1548658, _1548660, _1548662), -(hAPP(c_Fun_Ocomp(_1548660, _1548660, _1548660, hAPP(_1548662, _1548664)), hAPP(_1548662, _1548666)) = hAPP(c_Fun_Ocomp(_1548660, _1548660, _1548660, hAPP(_1548662, _1548666)), hAPP(_1548662, _1548664)))], (19564 ^ _779203) ^ [_1124189, _1124191, _1124193] : [19566 ^ _779203 : [(19569 ^ _779203) ^ [] : [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(_1124191, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 19565 ^ [_1124189, _1124191, _1124193]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1124191, 19565 ^ [_1124189, _1124191, _1124193])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19567 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19565 ^ [_1124189, _1124191, _1124193]), _1124189)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1124191, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1124193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1124193), hAPP(_1124191, _1124189))), 19579 ^ _779203 : [(19582 ^ _779203) ^ [] : [-(hAPP(_1124191, 19578 ^ [_1124189, _1124191, _1124193]) = _1124193)], (19580 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 19578 ^ [_1124189, _1124191, _1124193]), _1124189)))]]], (7627 ^ _779203) ^ [_905076, _905078, _905080] : [class_Orderings_Opreorder(_905076), 7630 ^ _779203 : [(7639 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905076), _905078), _905080))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905076), _905078), _905080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905076), _905080), _905078)))], (7631 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905076), _905078), _905080)), 7634 ^ _779203 : [(7637 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905076), _905080), _905078))], (7635 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905076), _905078), _905080)))]]]]], (15752 ^ _779203) ^ [_1055314, _1055316, _1055318, _1055320] : [class_Orderings_Olinorder(_1055314), 15755 ^ _779203 : [(15764 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055314), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1055314), _1055316), _1055318)), _1055320))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055314), _1055316), _1055320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055314), _1055318), _1055320))], (15756 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055314), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1055314), _1055316), _1055318)), _1055320)), 15759 ^ _779203 : [(15762 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055314), _1055318), _1055320)))], (15760 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055314), _1055316), _1055320)))]]]]], (52389 ^ _779203) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (9538 ^ _779203) ^ [_942025, _942027] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942025), _942027)), _942025) = _942027)], (28736 ^ _779203) ^ [_1287400, _1287402, _1287404, _1287406] : [hBOOL(hAPP(_1287400, _1287402)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287404, tc_HOL_Obool)), _1287400), _1287406)), -(hBOOL(hAPP(_1287406, _1287402)))], (30075 ^ _779203) ^ [_1314756, _1314758, _1314760, _1314762, _1314764] : [class_Groups_Ocomm__monoid__add(_1314756), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314758), _1314760)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314758), _1314762)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1314756), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1314758, _1314756), _1314764), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1314758, tc_HOL_Obool)), _1314760), _1314762))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1314758, _1314756), _1314764), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1314758, tc_HOL_Obool)), _1314760), _1314762))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1314756), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1314758, _1314756), _1314764), _1314760)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1314758, _1314756), _1314764), _1314762)))], (5602 ^ _779203) ^ [_864824, _864826] : [_864826 = _864824, -(c_Set_Oinsert(_864826) = c_Set_Oinsert(_864824))], (35926 ^ _779203) ^ [_1453360, _1453362, _1453364, _1453366, _1453368, _1453370, _1453372, _1453374, _1453376, _1453378] : [c_Equiv__Relations_Oequiv(_1453360, _1453362, _1453364), c_Equiv__Relations_Oequiv(_1453366, _1453368, _1453370), c_Equiv__Relations_Ocongruent2(_1453360, _1453366, tc_fun(_1453372, tc_HOL_Obool), _1453364, _1453370, _1453374), hBOOL(hAPP(hAPP(c_member(_1453360), _1453376), _1453362)), hBOOL(hAPP(hAPP(c_member(_1453366), _1453378), _1453368)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1453360, tc_fun(_1453372, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1453360, _1453360, _1453364), hAPP(hAPP(c_Set_Oinsert(_1453360), _1453376), c_Orderings_Obot__class_Obot(tc_fun(_1453360, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1453366, tc_fun(_1453372, tc_HOL_Obool)), tc_fun(_1453372, tc_HOL_Obool), _1453360), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1453366, tc_fun(_1453372, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1453366, _1453366, _1453370), hAPP(hAPP(c_Set_Oinsert(_1453366), _1453378), c_Orderings_Obot__class_Obot(tc_fun(_1453366, tc_HOL_Obool)))))), _1453374)) = hAPP(hAPP(_1453374, _1453376), _1453378))], (48320 ^ _779203) ^ [_1753532, _1753534, _1753536, _1753538] : [-(hBOOL(hAPP(hAPP(c_member(_1753532), _1753534), hAPP(c_List_Oset(_1753532), c_List_Oreplicate(_1753532, _1753536, _1753538))))), _1753534 = _1753538, -(_1753536 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21423 ^ _779203) ^ [] : [-(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)))], (37211 ^ _779203) ^ [_1481978, _1481980, _1481982, _1481984, _1481986] : [hBOOL(hAPP(hAPP(c_member(_1481978), _1481980), hAPP(c_Set_Ovimage(_1481978, _1481982, _1481984), _1481986))), -(hBOOL(hAPP(hAPP(c_member(_1481982), hAPP(_1481984, _1481980)), _1481986)))], (17356 ^ _779203) ^ [_1085148] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085148), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1085148)], (50256 ^ _779203) ^ [_1795575, _1795577] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795575), _1795577)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1795575, 50259 ^ [_1795575, _1795577], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1795575), _1795577)), _1795577))], (29952 ^ _779203) ^ [_1312328, _1312330, _1312332, _1312334] : [class_Orderings_Olinorder(_1312328), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312328, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1312328, _1312330, _1312332)), hAPP(c_SetInterval_Oord__class_OatLeast(_1312328), _1312334)) = c_SetInterval_Oord__class_OatLeastAtMost(_1312328, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1312328), _1312330), _1312334), _1312332))], (21493 ^ _779203) ^ [_1157607, _1157609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1157607), _1157609)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1157607)), c_Int_OBit0(_1157609))))], (340 ^ _779203) ^ [_784315, _784317] : [-(c_Nitpick_Ounknown(_784315)), _784317 = _784315, c_Nitpick_Ounknown(_784317)], (43516 ^ _779203) ^ [_1649211, _1649213] : [hAPP(c_List_Orotate1(_1649211), _1649213) = c_List_Olist_ONil(_1649211), -(_1649213 = c_List_Olist_ONil(_1649211))], (34318 ^ _779203) ^ [_1410068, _1410070, _1410072, _1410074, _1410076] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410068, tc_fun(_1410070, tc_HOL_Obool)), _1410072), hAPP(hAPP(c_COMBB(tc_fun(_1410070, tc_HOL_Obool), tc_fun(_1410070, tc_HOL_Obool), _1410068), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410070, tc_HOL_Obool)), _1410074)), _1410076)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1410070, tc_HOL_Obool)), _1410074), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410068, tc_fun(_1410070, tc_HOL_Obool)), _1410072), _1410076)))], (34845 ^ _779203) ^ [_1425531, _1425533, _1425535, _1425537] : [hBOOL(hAPP(hAPP(c_member(_1425533), _1425537), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425531, tc_fun(_1425533, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1425531, tc_HOL_Obool))), _1425535))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425531, tc_fun(_1425533, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1425531, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1425533, tc_HOL_Obool), tc_fun(_1425533, tc_HOL_Obool), _1425531), hAPP(c_COMBC(_1425533, tc_fun(_1425533, tc_HOL_Obool), tc_HOL_Obool), c_member(_1425533))), _1425535)), _1425537)))], (7983 ^ _779203) ^ [_910724, _910726, _910728, _910730, _910732, _910734, _910736] : [c_Nitpick_Ofold__graph_H(_910724, _910726, _910728, _910730, _910732, hAPP(hAPP(_910728, _910734), _910736)), 7988 ^ _779203 : [(7991 ^ _779203) ^ [] : [-(hAPP(hAPP(_910728, _910734), _910736) = _910730)], (7989 ^ _779203) ^ [] : [-(_910732 = c_Orderings_Obot__class_Obot(tc_fun(_910724, tc_HOL_Obool)))]], 7994 ^ _779203 : [(7999 ^ _779203) ^ [] : [-(c_Nitpick_Ofold__graph_H(_910724, _910726, _910728, _910730, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910724, tc_HOL_Obool)), _910732), hAPP(hAPP(c_Set_Oinsert(_910724), 7992 ^ [_910724, _910726, _910728, _910730, _910732, _910734, _910736]), c_Orderings_Obot__class_Obot(tc_fun(_910724, tc_HOL_Obool)))), 7993 ^ [_910724, _910726, _910728, _910730, _910732, _910734, _910736]))], (7997 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910724), 7992 ^ [_910724, _910726, _910728, _910730, _910732, _910734, _910736]), _910732)))], (7995 ^ _779203) ^ [] : [-(hAPP(hAPP(_910728, _910734), _910736) = hAPP(hAPP(_910728, 7992 ^ [_910724, _910726, _910728, _910730, _910732, _910734, _910736]), 7993 ^ [_910724, _910726, _910728, _910730, _910732, _910734, _910736]))]]], (39201 ^ _779203) ^ [_1539670, _1539672] : [-(c_Nitpick_Owf_H(_1539670, _1539672)), c_Wellfounded_Oacyclic(_1539670, _1539672), 39206 ^ _779203 : [(39209 ^ _779203) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (39207 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539670, _1539670)), _1539672))]]], (45424 ^ _779203) ^ [_1690849, _1690851, _1690853, _1690855] : [-(hAPP(c_List_OremoveAll(_1690849, _1690851), hAPP(hAPP(c_List_Oappend(_1690849), _1690853), _1690855)) = hAPP(hAPP(c_List_Oappend(_1690849), hAPP(c_List_OremoveAll(_1690849, _1690851), _1690853)), hAPP(c_List_OremoveAll(_1690849, _1690851), _1690855)))], (49877 ^ _779203) ^ [_1787895, _1787897, _1787899, _1787901, _1787903, _1787905] : [c_Fun_Obij__betw(_1787895, _1787897, _1787899, _1787901, _1787903), hBOOL(hAPP(hAPP(c_member(_1787895), _1787905), _1787901)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1787897, _1787895, _1787903, c_Hilbert__Choice_Oinv__into(_1787895, _1787897, _1787901, _1787899)), _1787905) = hAPP(_1787899, _1787905))], (40366 ^ _779203) ^ [_1569109, _1569111] : [-(c_Transitive__Closure_Ortrancl(_1569109, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569109, _1569109), tc_HOL_Obool)), _1569111), c_Relation_OId(_1569109))) = c_Transitive__Closure_Ortrancl(_1569109, _1569111))], (43237 ^ _779203) ^ [_1641934, _1641936, _1641938] : [-(c_List_Olist_ONil(_1641934) = hAPP(hAPP(c_List_Oappend(_1641934), _1641936), _1641938)), _1641936 = c_List_Olist_ONil(_1641934), _1641938 = c_List_Olist_ONil(_1641934)], (19834 ^ _779203) ^ [_1129022, _1129024, _1129026] : [class_Groups_Oordered__ab__group__add(_1129022), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129022), _1129024), _1129026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1129022), hAPP(c_Groups_Ouminus__class_Ouminus(_1129022), _1129026)), hAPP(c_Groups_Ouminus__class_Ouminus(_1129022), _1129024))))], (27996 ^ _779203) ^ [_1273413, _1273415] : [class_Orderings_Otop(_1273413), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273413), _1273415), c_Orderings_Otop__class_Otop(_1273413))))], (2278 ^ _779203) ^ [_812480, _812482, _812484, _812486, _812488, _812490] : [-(c_Nat_Onat_Onat__rec(_812490, _812486, _812482) = c_Nat_Onat_Onat__rec(_812488, _812484, _812480)), _812490 = _812488, _812486 = _812484, _812482 = _812480], (6407 ^ _779203) ^ [_882693, _882695, _882697, _882699] : [c_Finite__Set_Ofolding__one__idem(_882693, _882695, _882697), -(hAPP(hAPP(_882695, _882699), _882699) = _882699)], (33117 ^ _779203) ^ [_1385732, _1385734] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385732))), 33120 ^ _779203 : [(33127 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385734))), -(c_Divides_Odivmod__int(_1385732, _1385734) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385732), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385734))))], (33121 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385734)), -(c_Divides_Odivmod__int(_1385732, _1385734) = c_Divides_OnegDivAlg(_1385732, _1385734))]]], (2574 ^ _779203) ^ [_817076, _817078, _817080, _817082, _817084, _817086, _817088, _817090] : [-(c_Nitpick_Oprod(_817090, _817086, _817082, _817078) = c_Nitpick_Oprod(_817088, _817084, _817080, _817076)), _817090 = _817088, _817086 = _817084, _817082 = _817080, _817078 = _817076], (20498 ^ _779203) ^ [_1140744, _1140746] : [class_Rings_Oring__1(_1140744), hBOOL(hAPP(hAPP(c_member(_1140744), _1140746), c_Int_Oring__1__class_OInts(_1140744))), -(hBOOL(hAPP(hAPP(c_member(_1140744), hAPP(c_Groups_Ouminus__class_Ouminus(_1140744), _1140746)), c_Int_Oring__1__class_OInts(_1140744))))], (32819 ^ _779203) ^ [_1380104, _1380106, _1380108, _1380110, _1380112, _1380114] : [hBOOL(hAPP(hAPP(_1380104, _1380106), _1380108)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1380110, tc_fun(_1380112, tc_HOL_Obool))), _1380104), _1380114), _1380106), _1380108)))], (2498 ^ _779203) ^ [_815862, _815864, _815866, _815868, _815870, _815872, _815874, _815876, _815878, _815880] : [-(c_Finite__Set_Ofold__graph(_815880, _815876, _815872, _815868, _815864) = c_Finite__Set_Ofold__graph(_815878, _815874, _815870, _815866, _815862)), _815880 = _815878, _815876 = _815874, _815872 = _815870, _815868 = _815866, _815864 = _815862], (16258 ^ _779203) ^ [_1064686, _1064688, _1064690] : [class_Orderings_Olinorder(_1064686), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064686), _1064688)), hBOOL(hAPP(hAPP(c_member(_1064686), _1064690), _1064688)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1064686), _1064690), c_Big__Operators_Olinorder__class_OMax(_1064686, _1064688)) = c_Big__Operators_Olinorder__class_OMax(_1064686, _1064688))], (17712 ^ _779203) ^ [_1091376, _1091378, _1091380] : [class_Orderings_Olinorder(_1091376), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091376), _1091378)), -(c_Big__Operators_Olattice_OSup__fin(_1091376, c_Orderings_Oord__class_Omax(_1091376), hAPP(hAPP(c_Set_Oinsert(_1091376), _1091380), _1091378)) = hAPP(hAPP(c_Finite__Set_Ofold(_1091376, _1091376, c_Orderings_Oord__class_Omax(_1091376)), _1091380), _1091378))], (45809 ^ _779203) ^ [_1700681, _1700683] : [-(c_Random_Opick(_1700681, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1700681), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1700681, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1700681, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1700681)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1700683)) = c_Random_Opick(_1700681, _1700683))], (1200 ^ _779203) ^ [_797163, _797165] : [-(class_Rings_Olinordered__semiring__1(_797163)), _797165 = _797163, class_Rings_Olinordered__semiring__1(_797165)], (27875 ^ _779203) ^ [_1270947, _1270949, _1270951, _1270953] : [27876 ^ _779203 : [(27877 ^ _779203) ^ [_1271057] : [hBOOL(hAPP(hAPP(c_member(_1270947), _1271057), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270947, tc_HOL_Obool)), _1270949), _1270951))), hBOOL(hAPP(_1270953, _1271057))]], 27885 ^ _779203 : [(27888 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1270953, 27884 ^ [_1270947, _1270949, _1270951, _1270953])))], (27886 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1270947), 27884 ^ [_1270947, _1270949, _1270951, _1270953]), _1270949)))]], 27890 ^ _779203 : [(27893 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1270953, 27889 ^ [_1270947, _1270949, _1270951, _1270953])))], (27891 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1270947), 27889 ^ [_1270947, _1270949, _1270951, _1270953]), _1270951)))]]], (21247 ^ _779203) ^ [_1153847, _1153849] : [class_Int_Onumber__ring(_1153847), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1153847), _1153849), hAPP(c_Int_Onumber__class_Onumber__of(_1153847), c_Int_OBit1(c_Int_OPls))) = _1153849)], (39473 ^ _779203) ^ [_1547263, _1547265, _1547267, _1547269, _1547271, _1547273] : [-(hAPP(hAPP(c_Fun_Ocomp(_1547263, _1547265, _1547267, _1547269), _1547271), _1547273) = hAPP(_1547269, hAPP(_1547271, _1547273)))], (39119 ^ _779203) ^ [_1538035, _1538037] : [c_Wellfounded_Owf(_1538035, _1538037), -(c_Wellfounded_OwfP(_1538035, c_FunDef_Oin__rel(_1538035, _1538035, _1538037)))], (1890 ^ _779203) ^ [_805788, _805790] : [-(class_Groups_Ominus(_805788)), _805790 = _805788, class_Groups_Ominus(_805790)], (9843 ^ _779203) ^ [_947223, _947225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947223), _947225)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _947223), _947225)))], (50075 ^ _779203) ^ [_1792021, _1792023, _1792025, _1792027, _1792029] : [c_Fun_Obij__betw(_1792021, _1792023, _1792025, _1792027, _1792029), -(c_Fun_Obij__betw(_1792023, _1792021, c_Fun_Othe__inv__into(_1792021, _1792023, _1792027, _1792025), _1792029, _1792027))], (34342 ^ _779203) ^ [_1410953, _1410955, _1410957, _1410959, _1410961] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410953, tc_fun(_1410955, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410953, tc_HOL_Obool)), _1410957), _1410959)), _1410961) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410955, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410953, tc_fun(_1410955, tc_HOL_Obool)), _1410957), _1410961)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1410953, tc_fun(_1410955, tc_HOL_Obool)), _1410959), _1410961)))], (45819 ^ _779203) ^ [_1700968, _1700970, _1700972, _1700974] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1700968)), _1700970))), c_List_Ofoldr(tc_List_Olist(_1700972), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700972)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700972))), _1700974, 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(_1700968)), _1700970)), c_List_Ofoldr(tc_List_Olist(_1700972), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700972)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700972), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700972)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700972)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1700972), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700972)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700972), tc_List_Olist(_1700972), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700972)))), _1700974), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (42678 ^ _779203) ^ [_1629949, _1629951] : [-(c_List_Olistrelp(_1629949, _1629951, c_List_Olist_ONil(_1629949), c_List_Olist_ONil(_1629949)))], (42902 ^ _779203) ^ [_1634359, _1634361, _1634363, _1634365] : [-(hAPP(c_List_Olist_Olist__case(_1634359, _1634361, _1634363, _1634365), c_List_Olist_ONil(_1634361)) = _1634363)], (9779 ^ _779203) ^ [_946144, _946146] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _946144)), hAPP(c_Nat_OSuc, _946146))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946144), _946146)))], (30285 ^ _779203) ^ [_1319445, _1319447, _1319449, _1319451, _1319453] : [class_Groups_Ocomm__monoid__mult(_1319445), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319447), _1319449)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319447), _1319451)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319447, tc_HOL_Obool)), _1319449), _1319451) = c_Orderings_Obot__class_Obot(tc_fun(_1319447, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319447, _1319445), _1319453), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319447, tc_HOL_Obool)), _1319449), _1319451)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1319445), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319447, _1319445), _1319453), _1319449)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1319447, _1319445), _1319453), _1319451)))], (34596 ^ _779203) ^ [_1418396, _1418398, _1418400, _1418402, _1418404] : [hBOOL(hAPP(hAPP(c_member(_1418396), _1418398), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1418400, tc_fun(_1418396, tc_HOL_Obool)), _1418402), _1418404))), 34600 ^ _779203 : [(34603 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418396), _1418398), hAPP(_1418404, 34599 ^ [_1418396, _1418398, _1418400, _1418402, _1418404]))))], (34601 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418400), 34599 ^ [_1418396, _1418398, _1418400, _1418402, _1418404]), _1418402)))]]], (32235 ^ _779203) ^ [_1362239, _1362241, _1362243] : [class_Int_Onumber__ring(_1362239), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1362239), hAPP(c_Int_Onumber__class_Onumber__of(_1362239), _1362241)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1362243))) = hAPP(hAPP(c_HOL_OLet(_1362239, _1362239), hAPP(hAPP(c_Power_Opower__class_Opower(_1362239), hAPP(c_Int_Onumber__class_Onumber__of(_1362239), _1362241)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1362243))), hAPP(hAPP(c_COMBS(_1362239, _1362239, _1362239), c_Groups_Otimes__class_Otimes(_1362239)), c_COMBI(_1362239))))], (36228 ^ _779203) ^ [_1460736, _1460738, _1460740, _1460742, _1460744, _1460746] : [c_Fun_Oinj__on(_1460736, _1460738, _1460740, _1460742), hBOOL(hAPP(hAPP(c_member(_1460736), _1460744), _1460742)), hBOOL(hAPP(hAPP(c_member(_1460736), _1460746), _1460742)), 36239 ^ _779203 : [(36246 ^ _779203) ^ [] : [_1460744 = _1460746, -(hAPP(_1460740, _1460744) = hAPP(_1460740, _1460746))], (36240 ^ _779203) ^ [] : [hAPP(_1460740, _1460744) = hAPP(_1460740, _1460746), -(_1460744 = _1460746)]]], (27224 ^ _779203) ^ [_1258484] : [-(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)), _1258484)) = hAPP(c_Int_Onat, _1258484))], (35228 ^ _779203) ^ [_1435615, _1435617, _1435619, _1435621, _1435623] : [35230 ^ _779203 : [(35236 ^ _779203) ^ [] : [hBOOL(hAPP(_1435623, 35232 ^ [_1435615, _1435617, _1435619, _1435621, _1435623]))], (35234 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1435615), 35232 ^ [_1435615, _1435617, _1435619, _1435621, _1435623]), hAPP(_1435621, 35229 ^ [_1435615, _1435617, _1435619, _1435621, _1435623]))))], (35231 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1435617), 35229 ^ [_1435615, _1435617, _1435619, _1435621, _1435623]), _1435619)))]], 35237 ^ _779203 : [(35238 ^ _779203) ^ [_1435925] : [hBOOL(hAPP(hAPP(c_member(_1435615), _1435925), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1435617, tc_fun(_1435615, tc_HOL_Obool)), _1435619), _1435621))), -(hBOOL(hAPP(_1435623, _1435925)))]]], (22189 ^ _779203) ^ [_1171027, _1171029, _1171031, _1171033] : [class_Divides_Osemiring__div(_1171027), -(c_Divides_Odiv__class_Omod(_1171027, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171027), _1171029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171027), _1171031), _1171033)), _1171033) = c_Divides_Odiv__class_Omod(_1171027, _1171029, _1171033))], (11596 ^ _779203) ^ [_979194, _979196, _979198] : [class_Rings_Olinordered__ring__strict(_979194), 11599 ^ _779203 : [(11614 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979194), _979196), _979198)), c_Groups_Ozero__class_Ozero(_979194)))), 11615 ^ _779203 : [(11622 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979194), _979196), c_Groups_Ozero__class_Ozero(_979194))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979194), c_Groups_Ozero__class_Ozero(_979194)), _979198))], (11616 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979194), c_Groups_Ozero__class_Ozero(_979194)), _979196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979194), _979198), c_Groups_Ozero__class_Ozero(_979194)))]]], (11600 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_979194), _979196), _979198)), c_Groups_Ozero__class_Ozero(_979194))), 11605 ^ _779203 : [(11608 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979194), _979198), c_Groups_Ozero__class_Ozero(_979194))))], (11606 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979194), c_Groups_Ozero__class_Ozero(_979194)), _979196)))]], 11609 ^ _779203 : [(11612 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979194), c_Groups_Ozero__class_Ozero(_979194)), _979198)))], (11610 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_979194), _979196), c_Groups_Ozero__class_Ozero(_979194))))]]]]], (42359 ^ _779203) ^ [_1623136, _1623138, _1623140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1623136), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623138)), _1623140))), -(hAPP(hAPP(c_List_Otake(_1623138), _1623136), c_List_Obutlast(_1623138, _1623140)) = hAPP(hAPP(c_List_Otake(_1623138), _1623136), _1623140))], (28756 ^ _779203) ^ [_1287730, _1287732, _1287734, _1287736] : [hBOOL(hAPP(_1287730, _1287732)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1287734, tc_HOL_Obool)), _1287736), _1287730), _1287732)))], (42208 ^ _779203) ^ [_1619868, _1619870, _1619872] : [class_Groups_Omonoid__add(_1619868), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1619868), hAPP(hAPP(c_List_Olist_OCons(_1619868), _1619870), _1619872)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1619868), _1619870), hAPP(c_List_Omonoid__add__class_Olistsum(_1619868), _1619872)))], (12110 ^ _779203) ^ [_988496] : [class_Rings_Olinordered__semidom(_988496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988496), c_Groups_Oone__class_Oone(_988496)), c_Groups_Ozero__class_Ozero(_988496)))], (44781 ^ _779203) ^ [_1676637] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1676637)) = _1676637)], (44795 ^ _779203) ^ [_1676872, _1676874] : [hAPP(c_Code__Numeral_Onat__of, _1676872) = hAPP(c_Code__Numeral_Onat__of, _1676874), -(_1676872 = _1676874)], (37651 ^ _779203) ^ [_1493466, _1493468, _1493470, _1493472, _1493474] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1493466, _1493468), _1493470), hAPP(hAPP(c_COMBS(_1493466, tc_fun(_1493468, tc_HOL_Obool), tc_fun(_1493468, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1493468, tc_HOL_Obool), tc_fun(tc_fun(_1493468, tc_HOL_Obool), tc_fun(_1493468, tc_HOL_Obool)), _1493466), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493468, tc_HOL_Obool))), _1493472)), _1493474)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1493466, _1493468), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1493466, _1493468), _1493470), _1493472)), hAPP(hAPP(c_Product__Type_OSigma(_1493466, _1493468), _1493470), _1493474)))], (13561 ^ _779203) ^ [_1014739, _1014741] : [class_Rings_Odivision__ring(_1014739), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014739), c_Groups_Ozero__class_Ozero(_1014739)), _1014741) = c_Groups_Ozero__class_Ozero(_1014739))], (47807 ^ _779203) ^ [_1742683, _1742685, _1742687, _1742689] : [-(c_List_Olist__all(_1742683, _1742685, hAPP(hAPP(c_List_Oappend(_1742683), _1742687), _1742689))), c_List_Olist__all(_1742683, _1742685, _1742687), c_List_Olist__all(_1742683, _1742685, _1742689)], (13855 ^ _779203) ^ [_1020027, _1020029, _1020031, _1020033] : [class_Fields_Olinordered__field__inverse__zero(_1020027), 13858 ^ _779203 : [(13859 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020027), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1020027), _1020029), _1020031)), _1020033)), 13862 ^ _779203 : [(13869 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020027), c_Groups_Ozero__class_Ozero(_1020027)), _1020031))), 13872 ^ _779203 : [(13879 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020027), _1020031), c_Groups_Ozero__class_Ozero(_1020027)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020027), c_Groups_Ozero__class_Ozero(_1020027)), _1020033)))], (13873 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020027), _1020031), c_Groups_Ozero__class_Ozero(_1020027))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020027), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020027), _1020033), _1020031)), _1020029)))]]], (13863 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020027), c_Groups_Ozero__class_Ozero(_1020027)), _1020031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020027), _1020029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020027), _1020033), _1020031))))]]], (13885 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020027), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1020027), _1020029), _1020031)), _1020033))), 13888 ^ _779203 : [(13891 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020027), _1020029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020027), _1020033), _1020031)))], (13889 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020027), c_Groups_Ozero__class_Ozero(_1020027)), _1020031)))]], 13892 ^ _779203 : [(13895 ^ _779203) ^ [] : [13896 ^ _779203 : [(13899 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020027), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020027), _1020033), _1020031)), _1020029))], (13897 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020027), _1020031), c_Groups_Ozero__class_Ozero(_1020027))))]], 13900 ^ _779203 : [(13903 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020027), c_Groups_Ozero__class_Ozero(_1020027)), _1020033))], (13901 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020027), _1020031), c_Groups_Ozero__class_Ozero(_1020027)))]]], (13893 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1020027), c_Groups_Ozero__class_Ozero(_1020027)), _1020031))]]]]], (52291 ^ _779203) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (34236 ^ _779203) ^ [_1407806, _1407808, _1407810, _1407812, _1407814, _1407816] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1407806, tc_fun(_1407808, tc_HOL_Obool)), _1407810), _1407812), _1407814)), -(hBOOL(hAPP(hAPP(_1407812, _1407816), _1407814))), hBOOL(hAPP(hAPP(c_member(_1407806), _1407816), _1407810))], (19786 ^ _779203) ^ [_1128173, _1128175, _1128177] : [class_Groups_Oordered__ab__group__add(_1128173), 19789 ^ _779203 : [(19796 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128173), hAPP(c_Groups_Ouminus__class_Ouminus(_1128173), _1128177)), _1128175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128173), hAPP(c_Groups_Ouminus__class_Ouminus(_1128173), _1128175)), _1128177)))], (19790 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128173), hAPP(c_Groups_Ouminus__class_Ouminus(_1128173), _1128175)), _1128177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1128173), hAPP(c_Groups_Ouminus__class_Ouminus(_1128173), _1128177)), _1128175)))]]], (38274 ^ _779203) ^ [_1515898, _1515900] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1515898), _1515900)), -(_1515900 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1515898, 38278 ^ [_1515898, _1515900]), 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)), 38277 ^ [_1515898, _1515900]))))], (26374 ^ _779203) ^ [_1243064, _1243066] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243064), _1243066))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1243066, _1243064) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1243066), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1243066), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1243064)))], (36362 ^ _779203) ^ [_1463305, _1463307, _1463309, _1463311] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1463305), hAPP(c_Set_Oimage(_1463307, _1463305, _1463309), _1463311))), c_Fun_Oinj__on(_1463307, _1463305, _1463309, _1463311), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1463307), _1463311)))], (17022 ^ _779203) ^ [_1078880, _1078882, _1078884] : [class_Orderings_Olinorder(_1078880), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078880), _1078882)), -(hBOOL(hAPP(hAPP(c_member(_1078880), _1078884), _1078882))), -(_1078882 = c_Orderings_Obot__class_Obot(tc_fun(_1078880, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1078880, hAPP(hAPP(c_Set_Oinsert(_1078880), _1078884), _1078882)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1078880), _1078884), c_Big__Operators_Olinorder__class_OMin(_1078880, _1078882)))], (39580 ^ _779203) ^ [_1549703, _1549705, _1549707, _1549709, _1549711, _1549713] : [class_Groups_Ocomm__monoid__mult(_1549703), c_Fun_Oinj__on(_1549705, _1549707, _1549709, _1549711), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549707, _1549703), _1549713), hAPP(c_Set_Oimage(_1549705, _1549707, _1549709), _1549711)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549705, _1549703), hAPP(c_Fun_Ocomp(_1549707, _1549703, _1549705, _1549713), _1549709)), _1549711))], (38834 ^ _779203) ^ [_1531349, _1531351, _1531353] : [c_Wellfounded_Owf(_1531349, _1531351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531349, tc_HOL_Obool)), _1531353), hAPP(c_Relation_OImage(_1531349, _1531349, _1531351), _1531353))), -(_1531353 = c_Orderings_Obot__class_Obot(tc_fun(_1531349, tc_HOL_Obool)))], (37860 ^ _779203) ^ [_1499950, _1499952, _1499954, _1499956] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1499952, _1499950), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1499950, tc_prod(_1499952, _1499950), 37856 ^ [_1499950, _1499952, _1499954, _1499956]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1499952, tc_fun(_1499950, tc_HOL_Obool)), _1499954), _1499956))), hAPP(hAPP(c_Product__Type_OSigma(_1499952, _1499950), _1499954), _1499956))))], (9421 ^ _779203) ^ [_939792, _939794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939792), _939794)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939794), _939792)), -(_939792 = _939794)], (50279 ^ _779203) ^ [_1796081, _1796083, _1796085] : [c_Equiv__Relations_Oequivp(_1796081, _1796083), 50282 ^ _779203 : [(50283 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1796085, 50290 ^ [_1796081, _1796083, _1796085]))), 50284 ^ _779203 : [(50285 ^ _779203) ^ [_1796203] : [hBOOL(hAPP(hAPP(c_member(_1796081), _1796203), c_Quotient_ORespects(_1796081, _1796083))), hBOOL(hAPP(_1796085, _1796203))]]], (50294 ^ _779203) ^ [] : [50295 ^ _779203 : [(50296 ^ _779203) ^ [_1796370] : [hBOOL(hAPP(_1796085, _1796370))]], 50298 ^ _779203 : [(50301 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1796085, 50297 ^ [_1796081, _1796083, _1796085])))], (50299 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796081), 50297 ^ [_1796081, _1796083, _1796085]), c_Quotient_ORespects(_1796081, _1796083))))]]]]], (5326 ^ _779203) ^ [_860650, _860652, _860654, _860656, _860658, _860660] : [-(c_SetInterval_Oord_OatMost(_860660, _860656, _860652) = c_SetInterval_Oord_OatMost(_860658, _860654, _860650)), _860660 = _860658, _860656 = _860654, _860652 = _860650], (49441 ^ _779203) ^ [_1778310, _1778312] : [49442 ^ _779203 : [(49443 ^ _779203) ^ [_1778366] : [hBOOL(hAPP(hAPP(_1778310, _1778366), _1778366))]], c_Predicate_Osymp(_1778312, _1778310), c_Predicate_Otransp(_1778312, _1778310), -(c_Equiv__Relations_Opart__equivp(_1778312, _1778310))], (25472 ^ _779203) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19140 ^ _779203) ^ [_1116365, _1116367] : [class_Groups_Oordered__ab__group__add__abs(_1116365), 19143 ^ _779203 : [(19150 ^ _779203) ^ [] : [_1116367 = c_Groups_Ozero__class_Ozero(_1116365), -(hAPP(c_Groups_Oabs__class_Oabs(_1116365), _1116367) = c_Groups_Ozero__class_Ozero(_1116365))], (19144 ^ _779203) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1116365), _1116367) = c_Groups_Ozero__class_Ozero(_1116365), -(_1116367 = c_Groups_Ozero__class_Ozero(_1116365))]]], (20236 ^ _779203) ^ [_1136173, _1136175] : [class_Groups_Olinordered__ab__group__add(_1136173), 20239 ^ _779203 : [(20246 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136173), c_Groups_Ozero__class_Ozero(_1136173)), _1136175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136173), hAPP(c_Groups_Ouminus__class_Ouminus(_1136173), _1136175)), _1136175)))], (20240 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136173), hAPP(c_Groups_Ouminus__class_Ouminus(_1136173), _1136175)), _1136175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1136173), c_Groups_Ozero__class_Ozero(_1136173)), _1136175)))]]], (20664 ^ _779203) ^ [_1143792, _1143794, _1143796, _1143798] : [hBOOL(hAPP(hAPP(c_member(_1143792), _1143794), c_SetInterval_Oord_OgreaterThan(_1143792, _1143796, _1143798))), -(hBOOL(hAPP(hAPP(_1143796, _1143798), _1143794)))], (8567 ^ _779203) ^ [_923577, _923579] : [class_Groups_Omonoid__mult(_923577), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923577), c_Groups_Oone__class_Oone(_923577)), _923579) = _923579)], (45157 ^ _779203) ^ [_1685123, _1685125, _1685127, _1685129] : [c_List_Olist__all2(_1685123, _1685125, _1685127, c_List_Olist_ONil(_1685123), _1685129), -(_1685129 = c_List_Olist_ONil(_1685125))], (21839 ^ _779203) ^ [_1163684] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1163684), 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), _1163684), _1163684))], (44680 ^ _779203) ^ [_1674362, _1674364] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1674362)), hAPP(c_Code__Numeral_Oof__nat, _1674364)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1674362), _1674364)))], (9993 ^ _779203) ^ [_949853, _949855, _949857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949853), _949855)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949857), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949855), _949853)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _949857), _949853)), _949855))], (17500 ^ _779203) ^ [_1087775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1087775)), -(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)), _1087775))))], (22514 ^ _779203) ^ [_1176085] : [-(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)), _1176085)) = _1176085)], (18847 ^ _779203) ^ [_1111300, _1111302] : [class_Int_Onumber__ring(_1111300), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1111302)), -(hBOOL(hAPP(hAPP(c_member(_1111300), hAPP(c_Int_Onumber__class_Onumber__of(_1111300), _1111302)), c_Nat_Osemiring__1__class_ONats(_1111300))))], (38282 ^ _779203) ^ [_1516029, _1516031] : [38283 ^ _779203 : [(38284 ^ _779203) ^ [_1516093, _1516095] : [_1516031 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1516029, _1516093), 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)), _1516095)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1516029), _1516031)))], (48182 ^ _779203) ^ [_1750983, _1750985, _1750987, _1750989] : [-(hAPP(hAPP(c_List_Otake(_1750983), _1750985), c_List_Oreplicate(_1750983, _1750987, _1750989)) = c_List_Oreplicate(_1750983, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1750985), _1750987), _1750989))], (658 ^ _779203) ^ [_789082, _789084, _789086, _789088] : [-(c_FunDef_Ois__measure(_789086, _789082)), c_FunDef_Ois__measure(_789088, _789084), _789088 = _789086, _789084 = _789082], (29776 ^ _779203) ^ [_1308326, _1308328, _1308330] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308326, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308326, tc_HOL_Obool)), _1308328), _1308330)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308326, tc_HOL_Obool)), _1308328), _1308330)) = _1308328)], (21611 ^ _779203) ^ [_1159625, _1159627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1159625)), c_Int_OBit1(_1159627))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159625), _1159627)))], (44450 ^ _779203) ^ [_1669434, _1669436, _1669438, _1669440] : [-(_1669434 = c_List_Olist_ONil(_1669436)), -(hAPP(c_List_Ohd(_1669438), hAPP(hAPP(c_List_Omap(_1669436, _1669438), _1669440), _1669434)) = hAPP(_1669440, hAPP(c_List_Ohd(_1669436), _1669434)))], (52249 ^ _779203) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (32015 ^ _779203) ^ [_1356677, _1356679, _1356681, _1356683, _1356685] : [class_Groups_Ocomm__monoid__add(_1356677), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1356677), _1356679), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1356681), _1356683), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1356685), _1356683))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1356677), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1356677, tc_Nat_Onat), _1356679), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1356683))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1356681, _1356685)))], (3648 ^ _779203) ^ [_833809, _833811, _833813, _833815, _833817, _833819] : [-(c_List_Oinsert(_833819, _833815, _833811) = c_List_Oinsert(_833817, _833813, _833809)), _833819 = _833817, _833815 = _833813, _833811 = _833809], (19412 ^ _779203) ^ [_1121479] : [_1121479 = 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), _1121479)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (37477 ^ _779203) ^ [_1488596, _1488598, _1488600] : [-(hAPP(c_Set_OCollect(_1488596), hAPP(hAPP(c_COMBS(_1488596, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1488596), c_fconj), _1488598)), _1488600)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1488596, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1488596), _1488598)), hAPP(c_Set_OCollect(_1488596), _1488600)))], (43273 ^ _779203) ^ [_1642696, _1642698, _1642700, _1642702, _1642704] : [-(hAPP(hAPP(c_List_Olist__update(_1642696, hAPP(hAPP(c_List_Oappend(_1642696), _1642698), hAPP(hAPP(c_List_Olist_OCons(_1642696), _1642700), _1642702))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642696)), _1642698)), _1642704) = hAPP(hAPP(c_List_Oappend(_1642696), _1642698), hAPP(hAPP(c_List_Olist_OCons(_1642696), _1642704), _1642702)))], (24093 ^ _779203) ^ [_1203584, _1203586] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1203584))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203584)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203586)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20098 ^ _779203) ^ [_1133768, _1133770, _1133772] : [class_Fields_Ofield__inverse__zero(_1133768), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1133768), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133768), _1133770), _1133772)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133768), _1133770), hAPP(c_Groups_Ouminus__class_Ouminus(_1133768), _1133772)))], (41306 ^ _779203) ^ [_1592839] : [-(c_Nitpick_Odenom(_1592839) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1592839, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1592839)))], (38461 ^ _779203) ^ [_1521613, _1521615, _1521617, _1521619] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521613, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1521613, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521615, _1521613), _1521617)), hAPP(c_Relation_ORange(_1521615, _1521613), _1521619))), hAPP(c_Relation_ORange(_1521615, _1521613), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1521615, _1521613), tc_HOL_Obool)), _1521617), _1521619)))))], (17656 ^ _779203) ^ [_1090383, _1090385, _1090387] : [class_Orderings_Olinorder(_1090383), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090383), _1090385)), -(_1090387 = c_Orderings_Obot__class_Obot(tc_fun(_1090383, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1090383, tc_HOL_Obool)), _1090387), _1090385)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090383), c_Big__Operators_Olattice_OSup__fin(_1090383, c_Orderings_Oord__class_Omax(_1090383), _1090387)), c_Big__Operators_Olattice_OSup__fin(_1090383, c_Orderings_Oord__class_Omax(_1090383), _1090385)) = c_Big__Operators_Olattice_OSup__fin(_1090383, c_Orderings_Oord__class_Omax(_1090383), _1090385))], (18794 ^ _779203) ^ [_1110451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110451), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110451)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (32655 ^ _779203) ^ [_1374231, _1374233, _1374235, _1374237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool)), _1374235), _1374237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1374231, tc_fun(_1374233, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1374231, tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_fun(_1374233, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374233, tc_fun(tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_fun(_1374233, tc_HOL_Obool)), _1374231), c_COMBC(_1374233, tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374233, tc_prod(_1374231, _1374233)), tc_fun(_1374233, tc_fun(tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_HOL_Obool)), _1374231), hAPP(c_COMBB(tc_prod(_1374231, _1374233), tc_fun(tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_HOL_Obool), _1374233), c_member(tc_prod(_1374231, _1374233)))), c_Product__Type_OPair(_1374231, _1374233)))), _1374235)), hAPP(hAPP(c_COMBC(_1374231, tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_fun(_1374233, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374233, tc_fun(tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_fun(_1374233, tc_HOL_Obool)), _1374231), c_COMBC(_1374233, tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1374233, tc_prod(_1374231, _1374233)), tc_fun(_1374233, tc_fun(tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_HOL_Obool)), _1374231), hAPP(c_COMBB(tc_prod(_1374231, _1374233), tc_fun(tc_fun(tc_prod(_1374231, _1374233), tc_HOL_Obool), tc_HOL_Obool), _1374233), c_member(tc_prod(_1374231, _1374233)))), c_Product__Type_OPair(_1374231, _1374233)))), _1374237))))], (15740 ^ _779203) ^ [_1055100, _1055102, _1055104] : [class_Orderings_Olinorder(_1055100), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1055100), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1055100), _1055102), _1055104)), _1055104)))], (51791 ^ _779203) ^ [_1825180, _1825182] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1825180), 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)))), _1825182))), 51794 ^ _779203 : [(51797 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825182), _1825180))], (51795 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1825180), _1825182)))]]], (46957 ^ _779203) ^ [_1723863, _1723865, _1723867] : [class_Orderings_Olinorder(_1723863), c_List_Olinorder__class_Osorted(_1723863, _1723865), -(c_List_Olinorder__class_Osorted(_1723863, c_List_OdropWhile(_1723863, _1723867, _1723865)))], (13281 ^ _779203) ^ [_1009077, _1009079, _1009081, _1009083, _1009085, _1009087] : [class_Rings_Olinordered__semiring__1(_1009077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009077), _1009079), _1009081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009077), _1009083), _1009081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009077), c_Groups_Ozero__class_Ozero(_1009077)), _1009085)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009077), c_Groups_Ozero__class_Ozero(_1009077)), _1009087)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009077), _1009085), _1009087) = c_Groups_Oone__class_Oone(_1009077), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009077), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1009077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009077), _1009085), _1009079)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1009077), _1009087), _1009083))), _1009081)))], (42904 ^ _779203) ^ [_1634398, _1634400, _1634402] : [-(c_List_Olistset(_1634398, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1634398, tc_HOL_Obool)), _1634400), _1634402)) = c_List_Oset__Cons(_1634398, _1634400, c_List_Olistset(_1634398, _1634402)))], (17854 ^ _779203) ^ [_1093939, _1093941, _1093943] : [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), _1093939), _1093941)), _1093943))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1093943), _1093939)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1093939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1093941)))], (40618 ^ _779203) ^ [_1574980] : [-(c_Relation_OId(_1574980) = hAPP(c_Set_OCollect(tc_prod(_1574980, _1574980)), hAPP(hAPP(c_COMBB(tc_fun(_1574980, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1574980, _1574980)), c_HOL_OEx(_1574980)), hAPP(hAPP(c_COMBC(tc_prod(_1574980, _1574980), tc_fun(_1574980, tc_prod(_1574980, _1574980)), tc_fun(_1574980, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1574980, _1574980), tc_HOL_Obool), tc_fun(tc_fun(_1574980, tc_prod(_1574980, _1574980)), tc_fun(_1574980, tc_HOL_Obool)), tc_prod(_1574980, _1574980)), c_COMBB(tc_prod(_1574980, _1574980), tc_HOL_Obool, _1574980)), c_fequal)), hAPP(hAPP(c_COMBS(_1574980, _1574980, tc_prod(_1574980, _1574980)), c_Product__Type_OPair(_1574980, _1574980)), c_COMBI(_1574980))))))], (33899 ^ _779203) ^ [_1400301] : [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), _1400301))), -(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), _1400301)) = 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), _1400301))))], (50384 ^ _779203) ^ [_1798237, _1798239, _1798241, _1798243, _1798245] : [50386 ^ _779203 : [(50389 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1798241, tc_HOL_Obool)), _1798243), hAPP(_1798245, 50385 ^ [_1798237, _1798239, _1798241, _1798243, _1798245])))], (50387 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798237), 50385 ^ [_1798237, _1798239, _1798241, _1798243, _1798245]), _1798239)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1798241, tc_HOL_Obool)), _1798243), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1798237, tc_fun(_1798241, tc_HOL_Obool)), _1798239), _1798245))))], (43770 ^ _779203) ^ [_1654820, _1654822, _1654824] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654820)), hAPP(c_List_Orotate(_1654820, _1654822), _1654824)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654820)), _1654824))], (34887 ^ _779203) ^ [_1426729, _1426731, _1426733, _1426735, _1426737] : [_1426729 = c_Orderings_Obot__class_Obot(tc_fun(_1426731, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426731, tc_fun(_1426733, tc_HOL_Obool)), _1426729), hAPP(hAPP(c_COMBB(tc_fun(_1426733, tc_HOL_Obool), tc_fun(_1426733, tc_HOL_Obool), _1426731), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1426733, tc_HOL_Obool)), _1426735)), _1426737)) = c_Orderings_Obot__class_Obot(tc_fun(_1426733, tc_HOL_Obool)))], (40673 ^ _779203) ^ [_1576380, _1576382] : [-(c_Transitive__Closure_Ortrancl(_1576380, hAPP(c_Relation_Oconverse(_1576380, _1576380), _1576382)) = hAPP(c_Relation_Oconverse(_1576380, _1576380), c_Transitive__Closure_Ortrancl(_1576380, _1576382)))], (40113 ^ _779203) ^ [_1562271, _1562273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1562271), _1562273)), -(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), _1562271), _1562273)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (29786 ^ _779203) ^ [_1308567, _1308569] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308567, tc_HOL_Obool)), _1308569), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308567, tc_HOL_Obool)), _1308569)) = c_Orderings_Obot__class_Obot(tc_fun(_1308567, tc_HOL_Obool)))], (21949 ^ _779203) ^ [_1166146, _1166148] : [class_Divides_Osemiring__div(_1166146), -(c_Divides_Odiv__class_Omod(_1166146, _1166148, _1166148) = c_Groups_Ozero__class_Ozero(_1166146))], (41220 ^ _779203) ^ [_1590697, _1590699, _1590701, _1590703, _1590705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590697, tc_HOL_Obool)), _1590699), _1590701)), 41226 ^ _779203 : [(41231 ^ _779203) ^ [] : [hBOOL(hAPP(_1590705, 41225 ^ [_1590697, _1590699, _1590701, _1590703, _1590705]))], (41229 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1590703, 41225 ^ [_1590697, _1590699, _1590701, _1590703, _1590705])))], (41227 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1590697), 41225 ^ [_1590697, _1590699, _1590701, _1590703, _1590705]), _1590699)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1590697, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1590697, tc_HOL_Obool)), _1590699), hAPP(c_Set_OCollect(_1590697), _1590703))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1590697, tc_HOL_Obool)), _1590701), hAPP(c_Set_OCollect(_1590697), _1590705)))))], (29830 ^ _779203) ^ [_1309553, _1309555, _1309557] : [class_Lattices_Olattice(_1309553), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309553), _1309555)), hBOOL(hAPP(hAPP(c_member(_1309553), _1309557), _1309555)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1309553), _1309557), c_Big__Operators_Olattice__class_OSup__fin(_1309553, _1309555)) = _1309557)], (4412 ^ _779203) ^ [_846175, _846177] : [_846177 = _846175, -(c_Lazy__Sequence_Oyield(_846177) = c_Lazy__Sequence_Oyield(_846175))], (37918 ^ _779203) ^ [_1502258] : [-(c_Int_Oint__ge__less__than2(_1502258) = 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), _1502258)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (1520 ^ _779203) ^ [_801163, _801165] : [-(class_Finite__Set_Ofinite(_801163)), _801165 = _801163, class_Finite__Set_Ofinite(_801165)], (20889 ^ _779203) ^ [_1147778, _1147780] : [class_Rings_Osemiring__1(_1147778), 20892 ^ _779203 : [(20899 ^ _779203) ^ [] : [_1147780 = c_Groups_Ozero__class_Ozero(_1147778), -(c_Int_Oiszero(_1147778, _1147780))], (20893 ^ _779203) ^ [] : [c_Int_Oiszero(_1147778, _1147780), -(_1147780 = c_Groups_Ozero__class_Ozero(_1147778))]]], (8731 ^ _779203) ^ [_926412, _926414, _926416, _926418] : [class_Groups_Oordered__ab__semigroup__add(_926412), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926412), _926414), _926416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926412), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926412), _926414), _926418)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926412), _926416), _926418))))], (52259 ^ _779203) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (38487 ^ _779203) ^ [_1523166, _1523168, _1523170, _1523172] : [hBOOL(hAPP(hAPP(c_member(_1523166), _1523168), hAPP(c_Relation_ORange(_1523170, _1523166), _1523172))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1523170, _1523166)), hAPP(hAPP(c_Product__Type_OPair(_1523170, _1523166), 38490 ^ [_1523166, _1523168, _1523170, _1523172]), _1523168)), _1523172)))], (5228 ^ _779203) ^ [_859015, _859017, _859019, _859021, _859023, _859025, _859027, _859029] : [-(c_Lazy__Sequence_Omap(_859029, _859025, _859021, _859017) = c_Lazy__Sequence_Omap(_859027, _859023, _859019, _859015)), _859029 = _859027, _859025 = _859023, _859021 = _859019, _859017 = _859015], (25822 ^ _779203) ^ [_1233457, _1233459] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1233457, _1233459)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1233459), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1233457), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (9667 ^ _779203) ^ [_944404, _944406, _944408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944406), _944408)), -(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, _944404)), _944406)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _944404)), _944408))))], (31127 ^ _779203) ^ [_1336305, _1336307, _1336309, _1336311, _1336313] : [class_Groups_Ocomm__monoid__mult(_1336305), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336307), _1336309)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336307), _1336311)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1336307, tc_HOL_Obool)), _1336309), _1336311) = c_Orderings_Obot__class_Obot(tc_fun(_1336307, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1336305, _1336307, c_Groups_Otimes__class_Otimes(_1336305)), _1336313), c_Groups_Oone__class_Oone(_1336305)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1336307, tc_HOL_Obool)), _1336309), _1336311)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336305), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1336305, _1336307, c_Groups_Otimes__class_Otimes(_1336305)), _1336313), c_Groups_Oone__class_Oone(_1336305)), _1336309)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1336305, _1336307, c_Groups_Otimes__class_Otimes(_1336305)), _1336313), c_Groups_Oone__class_Oone(_1336305)), _1336311)))], (38372 ^ _779203) ^ [_1519051, _1519053, _1519055, _1519057, _1519059, _1519061, _1519063] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1519051, _1519053, _1519055), hAPP(hAPP(c_Relation_Orel__comp(_1519051, _1519057, _1519053), _1519059), _1519061)), _1519063) = hAPP(hAPP(c_Relation_Orel__comp(_1519051, _1519057, _1519055), _1519059), hAPP(hAPP(c_Relation_Orel__comp(_1519057, _1519053, _1519055), _1519061), _1519063)))], (37851 ^ _779203) ^ [_1499815, _1499817] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1499815))), -(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)), _1499815))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1499817)))) = 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)), _1499815))), 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, _1499817))))))], (34789 ^ _779203) ^ [_1424133, _1424135, _1424137, _1424139, _1424141, _1424143] : [hBOOL(hAPP(hAPP(c_member(_1424133), _1424135), _1424137)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1424133, tc_fun(_1424139, tc_HOL_Obool)), _1424137), hAPP(hAPP(c_COMBB(tc_fun(_1424139, tc_HOL_Obool), tc_fun(_1424139, tc_HOL_Obool), _1424133), hAPP(c_Set_Oinsert(_1424139), _1424141)), _1424143)) = hAPP(hAPP(c_Set_Oinsert(_1424139), _1424141), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1424133, tc_fun(_1424139, tc_HOL_Obool)), _1424137), _1424143)))], (46532 ^ _779203) ^ [_1714730, _1714732, _1714734, _1714736] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714730), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1714730))), _1714732))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714734), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714730))), c_List_Otranspose(_1714730, _1714732)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714736), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714730))), hAPP(c_List_Ofilter(tc_List_Olist(_1714730), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1714730)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714734)), c_Nat_Osize__class_Osize(tc_List_Olist(_1714730)))), _1714732)))), -(hAPP(hAPP(c_List_Onth(_1714730), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714730)), c_List_Otranspose(_1714730, _1714732)), _1714734)), _1714736) = hAPP(hAPP(c_List_Onth(_1714730), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714730)), _1714732), _1714736)), _1714734))], (28906 ^ _779203) ^ [_1290659, _1290661, _1290663] : [class_Lattices_Olattice(_1290659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290659), _1290661)), hBOOL(hAPP(hAPP(c_member(_1290659), _1290663), _1290661)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1290659), _1290663), c_Big__Operators_Olattice__class_OSup__fin(_1290659, _1290661)) = c_Big__Operators_Olattice__class_OSup__fin(_1290659, _1290661))], (50829 ^ _779203) ^ [_1808680, _1808682, _1808684, _1808686] : [class_Rings_Ocomm__ring(_1808680), class_Rings_Odvd(_1808680), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808680), _1808682), _1808684)), 50840 ^ _779203 : [(50847 ^ _779203) ^ [_1809106, _1809108] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808680), _1808682), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808680), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1808680), _1809108), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1808680), _1809106), _1808684))), _1808686))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808680), _1808682), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808680), _1809108), _1808686))))], (50841 ^ _779203) ^ [_1808933, _1808935] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808680), _1808682), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808680), _1808935), _1808686))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808680), _1808682), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808680), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1808680), _1808935), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1808680), _1808933), _1808684))), _1808686))))]]], (46682 ^ _779203) ^ [_1717906, _1717908] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717906)), hAPP(c_List_Orev(_1717906), _1717908)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717906)), _1717908))], (46610 ^ _779203) ^ [_1716391, _1716393, _1716395] : [-(hAPP(c_List_Orev(_1716391), hAPP(hAPP(c_List_Oappend(_1716391), _1716393), _1716395)) = hAPP(hAPP(c_List_Oappend(_1716391), hAPP(c_List_Orev(_1716391), _1716395)), hAPP(c_List_Orev(_1716391), _1716393)))], (12625 ^ _779203) ^ [_997019, _997021, _997023, _997025] : [class_Rings_Olinordered__ring__strict(_997019), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997019), _997021), c_Groups_Ozero__class_Ozero(_997019))), 12632 ^ _779203 : [(12639 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997019), _997025), _997023)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997019), _997021), _997023)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997019), _997021), _997025))))], (12633 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997019), _997021), _997023)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997019), _997021), _997025))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997019), _997025), _997023)))]]], (42696 ^ _779203) ^ [_1630263, _1630265] : [_1630265 = c_List_Olist_ONil(_1630263), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630263)), _1630265) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21729 ^ _779203) ^ [_1161660] : [-(c_Int_Osucc(c_Int_OBit1(_1161660)) = c_Int_OBit0(c_Int_Osucc(_1161660)))], (28152 ^ _779203) ^ [_1276664] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276664, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1276664, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1276664, tc_HOL_Obool)))], (33947 ^ _779203) ^ [_1401324, _1401326, _1401328] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1401324, _1401326), _1401328)), 33950 ^ _779203 : [(33959 ^ _779203) ^ [] : [-(_1401326 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 33962 ^ _779203 : [(33971 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1401326))), 33974 ^ _779203 : [(33977 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401328)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (33975 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1401326), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401328))))]]], (33963 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1401326)), 33966 ^ _779203 : [(33969 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401328)), _1401326)))], (33967 ^ _779203) ^ [] : [-(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), _1401328))))]]]]], (33953 ^ _779203) ^ [] : [_1401326 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1401328) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33951 ^ _779203) ^ [] : [-(_1401324 = 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), _1401328)), _1401326)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401328)))]]], (38576 ^ _779203) ^ [_1526187, _1526189, _1526191] : [-(c_Relation_Orefl__on(_1526187, _1526189, _1526191)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1526187, _1526187), tc_HOL_Obool)), _1526191), hAPP(hAPP(c_Product__Type_OSigma(_1526187, _1526187), _1526189), hAPP(c_COMBK(tc_fun(_1526187, tc_HOL_Obool), _1526187), _1526189)))), 38582 ^ _779203 : [(38585 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526187, _1526187)), hAPP(hAPP(c_Product__Type_OPair(_1526187, _1526187), 38581 ^ [_1526187, _1526189, _1526191]), 38581 ^ [_1526187, _1526189, _1526191])), _1526191))], (38583 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1526187), 38581 ^ [_1526187, _1526189, _1526191]), _1526189)))]]], (7353 ^ _779203) ^ [_900851, _900853, _900855] : [class_Orderings_Opreorder(_900851), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900851), _900853), _900855)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900851), _900855), _900853))], (34433 ^ _779203) ^ [_1413515, _1413517, _1413519, _1413521, _1413523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413515, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1413517, tc_fun(_1413515, tc_HOL_Obool)), _1413519), _1413521)), _1413523)), 34436 ^ _779203 : [(34437 ^ _779203) ^ [_1413648] : [hBOOL(hAPP(hAPP(c_member(_1413517), _1413648), _1413519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413515, tc_HOL_Obool)), hAPP(_1413521, _1413648)), _1413523)))]]], (52691 ^ _779203) ^ [_1836962, _1836964] : [hBOOL(hAPP(hAPP(c_fequal, _1836962), _1836964)), -(_1836962 = _1836964)], (34226 ^ _779203) ^ [_1407609, _1407611, _1407613, _1407615, _1407617, _1407619] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1407609, tc_fun(_1407611, tc_HOL_Obool)), _1407613), _1407615), _1407617)), hBOOL(hAPP(hAPP(c_member(_1407609), _1407619), _1407613)), -(hBOOL(hAPP(hAPP(_1407615, _1407619), _1407617)))], (39696 ^ _779203) ^ [_1552275, _1552277, _1552279, _1552281, _1552283, _1552285] : [c_Finite__Set_Ofolding(_1552275, _1552277, _1552279, _1552281), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552275), _1552283)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552275), _1552285)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1552275, tc_HOL_Obool)), _1552283), _1552285) = c_Orderings_Obot__class_Obot(tc_fun(_1552275, tc_HOL_Obool)), -(hAPP(_1552281, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1552275, tc_HOL_Obool)), _1552283), _1552285)) = hAPP(c_Fun_Ocomp(_1552277, _1552277, _1552277, hAPP(_1552281, _1552283)), hAPP(_1552281, _1552285)))], (14519 ^ _779203) ^ [_1031950, _1031952, _1031954, _1031956] : [class_Fields_Olinordered__field(_1031950), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031950), c_Groups_Ozero__class_Ozero(_1031950)), _1031952)), 14526 ^ _779203 : [(14533 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031950), _1031954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031950), _1031956), _1031952))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031950), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1031950), _1031954), _1031952)), _1031956)))], (14527 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031950), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1031950), _1031954), _1031952)), _1031956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1031950), _1031954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1031950), _1031956), _1031952))))]]], (12549 ^ _779203) ^ [_995622, _995624, _995626, _995628] : [class_Groups_Oordered__comm__monoid__add(_995622), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995622), c_Groups_Ozero__class_Ozero(_995622)), _995624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995622), _995626), _995628)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995622), _995626), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995622), _995624), _995628))))], (25306 ^ _779203) ^ [_1225485, _1225487, _1225489] : [class_Rings_Oring__1(_1225485), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1225485), hAPP(c_Groups_Ouminus__class_Ouminus(_1225485), _1225487)), _1225489) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1225485), hAPP(hAPP(c_Power_Opower__class_Opower(_1225485), hAPP(c_Groups_Ouminus__class_Ouminus(_1225485), c_Groups_Oone__class_Oone(_1225485))), _1225489)), hAPP(hAPP(c_Power_Opower__class_Opower(_1225485), _1225487), _1225489)))], (45446 ^ _779203) ^ [_1691254, _1691256, _1691258] : [hBOOL(hAPP(hAPP(c_member(_1691254), _1691256), hAPP(c_List_Oset(_1691254), _1691258))), -(c_List_Oremdups(_1691254, hAPP(hAPP(c_List_Olist_OCons(_1691254), _1691256), _1691258)) = c_List_Oremdups(_1691254, _1691258))], (42098 ^ _779203) ^ [_1617077, _1617079, _1617081, _1617083, _1617085] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1617077, _1617079)), _1617081), hAPP(hAPP(c_List_Ozip(_1617077, _1617079), _1617083), _1617085)) = hAPP(hAPP(c_List_Ozip(_1617077, _1617079), hAPP(hAPP(c_List_Otake(_1617077), _1617081), _1617083)), hAPP(hAPP(c_List_Otake(_1617079), _1617081), _1617085)))], (49826 ^ _779203) ^ [_1786931] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 49822 ^ [_1786931]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (29432 ^ _779203) ^ [_1301338, _1301340, _1301342] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301338, tc_HOL_Obool)), _1301340), _1301342)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301338, tc_HOL_Obool)), _1301342), _1301340) = _1301340)], (26418 ^ _779203) ^ [_1243794, _1243796, _1243798] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243794)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1243796), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1243798)), 26425 ^ _779203 : [(26426 ^ _779203) ^ [_1244002] : [26428 ^ _779203 : [(26434 ^ _779203) ^ [] : [-(_1244002 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26430 ^ [_1243794, _1243796, _1243798, _1244002]), 26427 ^ [_1243794, _1243796, _1243798, _1244002]))], (26432 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26430 ^ [_1243794, _1243796, _1243798, _1244002]), _1243798)))], (26429 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26427 ^ [_1243794, _1243796, _1243798, _1244002]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1243794))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1244002), _1243796)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244002), _1243794)), _1243796)))]]], (14093 ^ _779203) ^ [_1024433, _1024435, _1024437] : [class_Fields_Olinordered__field__inverse__zero(_1024433), 14096 ^ _779203 : [(14111 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024433), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1024433), _1024435), _1024437)), c_Groups_Ozero__class_Ozero(_1024433)))), 14112 ^ _779203 : [(14119 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024433), _1024435), c_Groups_Ozero__class_Ozero(_1024433))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024433), c_Groups_Ozero__class_Ozero(_1024433)), _1024437))], (14113 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024433), c_Groups_Ozero__class_Ozero(_1024433)), _1024435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024433), _1024437), c_Groups_Ozero__class_Ozero(_1024433)))]]], (14097 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024433), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1024433), _1024435), _1024437)), c_Groups_Ozero__class_Ozero(_1024433))), 14102 ^ _779203 : [(14105 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024433), _1024437), c_Groups_Ozero__class_Ozero(_1024433))))], (14103 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024433), c_Groups_Ozero__class_Ozero(_1024433)), _1024435)))]], 14106 ^ _779203 : [(14109 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024433), c_Groups_Ozero__class_Ozero(_1024433)), _1024437)))], (14107 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024433), _1024435), c_Groups_Ozero__class_Ozero(_1024433))))]]]]], (4960 ^ _779203) ^ [_854801, _854803, _854805, _854807, _854809, _854811] : [-(c_Product__Type_Oprod_Oprod__case(_854811, _854807, _854803) = c_Product__Type_Oprod_Oprod__case(_854809, _854805, _854801)), _854811 = _854809, _854807 = _854805, _854803 = _854801], (39457 ^ _779203) ^ [_1546825, _1546827, _1546829, _1546831, _1546833] : [hAPP(c_Set_Oimage(_1546825, _1546827, _1546829), c_Orderings_Otop__class_Otop(tc_fun(_1546825, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1546827, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1546827, _1546831, _1546833), c_Orderings_Otop__class_Otop(tc_fun(_1546827, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1546831, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1546825, _1546831, hAPP(c_Fun_Ocomp(_1546827, _1546831, _1546825, _1546833), _1546829)), c_Orderings_Otop__class_Otop(tc_fun(_1546825, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1546831, tc_HOL_Obool)))], (21731 ^ _779203) ^ [_1161691] : [-(c_Int_Osucc(c_Int_OBit0(_1161691)) = c_Int_OBit1(_1161691))], (18415 ^ _779203) ^ [] : [-(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))], (44209 ^ _779203) ^ [_1663585, _1663587, _1663589] : [-(_1663585 = c_List_Olist_ONil(_1663587)), -(c_List_Olast(_1663587, hAPP(hAPP(c_List_Oappend(_1663587), _1663589), _1663585)) = c_List_Olast(_1663587, _1663585))], (39500 ^ _779203) ^ [_1547773, _1547775, _1547777, _1547779, _1547781, _1547783, _1547785] : [hAPP(c_Fun_Ocomp(_1547773, _1547775, _1547777, _1547779), _1547781) = _1547783, -(hAPP(_1547779, hAPP(_1547781, _1547785)) = hAPP(_1547783, _1547785))], (30253 ^ _779203) ^ [_1318689, _1318691, _1318693, _1318695, _1318697] : [class_Groups_Oab__group__add(_1318689), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318691), _1318693)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318691), _1318695)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318691, _1318689), _1318697), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1318691, tc_HOL_Obool)), _1318693), _1318695)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1318689), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1318689), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318691, _1318689), _1318697), _1318693)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318691, _1318689), _1318697), _1318695))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318691, _1318689), _1318697), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318691, tc_HOL_Obool)), _1318693), _1318695))))], (10139 ^ _779203) ^ [_953037, _953039, _953041, _953043, _953045] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _953037), _953039)), -(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), _953037), _953041)), _953043)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _953039), _953041)), _953045)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _953043), 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), _953039), _953037)), _953041)), _953045)))], (41629 ^ _779203) ^ [_1603195, _1603197, _1603199, _1603201] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603195), tc_List_Olist(_1603195))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603195), tc_List_Olist(_1603195)), _1603197), _1603199)), c_List_Olistrel(_1603195, _1603201))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1603195), tc_List_Olist(_1603195))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1603195), tc_List_Olist(_1603195)), _1603197), _1603199)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1603195), c_List_Olistrel1(_1603195, _1603201)))))], (40293 ^ _779203) ^ [_1566831, _1566833, _1566835, _1566837] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1566831, tc_fun(_1566831, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1566831, tc_fun(tc_prod(_1566831, _1566831), tc_HOL_Obool), tc_fun(_1566831, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566831, tc_fun(tc_fun(tc_prod(_1566831, _1566831), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1566831, _1566831), tc_HOL_Obool), tc_fun(_1566831, tc_HOL_Obool)), _1566831), c_COMBC(_1566831, tc_fun(tc_prod(_1566831, _1566831), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1566831, tc_prod(_1566831, _1566831)), tc_fun(_1566831, tc_fun(tc_fun(tc_prod(_1566831, _1566831), tc_HOL_Obool), tc_HOL_Obool)), _1566831), hAPP(c_COMBB(tc_prod(_1566831, _1566831), tc_fun(tc_fun(tc_prod(_1566831, _1566831), tc_HOL_Obool), tc_HOL_Obool), _1566831), c_member(tc_prod(_1566831, _1566831)))), c_Product__Type_OPair(_1566831, _1566831)))), _1566833)), c_fequal), _1566835), _1566837)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1566831, _1566831)), hAPP(hAPP(c_Product__Type_OPair(_1566831, _1566831), _1566835), _1566837)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566831, _1566831), tc_HOL_Obool)), _1566833), c_Relation_OId(_1566831)))))], (23605 ^ _779203) ^ [] : [-(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))))], (40338 ^ _779203) ^ [_1568339, _1568341] : [-(c_Transitive__Closure_Otrancl(_1568339, _1568341) = hAPP(hAPP(c_Relation_Orel__comp(_1568339, _1568339, _1568339), _1568341), c_Transitive__Closure_Ortrancl(_1568339, _1568341)))], (8405 ^ _779203) ^ [_919729, _919731, _919733] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_919729), _919731)), hBOOL(hAPP(hAPP(c_member(_919729), _919733), _919731)), -(hAPP(c_Finite__Set_Ocard(_919729), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919729, tc_HOL_Obool)), _919731), hAPP(hAPP(c_Set_Oinsert(_919729), _919733), c_Orderings_Obot__class_Obot(tc_fun(_919729, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_919729), _919731)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (37765 ^ _779203) ^ [_1496823, _1496825, _1496827, _1496829] : [-(_1496823 = c_Orderings_Obot__class_Obot(tc_fun(_1496825, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1496827, _1496825), _1496827, c_Product__Type_Ofst(_1496827, _1496825)), hAPP(hAPP(c_Product__Type_OSigma(_1496827, _1496825), _1496829), hAPP(c_COMBK(tc_fun(_1496825, tc_HOL_Obool), _1496827), _1496823))) = _1496829)], (50571 ^ _779203) ^ [_1803812, _1803814, _1803816, _1803818, _1803820] : [class_Rings_Ocomm__semiring__1(_1803812), hBOOL(hAPP(c_Finite__Set_Ofinite(_1803814), _1803816)), hBOOL(hAPP(hAPP(c_member(_1803814), _1803818), _1803816)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1803812), hAPP(_1803820, _1803818)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1803814, _1803812), _1803820), _1803816))))], (45258 ^ _779203) ^ [_1687388, _1687390] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1687388))), c_Enum_Osublists(_1687388, _1687390)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687388)), _1687390)))], (45028 ^ _779203) ^ [_1682228, _1682230, _1682232, _1682234, _1682236] : [-(c_List_Olist__all2(_1682228, _1682230, _1682232, _1682234, _1682236)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682228)), _1682234) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682230)), _1682236), 45034 ^ _779203 : [(45037 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1682228, _1682230, tc_HOL_Obool), _1682232), 45033 ^ [_1682228, _1682230, _1682232, _1682234, _1682236]))], (45035 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682228, _1682230)), 45033 ^ [_1682228, _1682230, _1682232, _1682234, _1682236]), hAPP(c_List_Oset(tc_prod(_1682228, _1682230)), hAPP(hAPP(c_List_Ozip(_1682228, _1682230), _1682234), _1682236)))))]]], (15372 ^ _779203) ^ [_1048644, _1048646, _1048648] : [class_Orderings_Olinorder(_1048644), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1048644), _1048646), _1048648) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1048644), _1048648), _1048646))], (40227 ^ _779203) ^ [_1564903, _1564905] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564903, _1564903)), _1564905)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1564903, _1564903)), c_Transitive__Closure_Otrancl(_1564903, _1564905))))], (43734 ^ _779203) ^ [_1654132, _1654134, _1654136] : [-(_1654132 = c_List_Olist_ONil(_1654134)), -(hAPP(c_List_Ohd(_1654134), hAPP(c_List_Orotate(_1654134, _1654136), _1654132)) = hAPP(hAPP(c_List_Onth(_1654134), _1654132), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1654136, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1654134)), _1654132))))], (8431 ^ _779203) ^ [_920328, _920330, _920332, _920334, _920336] : [class_Groups_Ocomm__monoid__add(_920328), class_Groups_Oordered__cancel__ab__semigroup__add(_920328), hBOOL(hAPP(c_Finite__Set_Ofinite(_920330), _920332)), -(_920332 = c_Orderings_Obot__class_Obot(tc_fun(_920330, tc_HOL_Obool))), 8449 ^ _779203 : [(8452 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920328), hAPP(_920334, 8448 ^ [_920328, _920330, _920332, _920334, _920336])), hAPP(_920336, 8448 ^ [_920328, _920330, _920332, _920334, _920336])))], (8450 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_920330), 8448 ^ [_920328, _920330, _920332, _920334, _920336]), _920332)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_920328), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_920330, _920328), _920334), _920332)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_920330, _920328), _920336), _920332))))], (45163 ^ _779203) ^ [_1685214, _1685216, _1685218, _1685220] : [_1685220 = c_List_Olist_ONil(_1685216), -(c_List_Olist__all2(_1685214, _1685216, _1685218, c_List_Olist_ONil(_1685214), _1685220))], (5661 ^ _779203) ^ [_868499, _868501, _868503, _868505] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_868499), _868501)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_868503), hAPP(c_Set_Oimage(_868499, _868503, _868505), _868501))))], (47567 ^ _779203) ^ [_1737745, _1737747] : [class_Enum_Oenum(_1737745), 47570 ^ _779203 : [(47578 ^ _779203) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737745), _1737747)), 47581 ^ _779203 : [(47582 ^ _779203) ^ [_1737963] : [-(hBOOL(hAPP(_1737747, _1737963)))]]], (47571 ^ _779203) ^ [] : [hBOOL(hAPP(_1737747, 47572 ^ [_1737745, _1737747])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737745), _1737747)))]]], (32267 ^ _779203) ^ [_1362953, _1362955] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1362953))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1362955)), hAPP(c_Int_Onat, _1362953)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1362955), _1362953)), 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)))], (52685 ^ _779203) ^ [_1836803, _1836805, _1836807, _1836809, _1836811, _1836813] : [-(hAPP(hAPP(hAPP(c_COMBB(_1836803, _1836805, _1836807), _1836809), _1836811), _1836813) = hAPP(_1836809, hAPP(_1836811, _1836813)))], (43722 ^ _779203) ^ [_1654018, _1654020] : [-(_1654018 = c_List_Olist_ONil(_1654020)), -(hAPP(c_List_Ohd(_1654020), _1654018) = hAPP(hAPP(c_List_Onth(_1654020), _1654018), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33851 ^ _779203) ^ [_1399273, _1399275, _1399277] : [-(hAPP(c_Product__Type_Ofst(_1399273, _1399275), _1399277) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1399273, _1399275, _1399273), c_COMBK(_1399273, _1399275)), _1399277))], (20466 ^ _779203) ^ [_1140161, _1140163, _1140165] : [class_Groups_Olinordered__ab__group__add(_1140161), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1140161), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1140161), _1140163), _1140165)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1140161), hAPP(c_Groups_Ouminus__class_Ouminus(_1140161), _1140163)), hAPP(c_Groups_Ouminus__class_Ouminus(_1140161), _1140165)))], (46522 ^ _779203) ^ [_1714403, _1714405, _1714407] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714403), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1714403))), _1714405))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714407), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1714403))), _1714405))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1714403), _1714403), hAPP(hAPP(c_COMBC(tc_List_Olist(_1714403), tc_Nat_Onat, _1714403), c_List_Onth(_1714403)), _1714407)), hAPP(c_List_Ofilter(tc_List_Olist(_1714403), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1714403)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1714407)), c_Nat_Osize__class_Osize(tc_List_Olist(_1714403)))), c_List_Otranspose(_1714403, _1714405))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1714403)), _1714405), _1714407))], (21265 ^ _779203) ^ [_1154134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1154134))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1154134)))], (33327 ^ _779203) ^ [_1389439, _1389441, _1389443, _1389445, _1389447, _1389449] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389439, _1389441), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1389443), _1389445))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389439, _1389441), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1389447), _1389449))), -(_1389441 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1389443 = _1389447)], (35635 ^ _779203) ^ [_1446815, _1446817, _1446819] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446815), _1446817), _1446819) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446815, tc_HOL_Obool), tc_HOL_Obool)), -(_1446817 = c_Orderings_Obot__class_Obot(tc_fun(_1446815, tc_HOL_Obool)))], (17972 ^ _779203) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (38136 ^ _779203) ^ [_1510705, _1510707, _1510709] : [class_Lattices_Odistrib__lattice(_1510705), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510705), _1510707)), -(_1510707 = c_Orderings_Obot__class_Obot(tc_fun(_1510705, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1510705), _1510709)), -(_1510709 = c_Orderings_Obot__class_Obot(tc_fun(_1510705, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1510705), c_Big__Operators_Olattice__class_OSup__fin(_1510705, _1510707)), c_Big__Operators_Olattice__class_OSup__fin(_1510705, _1510709)) = c_Big__Operators_Olattice__class_OSup__fin(_1510705, hAPP(c_Set_OCollect(_1510705), hAPP(hAPP(c_COMBB(tc_fun(_1510705, tc_HOL_Obool), tc_HOL_Obool, _1510705), c_HOL_OEx(_1510705)), hAPP(hAPP(c_COMBB(tc_fun(_1510705, tc_fun(_1510705, tc_HOL_Obool)), tc_fun(_1510705, tc_HOL_Obool), _1510705), hAPP(c_COMBB(tc_fun(_1510705, tc_HOL_Obool), tc_HOL_Obool, _1510705), c_HOL_OEx(_1510705))), hAPP(hAPP(c_COMBC(_1510705, tc_fun(_1510705, tc_fun(_1510705, tc_HOL_Obool)), tc_fun(_1510705, tc_fun(_1510705, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1510705, tc_fun(tc_fun(_1510705, tc_HOL_Obool), tc_fun(_1510705, tc_HOL_Obool))), tc_fun(tc_fun(_1510705, tc_fun(_1510705, tc_HOL_Obool)), tc_fun(_1510705, tc_fun(_1510705, tc_HOL_Obool))), _1510705), c_COMBS(_1510705, tc_fun(_1510705, tc_HOL_Obool), tc_fun(_1510705, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1510705, tc_fun(_1510705, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1510705, tc_fun(tc_fun(_1510705, tc_HOL_Obool), tc_fun(_1510705, tc_HOL_Obool))), _1510705), hAPP(c_COMBB(tc_fun(_1510705, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1510705, tc_HOL_Obool), tc_fun(_1510705, tc_HOL_Obool)), _1510705), c_COMBS(_1510705, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1510705, tc_fun(_1510705, tc_HOL_Obool)), tc_fun(_1510705, tc_fun(_1510705, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1510705), hAPP(c_COMBB(tc_fun(_1510705, tc_HOL_Obool), tc_fun(_1510705, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1510705), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510705), c_fconj))), hAPP(hAPP(c_COMBC(_1510705, tc_fun(_1510705, tc_fun(_1510705, _1510705)), tc_fun(_1510705, tc_fun(_1510705, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1510705, _1510705), tc_fun(_1510705, tc_HOL_Obool)), tc_fun(tc_fun(_1510705, tc_fun(_1510705, _1510705)), tc_fun(_1510705, tc_fun(_1510705, tc_HOL_Obool))), _1510705), c_COMBB(tc_fun(_1510705, _1510705), tc_fun(_1510705, tc_HOL_Obool), _1510705)), hAPP(hAPP(c_COMBB(tc_fun(_1510705, tc_HOL_Obool), tc_fun(tc_fun(_1510705, _1510705), tc_fun(_1510705, tc_HOL_Obool)), _1510705), c_COMBB(_1510705, tc_HOL_Obool, _1510705)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1510705)))))), hAPP(hAPP(c_COMBC(_1510705, tc_fun(_1510705, tc_HOL_Obool), tc_fun(_1510705, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1510705, tc_HOL_Obool), tc_fun(_1510705, tc_HOL_Obool)), _1510705), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1510705)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1510705), c_fconj), hAPP(hAPP(c_COMBC(_1510705, tc_fun(_1510705, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510705)), _1510707)))), hAPP(hAPP(c_COMBC(_1510705, tc_fun(_1510705, tc_HOL_Obool), tc_HOL_Obool), c_member(_1510705)), _1510709))))))))], (21233 ^ _779203) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (52037 ^ _779203) ^ [_1829658, _1829660] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829658), _1829660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1829660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1829658), _1829660)))], (49026 ^ _779203) ^ [_1770895, _1770897, _1770899, _1770901, _1770903] : [c_Predicate_Otransp(_1770895, _1770897), hBOOL(hAPP(hAPP(_1770897, _1770899), _1770901)), hBOOL(hAPP(hAPP(_1770897, _1770901), _1770903)), -(hBOOL(hAPP(hAPP(_1770897, _1770899), _1770903)))], (29182 ^ _779203) ^ [_1295941, _1295943, _1295945] : [class_Lattices_Olattice(_1295941), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1295941), _1295943), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295941), _1295943), _1295945)) = _1295943)], (20584 ^ _779203) ^ [_1142222] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142222), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1142222) = _1142222)], (42668 ^ _779203) ^ [_1629772, _1629774] : [-(hAPP(hAPP(c_List_Otake(_1629772), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1629774) = c_List_Olist_ONil(_1629772))], (2780 ^ _779203) ^ [_820337, _820339] : [_820339 = _820337, -(c_Relation_OField(_820339) = c_Relation_OField(_820337))], (8248 ^ _779203) ^ [_916249, _916251, _916253, _916255] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_916249), _916251)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916249, tc_HOL_Obool)), _916251), _916253)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_916249, tc_Nat_Onat), _916255), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916249, tc_HOL_Obool)), _916253), _916251)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_916249, tc_Nat_Onat), _916255), _916253)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_916249, tc_Nat_Onat), _916255), _916251)))], (41953 ^ _779203) ^ [_1612195, _1612197, _1612199] : [-(hAPP(c_List_Oset(_1612195), hAPP(hAPP(c_List_Olist_OCons(_1612195), _1612197), _1612199)) = hAPP(hAPP(c_Set_Oinsert(_1612195), _1612197), hAPP(c_List_Oset(_1612195), _1612199)))], (45484 ^ _779203) ^ [_1692052, _1692054] : [-(c_List_Oconcat(_1692052, _1692054) = hAPP(c_List_Ofoldl(tc_List_Olist(_1692052), tc_List_Olist(_1692052), c_List_Oappend(_1692052), c_List_Olist_ONil(_1692052)), _1692054))], (39528 ^ _779203) ^ [_1548475, _1548477, _1548479, _1548481, _1548483, _1548485, _1548487] : [-(hAPP(c_Fun_Ocomp(_1548475, _1548477, _1548479, _1548481), c_Fun_Ofun__upd(_1548479, _1548475, _1548483, _1548485, _1548487)) = c_Fun_Ofun__upd(_1548479, _1548477, hAPP(c_Fun_Ocomp(_1548475, _1548477, _1548479, _1548481), _1548483), _1548485, hAPP(_1548481, _1548487)))], (40209 ^ _779203) ^ [_1564534, _1564536, _1564538] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1564534, _1564534)), _1564536), _1564538)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1564534, _1564534)), _1564536), c_Transitive__Closure_Otrancl(_1564534, _1564538))))], (19054 ^ _779203) ^ [_1114914, _1114916, _1114918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114914)), 19060 ^ _779203 : [(19063 ^ _779203) ^ [] : [hBOOL(hAPP(_1114916, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 19059 ^ [_1114914, _1114916, _1114918]), _1114914)))], (19061 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1114916, 19059 ^ [_1114914, _1114916, _1114918])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114918)), 19068 ^ _779203 : [(19069 ^ _779203) ^ [_1115203] : [hBOOL(hAPP(_1114916, _1115203)), -(hBOOL(hAPP(_1114916, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1115203), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1114918), _1114914)))))]]], (28102 ^ _779203) ^ [_1275535, _1275537, _1275539, _1275541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1275535, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1275535, tc_HOL_Obool)), _1275537), _1275539)), _1275541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1275535, tc_HOL_Obool)), _1275537), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275535, tc_HOL_Obool)), _1275539), _1275541))))], (43367 ^ _779203) ^ [_1645030, _1645032, _1645034, _1645036] : [-(c_List_Osublist(_1645030, hAPP(hAPP(c_List_Oappend(_1645030), _1645032), _1645034), _1645036) = hAPP(hAPP(c_List_Oappend(_1645030), c_List_Osublist(_1645030, _1645032, _1645036)), c_List_Osublist(_1645030, _1645034, 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(_1645030)), _1645032)))), _1645036)))))], (38625 ^ _779203) ^ [_1527190, _1527192] : [c_Wellfounded_Owf(_1527190, hAPP(hAPP(c_Relation_Orel__comp(_1527190, _1527190, _1527190), _1527192), _1527192)), -(c_Wellfounded_Owf(_1527190, _1527192))], (44239 ^ _779203) ^ [_1664079, _1664081, _1664083, _1664085] : [-(hAPP(hAPP(c_List_Oappend(_1664079), _1664081), hAPP(hAPP(c_List_Olist_OCons(_1664079), _1664083), c_List_Olist_ONil(_1664079))) = _1664085), -(_1664085 = c_List_Olist_ONil(_1664079)), c_List_Obutlast(_1664079, _1664085) = _1664081, c_List_Olast(_1664079, _1664085) = _1664083], (43209 ^ _779203) ^ [_1641437, _1641439, _1641441] : [_1641441 = c_List_Olist_ONil(_1641439), -(_1641437 = hAPP(hAPP(c_List_Oappend(_1641439), _1641441), _1641437))], (7793 ^ _779203) ^ [_907453, _907455, _907457] : [class_Orderings_Oorder(_907453), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907453), _907455), _907457)), -(_907455 = _907457), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907453), _907455), _907457)))], (34685 ^ _779203) ^ [_1421839, _1421841, _1421843, _1421845, _1421847] : [class_Complete__Lattice_Ocomplete__lattice(_1421839), class_Orderings_Olinorder(_1421839), 34692 ^ _779203 : [(34702 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421839), _1421841), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1421843, _1421839), _1421845), _1421847)))), 34703 ^ _779203 : [(34704 ^ _779203) ^ [_1422187] : [hBOOL(hAPP(hAPP(c_member(_1421843), _1422187), _1421845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421839), _1421841), hAPP(_1421847, _1422187)))]]], (34693 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421839), _1421841), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1421843, _1421839), _1421845), _1421847))), 34697 ^ _779203 : [(34700 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421839), _1421841), hAPP(_1421847, 34696 ^ [_1421839, _1421841, _1421843, _1421845, _1421847]))))], (34698 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1421843), 34696 ^ [_1421839, _1421841, _1421843, _1421845, _1421847]), _1421845)))]]]]], (27254 ^ _779203) ^ [_1258991, _1258993] : [-(_1258991 = _1258993), -(c_Random_Oinc__shift(_1258991, _1258993) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1258993), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (31943 ^ _779203) ^ [_1354756, _1354758, _1354760, _1354762, _1354764] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1354756), hAPP(c_Set_Oimage(_1354758, _1354756, _1354760), c_Orderings_Otop__class_Otop(tc_fun(_1354758, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1354762), hAPP(c_Set_Oimage(_1354758, _1354762, hAPP(hAPP(c_COMBB(_1354756, _1354762, _1354758), _1354764), _1354760)), c_Orderings_Otop__class_Otop(tc_fun(_1354758, tc_HOL_Obool))))))], (45302 ^ _779203) ^ [_1688438, _1688440, _1688442, _1688444, _1688446] : [45304 ^ _779203 : [(45307 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1688438, _1688440, tc_HOL_Obool), _1688446), 45303 ^ [_1688438, _1688440, _1688442, _1688444, _1688446]))], (45305 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1688438, _1688440)), 45303 ^ [_1688438, _1688440, _1688442, _1688444, _1688446]), hAPP(c_List_Oset(tc_prod(_1688438, _1688440)), hAPP(hAPP(c_List_Ozip(_1688438, _1688440), _1688442), _1688444)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688438)), _1688442) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688440)), _1688444), -(c_List_Olist__all2(_1688438, _1688440, _1688446, _1688442, _1688444))], (26888 ^ _779203) ^ [] : [-(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)))], (21567 ^ _779203) ^ [_1158850, _1158852] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1158850)), c_Int_OBit0(_1158852)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1158850), _1158852)))], (37179 ^ _779203) ^ [_1481150, _1481152, _1481154, _1481156, _1481158] : [-(hAPP(c_Set_Ovimage(_1481150, _1481152, _1481154), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481152, tc_HOL_Obool)), _1481156), _1481158)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1481150, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1481150, _1481152, _1481154), _1481156)), hAPP(c_Set_Ovimage(_1481150, _1481152, _1481154), _1481158)))], (25862 ^ _779203) ^ [_1234117, _1234119] : [c_Code__Numeral_OSuc__code__numeral(_1234117) = c_Code__Numeral_OSuc__code__numeral(_1234119), -(_1234117 = _1234119)], (44760 ^ _779203) ^ [_1676155, _1676157, _1676159, _1676161, _1676163] : [class_Groups_Omonoid__add(_1676155), class_Groups_Oordered__ab__semigroup__add(_1676155), 44770 ^ _779203 : [(44773 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676155), hAPP(_1676161, 44769 ^ [_1676155, _1676157, _1676159, _1676161, _1676163])), hAPP(_1676163, 44769 ^ [_1676155, _1676157, _1676159, _1676161, _1676163])))], (44771 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1676157), 44769 ^ [_1676155, _1676157, _1676159, _1676161, _1676163]), hAPP(c_List_Oset(_1676157), _1676159))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1676155), hAPP(c_List_Omonoid__add__class_Olistsum(_1676155), hAPP(hAPP(c_List_Omap(_1676157, _1676155), _1676161), _1676159))), hAPP(c_List_Omonoid__add__class_Olistsum(_1676155), hAPP(hAPP(c_List_Omap(_1676157, _1676155), _1676163), _1676159)))))], (5590 ^ _779203) ^ [_864654, _864656] : [_864656 = _864654, -(c_member(_864656) = c_member(_864654))], (50081 ^ _779203) ^ [_1792126, _1792128, _1792130, _1792132, _1792134] : [c_Fun_Obij__betw(_1792126, _1792128, _1792130, _1792132, _1792134), -(hAPP(c_Finite__Set_Ocard(_1792126), _1792132) = hAPP(c_Finite__Set_Ocard(_1792128), _1792134))], (11139 ^ _779203) ^ [_970945] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _970945) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52289 ^ _779203) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (9468 ^ _779203) ^ [_940646, _940648] : [9469 ^ _779203 : [(9470 ^ _779203) ^ [_940696] : [_940648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940646), _940696)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940646), _940648)))], (43452 ^ _779203) ^ [_1647653, _1647655, _1647657, _1647659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647653), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647655)), _1647657))), -(hAPP(hAPP(c_List_Olist__update(_1647655, _1647657), _1647653), _1647659) = hAPP(hAPP(c_List_Oappend(_1647655), hAPP(hAPP(c_List_Otake(_1647655), _1647653), _1647657)), hAPP(hAPP(c_List_Olist_OCons(_1647655), _1647659), hAPP(hAPP(c_List_Odrop(_1647655), hAPP(c_Nat_OSuc, _1647653)), _1647657))))], (48733 ^ _779203) ^ [_1762988, _1762990, _1762992, _1762994] : [-(hAPP(c_Relation_OImage(_1762988, _1762990, hAPP(c_Set_OCollect(tc_prod(_1762988, _1762990)), hAPP(c_Product__Type_Oprod_Oprod__case(_1762988, _1762990, tc_HOL_Obool), _1762992))), _1762994) = hAPP(c_Set_OCollect(_1762990), hAPP(hAPP(c_COMBB(tc_fun(_1762988, tc_HOL_Obool), tc_HOL_Obool, _1762990), c_HOL_OEx(_1762988)), hAPP(hAPP(c_COMBB(tc_fun(_1762988, tc_HOL_Obool), tc_fun(_1762988, tc_HOL_Obool), _1762990), hAPP(c_COMBS(_1762988, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1762988), c_fconj), hAPP(hAPP(c_COMBC(_1762988, tc_fun(_1762988, tc_HOL_Obool), tc_HOL_Obool), c_member(_1762988)), _1762994)))), hAPP(c_COMBC(_1762988, _1762990, tc_HOL_Obool), _1762992)))))], (228 ^ _779203) ^ [_782691, _782693, _782695, _782697, _782699, _782701, _782703, _782705, _782707, _782709, _782711, _782713] : [-(c_Finite__Set_Ofolding__image__simple(_782711, _782707, _782703, _782699, _782695, _782691)), c_Finite__Set_Ofolding__image__simple(_782713, _782709, _782705, _782701, _782697, _782693), _782713 = _782711, _782709 = _782707, _782705 = _782703, _782701 = _782699, _782697 = _782695, _782693 = _782691], (350 ^ _779203) ^ [_784440, _784442, _784444, _784446] : [-(c_Wellfounded_OwfP(_784444, _784440)), c_Wellfounded_OwfP(_784446, _784442), _784446 = _784444, _784442 = _784440], (52603 ^ _779203) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (30670 ^ _779203) ^ [_1327110, _1327112, _1327114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1327110, tc_HOL_Obool), tc_HOL_Obool)), _1327112), _1327114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1327110, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1327110, tc_HOL_Obool), _1327112)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1327110, tc_HOL_Obool), _1327114))))], (44756 ^ _779203) ^ [_1675983, _1675985] : [-(c_Random_Oselect__weight(_1675983, _1675985) = 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(_1675983, 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, _1675983), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1675983)), _1675985)))), hAPP(hAPP(c_COMBB(_1675983, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1675983, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1675983, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1675983, _1675985))))], (37825 ^ _779203) ^ [_1498546, _1498548, _1498550, _1498552, _1498554, _1498556, _1498558, _1498560] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1498546, _1498548), tc_fun(tc_prod(_1498550, _1498552), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1498546, _1498548), _1498554), hAPP(c_COMBK(tc_fun(_1498548, tc_HOL_Obool), _1498546), _1498556))), hAPP(c_Product__Type_Oprod_Oprod__case(_1498546, _1498548, tc_fun(tc_prod(_1498550, _1498552), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1498546, tc_fun(_1498548, tc_fun(_1498550, tc_fun(_1498552, tc_HOL_Obool))), tc_fun(_1498548, tc_fun(tc_prod(_1498550, _1498552), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1498550, tc_fun(_1498552, tc_HOL_Obool)), tc_fun(tc_prod(_1498550, _1498552), tc_HOL_Obool)), tc_fun(tc_fun(_1498548, tc_fun(_1498550, tc_fun(_1498552, tc_HOL_Obool))), tc_fun(_1498548, tc_fun(tc_prod(_1498550, _1498552), tc_HOL_Obool))), _1498546), c_COMBB(tc_fun(_1498550, tc_fun(_1498552, tc_HOL_Obool)), tc_fun(tc_prod(_1498550, _1498552), tc_HOL_Obool), _1498548)), hAPP(hAPP(c_COMBB(tc_fun(_1498550, tc_HOL_Obool), tc_fun(tc_fun(_1498550, tc_fun(_1498552, tc_HOL_Obool)), tc_fun(tc_prod(_1498550, _1498552), tc_HOL_Obool)), _1498546), c_Product__Type_OSigma(_1498550, _1498552)), _1498558))), hAPP(hAPP(c_COMBB(tc_fun(_1498552, tc_HOL_Obool), tc_fun(_1498550, tc_fun(_1498552, tc_HOL_Obool)), _1498548), c_COMBK(tc_fun(_1498552, tc_HOL_Obool), _1498550)), _1498560)))) = hAPP(hAPP(c_Product__Type_OSigma(_1498550, _1498552), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1498546, tc_fun(_1498550, tc_HOL_Obool)), _1498554), _1498558)), hAPP(c_COMBK(tc_fun(_1498552, tc_HOL_Obool), _1498550), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1498548, tc_fun(_1498552, tc_HOL_Obool)), _1498556), _1498560))))], (21967 ^ _779203) ^ [_1166411, _1166413, _1166415] : [class_Divides_Osemiring__div(_1166411), -(c_Divides_Odiv__class_Omod(_1166411, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166411), _1166413), _1166415), _1166415) = c_Divides_Odiv__class_Omod(_1166411, _1166413, _1166415))], (4050 ^ _779203) ^ [_840458, _840460, _840462, _840464, _840466, _840468, _840470, _840472] : [-(c_New__Random__Sequence_Opos__map(_840472, _840468, _840464, _840460) = c_New__Random__Sequence_Opos__map(_840470, _840466, _840462, _840458)), _840472 = _840470, _840468 = _840466, _840464 = _840462, _840460 = _840458], (6997 ^ _779203) ^ [_894256, _894258, _894260, _894262, _894264] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_894256, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894256, tc_HOL_Obool)), hAPP(c_Set_Oimage(_894258, _894256, _894260), _894262)), hAPP(c_Set_Oimage(_894258, _894256, _894260), _894264))), hAPP(c_Set_Oimage(_894258, _894256, _894260), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894258, tc_HOL_Obool)), _894262), _894264)))))], (46945 ^ _779203) ^ [_1723523, _1723525, _1723527] : [hBOOL(hAPP(c_List_Odistinct(_1723523), _1723525)), hBOOL(hAPP(hAPP(c_member(_1723523), _1723527), hAPP(c_List_Oset(_1723523), _1723525))), -(c_List_OdropWhile(_1723523, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723523), c_fNot), hAPP(hAPP(c_COMBC(_1723523, _1723523, tc_HOL_Obool), c_fequal), _1723527)), hAPP(c_List_Orev(_1723523), _1723525)) = hAPP(hAPP(c_List_Olist_OCons(_1723523), _1723527), hAPP(c_List_Orev(_1723523), c_List_OtakeWhile(_1723523, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1723523), c_fNot), hAPP(hAPP(c_COMBC(_1723523, _1723523, tc_HOL_Obool), c_fequal), _1723527)), _1723525))))], (51159 ^ _779203) ^ [_1814518, _1814520] : [_1814518 = _1814520, 51162 ^ _779203 : [(51165 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814520), _1814518)))], (51163 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814518), _1814520)))]]], (3216 ^ _779203) ^ [_827113, _827115, _827117, _827119] : [-(c_Random_Oselect(_827119, _827115) = c_Random_Oselect(_827117, _827113)), _827119 = _827117, _827115 = _827113], (39018 ^ _779203) ^ [] : [-(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))))], (19180 ^ _779203) ^ [_1117113, _1117115, _1117117] : [class_Groups_Oordered__ab__group__add__abs(_1117113), -(hAPP(c_Groups_Oabs__class_Oabs(_1117113), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1117113), _1117115), _1117117)) = hAPP(c_Groups_Oabs__class_Oabs(_1117113), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1117113), _1117117), _1117115)))], (25454 ^ _779203) ^ [_1228009] : [c_Int_OBit0(_1228009) = c_Int_OMin], (40622 ^ _779203) ^ [_1575165, _1575167] : [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), _1575165), _1575167)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1575165), _1575167)))], (1350 ^ _779203) ^ [_799038, _799040] : [-(class_Rings_Oring__1(_799038)), _799040 = _799038, class_Rings_Oring__1(_799040)], (47044 ^ _779203) ^ [_1725551, _1725553, _1725555] : [-(c_List_OdropWhile(_1725551, _1725553, _1725555) = hAPP(hAPP(c_List_Odrop(_1725551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725551)), c_List_OtakeWhile(_1725551, _1725553, _1725555))), _1725555))], (24253 ^ _779203) ^ [_1206533, _1206535, _1206537] : [-(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, _1206533, _1206535)), _1206537), _1206535) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1206533), _1206537), _1206535))], (30678 ^ _779203) ^ [_1327320, _1327322] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1327320, tc_HOL_Obool), tc_HOL_Obool)), _1327322), hAPP(c_Set_OPow(_1327320), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1327320, tc_HOL_Obool), _1327322)))))], (1006 ^ _779203) ^ [_794330, _794332, _794334, _794336, _794338, _794340, _794342, _794344] : [-(c_Equiv__Relations_Ocongruent(_794342, _794338, _794334, _794330)), c_Equiv__Relations_Ocongruent(_794344, _794340, _794336, _794332), _794344 = _794342, _794340 = _794338, _794336 = _794334, _794332 = _794330], (31446 ^ _779203) ^ [_1343073] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1343073, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1343073, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1343073, tc_HOL_Obool)))], (34381 ^ _779203) ^ [_1412133, _1412135, _1412137, _1412139] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1412133, tc_fun(_1412135, tc_HOL_Obool)), _1412137), _1412139) = c_Orderings_Obot__class_Obot(tc_fun(_1412135, tc_HOL_Obool)), 34384 ^ _779203 : [(34385 ^ _779203) ^ [_1412249] : [hBOOL(hAPP(hAPP(c_member(_1412133), _1412249), _1412137)), -(hAPP(_1412139, _1412249) = c_Orderings_Obot__class_Obot(tc_fun(_1412135, tc_HOL_Obool)))]]], (21329 ^ _779203) ^ [] : [-(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)))))], (24758 ^ _779203) ^ [_1215521, _1215523] : [c_Nat__Transfer_Onat__set(_1215521), c_Nat__Transfer_Onat__set(_1215523), 24765 ^ _779203 : [(24772 ^ _779203) ^ [] : [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), _1215521)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1215523))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1215521), _1215523)))], (24766 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1215521), _1215523)), -(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), _1215521)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1215523))))]]], (40011 ^ _779203) ^ [_1559695, _1559697, _1559699, _1559701] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1559695, tc_HOL_Obool), tc_fun(_1559695, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1559695, tc_HOL_Obool), tc_fun(_1559695, tc_HOL_Obool)), _1559697), _1559699)), c_Wellfounded_Omax__ext(_1559695, _1559701))), 40014 ^ _779203 : [(40017 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1559695), _1559699)))], (40019 ^ _779203) ^ [] : [_1559699 = c_Orderings_Obot__class_Obot(tc_fun(_1559695, tc_HOL_Obool))], (40021 ^ _779203) ^ [_1559989] : [hBOOL(hAPP(hAPP(c_member(_1559695), _1559989), _1559697)), 40025 ^ _779203 : [(40028 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559695, _1559695)), hAPP(hAPP(c_Product__Type_OPair(_1559695, _1559695), _1559989), 40024 ^ [_1559695, _1559697, _1559699, _1559701, _1559989])), _1559701)))], (40026 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559695), 40024 ^ [_1559695, _1559697, _1559699, _1559701, _1559989]), _1559699)))]]], (40015 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1559695), _1559697)))]]], (15408 ^ _779203) ^ [_1049390, _1049392] : [class_Orderings_Olinorder(_1049390), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049390), _1049392), _1049392) = _1049392)], (21325 ^ _779203) ^ [] : [-(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))))))], (29642 ^ _779203) ^ [_1305230, _1305232, _1305234, _1305236] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1305230, tc_HOL_Obool)), _1305232), _1305234), _1305236)), -(hBOOL(hAPP(_1305232, _1305236)))], (27230 ^ _779203) ^ [_1258600, _1258602] : [class_Groups_Oordered__ab__group__add(_1258600), -(hAPP(c_Set_Oimage(_1258600, _1258600, c_Groups_Ouminus__class_Ouminus(_1258600)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1258600), _1258602)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1258600), hAPP(c_Groups_Ouminus__class_Ouminus(_1258600), _1258602)))], (46883 ^ _779203) ^ [_1722158, _1722160, _1722162, _1722164, _1722166] : [hBOOL(hAPP(hAPP(c_member(_1722158), _1722160), hAPP(c_List_Oset(_1722158), _1722162))), -(hBOOL(hAPP(_1722164, _1722160))), -(c_List_OtakeWhile(_1722158, _1722164, hAPP(hAPP(c_List_Oappend(_1722158), _1722162), _1722166)) = c_List_OtakeWhile(_1722158, _1722164, _1722162))], (14663 ^ _779203) ^ [_1034705, _1034707, _1034709, _1034711] : [class_Fields_Ofield__inverse__zero(_1034705), -(_1034707 = c_Groups_Ozero__class_Ozero(_1034705)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034705), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034705), _1034709), _1034707)), _1034711) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034705), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034705), _1034709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034705), _1034711), _1034707))), _1034707))], (15045 ^ _779203) ^ [_1042094, _1042096, _1042098] : [class_Orderings_Olinorder(_1042094), hBOOL(hAPP(c_Finite__Set_Ofinite(_1042094), _1042096)), hBOOL(hAPP(hAPP(c_member(_1042094), _1042098), _1042096)), 15056 ^ _779203 : [(15063 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042094, tc_HOL_Obool)), _1042096), hAPP(hAPP(c_Set_Oinsert(_1042094), _1042098), c_Orderings_Obot__class_Obot(tc_fun(_1042094, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1042094, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1042094, _1042096) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1042094), _1042098), c_Big__Operators_Olinorder__class_OMin(_1042094, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042094, tc_HOL_Obool)), _1042096), hAPP(hAPP(c_Set_Oinsert(_1042094), _1042098), c_Orderings_Obot__class_Obot(tc_fun(_1042094, tc_HOL_Obool)))))))], (15057 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042094, tc_HOL_Obool)), _1042096), hAPP(hAPP(c_Set_Oinsert(_1042094), _1042098), c_Orderings_Obot__class_Obot(tc_fun(_1042094, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1042094, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1042094, _1042096) = _1042098)]]], (3742 ^ _779203) ^ [_835316, _835318] : [_835318 = _835316, -(c_New__DSequence_Opos__not__seq(_835318) = c_New__DSequence_Opos__not__seq(_835316))], (45671 ^ _779203) ^ [_1696938, _1696940, _1696942, _1696944] : [-(hAPP(c_List_Ofilter(_1696938, _1696940), c_List_Oremove1(_1696938, _1696942, _1696944)) = c_List_Oremove1(_1696938, _1696942, hAPP(c_List_Ofilter(_1696938, _1696940), _1696944)))], (32583 ^ _779203) ^ [_1370544, _1370546] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1370544), hAPP(c_Nat_OSuc, _1370546)) = 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)), _1370546)), _1370544))], (6092 ^ _779203) ^ [_876342, _876344, _876346] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_876342), hAPP(hAPP(c_Set_Oinsert(_876342), _876344), _876346))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_876342), _876346)))], (10979 ^ _779203) ^ [_968695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968695), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31965 ^ _779203) ^ [_1355326, _1355328, _1355330, _1355332] : [-(_1355326 = c_Orderings_Obot__class_Obot(tc_fun(_1355328, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1355328, _1355330, hAPP(c_COMBK(_1355330, _1355328), _1355332)), _1355326) = hAPP(hAPP(c_Set_Oinsert(_1355330), _1355332), c_Orderings_Obot__class_Obot(tc_fun(_1355330, tc_HOL_Obool))))], (7739 ^ _779203) ^ [_906706, _906708, _906710] : [class_Orderings_Olinorder(_906706), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906706), _906708), _906710)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906706), _906710), _906708))], (33211 ^ _779203) ^ [_1387452, _1387454] : [-(c_Divides_Odivmod__nat(_1387454, _1387452) = 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), _1387454), _1387452), _1387452))), -(_1387452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1387454), _1387452)))], (32421 ^ _779203) ^ [_1366511, _1366513] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1366511)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366513)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1366513))), 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, _1366511))), 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), _1366511)), c_Int_Onat)))))], (45470 ^ _779203) ^ [_1691794, _1691796] : [class_Orderings_Olinorder(_1691794), -(c_List_Olinorder__class_Osorted__list__of__set(_1691794, hAPP(c_List_Oset(_1691794), _1691796)) = c_List_Olinorder__class_Osort__key(_1691794, _1691794, c_COMBI(_1691794), c_List_Oremdups(_1691794, _1691796)))], (37579 ^ _779203) ^ [_1491652, _1491654] : [-(hAPP(c_Set_OCollect(_1491652), hAPP(hAPP(c_COMBC(_1491652, _1491652, tc_HOL_Obool), c_fequal), _1491654)) = hAPP(hAPP(c_Set_Oinsert(_1491652), _1491654), c_Orderings_Obot__class_Obot(tc_fun(_1491652, tc_HOL_Obool))))], (35027 ^ _779203) ^ [_1430259, _1430261, _1430263, _1430265] : [-(hAPP(c_Set_Oimage(_1430259, _1430261, _1430263), _1430265) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1430259, tc_fun(_1430261, tc_HOL_Obool)), _1430265), hAPP(hAPP(c_COMBC(_1430259, tc_fun(_1430261, tc_HOL_Obool), tc_fun(_1430261, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1430261, tc_fun(tc_fun(_1430261, tc_HOL_Obool), tc_fun(_1430261, tc_HOL_Obool)), _1430259), c_Set_Oinsert(_1430261)), _1430263)), c_Orderings_Obot__class_Obot(tc_fun(_1430261, tc_HOL_Obool)))))], (47183 ^ _779203) ^ [_1728491, _1728493, _1728495] : [-(c_List_Oinsert(_1728491, _1728493, c_List_Oremdups(_1728491, _1728495)) = c_List_Oremdups(_1728491, c_List_Oinsert(_1728491, _1728493, _1728495)))], (35371 ^ _779203) ^ [_1439417, _1439419] : [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), _1439417), _1439419)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1439417), _1439419)))], (45562 ^ _779203) ^ [_1693657, _1693659, _1693661, _1693663, _1693665] : [class_Orderings_Olinorder(_1693657), -(c_List_Olinorder__class_Osort__key(_1693659, _1693657, _1693661, hAPP(hAPP(c_List_Olist_OCons(_1693659), _1693663), _1693665)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1693659, _1693657, _1693661), _1693663), c_List_Olinorder__class_Osort__key(_1693659, _1693657, _1693661, _1693665)))], (51427 ^ _779203) ^ [_1818805, _1818807] : [_1818805 = _1818807, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818805), _1818807)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1818807), _1818805)))], (34763 ^ _779203) ^ [_1423692, _1423694, _1423696, _1423698, _1423700] : [hBOOL(hAPP(hAPP(c_member(_1423692), _1423694), _1423696)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1423698, tc_HOL_Obool)), hAPP(_1423700, _1423694)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423692, tc_fun(_1423698, tc_HOL_Obool)), _1423696), _1423700)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423692, tc_fun(_1423698, tc_HOL_Obool)), _1423696), _1423700))], (1280 ^ _779203) ^ [_798163, _798165] : [-(class_Groups_Ogroup__add(_798163)), _798165 = _798163, class_Groups_Ogroup__add(_798165)], (33615 ^ _779203) ^ [_1394475, _1394477, _1394479] : [33617 ^ _779203 : [(33620 ^ _779203) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1394475, _1394477), 33616 ^ [_1394475, _1394477, _1394479]))], (33618 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1394477, 33616 ^ [_1394475, _1394477, _1394479]), _1394479)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1394475, _1394477), _1394479)))], (19270 ^ _779203) ^ [_1118575, _1118577] : [class_Groups_Oordered__ab__group__add__abs(_1118575), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118575), hAPP(c_Groups_Oabs__class_Oabs(_1118575), _1118577)), c_Groups_Ozero__class_Ozero(_1118575)))], (29542 ^ _779203) ^ [_1303348, _1303350, _1303352, _1303354] : [class_Lattices_Osemilattice__inf(_1303348), 29545 ^ _779203 : [(29554 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303348), _1303350), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1303348), _1303352), _1303354)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303348), _1303350), _1303352)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303348), _1303350), _1303354))], (29546 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303348), _1303350), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1303348), _1303352), _1303354))), 29549 ^ _779203 : [(29552 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303348), _1303350), _1303354)))], (29550 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303348), _1303350), _1303352)))]]]]], (18308 ^ _779203) ^ [_1102183, _1102185] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1102183)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1102185)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1102183), _1102185)))], (4328 ^ _779203) ^ [_844863, _844865] : [_844865 = _844863, -(c_Lazy__Sequence_Oempty(_844865) = c_Lazy__Sequence_Oempty(_844863))], (21511 ^ _779203) ^ [_1157952, _1157954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1157952)), c_Int_OBit0(_1157954))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1157952), _1157954)))], (51177 ^ _779203) ^ [_1814803, _1814805] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814803), _1814805)), 51182 ^ _779203 : [(51185 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814805), _1814803))], (51183 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1814803), _1814805)))]], -(_1814803 = _1814805)], (30694 ^ _779203) ^ [_1327646] : [class_Complete__Lattice_Ocomplete__lattice(_1327646), -(c_Complete__Lattice_OSup__class_OSup(_1327646, c_Orderings_Obot__class_Obot(tc_fun(_1327646, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1327646))], (5070 ^ _779203) ^ [_856534, _856536, _856538, _856540] : [-(c_Transitive__Closure_Otrancl(_856540, _856536) = c_Transitive__Closure_Otrancl(_856538, _856534)), _856540 = _856538, _856536 = _856534], (50039 ^ _779203) ^ [_1791384, _1791386, _1791388, _1791390] : [c_Fun_Oinj__on(_1791384, _1791386, _1791388, _1791390), -(c_Fun_Obij__betw(_1791384, _1791386, _1791388, _1791390, hAPP(c_Set_Oimage(_1791384, _1791386, _1791388), _1791390)))], (35543 ^ _779203) ^ [_1444298, _1444300] : [-(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), _1444298), _1444300)), 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), _1444298), _1444300))], (48136 ^ _779203) ^ [_1749598, _1749600, _1749602, _1749604, _1749606] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749598, _1749600, hAPP(hAPP(c_COMBC(_1749598, tc_fun(tc_prod(_1749598, _1749600), tc_HOL_Obool), tc_fun(_1749600, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749600, tc_fun(tc_fun(tc_prod(_1749598, _1749600), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1749598, _1749600), tc_HOL_Obool), tc_fun(_1749600, tc_HOL_Obool)), _1749598), c_COMBC(_1749600, tc_fun(tc_prod(_1749598, _1749600), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749600, tc_prod(_1749598, _1749600)), tc_fun(_1749600, tc_fun(tc_fun(tc_prod(_1749598, _1749600), tc_HOL_Obool), tc_HOL_Obool)), _1749598), hAPP(c_COMBB(tc_prod(_1749598, _1749600), tc_fun(tc_fun(tc_prod(_1749598, _1749600), tc_HOL_Obool), tc_HOL_Obool), _1749600), c_member(tc_prod(_1749598, _1749600)))), c_Product__Type_OPair(_1749598, _1749600)))), _1749602)), _1749604), _1749606)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1749600, _1749598)), hAPP(hAPP(c_Product__Type_OPair(_1749600, _1749598), _1749604), _1749606)), hAPP(c_Relation_Oconverse(_1749598, _1749600), _1749602))))], (44129 ^ _779203) ^ [_1662314, _1662316, _1662318] : [class_Orderings_Olinorder(_1662314), -(hAPP(c_List_Oset(_1662314), c_List_Olinorder__class_Oinsort__insert__key(_1662314, _1662314, c_COMBI(_1662314), _1662316, _1662318)) = hAPP(hAPP(c_Set_Oinsert(_1662314), _1662316), hAPP(c_List_Oset(_1662314), _1662318)))], (18600 ^ _779203) ^ [_1107236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1107236)), -(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), _1107236))))], (6215 ^ _779203) ^ [_878964, _878966, _878968] : [_878966 = _878968, -(hBOOL(hAPP(hAPP(c_member(_878964), _878966), hAPP(hAPP(c_Set_Oinsert(_878964), _878968), c_Orderings_Obot__class_Obot(tc_fun(_878964, tc_HOL_Obool))))))], (23613 ^ _779203) ^ [_1194985, _1194987] : [-(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), _1194985)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1194987))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1194985))) = 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), _1194987)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194985)))], (52683 ^ _779203) ^ [_1836765, _1836767, _1836769, _1836771] : [-(hAPP(hAPP(c_COMBK(_1836765, _1836767), _1836769), _1836771) = _1836769)], (31109 ^ _779203) ^ [_1335711, _1335713, _1335715] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1335711, tc_HOL_Obool)), _1335713), _1335715))), 31115 ^ _779203 : [(31119 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1335711, tc_HOL_Obool)), 31117 ^ [_1335711, _1335713, _1335715]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1335711, tc_HOL_Obool)), _1335713), _1335715))))], (31121 ^ _779203) ^ [] : [31114 ^ [_1335711, _1335713, _1335715] = 31117 ^ [_1335711, _1335713, _1335715]], (31123 ^ _779203) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335711, tc_HOL_Obool)), 31114 ^ [_1335711, _1335713, _1335715]), 31117 ^ [_1335711, _1335713, _1335715]) = c_Orderings_Obot__class_Obot(tc_fun(_1335711, tc_HOL_Obool))], (31116 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1335711, tc_HOL_Obool)), 31114 ^ [_1335711, _1335713, _1335715]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1335711, tc_HOL_Obool)), _1335713), _1335715))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1335711, tc_HOL_Obool)), _1335713), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1335711, tc_HOL_Obool), _1335715)) = c_Orderings_Obot__class_Obot(tc_fun(_1335711, tc_HOL_Obool)))], (32521 ^ _779203) ^ [_1369137, _1369139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369137), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369139)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369137)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369139))], (27494 ^ _779203) ^ [_1263590, _1263592, _1263594, _1263596] : [class_Lattices_Osemilattice__sup(_1263590), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263590), _1263592), _1263594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263590), _1263596), _1263594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263590), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263590), _1263592), _1263596)), _1263594)))], (49548 ^ _779203) ^ [_1780241, _1780243] : [c_Equiv__Relations_Opart__equivp(_1780241, _1780243), 49552 ^ _779203 : [(49557 ^ _779203) ^ [] : [-(c_Predicate_Otransp(_1780241, _1780243))], (49555 ^ _779203) ^ [] : [-(c_Predicate_Osymp(_1780241, _1780243))], (49553 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1780243, 49551 ^ [_1780241, _1780243]), 49551 ^ [_1780241, _1780243])))]]], (29910 ^ _779203) ^ [_1311351, _1311353, _1311355, _1311357] : [class_Orderings_Oorder(_1311351), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311351, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1311351, _1311353, _1311355)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1311351, _1311355), _1311357)) = c_Orderings_Obot__class_Obot(tc_fun(_1311351, tc_HOL_Obool)))], (33439 ^ _779203) ^ [_1390960, _1390962, _1390964, _1390966, _1390968, _1390970, _1390972] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390960, _1390962), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1390964), _1390966))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390968, _1390962), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1390970), _1390972))), -(_1390962 = 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), _1390960), _1390968), _1390962), 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), _1390964), _1390970)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1390966), _1390972)), _1390962))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1390966), _1390972), _1390962)))))], (28128 ^ _779203) ^ [_1276171, _1276173, _1276175, _1276177] : [-(hBOOL(hAPP(hAPP(c_member(_1276171), hAPP(_1276173, _1276175)), hAPP(c_Set_Oimage(_1276177, _1276171, _1276173), c_Orderings_Otop__class_Otop(tc_fun(_1276177, tc_HOL_Obool))))))], (25982 ^ _779203) ^ [_1236060, _1236062, _1236064] : [class_Rings_Oring__1(_1236060), -(hAPP(c_Int_Oring__1__class_Oof__int(_1236060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1236062), _1236064)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1236060), hAPP(c_Int_Oring__1__class_Oof__int(_1236060), _1236062)), hAPP(c_Int_Oring__1__class_Oof__int(_1236060), _1236064)))], (23635 ^ _779203) ^ [_1195265, _1195267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195265)), -(c_SMT_Oz3div(_1195267, _1195265) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195267), _1195265))], (20778 ^ _779203) ^ [_1145962, _1145964, _1145966, _1145968, _1145970, _1145972] : [hBOOL(hAPP(hAPP(c_member(_1145962), _1145964), c_SetInterval_Oord_OgreaterThanAtMost(_1145962, _1145966, _1145968, _1145970, _1145972))), 20781 ^ _779203 : [(20784 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1145966, _1145964), _1145972)))], (20782 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1145968, _1145970), _1145964)))]]], (48028 ^ _779203) ^ [_1746882, _1746884, _1746886, _1746888, _1746890, _1746892, _1746894] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1746882, _1746884, _1746886, _1746888, _1746890, _1746892, _1746894) = c_New__DSequence_Oneg__decr__bind(_1746882, _1746884, hAPP(hAPP(hAPP(_1746886, _1746890), _1746892), _1746894), hAPP(hAPP(c_COMBC(_1746882, 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(_1746884)))), hAPP(hAPP(c_COMBC(_1746882, 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(_1746884))))), hAPP(hAPP(c_COMBC(_1746882, 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(_1746884)))))), _1746888), _1746890)), _1746892)), _1746894)))], (21221 ^ _779203) ^ [_1153408] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1153408)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1153408))))], (36052 ^ _779203) ^ [_1456298, _1456300, _1456302, _1456304, _1456306, _1456308, _1456310, _1456312, _1456314, _1456316] : [c_Equiv__Relations_Ocongruent2(_1456298, _1456300, _1456302, _1456304, _1456306, _1456308), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456298, _1456298)), hAPP(hAPP(c_Product__Type_OPair(_1456298, _1456298), _1456310), _1456312)), _1456304)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456300, _1456300)), hAPP(hAPP(c_Product__Type_OPair(_1456300, _1456300), _1456314), _1456316)), _1456306)), -(hAPP(hAPP(_1456308, _1456310), _1456314) = hAPP(hAPP(_1456308, _1456312), _1456316))], (3768 ^ _779203) ^ [_835707, _835709, _835711, _835713, _835715, _835717] : [-(c_List_OtakeWhile(_835717, _835713, _835709) = c_List_OtakeWhile(_835715, _835711, _835707)), _835717 = _835715, _835713 = _835711, _835709 = _835707], (23840 ^ _779203) ^ [_1198781, _1198783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1198781)), 23843 ^ _779203 : [(23850 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198783), _1198781))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1198783), _1198781) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1198783), _1198781)), _1198781)))], (23844 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198783), _1198781)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1198783), _1198781) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (24888 ^ _779203) ^ [_1217857, _1217859] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1217857), _1217859) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1217859 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1217857 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (32831 ^ _779203) ^ [_1380370, _1380372, _1380374] : [_1380370 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1380372, _1380372), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1380372, _1380372), tc_HOL_Obool)), _1380370), _1380374)))], (34051 ^ _779203) ^ [_1403424, _1403426, _1403428, _1403430, _1403432, _1403434, _1403436, _1403438] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1403424, _1403426), tc_prod(_1403424, _1403426))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1403424, _1403426), tc_prod(_1403424, _1403426)), hAPP(hAPP(c_Product__Type_OPair(_1403424, _1403426), _1403428), _1403430)), hAPP(hAPP(c_Product__Type_OPair(_1403424, _1403426), _1403432), _1403434))), c_Wellfounded_Olex__prod(_1403424, _1403426, _1403436, _1403438)))), 34052 ^ _779203 : [(34055 ^ _779203) ^ [] : [_1403428 = _1403432, hBOOL(hAPP(hAPP(c_member(tc_prod(_1403426, _1403426)), hAPP(hAPP(c_Product__Type_OPair(_1403426, _1403426), _1403430), _1403434)), _1403438))], (34053 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1403424, _1403424)), hAPP(hAPP(c_Product__Type_OPair(_1403424, _1403424), _1403428), _1403432)), _1403436))]]], (11043 ^ _779203) ^ [_969531] : [_969531 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969531), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42640 ^ _779203) ^ [_1629332, _1629334, _1629336] : [c_List_Olist_ONil(_1629332) = hAPP(hAPP(c_List_Olist_OCons(_1629332), _1629334), _1629336)], (52593 ^ _779203) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (19688 ^ _779203) ^ [_1126569, _1126571] : [class_Lattices_Oboolean__algebra(_1126569), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1126569), hAPP(c_Groups_Ouminus__class_Ouminus(_1126569), _1126571)) = _1126571)], (52315 ^ _779203) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (21277 ^ _779203) ^ [_1154318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1154318)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154318), c_Int_OPls)))], (41298 ^ _779203) ^ [_1592687, _1592689, _1592691] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592687), c_Nitpick_Oplus__frac(_1592687, _1592689, c_Nitpick_Ouminus__frac(_1592687, _1592691)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1592687, _1592689, _1592691))], (44458 ^ _779203) ^ [_1669563] : [-(hAPP(c_List_Omap(_1669563, _1669563), c_COMBI(_1669563)) = c_Fun_Oid(tc_List_Olist(_1669563)))], (27746 ^ _779203) ^ [_1268268, _1268270, _1268272, _1268274] : [class_Lattices_Osemilattice__sup(_1268268), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268268), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268268), _1268270), _1268272)), _1268274) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268268), _1268270), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268268), _1268272), _1268274)))], (49078 ^ _779203) ^ [_1771626, _1771628, _1771630, _1771632] : [c_Predicate_Osymp(_1771626, _1771628), hBOOL(hAPP(hAPP(_1771628, _1771630), _1771632)), -(hBOOL(hAPP(hAPP(_1771628, _1771632), _1771630)))], (5090 ^ _779203) ^ [_856832, _856834, _856836, _856838] : [-(c_Transitive__Closure_Ortrancl(_856838, _856834) = c_Transitive__Closure_Ortrancl(_856836, _856832)), _856838 = _856836, _856834 = _856832], (31243 ^ _779203) ^ [_1338605, _1338607, _1338609, _1338611] : [class_Groups_Ocomm__monoid__mult(_1338605), 31246 ^ _779203 : [(31253 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1338607), _1338609))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338607, _1338605), _1338611), _1338609) = c_Groups_Oone__class_Oone(_1338605))], (31247 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1338607), _1338609)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1338607, _1338605), _1338611), _1338609) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1338605, _1338607, c_Groups_Otimes__class_Otimes(_1338605)), _1338611), c_Groups_Oone__class_Oone(_1338605)), _1338609))]]], (27782 ^ _779203) ^ [_1269090, _1269092, _1269094] : [class_Lattices_Osemilattice__sup(_1269090), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269090), _1269092), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269090), _1269092), _1269094)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269090), _1269092), _1269094))], (34367 ^ _779203) ^ [_1411834, _1411836, _1411838] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411834, tc_fun(_1411836, tc_HOL_Obool)), _1411838), hAPP(c_COMBK(tc_fun(_1411836, tc_HOL_Obool), _1411834), c_Orderings_Obot__class_Obot(tc_fun(_1411836, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1411836, tc_HOL_Obool)))], (36094 ^ _779203) ^ [_1457261, _1457263, _1457265, _1457267, _1457269, _1457271, _1457273] : [c_Equiv__Relations_Oequiv(_1457261, _1457263, _1457265), c_Equiv__Relations_Ocongruent(_1457261, tc_fun(_1457267, tc_HOL_Obool), _1457265, _1457269), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1457261, tc_fun(_1457267, tc_HOL_Obool)), _1457271), _1457269) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1457261, tc_fun(_1457267, tc_HOL_Obool)), _1457273), _1457269), hBOOL(hAPP(hAPP(c_member(tc_fun(_1457261, tc_HOL_Obool)), _1457271), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457261), _1457263), _1457265))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1457261, tc_HOL_Obool)), _1457273), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1457261), _1457263), _1457265))), 36116 ^ _779203 : [(36120 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457261), 36118 ^ [_1457261, _1457263, _1457265, _1457267, _1457269, _1457271, _1457273]), _1457263)))], (36122 ^ _779203) ^ [] : [-(hAPP(_1457269, 36115 ^ [_1457261, _1457263, _1457265, _1457267, _1457269, _1457271, _1457273]) = hAPP(_1457269, 36118 ^ [_1457261, _1457263, _1457265, _1457267, _1457269, _1457271, _1457273]))], (36124 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1457261, _1457261)), hAPP(hAPP(c_Product__Type_OPair(_1457261, _1457261), 36115 ^ [_1457261, _1457263, _1457265, _1457267, _1457269, _1457271, _1457273]), 36118 ^ [_1457261, _1457263, _1457265, _1457267, _1457269, _1457271, _1457273])), _1457265))], (36117 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1457261), 36115 ^ [_1457261, _1457263, _1457265, _1457267, _1457269, _1457271, _1457273]), _1457263)))]], -(_1457271 = _1457273)], (23086 ^ _779203) ^ [_1185572, _1185574] : [hAPP(c_Int_Onat, _1185572) = _1185574, 23089 ^ _779203 : [(23096 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185572))), -(_1185574 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23090 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185572)), -(_1185572 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185574))]]], (27988 ^ _779203) ^ [_1273310] : [class_Lattices_Osemilattice__sup(_1273310), -(c_Finite__Set_Ofun__left__comm__idem(_1273310, _1273310, c_Lattices_Osemilattice__sup__class_Osup(_1273310)))], (14229 ^ _779203) ^ [_1026601, _1026603, _1026605, _1026607] : [class_Fields_Ofield__inverse__zero(_1026601), -(_1026603 = c_Groups_Ozero__class_Ozero(_1026601)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026601), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026601), _1026605), _1026603)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026601), _1026607), _1026603)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026601), _1026605), _1026607))], (42353 ^ _779203) ^ [_1622997, _1622999, _1623001, _1623003] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622997), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622999)), _1623001))), -(hAPP(hAPP(c_List_Onth(_1622999), hAPP(hAPP(c_List_Olist__update(_1622999, _1623001), _1622997), _1623003)), _1622997) = _1623003)], (42896 ^ _779203) ^ [_1634027] : [-(c_List_Olistset(_1634027, c_List_Olist_ONil(tc_fun(_1634027, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1634027)), c_List_Olist_ONil(_1634027)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1634027), tc_HOL_Obool))))], (38981 ^ _779203) ^ [_1535004, _1535006, _1535008, _1535010] : [hBOOL(hAPP(hAPP(c_member(_1535004), _1535010), hAPP(c_Relation_ODomain(_1535004, _1535006), _1535008))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1535004, _1535006, hAPP(hAPP(c_COMBC(_1535004, tc_fun(tc_prod(_1535004, _1535006), tc_HOL_Obool), tc_fun(_1535006, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535006, tc_fun(tc_fun(tc_prod(_1535004, _1535006), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1535004, _1535006), tc_HOL_Obool), tc_fun(_1535006, tc_HOL_Obool)), _1535004), c_COMBC(_1535006, tc_fun(tc_prod(_1535004, _1535006), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535006, tc_prod(_1535004, _1535006)), tc_fun(_1535006, tc_fun(tc_fun(tc_prod(_1535004, _1535006), tc_HOL_Obool), tc_HOL_Obool)), _1535004), hAPP(c_COMBB(tc_prod(_1535004, _1535006), tc_fun(tc_fun(tc_prod(_1535004, _1535006), tc_HOL_Obool), tc_HOL_Obool), _1535006), c_member(tc_prod(_1535004, _1535006)))), c_Product__Type_OPair(_1535004, _1535006)))), _1535008)), _1535010)))], (1880 ^ _779203) ^ [_805663, _805665] : [-(class_Orderings_Oord(_805663)), _805665 = _805663, class_Orderings_Oord(_805665)], (36500 ^ _779203) ^ [_1465960, _1465962, _1465964] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1465960), _1465962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1465960, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1465960, _1465960, _1465964), _1465962)), _1465962)), c_Fun_Oinj__on(_1465960, _1465960, _1465964, _1465962), -(hAPP(c_Set_Oimage(_1465960, _1465960, _1465964), _1465962) = _1465962)], (21705 ^ _779203) ^ [_1161307] : [-(c_Int_Opred(c_Int_OBit0(_1161307)) = c_Int_OBit1(c_Int_Opred(_1161307)))], (33729 ^ _779203) ^ [_1396738, _1396740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396738)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396740)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396738, _1396740) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1396738, _1396740)))], (11049 ^ _779203) ^ [_969618] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _969618) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18312 ^ _779203) ^ [_1102290, _1102292] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102290), _1102292)), -(_1102292 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1102290), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 18315 ^ [_1102290, _1102292])))], (3538 ^ _779203) ^ [_832114, _832116, _832118, _832120, _832122, _832124] : [-(c_List_Oremove1(_832124, _832120, _832116) = c_List_Oremove1(_832122, _832118, _832114)), _832124 = _832122, _832120 = _832118, _832116 = _832114], (32793 ^ _779203) ^ [_1379506, _1379508, _1379510, _1379512, _1379514] : [hBOOL(hAPP(hAPP(_1379506, _1379508), _1379510)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1379512, _1379514, tc_HOL_Obool), _1379506), hAPP(hAPP(c_Product__Type_OPair(_1379512, _1379514), _1379508), _1379510))))], (35539 ^ _779203) ^ [_1444153] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1444153) = 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), _1444153), 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))))))], (26028 ^ _779203) ^ [_1236929] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1236929)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1236929)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29784 ^ _779203) ^ [_1308521, _1308523] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1308521), _1308523) = 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)), _1308521)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1308523))))], (4242 ^ _779203) ^ [_843382, _843384] : [_843384 = _843382, -(c_If(_843384) = c_If(_843382))], (12446 ^ _779203) ^ [_993898, _993900] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _993898), _993900) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993898), _993900)))], (21891 ^ _779203) ^ [_1164753, _1164755, _1164757] : [class_Divides_Osemiring__div(_1164753), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1164753), c_Divides_Odiv__class_Omod(_1164753, _1164755, _1164757)), _1164757) = c_Groups_Ozero__class_Ozero(_1164753))], (41709 ^ _779203) ^ [_1605876, _1605878, _1605880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1605876, _1605876), tc_HOL_Obool)), _1605878), hAPP(hAPP(c_Product__Type_OSigma(_1605876, _1605876), _1605880), hAPP(c_COMBK(tc_fun(_1605876, tc_HOL_Obool), _1605876), _1605880)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1605876), tc_List_Olist(_1605876)), tc_HOL_Obool)), c_List_Olistrel(_1605876, _1605878)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1605876), tc_List_Olist(_1605876)), c_List_Olists(_1605876, _1605880)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1605876), tc_HOL_Obool), tc_List_Olist(_1605876)), c_List_Olists(_1605876, _1605880))))))], (21391 ^ _779203) ^ [_1155994, _1155996] : [class_Int_Onumber__ring(_1155994), class_Rings_Olinordered__idom(_1155994), 21398 ^ _779203 : [(21405 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1155996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155994), c_Groups_Oone__class_Oone(_1155994)), hAPP(c_Int_Onumber__class_Onumber__of(_1155994), _1155996))))], (21399 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155994), c_Groups_Oone__class_Oone(_1155994)), hAPP(c_Int_Onumber__class_Onumber__of(_1155994), _1155996))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1155996)))]]], (52293 ^ _779203) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (47679 ^ _779203) ^ [_1739957, _1739959, _1739961, _1739963] : [47680 ^ _779203 : [(47683 ^ _779203) ^ [] : [c_List_Olist__ex(_1739957, _1739959, _1739963)], (47681 ^ _779203) ^ [] : [c_List_Olist__ex(_1739957, _1739959, _1739961)]], -(c_List_Olist__ex(_1739957, _1739959, hAPP(hAPP(c_List_Oappend(_1739957), _1739961), _1739963)))], (13567 ^ _779203) ^ [_1014838, _1014840] : [class_Rings_Odivision__ring__inverse__zero(_1014838), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1014838), _1014840), c_Groups_Ozero__class_Ozero(_1014838)) = c_Groups_Ozero__class_Ozero(_1014838))], (49232 ^ _779203) ^ [_1774604, _1774606] : [c_Wellfounded_Oacyclic(_1774604, _1774606), -(c_Relation_Oantisym(_1774604, c_Transitive__Closure_Ortrancl(_1774604, _1774606)))], (14843 ^ _779203) ^ [_1038099, _1038101] : [-(hBOOL(hAPP(_1038099, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1038099, _1038101)), 14851 ^ _779203 : [(14854 ^ _779203) ^ [_1038337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1038337), 14850 ^ [_1038099, _1038101])), hBOOL(hAPP(_1038099, _1038337))], (14860 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1038099, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 14850 ^ [_1038099, _1038101]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (14852 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14850 ^ [_1038099, _1038101]), _1038101)))]]], (20712 ^ _779203) ^ [_1144763, _1144765, _1144767, _1144769, _1144771, _1144773] : [hBOOL(hAPP(hAPP(c_member(_1144763), _1144765), c_SetInterval_Oord_OatLeastLessThan(_1144763, _1144767, _1144769, _1144771, _1144773))), 20715 ^ _779203 : [(20718 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1144769, _1144765), _1144773)))], (20716 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1144767, _1144771), _1144765)))]]], (9027 ^ _779203) ^ [_932071, _932073, _932075] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_932071), _932073)), -(hAPP(c_Finite__Set_Ocard(_932071), hAPP(hAPP(c_Set_Oinsert(_932071), _932075), _932073)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_932071), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_932071, tc_HOL_Obool)), _932073), hAPP(hAPP(c_Set_Oinsert(_932071), _932075), c_Orderings_Obot__class_Obot(tc_fun(_932071, tc_HOL_Obool)))))))], (43800 ^ _779203) ^ [_1655366, _1655368, _1655370] : [-(hAPP(c_List_Orotate(_1655366, _1655368), _1655370) = hAPP(c_List_Orotate(_1655366, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1655368, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655366)), _1655370))), _1655370))], (46373 ^ _779203) ^ [_1711492, _1711494, _1711496, _1711498, _1711500, _1711502] : [class_Orderings_Olinorder(_1711492), c_List_Olinorder__class_Osorted(_1711492, hAPP(hAPP(c_List_Omap(_1711494, _1711492), _1711496), _1711498)), hBOOL(hAPP(_1711500, _1711502)), -(hAPP(c_List_Ofilter(_1711494, _1711500), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1711494, _1711492, _1711496), _1711502), _1711498)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1711494, _1711492, _1711496), _1711502), hAPP(c_List_Ofilter(_1711494, _1711500), _1711498)))], (28944 ^ _779203) ^ [_1291259, _1291261, _1291263] : [class_Lattices_Olattice(_1291259), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291259), _1291261)), -(_1291263 = c_Orderings_Obot__class_Obot(tc_fun(_1291259, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1291259, tc_HOL_Obool)), _1291263), _1291261)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291259), c_Big__Operators_Olattice__class_OSup__fin(_1291259, _1291263)), c_Big__Operators_Olattice__class_OSup__fin(_1291259, _1291261)) = c_Big__Operators_Olattice__class_OSup__fin(_1291259, _1291261))], (49763 ^ _779203) ^ [_1785332, _1785334, _1785336, _1785338, _1785340] : [c_Fun_Oinj__on(_1785332, _1785334, _1785336, c_Orderings_Otop__class_Otop(tc_fun(_1785332, tc_HOL_Obool))), 49769 ^ _779203 : [(49772 ^ _779203) ^ [] : [hBOOL(hAPP(_1785338, hAPP(c_Hilbert__Choice_Oinv__into(_1785332, _1785334, c_Orderings_Otop__class_Otop(tc_fun(_1785332, tc_HOL_Obool)), _1785336), 49768 ^ [_1785332, _1785334, _1785336, _1785338, _1785340])))], (49770 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1785334), 49768 ^ [_1785332, _1785334, _1785336, _1785338, _1785340]), hAPP(c_Set_Oimage(_1785332, _1785334, _1785336), c_Orderings_Otop__class_Otop(tc_fun(_1785332, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1785338, _1785340)))], (15806 ^ _779203) ^ [_1056222, _1056224, _1056226, _1056228] : [class_Orderings_Olinorder(_1056222), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056222), _1056224), _1056226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056222), _1056224), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1056222), _1056228), _1056226))))], (15950 ^ _779203) ^ [_1058955, _1058957, _1058959] : [class_Int_Onumber__ring(_1058955), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058955), hAPP(c_Int_Onumber__class_Onumber__of(_1058955), _1058957)), hAPP(c_Int_Onumber__class_Onumber__of(_1058955), _1058959)) = hAPP(c_Int_Onumber__class_Onumber__of(_1058955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1058957), _1058959)))], (31799 ^ _779203) ^ [_1350992, _1350994, _1350996, _1350998, _1351000] : [class_Groups_Ocomm__monoid__add(_1350992), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350994, _1350992), hAPP(hAPP(c_COMBS(_1350994, _1350992, _1350992), hAPP(hAPP(c_COMBB(_1350992, tc_fun(_1350992, _1350992), _1350994), c_Groups_Oplus__class_Oplus(_1350992)), _1350996)), _1350998)), _1351000) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1350992), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350994, _1350992), _1350996), _1351000)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1350994, _1350992), _1350998), _1351000)))], (16068 ^ _779203) ^ [_1061441, _1061443, _1061445, _1061447] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061441), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1061441), _1061443), _1061445)), hAPP(c_Int_Onumber__class_Onumber__of(_1061441), _1061447)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1061441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061441), _1061443), hAPP(c_Int_Onumber__class_Onumber__of(_1061441), _1061447))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061441), _1061445), hAPP(c_Int_Onumber__class_Onumber__of(_1061441), _1061447)))), class_Int_Onumber(_1061441), class_Rings_Oring(_1061441)], (4584 ^ _779203) ^ [_848879, _848881, _848883, _848885, _848887, _848889] : [-(c_Random__Sequence_Oempty(_848889, _848885, _848881) = c_Random__Sequence_Oempty(_848887, _848883, _848879)), _848889 = _848887, _848885 = _848883, _848881 = _848879], (42846 ^ _779203) ^ [_1633117, _1633119] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633117)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633119))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633117), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633119)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633117)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633117)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633119))))], (41152 ^ _779203) ^ [_1588544, _1588546, _1588548, _1588550, _1588552] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588544, _1588544)), hAPP(hAPP(c_Product__Type_OPair(_1588544, _1588544), _1588546), _1588548)), c_Transitive__Closure_Ortrancl(_1588544, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588544, _1588544), tc_HOL_Obool)), _1588550), _1588552)))), 41158 ^ _779203 : [(41164 ^ _779203) ^ [] : [41157 ^ [_1588544, _1588546, _1588548, _1588550, _1588552] = 41160 ^ [_1588544, _1588546, _1588548, _1588550, _1588552]], (41162 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588544, _1588544)), hAPP(hAPP(c_Product__Type_OPair(_1588544, _1588544), 41157 ^ [_1588544, _1588546, _1588548, _1588550, _1588552]), 41160 ^ [_1588544, _1588546, _1588548, _1588550, _1588552])), _1588552)))], (41159 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588544, _1588544)), hAPP(hAPP(c_Product__Type_OPair(_1588544, _1588544), _1588546), 41157 ^ [_1588544, _1588546, _1588548, _1588550, _1588552])), c_Transitive__Closure_Ortrancl(_1588544, _1588550))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588544, _1588544)), hAPP(hAPP(c_Product__Type_OPair(_1588544, _1588544), _1588546), _1588548)), c_Transitive__Closure_Ortrancl(_1588544, _1588550))))], (30969 ^ _779203) ^ [_1333151, _1333153] : [class_Lattices_Olattice(_1333151), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333151), _1333153)), -(_1333153 = c_Orderings_Obot__class_Obot(tc_fun(_1333151, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1333151), c_Big__Operators_Olattice__class_OInf__fin(_1333151, _1333153)), c_Big__Operators_Olattice__class_OSup__fin(_1333151, _1333153))))], (35360 ^ _779203) ^ [_1439140, _1439142, _1439144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439140, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1439140, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35361 ^ [_1439140, _1439142, _1439144])), _1439142)), _1439144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1439140, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1439140, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1439142)), _1439144)))], (49596 ^ _779203) ^ [_1781467, _1781469, _1781471, _1781473] : [c_Fun_Oinj__on(_1781467, _1781469, _1781471, c_Orderings_Otop__class_Otop(tc_fun(_1781467, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1781469, _1781467, c_Hilbert__Choice_Oinv__into(_1781467, _1781469, c_Orderings_Otop__class_Otop(tc_fun(_1781467, tc_HOL_Obool)), _1781471)), hAPP(c_Set_Oimage(_1781467, _1781469, _1781471), _1781473)) = _1781473)], (24964 ^ _779203) ^ [_1219186, _1219188, _1219190, _1219192] : [class_Fields_Ofield__inverse__zero(_1219186), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1219186), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219186), _1219188), _1219190)), _1219192) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1219186), hAPP(hAPP(c_Power_Opower__class_Opower(_1219186), _1219188), _1219192)), hAPP(hAPP(c_Power_Opower__class_Opower(_1219186), _1219190), _1219192)))], (24452 ^ _779203) ^ [_1209897, _1209899] : [class_Groups_Omonoid__mult(_1209897), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1209897), _1209899), 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(_1209897), _1209899), _1209899))], (48150 ^ _779203) ^ [_1750487, _1750489, _1750491] : [-(_1750487 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1750489), c_List_Oreplicate(_1750489, _1750487, _1750491)) = c_List_Oreplicate(_1750489, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1750487), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1750491))], (6162 ^ _779203) ^ [_877689, _877691, _877693, _877695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877689, tc_HOL_Obool)), _877691), _877693)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877689, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_877689), _877695), _877691)), hAPP(hAPP(c_Set_Oinsert(_877689), _877695), _877693))))], (15342 ^ _779203) ^ [_1048083, _1048085, _1048087] : [class_Orderings_Olinorder(_1048083), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1048083), _1048085), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1048083), _1048085), _1048087)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1048083), _1048085), _1048087))], (20172 ^ _779203) ^ [_1135089, _1135091] : [class_Groups_Olinordered__ab__group__add(_1135089), 20175 ^ _779203 : [(20182 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135089), c_Groups_Ozero__class_Ozero(_1135089)), _1135091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135089), hAPP(c_Groups_Ouminus__class_Ouminus(_1135089), _1135091)), _1135091)))], (20176 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135089), hAPP(c_Groups_Ouminus__class_Ouminus(_1135089), _1135091)), _1135091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135089), c_Groups_Ozero__class_Ozero(_1135089)), _1135091)))]]], (38056 ^ _779203) ^ [_1507382, _1507384] : [-(hAPP(c_Set_OPow(_1507382), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1507382, tc_HOL_Obool)), _1507384)) = hAPP(c_Set_OCollect(tc_fun(_1507382, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1507382, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1507382, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1507382, tc_HOL_Obool), tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1507382, tc_HOL_Obool)), c_COMBS(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1507382, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1507382, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1507382, tc_HOL_Obool), tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_fun(_1507382, tc_HOL_Obool)), tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_fun(_1507382, tc_HOL_Obool)), tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1507382, tc_HOL_Obool)), c_COMBB(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1507382, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1507382, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1507382, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1507382, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1507382, tc_HOL_Obool)), _1507384)), c_Set_OPow(_1507382))))))], (26898 ^ _779203) ^ [_1252950, _1252952, _1252954] : [class_Orderings_Oord(_1252950), 26901 ^ _779203 : [(26908 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252950), _1252952), _1252954)), -(hBOOL(hAPP(hAPP(c_member(_1252950), _1252952), hAPP(c_SetInterval_Oord__class_OatMost(_1252950), _1252954))))], (26902 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1252950), _1252952), hAPP(c_SetInterval_Oord__class_OatMost(_1252950), _1252954))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252950), _1252952), _1252954)))]]], (40219 ^ _779203) ^ [_1564741, _1564743] : [-(hAPP(c_Relation_ORange(_1564741, _1564741), c_Transitive__Closure_Otrancl(_1564741, _1564743)) = hAPP(c_Relation_ORange(_1564741, _1564741), _1564743))], (31939 ^ _779203) ^ [_1354658, _1354660, _1354662, _1354664, _1354666, _1354668] : [-(hAPP(c_Set_Oimage(_1354658, _1354660, _1354662), hAPP(c_Set_Oimage(_1354664, _1354658, _1354666), _1354668)) = hAPP(c_Set_Oimage(_1354664, _1354660, hAPP(hAPP(c_COMBB(_1354658, _1354660, _1354664), _1354662), _1354666)), _1354668))], (15682 ^ _779203) ^ [_1054106, _1054108, _1054110, _1054112] : [class_Orderings_Olinorder(_1054106), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054106), _1054108), _1054110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054106), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1054106), _1054112), _1054108)), _1054110)))], (35260 ^ _779203) ^ [_1436211, _1436213, _1436215, _1436217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1436211), _1436213)), -(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), _1436211), _1436215)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1436213), _1436217))), c_FunDef_Opair__leq)))], (9875 ^ _779203) ^ [_947720, _947722] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947720), _947722))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _947720), _947722)), -(_947720 = _947722)], (22874 ^ _779203) ^ [_1182182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182182)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1182182)) = _1182182)], (40002 ^ _779203) ^ [_1559436, _1559438, _1559440] : [40004 ^ _779203 : [(40007 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1559436), 40003 ^ [_1559436, _1559438, _1559440]), c_Wellfounded_Oacc(_1559436, _1559440)))], (40005 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1559436, _1559436)), hAPP(hAPP(c_Product__Type_OPair(_1559436, _1559436), 40003 ^ [_1559436, _1559438, _1559440]), _1559438)), _1559440)))]], -(hBOOL(hAPP(hAPP(c_member(_1559436), _1559438), c_Wellfounded_Oacc(_1559436, _1559440))))], (28088 ^ _779203) ^ [_1275237, _1275239, _1275241, _1275243] : [class_Orderings_Olinorder(_1275237), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275237), _1275239), _1275241)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1275237), _1275241), _1275243)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275237, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1275237, _1275239), _1275241)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1275237, _1275241), _1275243)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1275237, _1275239), _1275243))], (37623 ^ _779203) ^ [_1492630, _1492632, _1492634] : [-(hAPP(hAPP(c_Set_Oinsert(_1492630), _1492632), _1492634) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1492630, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1492630), hAPP(hAPP(c_COMBC(_1492630, _1492630, tc_HOL_Obool), c_fequal), _1492632))), _1492634))], (20676 ^ _779203) ^ [_1144040, _1144042, _1144044, _1144046, _1144048] : [hBOOL(hAPP(hAPP(c_member(_1144040), _1144042), c_SetInterval_Oord_OatLeastAtMost(_1144040, _1144044, _1144046, _1144048))), 20679 ^ _779203 : [(20682 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1144044, _1144042), _1144048)))], (20680 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1144044, _1144046), _1144042)))]]], (21235 ^ _779203) ^ [_1153601, _1153603] : [class_Int_Onumber__ring(_1153601), -(hAPP(c_Int_Onumber__class_Onumber__of(_1153601), c_Int_OBit1(_1153603)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153601), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153601), c_Groups_Oone__class_Oone(_1153601)), hAPP(c_Int_Onumber__class_Onumber__of(_1153601), _1153603))), hAPP(c_Int_Onumber__class_Onumber__of(_1153601), _1153603)))], (38717 ^ _779203) ^ [_1528768, _1528770, _1528772] : [c_Wellfounded_Owf(_1528768, _1528770), c_Wellfounded_Owf(_1528768, _1528772), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1528768, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1528768, _1528768), _1528770)), hAPP(c_Relation_ORange(_1528768, _1528768), _1528772)) = c_Orderings_Obot__class_Obot(tc_fun(_1528768, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1528768, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1528768, _1528768), tc_HOL_Obool)), _1528770), _1528772)))], (35087 ^ _779203) ^ [_1431856, _1431858, _1431860, _1431862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1431856), _1431858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1431860), _1431862)), -(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), _1431856), _1431860)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1431858), _1431862))), c_FunDef_Opair__leq)))], (22916 ^ _779203) ^ [_1182799, _1182801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1182799)), _1182801)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1182799), hAPP(c_Int_Onat, _1182801))))], (35302 ^ _779203) ^ [_1437048, _1437050] : [_1437048 = _1437050, -(hAPP(c_Int_ORep__Integ, _1437048) = hAPP(c_Int_ORep__Integ, _1437050))], (3594 ^ _779203) ^ [_833022, _833024] : [_833024 = _833022, -(c_Orderings_Oord__class_Omax(_833024) = c_Orderings_Oord__class_Omax(_833022))], (9309 ^ _779203) ^ [_938032, _938034] : [-(_938032 = _938034), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938032), _938034))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938034), _938032)))], (38647 ^ _779203) ^ [] : [-(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)))))], (21763 ^ _779203) ^ [_1162326, _1162328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1162326)), c_Int_OBit1(_1162328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1162326), _1162328)))], (41729 ^ _779203) ^ [_1606393, _1606395, _1606397] : [c_Relation_Orefl__on(_1606393, _1606395, _1606397), -(c_Relation_Orefl__on(tc_List_Olist(_1606393), c_List_Olists(_1606393, _1606395), c_List_Olistrel(_1606393, _1606397)))], (51691 ^ _779203) ^ [_1823386, _1823388, _1823390, _1823392] : [-(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), _1823386, _1823388)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823390, _1823392)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823390), _1823392)), 51694 ^ _779203 : [(51697 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823390), _1823386)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823388), _1823392)), 51704 ^ _779203 : [(51711 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823388), _1823392)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823392), _1823388)))], (51705 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823390), _1823386)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823386), _1823390)))]]], (51695 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1823386), _1823388)))]]], (52653 ^ _779203) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (21605 ^ _779203) ^ [_1159509] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159509), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1159509)), c_Int_OPls)))], (49909 ^ _779203) ^ [_1788673, _1788675, _1788677, _1788679, _1788681, _1788683, _1788685, _1788687] : [c_Fun_Obij__betw(_1788673, _1788675, _1788677, _1788679, _1788681), 49912 ^ _779203 : [(49919 ^ _779203) ^ [] : [c_Fun_Obij__betw(_1788673, _1788683, hAPP(c_Fun_Ocomp(_1788675, _1788683, _1788673, _1788685), _1788677), _1788679, _1788687), -(c_Fun_Obij__betw(_1788675, _1788683, _1788685, _1788681, _1788687))], (49913 ^ _779203) ^ [] : [c_Fun_Obij__betw(_1788675, _1788683, _1788685, _1788681, _1788687), -(c_Fun_Obij__betw(_1788673, _1788683, hAPP(c_Fun_Ocomp(_1788675, _1788683, _1788673, _1788685), _1788677), _1788679, _1788687))]]], (44406 ^ _779203) ^ [_1668372, _1668374, _1668376, _1668378, _1668380] : [class_Groups_Oab__group__add(_1668372), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1668372), hAPP(hAPP(c_List_Omap(_1668374, _1668372), hAPP(hAPP(c_COMBS(_1668374, _1668372, _1668372), hAPP(hAPP(c_COMBB(_1668372, tc_fun(_1668372, _1668372), _1668374), c_Groups_Ominus__class_Ominus(_1668372)), _1668376)), _1668378)), _1668380)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1668372), hAPP(c_List_Omonoid__add__class_Olistsum(_1668372), hAPP(hAPP(c_List_Omap(_1668374, _1668372), _1668376), _1668380))), hAPP(c_List_Omonoid__add__class_Olistsum(_1668372), hAPP(hAPP(c_List_Omap(_1668374, _1668372), _1668378), _1668380))))], (12356 ^ _779203) ^ [_992250, _992252, _992254] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992250), _992252)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992250), _992254)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992252), _992254))], (6255 ^ _779203) ^ [_879795, _879797, _879799, _879801, _879803] : [hBOOL(hAPP(hAPP(c_member(_879795), _879797), _879799)), -(hAPP(hAPP(c_Set_Oinsert(_879801), hAPP(_879803, _879797)), hAPP(c_Set_Oimage(_879795, _879801, _879803), _879799)) = hAPP(c_Set_Oimage(_879795, _879801, _879803), _879799))], (47962 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45412 ^ _779203) ^ [_1690664, _1690666, _1690668, _1690670] : [_1690664 = _1690666, -(hAPP(c_List_OremoveAll(_1690668, _1690664), hAPP(hAPP(c_List_Olist_OCons(_1690668), _1690666), _1690670)) = hAPP(c_List_OremoveAll(_1690668, _1690664), _1690670))], (37413 ^ _779203) ^ [_1487226, _1487228, _1487230, _1487232, _1487234, _1487236] : [hBOOL(hAPP(hAPP(c_member(_1487226), _1487228), _1487230)), 37416 ^ _779203 : [(37423 ^ _779203) ^ [] : [_1487234 = _1487236, -(hAPP(hAPP(c_Product__Type_OSigma(_1487232, _1487226), _1487234), hAPP(c_COMBK(tc_fun(_1487226, tc_HOL_Obool), _1487232), _1487230)) = hAPP(hAPP(c_Product__Type_OSigma(_1487232, _1487226), _1487236), hAPP(c_COMBK(tc_fun(_1487226, tc_HOL_Obool), _1487232), _1487230)))], (37417 ^ _779203) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1487232, _1487226), _1487234), hAPP(c_COMBK(tc_fun(_1487226, tc_HOL_Obool), _1487232), _1487230)) = hAPP(hAPP(c_Product__Type_OSigma(_1487232, _1487226), _1487236), hAPP(c_COMBK(tc_fun(_1487226, tc_HOL_Obool), _1487232), _1487230)), -(_1487234 = _1487236)]]], (27740 ^ _779203) ^ [_1268125, _1268127, _1268129, _1268131] : [class_Lattices_Olattice(_1268125), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268125), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268125), _1268127), _1268129)), _1268131) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268125), _1268127), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268125), _1268129), _1268131)))], (5867 ^ _779203) ^ [_872127, _872129, _872131] : [_872127 = _872129, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872131, tc_HOL_Obool)), _872129), _872127)))], (8188 ^ _779203) ^ [_915145, _915147, _915149, _915151, _915153] : [hAPP(_915145, _915147) = _915149, -(c_Fun_Ofun__upd(_915151, _915153, _915145, _915147, _915149) = _915145)], (52465 ^ _779203) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (26536 ^ _779203) ^ [_1246178, _1246180] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1246178, _1246180) = 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), _1246178), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1246180))))], (10165 ^ _779203) ^ [_953660, _953662] : [class_Rings_Olinordered__semidom(_953660), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_953660), _953662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_953660), _953662), c_Groups_Oone__class_Oone(_953660)))))], (1490 ^ _779203) ^ [_800788, _800790] : [-(class_Orderings_Obot(_800788)), _800790 = _800788, class_Orderings_Obot(_800790)], (8631 ^ _779203) ^ [_924624, _924626, _924628, _924630] : [class_Groups_Oab__semigroup__mult(_924624), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924624), _924626), _924628)), _924630) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924624), _924626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924624), _924628), _924630)))], (48715 ^ _779203) ^ [_1762459, _1762461, _1762463, _1762465] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1762459), _1762461), _1762463), _1762465) = 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(_1762459)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1762459), _1762461)))], (18192 ^ _779203) ^ [_1100149] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1100149) = c_Int_OPls)], (25348 ^ _779203) ^ [_1226308, _1226310, _1226312] : [class_Rings_Olinordered__semidom(_1226308), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226308), c_Groups_Ozero__class_Ozero(_1226308)), _1226310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226308), _1226310), c_Groups_Oone__class_Oone(_1226308))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226308), hAPP(hAPP(c_Power_Opower__class_Opower(_1226308), _1226310), hAPP(c_Nat_OSuc, _1226312))), c_Groups_Oone__class_Oone(_1226308))))], (34332 ^ _779203) ^ [_1410453, _1410455, _1410457, _1410459, _1410461] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410453, tc_fun(_1410455, tc_HOL_Obool)), _1410457), hAPP(hAPP(c_COMBB(tc_fun(_1410455, tc_HOL_Obool), tc_fun(_1410455, tc_HOL_Obool), _1410453), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410455, tc_HOL_Obool)), _1410459)), _1410461)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410455, tc_HOL_Obool)), _1410459), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410453, tc_fun(_1410455, tc_HOL_Obool)), _1410457), _1410461)))], (31937 ^ _779203) ^ [_1354600, _1354602, _1354604] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354600, tc_Nat_Onat), _1354602), _1354604)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354600, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1354600), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1354602)), _1354604))], (41830 ^ _779203) ^ [_1609078, _1609080, _1609082, _1609084] : [_1609078 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1609080), hAPP(hAPP(c_List_Olist_OCons(_1609080), _1609082), _1609084)), _1609078) = _1609082)], (9321 ^ _779203) ^ [_938122, _938124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938122), _938124)), _938124 = _938122], (30545 ^ _779203) ^ [_1324483, _1324485, _1324487] : [class_Orderings_Olinorder(_1324483), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324483), _1324485)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324483), _1324487)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324483, tc_HOL_Obool)), _1324485), _1324487) = c_Orderings_Obot__class_Obot(tc_fun(_1324483, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1324483), c_Big__Operators_Olattice_OSup__fin(_1324483, c_Orderings_Oord__class_Omax(_1324483), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1324483, tc_HOL_Obool)), _1324485), _1324487))), c_Big__Operators_Olattice_OSup__fin(_1324483, c_Orderings_Oord__class_Omax(_1324483), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1324483, tc_HOL_Obool)), _1324485), _1324487))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1324483), c_Big__Operators_Olattice_OSup__fin(_1324483, c_Orderings_Oord__class_Omax(_1324483), _1324485)), c_Big__Operators_Olattice_OSup__fin(_1324483, c_Orderings_Oord__class_Omax(_1324483), _1324487)))], (42868 ^ _779203) ^ [_1633643, _1633645, _1633647] : [-(hBOOL(hAPP(hAPP(c_member(_1633643), _1633645), hAPP(c_List_Oset(_1633643), _1633647)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633643)), c_List_Oremove1(_1633643, _1633645, _1633647)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633643)), _1633647))], (41651 ^ _779203) ^ [_1604139, _1604141, _1604143, _1604145] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604139), tc_List_Olist(_1604139))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604139), tc_List_Olist(_1604139)), _1604143), _1604145)), c_List_Olistrel(_1604139, _1604141))), -(c_List_Olistrelp(_1604139, hAPP(hAPP(c_COMBC(_1604139, tc_fun(tc_prod(_1604139, _1604139), tc_HOL_Obool), tc_fun(_1604139, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604139, tc_fun(tc_fun(tc_prod(_1604139, _1604139), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1604139, _1604139), tc_HOL_Obool), tc_fun(_1604139, tc_HOL_Obool)), _1604139), c_COMBC(_1604139, tc_fun(tc_prod(_1604139, _1604139), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604139, tc_prod(_1604139, _1604139)), tc_fun(_1604139, tc_fun(tc_fun(tc_prod(_1604139, _1604139), tc_HOL_Obool), tc_HOL_Obool)), _1604139), hAPP(c_COMBB(tc_prod(_1604139, _1604139), tc_fun(tc_fun(tc_prod(_1604139, _1604139), tc_HOL_Obool), tc_HOL_Obool), _1604139), c_member(tc_prod(_1604139, _1604139)))), c_Product__Type_OPair(_1604139, _1604139)))), _1604141), _1604143, _1604145))], (33235 ^ _779203) ^ [_1387721, _1387723, _1387725, _1387727, _1387729] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1387721, _1387723), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1387725), _1387727))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1387723)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1387729)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1387721, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1387723), _1387729)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1387725), _1387729)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1387723), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1387725, _1387729))), _1387727)))))], (47092 ^ _779203) ^ [_1726671, _1726673, _1726675, _1726677] : [47094 ^ _779203 : [(47099 ^ _779203) ^ [] : [hBOOL(hAPP(_1726677, hAPP(hAPP(c_List_Onth(_1726673), _1726675), 47093 ^ [_1726671, _1726673, _1726675, _1726677])))], (47097 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47093 ^ [_1726671, _1726673, _1726675, _1726677]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726673)), _1726675))))], (47095 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47093 ^ [_1726671, _1726673, _1726675, _1726677]), _1726671)))]], 47102 ^ _779203 : [(47105 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1726677, hAPP(hAPP(c_List_Onth(_1726673), _1726675), _1726671))))], (47103 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1726671), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726673)), _1726675))))]], -(c_List_OtakeWhile(_1726673, _1726677, _1726675) = hAPP(hAPP(c_List_Otake(_1726673), _1726671), _1726675))], (17624 ^ _779203) ^ [_1089831, _1089833, _1089835] : [class_Orderings_Olinorder(_1089831), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089831), _1089833)), -(_1089833 = c_Orderings_Obot__class_Obot(tc_fun(_1089831, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1089831, c_Orderings_Oord__class_Omax(_1089831), hAPP(hAPP(c_Set_Oinsert(_1089831), _1089835), _1089833)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1089831), _1089835), c_Big__Operators_Olattice_OSup__fin(_1089831, c_Orderings_Oord__class_Omax(_1089831), _1089833)))], (41062 ^ _779203) ^ [_1586179, _1586181, _1586183] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586179, _1586179)), _1586181), c_Transitive__Closure_Otrancl(_1586179, _1586183)))), 41063 ^ _779203 : [(41064 ^ _779203) ^ [_1586258] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1586258)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1586179, _1586179)), _1586181), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1586179, _1586179), tc_HOL_Obool), _1586258), _1586183)))]]], (26442 ^ _779203) ^ [_1244278, _1244280, _1244282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244278)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1244280), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1244282)), 26452 ^ _779203 : [(26458 ^ _779203) ^ [] : [-(_1244280 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26454 ^ [_1244278, _1244280, _1244282]), 26451 ^ [_1244278, _1244280, _1244282]))], (26456 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26454 ^ [_1244278, _1244280, _1244282]), _1244282)))], (26453 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26451 ^ [_1244278, _1244280, _1244282]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1244278))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1244280), _1244278) = _1244280)], (29604 ^ _779203) ^ [_1304412, _1304414, _1304416, _1304418] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304412, tc_HOL_Obool)), _1304414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304412, tc_HOL_Obool)), _1304416), _1304418)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304412, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304412, tc_HOL_Obool)), _1304414), _1304416)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304412, tc_HOL_Obool)), _1304414), _1304418)))], (38731 ^ _779203) ^ [_1529054, _1529056] : [c_Wellfounded_Owf(_1529054, _1529056), 38734 ^ _779203 : [(38735 ^ _779203) ^ [_1529123] : [-(hBOOL(hAPP(hAPP(c_member(_1529054), _1529123), c_Wellfounded_Oacc(_1529054, _1529056))))]]], (3448 ^ _779203) ^ [_830663, _830665] : [_830665 = _830663, -(c_SetInterval_Oord__class_OlessThan(_830665) = c_SetInterval_Oord__class_OlessThan(_830663))], (23754 ^ _779203) ^ [_1197292, _1197294] : [23755 ^ _779203 : [(23756 ^ _779203) ^ [_1197341] : [_1197292 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1197294), _1197341)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197292, _1197294) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10223 ^ _779203) ^ [_954921, _954923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _954921), _954923)), 10226 ^ _779203 : [(10233 ^ _779203) ^ [] : [_954923 = _954921, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _954923), hAPP(c_Nat_OSuc, _954921))))], (10227 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _954923), hAPP(c_Nat_OSuc, _954921))), -(_954923 = _954921)]]], (19732 ^ _779203) ^ [_1127263, _1127265, _1127267] : [class_Groups_Ogroup__add(_1127263), 19735 ^ _779203 : [(19742 ^ _779203) ^ [] : [_1127265 = _1127267, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1127263), _1127265) = hAPP(c_Groups_Ouminus__class_Ouminus(_1127263), _1127267))], (19736 ^ _779203) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1127263), _1127265) = hAPP(c_Groups_Ouminus__class_Ouminus(_1127263), _1127267), -(_1127265 = _1127267)]]], (8162 ^ _779203) ^ [_914811, _914813, _914815, _914817, _914819] : [-(hAPP(c_Fun_Ofun__upd(_914811, _914813, _914815, _914817, _914819), _914817) = _914819)], (21955 ^ _779203) ^ [_1166233, _1166235] : [class_Divides_Osemiring__div(_1166233), -(c_Divides_Odiv__class_Omod(_1166233, _1166235, c_Groups_Ozero__class_Ozero(_1166233)) = _1166235)], (29170 ^ _779203) ^ [_1295623, _1295625, _1295627, _1295629] : [class_Lattices_Odistrib__lattice(_1295623), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1295623), _1295625), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295623), _1295627), _1295629)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295623), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1295623), _1295625), _1295627)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1295623), _1295625), _1295629)))], (31731 ^ _779203) ^ [_1349149, _1349151, _1349153, _1349155] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349149, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1349149, tc_fun(_1349149, tc_HOL_Obool), tc_HOL_Obool), c_member(_1349149)), _1349151)), hAPP(hAPP(c_COMBC(_1349149, tc_fun(_1349149, tc_HOL_Obool), tc_HOL_Obool), c_member(_1349149)), _1349153)), _1349155)), -(hBOOL(hAPP(hAPP(c_member(_1349149), _1349155), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349149, tc_HOL_Obool)), _1349151), _1349153))))], (41557 ^ _779203) ^ [_1601077, _1601079, _1601081, _1601083, _1601085] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601077, _1601077)), hAPP(hAPP(c_Product__Type_OPair(_1601077, _1601077), _1601079), _1601081)), _1601083)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601077), tc_List_Olist(_1601077))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601077), tc_List_Olist(_1601077)), hAPP(hAPP(c_List_Olist_OCons(_1601077), _1601079), _1601085)), hAPP(hAPP(c_List_Olist_OCons(_1601077), _1601081), _1601085))), c_List_Olistrel1(_1601077, _1601083))))], (27282 ^ _779203) ^ [_1259439, _1259441, _1259443, _1259445] : [27283 ^ _779203 : [(27286 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1259439), _1259441), _1259445))], (27284 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1259439), _1259441), _1259443))]], -(hBOOL(hAPP(hAPP(c_member(_1259439), _1259441), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259439, tc_HOL_Obool)), _1259445), _1259443))))], (24396 ^ _779203) ^ [_1209056, _1209058] : [-(_1209056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1209058), _1209056) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1209058), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1209058), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1209056), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (40769 ^ _779203) ^ [_1578641, _1578643] : [c_Wellfounded_Owf(_1578641, hAPP(c_Relation_Oconverse(_1578641, _1578641), _1578643)), -(c_Wellfounded_Owf(_1578641, hAPP(c_Relation_Oconverse(_1578641, _1578641), c_Transitive__Closure_Otrancl(_1578641, _1578643))))], (52499 ^ _779203) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (27322 ^ _779203) ^ [_1260222, _1260224, _1260226, _1260228] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260222, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260222, tc_HOL_Obool)), _1260224), _1260226)), _1260228) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260222, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260222, tc_HOL_Obool)), _1260224), _1260228)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1260222, tc_HOL_Obool)), _1260226), _1260228)))], (44614 ^ _779203) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (618 ^ _779203) ^ [_788444, _788446, _788448, _788450, _788452, _788454, _788456, _788458, _788460, _788462] : [-(c_List_Olist__all2(_788460, _788456, _788452, _788448, _788444)), c_List_Olist__all2(_788462, _788458, _788454, _788450, _788446), _788462 = _788460, _788458 = _788456, _788454 = _788452, _788450 = _788448, _788446 = _788444], (35740 ^ _779203) ^ [_1449284, _1449286, _1449288, _1449290, _1449292] : [c_Equiv__Relations_Oequiv(_1449284, _1449286, _1449288), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449284, tc_HOL_Obool)), _1449290), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449284), _1449286), _1449288))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1449284, tc_HOL_Obool)), _1449292), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1449284), _1449286), _1449288))), -(_1449290 = _1449292), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1449284, tc_HOL_Obool)), _1449290), _1449292) = c_Orderings_Obot__class_Obot(tc_fun(_1449284, tc_HOL_Obool)))], (35127 ^ _779203) ^ [_1432740, _1432742, _1432744, _1432746, _1432748, _1432750] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432740, tc_fun(_1432742, tc_HOL_Obool)), _1432744), hAPP(hAPP(c_COMBC(_1432740, tc_fun(_1432746, tc_fun(_1432742, tc_HOL_Obool)), tc_fun(_1432742, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432746, tc_HOL_Obool), tc_fun(tc_fun(_1432746, tc_fun(_1432742, tc_HOL_Obool)), tc_fun(_1432742, tc_HOL_Obool)), _1432740), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432746, tc_fun(_1432742, tc_HOL_Obool))), _1432748)), _1432750)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432746, tc_fun(_1432742, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432740, tc_fun(_1432746, tc_HOL_Obool)), _1432744), _1432748)), _1432750))], (7235 ^ _779203) ^ [_899422, _899424] : [class_Orderings_Opreorder(_899422), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899422), _899424), _899424))], (14239 ^ _779203) ^ [_1026763, _1026765, _1026767, _1026769] : [class_Fields_Ofield__inverse__zero(_1026763), -(_1026765 = c_Groups_Ozero__class_Ozero(_1026763)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026763), _1026765), _1026767)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026763), _1026765), _1026769)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026763), _1026767), _1026769))], (25880 ^ _779203) ^ [_1234380] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1234380) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1234380))], (22041 ^ _779203) ^ [_1168008, _1168010, _1168012, _1168014] : [class_Divides_Osemiring__div(_1168008), -(c_Divides_Odiv__class_Omod(_1168008, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168008), _1168010), _1168012), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168008), _1168010), _1168014)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168008), _1168010), c_Divides_Odiv__class_Omod(_1168008, _1168012, _1168014)))], (38072 ^ _779203) ^ [_1508148, _1508150, _1508152] : [class_Groups_Olinordered__ab__semigroup__add(_1508148), hBOOL(hAPP(c_Finite__Set_Ofinite(_1508148), _1508150)), -(_1508150 = c_Orderings_Obot__class_Obot(tc_fun(_1508148, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1508148), _1508152), c_Big__Operators_Olinorder__class_OMin(_1508148, _1508150)) = c_Big__Operators_Olinorder__class_OMin(_1508148, hAPP(c_Set_OCollect(_1508148), hAPP(hAPP(c_COMBB(tc_fun(_1508148, tc_HOL_Obool), tc_HOL_Obool, _1508148), c_HOL_OEx(_1508148)), hAPP(hAPP(c_COMBC(_1508148, tc_fun(_1508148, tc_HOL_Obool), tc_fun(_1508148, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1508148, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1508148, tc_HOL_Obool), tc_fun(_1508148, tc_HOL_Obool)), _1508148), c_COMBS(_1508148, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1508148, tc_HOL_Obool), tc_fun(_1508148, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1508148), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1508148), c_fconj)), hAPP(hAPP(c_COMBC(_1508148, tc_fun(_1508148, _1508148), tc_fun(_1508148, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1508148, tc_HOL_Obool), tc_fun(tc_fun(_1508148, _1508148), tc_fun(_1508148, tc_HOL_Obool)), _1508148), c_COMBB(_1508148, tc_HOL_Obool, _1508148)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1508148), _1508152))))), hAPP(hAPP(c_COMBC(_1508148, tc_fun(_1508148, tc_HOL_Obool), tc_HOL_Obool), c_member(_1508148)), _1508150))))))], (38762 ^ _779203) ^ [_1529718, _1529720, _1529722] : [c_Wellfounded_Owf(_1529718, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529718, _1529718), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529718, _1529718), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1529718, _1529718, _1529718), _1529720), _1529720)), hAPP(hAPP(c_Relation_Orel__comp(_1529718, _1529718, _1529718), _1529722), _1529720))), _1529722)), -(c_Wellfounded_Owf(_1529718, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529718, _1529718), tc_HOL_Obool)), _1529720), _1529722)))], (34526 ^ _779203) ^ [_1416672, _1416674, _1416676, _1416678] : [34528 ^ _779203 : [(34531 ^ _779203) ^ [] : [hAPP(_1416678, 34527 ^ [_1416672, _1416674, _1416676, _1416678]) = c_Orderings_Otop__class_Otop(tc_fun(_1416674, tc_HOL_Obool))], (34529 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1416672), 34527 ^ [_1416672, _1416674, _1416676, _1416678]), _1416676)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416672, tc_fun(_1416674, tc_HOL_Obool)), _1416676), _1416678) = c_Orderings_Otop__class_Otop(tc_fun(_1416674, tc_HOL_Obool)))], (45334 ^ _779203) ^ [_1689224, _1689226, _1689228, _1689230, _1689232] : [c_Fun_Oinj__on(_1689224, _1689226, _1689228, hAPP(hAPP(c_Set_Oinsert(_1689224), _1689230), hAPP(c_List_Oset(_1689224), _1689232))), -(hAPP(hAPP(c_List_Omap(_1689224, _1689226), _1689228), hAPP(c_List_OremoveAll(_1689224, _1689230), _1689232)) = hAPP(c_List_OremoveAll(_1689226, hAPP(_1689228, _1689230)), hAPP(hAPP(c_List_Omap(_1689224, _1689226), _1689228), _1689232)))], (37799 ^ _779203) ^ [_1497675, _1497677, _1497679, _1497681, _1497683, _1497685] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1497675, _1497677), hAPP(hAPP(c_Set_Oinsert(_1497675), _1497679), _1497681)), hAPP(c_COMBK(tc_fun(_1497677, tc_HOL_Obool), _1497675), hAPP(hAPP(c_Set_Oinsert(_1497677), _1497683), _1497685))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1497675, _1497677)), hAPP(hAPP(c_Product__Type_OPair(_1497675, _1497677), _1497679), _1497683)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1497675, _1497677), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1497675, _1497677), _1497681), hAPP(c_COMBK(tc_fun(_1497677, tc_HOL_Obool), _1497675), hAPP(hAPP(c_Set_Oinsert(_1497677), _1497683), _1497685)))), hAPP(hAPP(c_Product__Type_OSigma(_1497675, _1497677), hAPP(hAPP(c_Set_Oinsert(_1497675), _1497679), _1497681)), hAPP(c_COMBK(tc_fun(_1497677, tc_HOL_Obool), _1497675), _1497685)))))], (9155 ^ _779203) ^ [_935284, _935286, _935288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935284), _935286)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _935284), _935288)), 9162 ^ _779203 : [(9169 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935286), _935288)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935286), _935284)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935288), _935284))))], (9163 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935286), _935284)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _935288), _935284))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _935286), _935288)))]]], (38370 ^ _779203) ^ [_1518960, _1518962, _1518964, _1518966, _1518968, _1518970] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1518960, _1518962, _1518964), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518960, _1518962), tc_HOL_Obool)), _1518966), _1518968)), _1518970) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1518960, _1518964), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1518960, _1518962, _1518964), _1518966), _1518970)), hAPP(hAPP(c_Relation_Orel__comp(_1518960, _1518962, _1518964), _1518968), _1518970)))], (52673 ^ _779203) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (27764 ^ _779203) ^ [_1268697, _1268699, _1268701, _1268703] : [class_Lattices_Osemilattice__sup(_1268697), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268697), _1268699), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268697), _1268701), _1268703)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268697), _1268701), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268697), _1268699), _1268703)))], (17354 ^ _779203) ^ [_1085122] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1085122) = _1085122)], (34500 ^ _779203) ^ [_1415857, _1415859, _1415861, _1415863, _1415865, _1415867] : [class_Complete__Lattice_Ocomplete__lattice(_1415857), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415859, tc_fun(_1415861, _1415857)), _1415863), _1415865), _1415867) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415859, _1415857), _1415863), hAPP(hAPP(c_COMBC(_1415859, _1415861, _1415857), _1415865), _1415867)))], (48871 ^ _779203) ^ [_1766264, _1766266] : [-(hBOOL(hAPP(_1766266, 48878 ^ [_1766264, _1766266]))), 48872 ^ _779203 : [(48873 ^ _779203) ^ [_1766325] : [hBOOL(hAPP(hAPP(c_member(_1766264), _1766325), c_Orderings_Otop__class_Otop(tc_fun(_1766264, tc_HOL_Obool)))), hBOOL(hAPP(_1766266, _1766325))]]], (9289 ^ _779203) ^ [_937636, _937638] : [9290 ^ _779203 : [(9293 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _937638), _937636))], (9291 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _937636), _937638))]], _937636 = _937638], (24736 ^ _779203) ^ [_1215068, _1215070, _1215072] : [class_Groups_Omonoid__mult(_1215068), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1215068), _1215070), 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)))), _1215072))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215068), _1215070), hAPP(hAPP(c_Power_Opower__class_Opower(_1215068), hAPP(hAPP(c_Power_Opower__class_Opower(_1215068), _1215070), _1215072)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (43101 ^ _779203) ^ [_1639238, _1639240, _1639242, _1639244] : [hAPP(hAPP(c_List_Oappend(_1639238), _1639240), _1639242) = hAPP(hAPP(c_List_Oappend(_1639238), _1639240), _1639244), -(_1639242 = _1639244)], (36780 ^ _779203) ^ [_1472379, _1472381, _1472383, _1472385, _1472387, _1472389] : [c_Fun_Oinj__on(_1472379, _1472381, _1472383, _1472385), hBOOL(hAPP(hAPP(c_member(_1472381), _1472387), hAPP(c_Set_Oimage(_1472379, _1472381, _1472383), _1472385))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472379, tc_HOL_Obool)), _1472385), _1472389)), -(hBOOL(hAPP(hAPP(c_member(_1472379), hAPP(c_Fun_Othe__inv__into(_1472379, _1472381, _1472385, _1472383), _1472387)), _1472389)))], (37462 ^ _779203) ^ [_1488358, _1488360] : [c_Orderings_Obot__class_Obot(tc_fun(_1488358, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1488358), _1488360), 37465 ^ _779203 : [(37466 ^ _779203) ^ [_1488443] : [hBOOL(hAPP(_1488360, _1488443))]]], (36586 ^ _779203) ^ [_1467740, _1467742, _1467744, _1467746] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467740), _1467742)), hAPP(c_Finite__Set_Ocard(_1467744), hAPP(c_Set_Oimage(_1467740, _1467744, _1467746), _1467742)) = hAPP(c_Finite__Set_Ocard(_1467740), _1467742), -(c_Fun_Oinj__on(_1467740, _1467744, _1467746, _1467742))], (48775 ^ _779203) ^ [_1764121, _1764123] : [48778 ^ _779203 : [(48784 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764121, _1764121)), hAPP(hAPP(c_Product__Type_OPair(_1764121, _1764121), 48776 ^ [_1764121, _1764123]), 48780 ^ [_1764121, _1764123])), _1764123))], (48782 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764121, _1764121)), hAPP(hAPP(c_Product__Type_OPair(_1764121, _1764121), 48777 ^ [_1764121, _1764123]), 48780 ^ [_1764121, _1764123])), _1764123)))], (48779 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764121, _1764121)), hAPP(hAPP(c_Product__Type_OPair(_1764121, _1764121), 48776 ^ [_1764121, _1764123]), 48777 ^ [_1764121, _1764123])), _1764123)))]], -(c_Relation_Otrans(_1764121, _1764123))], (14683 ^ _779203) ^ [_1035061, _1035063, _1035065, _1035067, _1035069] : [class_Fields_Ofield(_1035061), -(_1035063 = c_Groups_Ozero__class_Ozero(_1035061)), -(_1035065 = c_Groups_Ozero__class_Ozero(_1035061)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035061), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035061), _1035067), _1035063)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035061), _1035069), _1035065)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035061), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1035061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035061), _1035067), _1035065)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035061), _1035069), _1035063))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035061), _1035063), _1035065)))], (4 ^ _779203) ^ [_779253, _779255] : [_779255 = _779253, -(_779253 = _779255)], (8573 ^ _779203) ^ [_923672, _923674] : [class_Groups_Ocomm__monoid__mult(_923672), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923672), c_Groups_Oone__class_Oone(_923672)), _923674) = _923674)], (9195 ^ _779203) ^ [_936047, _936049, _936051] : [_936049 = _936051, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936047), _936049) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936047), _936051))], (14697 ^ _779203) ^ [_1035308, _1035310, _1035312, _1035314] : [class_Fields_Ofield(_1035308), -(_1035310 = c_Groups_Ozero__class_Ozero(_1035308)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035308), _1035312), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035308), _1035314), _1035310)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035308), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035308), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035308), _1035310), _1035312)), _1035314)), _1035310))], (12925 ^ _779203) ^ [_1002695, _1002697] : [12926 ^ _779203 : [(12929 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1002695), _1002697)))], (12927 ^ _779203) ^ [] : [_1002697 = c_Orderings_Obot__class_Obot(tc_fun(_1002695, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1002695), _1002697) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52677 ^ _779203) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (8368 ^ _779203) ^ [_918937, _918939, _918941] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_918937), _918939)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918937, tc_HOL_Obool)), _918939), _918941)), -(hAPP(c_Finite__Set_Ocard(_918937), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918937, tc_HOL_Obool)), _918941), _918939)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_918937), _918941)), hAPP(c_Finite__Set_Ocard(_918937), _918939)))], (18106 ^ _779203) ^ [_1098647, _1098649, _1098651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098647), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098647)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098649)), _1098651)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31685 ^ _779203) ^ [_1348008, _1348010, _1348012, _1348014] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1348008, _1348010)), c_Nitpick_Opair__box_OPairBox(_1348008, _1348010, _1348012, _1348014)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52257 ^ _779203) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (1500 ^ _779203) ^ [_800913, _800915] : [-(class_Groups_Ouminus(_800913)), _800915 = _800913, class_Groups_Ouminus(_800915)], (34063 ^ _779203) ^ [_1403799] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1403799) = _1403799)], (9885 ^ _779203) ^ [_947874, _947876] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _947874)), hAPP(c_Nat_OSuc, _947876)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947874), _947876))], (4424 ^ _779203) ^ [_846345, _846347] : [_846347 = _846345, -(c_List_Olist_OCons(_846347) = c_List_Olist_OCons(_846345))], (11300 ^ _779203) ^ [_973744, _973746, _973748] : [class_Groups_Oordered__comm__monoid__add(_973744), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973744), c_Groups_Ozero__class_Ozero(_973744)), _973746)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973744), c_Groups_Ozero__class_Ozero(_973744)), _973748)), 11311 ^ _779203 : [(11320 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973744), _973746), _973748) = c_Groups_Ozero__class_Ozero(_973744)), _973746 = c_Groups_Ozero__class_Ozero(_973744), _973748 = c_Groups_Ozero__class_Ozero(_973744)], (11312 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973744), _973746), _973748) = c_Groups_Ozero__class_Ozero(_973744), 11315 ^ _779203 : [(11318 ^ _779203) ^ [] : [-(_973748 = c_Groups_Ozero__class_Ozero(_973744))], (11316 ^ _779203) ^ [] : [-(_973746 = c_Groups_Ozero__class_Ozero(_973744))]]]]], (29300 ^ _779203) ^ [_1298600, _1298602, _1298604, _1298606] : [class_Lattices_Osemilattice__inf(_1298600), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298600), _1298602), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298600), _1298604), _1298606)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298600), _1298604), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298600), _1298602), _1298606)))], (21599 ^ _779203) ^ [_1159414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1159414)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159414), c_Int_OPls)))], (32857 ^ _779203) ^ [_1380873, _1380875, _1380877, _1380879, _1380881, _1380883] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1380873, tc_fun(_1380875, tc_HOL_Obool))), _1380877), _1380879), _1380881), _1380883)), -(hBOOL(hAPP(hAPP(_1380879, _1380881), _1380883)))], (12098 ^ _779203) ^ [_988305] : [class_Rings_Olinordered__semidom(_988305), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988305), c_Groups_Ozero__class_Ozero(_988305)), c_Groups_Oone__class_Oone(_988305))))], (1180 ^ _779203) ^ [_796913, _796915] : [-(class_Rings_Olinordered__ring__strict(_796913)), _796915 = _796913, class_Rings_Olinordered__ring__strict(_796915)], (40446 ^ _779203) ^ [_1571007, _1571009, _1571011] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1571007, _1571009, _1571009), _1571011), c_Relation_OId(_1571009)) = _1571011)], (36204 ^ _779203) ^ [_1460344, _1460346] : [class_Groups_Oordered__ab__group__add(_1460344), -(c_Fun_Oinj__on(_1460344, _1460344, c_Groups_Ouminus__class_Ouminus(_1460344), _1460346))], (42956 ^ _779203) ^ [_1635873, _1635875, _1635877, _1635879] : [-(c_List_Osublist(_1635873, hAPP(hAPP(c_List_Olist_OCons(_1635873), _1635875), _1635877), _1635879) = hAPP(hAPP(c_List_Oappend(_1635873), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1635873)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1635879)), hAPP(hAPP(c_List_Olist_OCons(_1635873), _1635875), c_List_Olist_ONil(_1635873))), c_List_Olist_ONil(_1635873))), c_List_Osublist(_1635873, _1635877, 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)), _1635879)))))], (35541 ^ _779203) ^ [_1444197, _1444199, _1444201, _1444203] : [-(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), _1444197), _1444199)), 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), _1444201), _1444203)), 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), _1444197), _1444201)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444199), _1444203))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (52147 ^ _779203) ^ [_1831298, _1831300] : [class_Lattices_Odistrib__lattice(_1831298), -(class_Lattices_Odistrib__lattice(tc_fun(_1831300, _1831298)))], (7931 ^ _779203) ^ [_909739, _909741, _909743, _909745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_909739, tc_HOL_Obool)), _909741), _909743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909739, tc_HOL_Obool)), _909743), _909745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_909739, tc_HOL_Obool)), _909741), _909745)))], (20494 ^ _779203) ^ [_1140664, _1140666] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1140664), _1140666) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1140664), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1140666)))], (40352 ^ _779203) ^ [_1568706, _1568708] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1568706, _1568706, _1568706), c_Transitive__Closure_Ortrancl(_1568706, _1568708)), c_Transitive__Closure_Ortrancl(_1568706, _1568708)) = c_Transitive__Closure_Ortrancl(_1568706, _1568708))], (9705 ^ _779203) ^ [_945024, _945026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945024), _945026)), -(hAPP(c_Nat_OSuc, _945024) = _945026), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _945024)), _945026)))], (38296 ^ _779203) ^ [_1516425, _1516427] : [-(c_Product__Type_Omap__pair(_1516425, _1516425, _1516427, _1516427, c_COMBI(_1516425), c_COMBI(_1516427)) = c_Fun_Oid(tc_prod(_1516425, _1516427)))], (17524 ^ _779203) ^ [_1088151, _1088153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1088151), _1088153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1088151), _1088153)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21475 ^ _779203) ^ [_1157323, _1157325] : [c_Int_OBit0(_1157323) = c_Int_OBit0(_1157325), -(_1157323 = _1157325)], (43425 ^ _779203) ^ [_1646835, _1646837, _1646839, _1646841] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1646835), tc_List_Olist(_1646835))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1646835), tc_List_Olist(_1646835)), _1646837), _1646839)), c_List_Olistrel1(_1646835, _1646841))), 43430 ^ _779203 : [(43437 ^ _779203) ^ [] : [-(_1646839 = hAPP(hAPP(c_List_Oappend(_1646835), 43432 ^ [_1646835, _1646837, _1646839, _1646841]), hAPP(hAPP(c_List_Olist_OCons(_1646835), 43429 ^ [_1646835, _1646837, _1646839, _1646841]), 43433 ^ [_1646835, _1646837, _1646839, _1646841])))], (43435 ^ _779203) ^ [] : [-(_1646837 = hAPP(hAPP(c_List_Oappend(_1646835), 43432 ^ [_1646835, _1646837, _1646839, _1646841]), hAPP(hAPP(c_List_Olist_OCons(_1646835), 43428 ^ [_1646835, _1646837, _1646839, _1646841]), 43433 ^ [_1646835, _1646837, _1646839, _1646841])))], (43431 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1646835, _1646835)), hAPP(hAPP(c_Product__Type_OPair(_1646835, _1646835), 43428 ^ [_1646835, _1646837, _1646839, _1646841]), 43429 ^ [_1646835, _1646837, _1646839, _1646841])), _1646841)))]]], (39242 ^ _779203) ^ [_1540948, _1540950, _1540952] : [-(c_Relation_Orefl__on(_1540948, _1540950, _1540952)), 39246 ^ _779203 : [(39249 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1540948, _1540948, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1540948, tc_fun(_1540948, tc_HOL_Obool), tc_fun(_1540948, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1540948, tc_HOL_Obool), tc_fun(_1540948, tc_HOL_Obool)), _1540948), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1540948)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1540948), c_fconj), hAPP(hAPP(c_COMBC(_1540948, tc_fun(_1540948, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540948)), _1540950)))), hAPP(hAPP(c_COMBC(_1540948, tc_fun(_1540948, tc_HOL_Obool), tc_HOL_Obool), c_member(_1540948)), _1540950))), 39245 ^ [_1540948, _1540950, _1540952]))], (39247 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540948, _1540948)), 39245 ^ [_1540948, _1540950, _1540952]), _1540952)))]], 39251 ^ _779203 : [(39254 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540948, _1540948)), hAPP(hAPP(c_Product__Type_OPair(_1540948, _1540948), 39250 ^ [_1540948, _1540950, _1540952]), 39250 ^ [_1540948, _1540950, _1540952])), _1540952))], (39252 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1540948), 39250 ^ [_1540948, _1540950, _1540952]), _1540950)))]]], (38356 ^ _779203) ^ [_1518578, _1518580, _1518582, _1518584, _1518586] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1518578, _1518580)), hAPP(hAPP(c_Product__Type_OPair(_1518578, _1518580), _1518582), _1518584)), _1518586)), -(hBOOL(hAPP(hAPP(c_member(_1518580), _1518584), hAPP(c_Relation_ORange(_1518578, _1518580), _1518586))))], (40891 ^ _779203) ^ [_1581925, _1581927, _1581929, _1581931, _1581933, _1581935] : [c_Relation_Osingle__valued(_1581925, _1581927, hAPP(c_Relation_Oconverse(_1581927, _1581925), _1581929)), -(_1581931 = c_Orderings_Obot__class_Obot(tc_fun(_1581933, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1581927, _1581925, _1581929), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581933, tc_fun(_1581927, tc_HOL_Obool)), _1581931), _1581935)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1581933, tc_fun(_1581925, tc_HOL_Obool)), _1581931), hAPP(hAPP(c_COMBB(tc_fun(_1581927, tc_HOL_Obool), tc_fun(_1581925, tc_HOL_Obool), _1581933), c_Relation_OImage(_1581927, _1581925, _1581929)), _1581935)))], (33565 ^ _779203) ^ [_1393472, _1393474, _1393476] : [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), _1393472), _1393474))), -(hBOOL(hAPP(hAPP(_1393476, _1393472), _1393474))), 33572 ^ _779203 : [(33575 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1393476, 33570 ^ [_1393472, _1393474, _1393476]), 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)))), 33571 ^ [_1393472, _1393474, _1393476])))), -(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), 33570 ^ [_1393472, _1393474, _1393476]), 33571 ^ [_1393472, _1393474, _1393476])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 33571 ^ [_1393472, _1393474, _1393476]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33585 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1393476, 33570 ^ [_1393472, _1393474, _1393476]), 33571 ^ [_1393472, _1393474, _1393476]))], (33573 ^ _779203) ^ [] : [-(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), 33570 ^ [_1393472, _1393474, _1393476]), 33571 ^ [_1393472, _1393474, _1393476]))))]]], (13373 ^ _779203) ^ [_1010812, _1010814, _1010816, _1010818] : [c_Big__Operators_Osemilattice__big(_1010812, _1010814, _1010816), hBOOL(hAPP(c_Finite__Set_Ofinite(_1010812), _1010818)), -(hAPP(_1010816, _1010818) = hAPP(c_Finite__Set_Ofold1(_1010812, _1010814), _1010818))], (8819 ^ _779203) ^ [_928124, _928126, _928128, _928130] : [class_Groups_Oordered__cancel__ab__semigroup__add(_928124), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928124), _928126), _928128)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928124), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928124), _928130), _928126)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928124), _928130), _928128))))], (25904 ^ _779203) ^ [_1234735, _1234737] : [class_Int_Oring__char__0(_1234735), 25907 ^ _779203 : [(25914 ^ _779203) ^ [] : [_1234737 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1234735) = hAPP(c_Int_Oring__1__class_Oof__int(_1234735), _1234737))], (25908 ^ _779203) ^ [] : [c_Groups_Ozero__class_Ozero(_1234735) = hAPP(c_Int_Oring__1__class_Oof__int(_1234735), _1234737), -(_1234737 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (35431 ^ _779203) ^ [_1441356, _1441358, _1441360, _1441362, _1441364] : [class_Groups_Ocomm__monoid__add(_1441356), class_Groups_Ocomm__monoid__mult(_1441356), _1441358 = _1441360, c_Nat__Transfer_Onat__set(_1441360), 35449 ^ _779203 : [(35452 ^ _779203) ^ [] : [hAPP(_1441362, 35448 ^ [_1441356, _1441358, _1441360, _1441362, _1441364]) = hAPP(_1441364, 35448 ^ [_1441356, _1441358, _1441360, _1441362, _1441364])], (35450 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35448 ^ [_1441356, _1441358, _1441360, _1441362, _1441364])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1441356), _1441362), _1441358) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1441356), _1441364), _1441360))], (15366 ^ _779203) ^ [_1048535, _1048537, _1048539] : [class_Orderings_Olinorder(_1048535), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048535), _1048537), _1048539) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048535), _1048539), _1048537))], (6489 ^ _779203) ^ [_883897, _883899, _883901, _883903] : [class_Orderings_Oorder(_883897), _883899 = _883901, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883897), _883903), _883901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883897), _883903), _883899)))], (46331 ^ _779203) ^ [_1710644, _1710646, _1710648] : [class_Orderings_Olinorder(_1710644), 46334 ^ _779203 : [(46353 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710644, hAPP(hAPP(c_List_Oappend(_1710644), _1710646), _1710648))), c_List_Olinorder__class_Osorted(_1710644, _1710646), c_List_Olinorder__class_Osorted(_1710644, _1710648), 46363 ^ _779203 : [(46369 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710644), 46362 ^ [_1710644, _1710646, _1710648]), 46365 ^ [_1710644, _1710646, _1710648]))], (46367 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1710644), 46365 ^ [_1710644, _1710646, _1710648]), hAPP(c_List_Oset(_1710644), _1710648))))], (46364 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1710644), 46362 ^ [_1710644, _1710646, _1710648]), hAPP(c_List_Oset(_1710644), _1710646))))]]], (46335 ^ _779203) ^ [] : [c_List_Olinorder__class_Osorted(_1710644, hAPP(hAPP(c_List_Oappend(_1710644), _1710646), _1710648)), 46338 ^ _779203 : [(46343 ^ _779203) ^ [_1710880] : [hBOOL(hAPP(hAPP(c_member(_1710644), _1710880), hAPP(c_List_Oset(_1710644), _1710646))), 46346 ^ _779203 : [(46347 ^ _779203) ^ [_1710990] : [hBOOL(hAPP(hAPP(c_member(_1710644), _1710990), hAPP(c_List_Oset(_1710644), _1710648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710644), _1710880), _1710990)))]]], (46341 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710644, _1710648))], (46339 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710644, _1710646))]]]]], (24099 ^ _779203) ^ [_1203689, _1203691] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1203689)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203689)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203691)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1203689)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1203691))))], (9492 ^ _779203) ^ [_941133, _941135, _941137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941133), _941135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941133), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941137), _941135))))], (21931 ^ _779203) ^ [_1165643, _1165645, _1165647, _1165649] : [class_Divides_Osemiring__div(_1165643), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165643), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165643), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165643), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1165643), _1165645), _1165647)), _1165647)), c_Divides_Odiv__class_Omod(_1165643, _1165645, _1165647))), _1165649) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165643), _1165645), _1165649))], (42096 ^ _779203) ^ [_1616852, _1616854, _1616856, _1616858] : [-(hAPP(c_List_Oset(tc_prod(_1616852, _1616854)), hAPP(hAPP(c_List_Ozip(_1616852, _1616854), _1616856), _1616858)) = hAPP(c_Set_OCollect(tc_prod(_1616852, _1616854)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1616852, _1616854)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1616852, _1616854), 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(_1616852, _1616854)), 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(_1616852, _1616854)), 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(_1616852, _1616854), tc_fun(tc_Nat_Onat, tc_prod(_1616852, _1616854)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1616852, _1616854), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1616852, _1616854)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1616852, _1616854)), c_COMBB(tc_prod(_1616852, _1616854), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1616854, tc_prod(_1616852, _1616854)), hAPP(hAPP(c_COMBB(_1616852, tc_fun(_1616854, tc_prod(_1616852, _1616854)), tc_Nat_Onat), c_Product__Type_OPair(_1616852, _1616854)), hAPP(c_List_Onth(_1616852), _1616856))), hAPP(c_List_Onth(_1616854), _1616858)))))), 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(_1616852)), _1616856)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1616854)), _1616858)))))))], (10917 ^ _779203) ^ [_967735, _967737] : [class_Groups_Ogroup__add(_967735), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967735), _967737), _967737) = c_Groups_Ozero__class_Ozero(_967735))], (40402 ^ _779203) ^ [_1569932, _1569934, _1569936, _1569938, _1569940] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569932, _1569932)), hAPP(hAPP(c_Product__Type_OPair(_1569932, _1569932), _1569934), _1569936)), c_Transitive__Closure_Ortrancl(_1569932, _1569938))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1569932, _1569932)), hAPP(hAPP(c_Product__Type_OPair(_1569932, _1569932), _1569936), _1569940)), c_Transitive__Closure_Ortrancl(_1569932, _1569938))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1569932, _1569932)), hAPP(hAPP(c_Product__Type_OPair(_1569932, _1569932), _1569934), _1569940)), c_Transitive__Closure_Ortrancl(_1569932, _1569938))))], (32533 ^ _779203) ^ [_1369321, _1369323, _1369325, _1369327, _1369329] : [-(c_Nat_Onat_Onat__case(_1369321, _1369323, _1369325, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369327)), _1369329)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1369321), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1369327))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1369321, _1369321), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1369321, tc_fun(_1369321, _1369321)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1369321, tc_fun(_1369321, _1369321)), tc_Int_Oint), c_If(_1369321)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1369321, _1369323, _1369325, _1369329))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1369321, tc_Int_Oint), _1369325), 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)), _1369329)))))], (12452 ^ _779203) ^ [_993993, _993995] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _993993), _993995)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _993993), _993995) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44315 ^ _779203) ^ [_1665519, _1665521] : [-(hAPP(hAPP(c_List_Ozip(_1665519, _1665519), _1665521), _1665521) = hAPP(hAPP(c_List_Omap(_1665519, tc_prod(_1665519, _1665519)), hAPP(hAPP(c_COMBS(_1665519, _1665519, tc_prod(_1665519, _1665519)), c_Product__Type_OPair(_1665519, _1665519)), c_COMBI(_1665519))), _1665521))], (52255 ^ _779203) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (29684 ^ _779203) ^ [_1306087, _1306089, _1306091] : [class_Lattices_Oboolean__algebra(_1306087), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1306087), _1306089), _1306091) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1306087), _1306089), hAPP(c_Groups_Ouminus__class_Ouminus(_1306087), _1306091)))], (23786 ^ _779203) ^ [_1197772, _1197774] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1197772), _1197774)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197772)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197774)))], (46574 ^ _779203) ^ [_1715655, _1715657] : [hAPP(c_List_Orev(_1715655), _1715657) = c_List_Olist_ONil(_1715655), -(_1715657 = c_List_Olist_ONil(_1715655))], (21183 ^ _779203) ^ [_1152786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1152786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1152786)))], (9399 ^ _779203) ^ [_939496, _939498] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939496), _939498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939498), _939496)))], (17868 ^ _779203) ^ [_1094172, _1094174, _1094176] : [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), _1094172), _1094174)), _1094176)), 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)), _1094176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1094172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1094174), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (52275 ^ _779203) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (19666 ^ _779203) ^ [_1126171, _1126173] : [-(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), _1126171))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1126173))))], (33203 ^ _779203) ^ [_1387321, _1387323] : [33204 ^ _779203 : [(33207 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1387323), _1387321))], (33205 ^ _779203) ^ [] : [_1387321 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1387323, _1387321) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1387323))], (44724 ^ _779203) ^ [_1675324, _1675326, _1675328] : [-(c_List_Olist_Olist__size(_1675324, _1675326, _1675328) = 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(_1675324, tc_Nat_Onat), _1675326), _1675328))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675324)), _1675328)))], (47786 ^ _779203) ^ [_1742283, _1742285, _1742287] : [47788 ^ _779203 : [(47791 ^ _779203) ^ [] : [hBOOL(hAPP(_1742285, hAPP(hAPP(c_List_Onth(_1742283), _1742287), 47787 ^ [_1742283, _1742285, _1742287])))], (47789 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47787 ^ [_1742283, _1742285, _1742287]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1742283)), _1742287))))]], -(c_List_Olist__all(_1742283, _1742285, _1742287))], (22984 ^ _779203) ^ [_1183904, _1183906] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183904, _1183906) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183904, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1183906)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20762 ^ _779203) ^ [_1145676, _1145678] : [class_Int_Onumber__ring(_1145676), 20765 ^ _779203 : [(20772 ^ _779203) ^ [] : [c_Int_Oiszero(_1145676, hAPP(c_Int_Onumber__class_Onumber__of(_1145676), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1145678), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1145676), _1145678) = c_Groups_Ozero__class_Ozero(_1145676))], (20766 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1145676), _1145678) = c_Groups_Ozero__class_Ozero(_1145676), -(c_Int_Oiszero(_1145676, hAPP(c_Int_Onumber__class_Onumber__of(_1145676), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1145678), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (17288 ^ _779203) ^ [_1084170, _1084172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084170), _1084172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084170)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1084172))))], (7595 ^ _779203) ^ [_904622, _904624, _904626] : [class_Orderings_Olinorder(_904622), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904622), _904624), _904626))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904622), _904626), _904624)))], (46624 ^ _779203) ^ [_1716794, _1716796] : [-(hAPP(c_List_Oset(_1716794), hAPP(c_List_Orev(_1716794), _1716796)) = hAPP(c_List_Oset(_1716794), _1716796))], (32031 ^ _779203) ^ [_1357063, _1357065, _1357067] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1357063, tc_Nat_Onat), _1357065), _1357067) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1357063, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1357063), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1357065)), _1357067)))], (52433 ^ _779203) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (41595 ^ _779203) ^ [_1602224, _1602226, _1602228, _1602230] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602224), tc_List_Olist(_1602224))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602224), tc_List_Olist(_1602224)), _1602226), _1602228)), c_List_Olistrel(_1602224, _1602230))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602224)), _1602226) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1602224)), _1602228))], (3434 ^ _779203) ^ [_830442, _830444, _830446, _830448, _830450, _830452] : [-(c_List_Osublist(_830452, _830448, _830444) = c_List_Osublist(_830450, _830446, _830442)), _830452 = _830450, _830448 = _830446, _830444 = _830442], (51105 ^ _779203) ^ [_1813620, _1813622, _1813624] : [class_Rings_Olinordered__idom(_1813620), hAPP(c_Groups_Oabs__class_Oabs(_1813620), _1813622) = hAPP(c_Groups_Oabs__class_Oabs(_1813620), _1813624), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813620), _1813622), _1813624)))], (37641 ^ _779203) ^ [_1493130, _1493132, _1493134] : [c_Equiv__Relations_Oequiv(_1493130, _1493132, _1493134), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1493130, _1493130), tc_HOL_Obool)), _1493134), hAPP(hAPP(c_Product__Type_OSigma(_1493130, _1493130), _1493132), hAPP(c_COMBK(tc_fun(_1493130, tc_HOL_Obool), _1493130), _1493132)))))], (12577 ^ _779203) ^ [_996128, _996130, _996132] : [class_Groups_Oordered__comm__monoid__add(_996128), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996128), _996130), c_Groups_Ozero__class_Ozero(_996128))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996128), _996132), c_Groups_Ozero__class_Ozero(_996128))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996128), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996128), _996130), _996132)), c_Groups_Ozero__class_Ozero(_996128))))], (33189 ^ _779203) ^ [_1387035, _1387037, _1387039, _1387041, _1387043, _1387045] : [-(hAPP(c_Product__Type_Oapsnd(_1387035, _1387037, _1387039, _1387041), hAPP(hAPP(c_Product__Type_OPair(_1387039, _1387035), _1387043), _1387045)) = hAPP(hAPP(c_Product__Type_OPair(_1387039, _1387037), _1387043), hAPP(_1387041, _1387045)))], (6282 ^ _779203) ^ [_880315, _880317, _880319, _880321, _880323] : [c_Finite__Set_Ofolding__one(_880315, _880317, _880319), hBOOL(hAPP(c_Finite__Set_Ofinite(_880315), _880321)), -(hBOOL(hAPP(hAPP(c_member(_880315), _880323), _880321))), -(_880321 = c_Orderings_Obot__class_Obot(tc_fun(_880315, tc_HOL_Obool))), -(hAPP(_880319, hAPP(hAPP(c_Set_Oinsert(_880315), _880323), _880321)) = hAPP(hAPP(_880317, _880323), hAPP(_880319, _880321)))], (34997 ^ _779203) ^ [_1429470, _1429472, _1429474, _1429476, _1429478] : [-(_1429470 = c_Orderings_Obot__class_Obot(tc_fun(_1429472, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429472, tc_fun(_1429474, tc_HOL_Obool)), _1429470), hAPP(hAPP(c_COMBC(_1429472, tc_fun(_1429474, tc_HOL_Obool), tc_fun(_1429474, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429474, tc_HOL_Obool), tc_fun(tc_fun(_1429474, tc_HOL_Obool), tc_fun(_1429474, tc_HOL_Obool)), _1429472), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429474, tc_HOL_Obool))), _1429476)), _1429478)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429474, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429472, tc_fun(_1429474, tc_HOL_Obool)), _1429470), _1429476)), _1429478))], (38232 ^ _779203) ^ [_1514910, _1514912, _1514914, _1514916] : [class_Groups_Ocomm__monoid__add(_1514910), c_Fun_Oinj__on(_1514912, _1514910, _1514914, _1514916), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514912, _1514910), _1514914), _1514916) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1514910, _1514910), c_Fun_Oid(_1514910)), hAPP(c_Set_Oimage(_1514912, _1514910, _1514914), _1514916)))], (40442 ^ _779203) ^ [_1570934, _1570936] : [-(hAPP(c_Relation_OImage(_1570934, _1570934, c_Relation_OId(_1570934)), _1570936) = _1570936)], (52381 ^ _779203) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (32439 ^ _779203) ^ [_1366941, _1366943, _1366945, _1366947, _1366949, _1366951] : [class_Groups_Ocomm__monoid__mult(_1366941), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366943), _1366945)), 32446 ^ _779203 : [(32453 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366943), _1366947), _1366945))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366943, _1366941), hAPP(hAPP(c_COMBC(_1366943, _1366941, _1366941), hAPP(hAPP(c_COMBS(_1366943, _1366941, tc_fun(_1366941, _1366941)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1366941, tc_fun(_1366941, _1366941)), _1366943), c_If(_1366941)), hAPP(hAPP(c_COMBC(_1366943, _1366943, tc_HOL_Obool), c_fequal), _1366947))), _1366949)), _1366951)), _1366945) = hAPP(hAPP(c_Power_Opower__class_Opower(_1366941), _1366951), hAPP(c_Finite__Set_Ocard(_1366943), _1366945)))], (32447 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1366943), _1366947), _1366945)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366943, _1366941), hAPP(hAPP(c_COMBC(_1366943, _1366941, _1366941), hAPP(hAPP(c_COMBS(_1366943, _1366941, tc_fun(_1366941, _1366941)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1366941, tc_fun(_1366941, _1366941)), _1366943), c_If(_1366941)), hAPP(hAPP(c_COMBC(_1366943, _1366943, tc_HOL_Obool), c_fequal), _1366947))), _1366949)), _1366951)), _1366945) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366941), hAPP(_1366949, _1366947)), hAPP(hAPP(c_Power_Opower__class_Opower(_1366941), _1366951), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1366943), _1366945)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (24712 ^ _779203) ^ [_1214423, _1214425, _1214427] : [class_Rings_Olinordered__idom(_1214423), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214423), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214423), hAPP(hAPP(c_Power_Opower__class_Opower(_1214423), _1214425), 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(_1214423), _1214427), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1214423)))], (9813 ^ _779203) ^ [_946708, _946710, _946712] : [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, _946708)), _946710)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _946708)), _946712))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946710), _946712)))], (50309 ^ _779203) ^ [_1796602, _1796604, _1796606] : [hBOOL(hAPP(hAPP(_1796606, _1796604), _1796604)), -(hBOOL(hAPP(hAPP(c_member(_1796602), _1796604), c_Quotient_ORespects(_1796602, _1796606))))], (44333 ^ _779203) ^ [_1666448, _1666450, _1666452, _1666454] : [_1666454 = c_List_Olist_ONil(_1666450), -(c_List_Olist_ONil(_1666448) = hAPP(hAPP(c_List_Omap(_1666450, _1666448), _1666452), _1666454))], (23679 ^ _779203) ^ [_1195984, _1195986] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195984), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1195986), _1195984)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1195986), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1195986, _1195984)))], (3016 ^ _779203) ^ [_823961, _823963, _823965, _823967, _823969, _823971] : [-(c_List_Oset__Cons(_823971, _823967, _823963) = c_List_Oset__Cons(_823969, _823965, _823961)), _823971 = _823969, _823967 = _823965, _823963 = _823961], (39477 ^ _779203) ^ [_1547344, _1547346] : [-(c_Hilbert__Choice_OEps(_1547344, hAPP(hAPP(c_COMBC(_1547344, _1547344, tc_HOL_Obool), c_fequal), _1547346)) = _1547346)], (42804 ^ _779203) ^ [_1632337, _1632339, _1632341] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632337), tc_List_Olist(_1632337))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632337), tc_List_Olist(_1632337)), c_List_Olist_ONil(_1632337)), _1632339)), c_List_Olex(_1632337, _1632341)))], (49098 ^ _779203) ^ [_1771935, _1771937, _1771939, _1771941] : [c_Wellfounded_Omax__extp(_1771935, _1771937, _1771939, _1771941), 49101 ^ _779203 : [(49104 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1771935), _1771941)))], (49106 ^ _779203) ^ [] : [_1771941 = c_Orderings_Obot__class_Obot(tc_fun(_1771935, tc_HOL_Obool))], (49108 ^ _779203) ^ [_1772151] : [hBOOL(hAPP(hAPP(c_member(_1771935), _1772151), _1771939)), 49112 ^ _779203 : [(49115 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1771937, _1772151), 49111 ^ [_1771935, _1771937, _1771939, _1771941, _1772151])))], (49113 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771935), 49111 ^ [_1771935, _1771937, _1771939, _1771941, _1772151]), _1771941)))]]], (49102 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1771935), _1771939)))]]], (730 ^ _779203) ^ [_790166, _790168, _790170, _790172] : [-(c_Predicate_Oreflp(_790170, _790166)), c_Predicate_Oreflp(_790172, _790168), _790172 = _790170, _790168 = _790166], (52485 ^ _779203) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (43514 ^ _779203) ^ [_1649141, _1649143, _1649145] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1649141, tc_HOL_Obool)), hAPP(c_List_Oset(_1649141), hAPP(hAPP(c_List_Odrop(_1649141), _1649143), _1649145))), hAPP(c_List_Oset(_1649141), _1649145))))], (45599 ^ _779203) ^ [_1694722, _1694724, _1694726] : [c_List_Oconcat(_1694722, _1694724) = c_List_Oconcat(_1694722, _1694726), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694722))), _1694724) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1694722))), _1694726), 45609 ^ _779203 : [(45612 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1694722), tc_List_Olist(_1694722), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1694722), tc_fun(tc_List_Olist(_1694722), tc_Nat_Onat), tc_fun(tc_List_Olist(_1694722), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1694722), tc_Nat_Onat), tc_fun(tc_List_Olist(_1694722), tc_HOL_Obool)), tc_List_Olist(_1694722)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1694722))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1694722)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1694722))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1694722)))), 45608 ^ [_1694722, _1694724, _1694726]))], (45610 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694722), tc_List_Olist(_1694722))), 45608 ^ [_1694722, _1694724, _1694726]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1694722), tc_List_Olist(_1694722))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1694722), tc_List_Olist(_1694722)), _1694724), _1694726)))))]], -(_1694724 = _1694726)], (5320 ^ _779203) ^ [_860565, _860567] : [_860567 = _860565, -(c_Groups_Oplus__class_Oplus(_860567) = c_Groups_Oplus__class_Oplus(_860565))], (23709 ^ _779203) ^ [_1196595, _1196597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1196595), _1196597)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1196595), _1196597) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28654 ^ _779203) ^ [_1286124, _1286126] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1286124, _1286126))))], (29282 ^ _779203) ^ [_1298189, _1298191, _1298193] : [class_Lattices_Osemilattice__inf(_1298189), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298189), _1298191), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298189), _1298191), _1298193)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298189), _1298191), _1298193))], (43281 ^ _779203) ^ [_1642937, _1642939, _1642941, _1642943] : [-(hBOOL(hAPP(hAPP(c_member(_1642937), _1642939), hAPP(c_List_Oset(_1642937), _1642941)))), -(c_List_Oremove1(_1642937, _1642939, hAPP(hAPP(c_List_Oappend(_1642937), _1642941), _1642943)) = hAPP(hAPP(c_List_Oappend(_1642937), _1642941), c_List_Oremove1(_1642937, _1642939, _1642943)))], (29128 ^ _779203) ^ [_1294815, _1294817, _1294819] : [29129 ^ _779203 : [(29132 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1294815), _1294819))], (29130 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1294815), _1294817))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1294815), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1294815, tc_HOL_Obool)), _1294817), _1294819))))], (35659 ^ _779203) ^ [_1447428, _1447430, _1447432, _1447434] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1447428, _1447428)), hAPP(hAPP(c_Product__Type_OPair(_1447428, _1447428), _1447430), _1447432)), c_Relation_OId__on(_1447428, _1447434))), 35662 ^ _779203 : [(35665 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1447428), _1447430), _1447434)))], (35663 ^ _779203) ^ [] : [-(_1447430 = _1447432)]]], (39612 ^ _779203) ^ [_1550449, _1550451, _1550453, _1550455, _1550457] : [class_Groups_Ocomm__monoid__add(_1550449), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550451), _1550453)), c_Fun_Oinj__on(_1550451, _1550451, _1550455, _1550453), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550451, _1550449), _1550457), hAPP(c_Set_Oimage(_1550451, _1550451, _1550455), _1550453)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550451, _1550449), hAPP(c_Fun_Ocomp(_1550451, _1550449, _1550451, _1550457), _1550455)), _1550453))], (25708 ^ _779203) ^ [_1231752] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1231752, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36192 ^ _779203) ^ [_1459961, _1459963, _1459965] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1459961), _1459963)), c_Fun_Oinj__on(_1459961, tc_fun(tc_fun(_1459961, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1459961, tc_fun(tc_prod(_1459961, _1459961), tc_HOL_Obool), tc_fun(tc_fun(_1459961, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1459961, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1459961, _1459961), tc_HOL_Obool), tc_fun(tc_fun(_1459961, tc_HOL_Obool), tc_HOL_Obool)), _1459961), c_Equiv__Relations_Oquotient(_1459961)), hAPP(hAPP(c_COMBC(_1459961, tc_fun(_1459961, tc_HOL_Obool), tc_fun(_1459961, tc_HOL_Obool)), c_Set_Oinsert(_1459961)), c_Orderings_Obot__class_Obot(tc_fun(_1459961, tc_HOL_Obool))))), _1459965), _1459963), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1459961, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1459961), _1459963), _1459965)) = hAPP(c_Finite__Set_Ocard(_1459961), _1459963))], (17584 ^ _779203) ^ [_1089172, _1089174] : [class_Orderings_Olinorder(_1089172), -(c_Big__Operators_Olattice_OSup__fin(_1089172, c_Orderings_Oord__class_Omax(_1089172), hAPP(hAPP(c_Set_Oinsert(_1089172), _1089174), c_Orderings_Obot__class_Obot(tc_fun(_1089172, tc_HOL_Obool)))) = _1089174)], (44696 ^ _779203) ^ [_1674685, _1674687, _1674689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1674685), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674687), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1674687)), _1674689)))), -(hBOOL(hAPP(hAPP(c_member(_1674687), hAPP(c_Random_Opick(_1674687, _1674689), _1674685)), hAPP(c_List_Oset(_1674687), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1674687), _1674687), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1674687)), _1674689)))))], (2132 ^ _779203) ^ [_810027, _810029, _810031, _810033, _810035, _810037, _810039, _810041] : [-(c_Sum__Type_OPlus(_810041, _810037, _810033, _810029) = c_Sum__Type_OPlus(_810039, _810035, _810031, _810027)), _810041 = _810039, _810037 = _810035, _810033 = _810031, _810029 = _810027], (30149 ^ _779203) ^ [_1316691, _1316693, _1316695, _1316697, _1316699] : [c_Finite__Set_Ofolding__one(_1316691, _1316693, _1316695), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316691), _1316697)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316691), _1316699)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316691, tc_HOL_Obool)), _1316697), _1316699) = c_Orderings_Obot__class_Obot(tc_fun(_1316691, tc_HOL_Obool))), -(hAPP(hAPP(_1316693, hAPP(_1316695, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1316691, tc_HOL_Obool)), _1316697), _1316699))), hAPP(_1316695, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1316691, tc_HOL_Obool)), _1316697), _1316699))) = hAPP(hAPP(_1316693, hAPP(_1316695, _1316697)), hAPP(_1316695, _1316699)))], (40901 ^ _779203) ^ [_1582151, _1582153, _1582155] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582151, _1582151)), _1582153), c_Transitive__Closure_Ortrancl(_1582151, _1582155))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582151, _1582151)), _1582153), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1582151, _1582151), 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(_1582151, _1582151), tc_HOL_Obool), tc_fun(tc_prod(_1582151, _1582151), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1582151, _1582151), tc_HOL_Obool)), _1582155)))))], (44470 ^ _779203) ^ [_1669932] : [-(hAPP(c_List_Omap(_1669932, _1669932), c_Fun_Oid(_1669932)) = c_Fun_Oid(tc_List_Olist(_1669932)))], (33699 ^ _779203) ^ [_1396110, _1396112, _1396114, _1396116, _1396118, _1396120] : [hAPP(c_Product__Type_Oapsnd(_1396110, _1396112, _1396114, _1396116), _1396118) = hAPP(c_Product__Type_Oapsnd(_1396110, _1396112, _1396114, _1396120), _1396118), -(hAPP(_1396116, hAPP(c_Product__Type_Osnd(_1396114, _1396110), _1396118)) = hAPP(_1396120, hAPP(c_Product__Type_Osnd(_1396114, _1396110), _1396118)))], (10353 ^ _779203) ^ [_957412, _957414, _957416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957412), _957414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _957412), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957414), _957416))))], (43221 ^ _779203) ^ [_1641651, _1641653, _1641655] : [_1641655 = c_List_Olist_ONil(_1641653), -(_1641651 = hAPP(hAPP(c_List_Oappend(_1641653), _1641651), _1641655))], (36971 ^ _779203) ^ [_1476343, _1476345, _1476347, _1476349] : [c_Wellfounded_Omax__extp(_1476343, _1476345, _1476347, _1476349), 36974 ^ _779203 : [(36977 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1476343), _1476349)))], (36979 ^ _779203) ^ [] : [_1476349 = c_Orderings_Obot__class_Obot(tc_fun(_1476343, tc_HOL_Obool))], (36981 ^ _779203) ^ [_1476559] : [hBOOL(hAPP(hAPP(c_member(_1476343), _1476559), _1476347)), 36985 ^ _779203 : [(36988 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1476345, _1476559), 36984 ^ [_1476343, _1476345, _1476347, _1476349, _1476559])))], (36986 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1476343), 36984 ^ [_1476343, _1476345, _1476347, _1476349, _1476559]), _1476349)))]]], (36975 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1476343), _1476347)))]]], (39058 ^ _779203) ^ [_1536719, _1536721, _1536723, _1536725] : [39060 ^ _779203 : [(39063 ^ _779203) ^ [] : [c_Wellfounded_Owf(_1536721, hAPP(_1536723, 39059 ^ [_1536719, _1536721, _1536723, _1536725]))], (39061 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1536719, 39059 ^ [_1536719, _1536721, _1536723, _1536725])))]], -(c_Wellfounded_Owf(tc_prod(_1536725, _1536721), c_Recdef_Osame__fst(_1536725, _1536721, _1536719, _1536723)))], (8751 ^ _779203) ^ [_926802, _926804, _926806, _926808, _926810] : [class_Groups_Oordered__ab__semigroup__add(_926802), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926802), _926804), _926806)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926802), _926808), _926810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926802), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926802), _926804), _926808)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926802), _926806), _926810))))], (8466 ^ _779203) ^ [_921088, _921090, _921092, _921094, _921096] : [class_Groups_Ocomm__monoid__add(_921088), hBOOL(hAPP(c_Finite__Set_Ofinite(_921090), _921092)), hBOOL(hAPP(hAPP(c_member(_921090), _921094), _921092)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_921090, _921088), _921096), _921092) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921088), hAPP(_921096, _921094)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_921090, _921088), _921096), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921090, tc_HOL_Obool)), _921092), hAPP(hAPP(c_Set_Oinsert(_921090), _921094), c_Orderings_Obot__class_Obot(tc_fun(_921090, tc_HOL_Obool)))))))], (24091 ^ _779203) ^ [_1203538] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1203538)), 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, _1203538, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (11684 ^ _779203) ^ [_980736, _980738] : [class_Groups_Olinordered__ab__group__add(_980736), 11687 ^ _779203 : [(11694 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980736), c_Groups_Ozero__class_Ozero(_980736)), _980738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980736), c_Groups_Ozero__class_Ozero(_980736)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980736), _980738), _980738))))], (11688 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980736), c_Groups_Ozero__class_Ozero(_980736)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_980736), _980738), _980738))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_980736), c_Groups_Ozero__class_Ozero(_980736)), _980738)))]]], (15270 ^ _779203) ^ [_1046389, _1046391, _1046393, _1046395] : [class_Orderings_Olinorder(_1046389), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046389), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046389), _1046391), _1046393)), _1046395) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046389), _1046391), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046389), _1046393), _1046395)))], (23980 ^ _779203) ^ [_1201427, _1201429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1201427)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1201427), _1201429)), _1201427) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (37653 ^ _779203) ^ [_1493581, _1493583, _1493585] : [-(hAPP(c_Set_OCollect(_1493581), hAPP(hAPP(c_COMBS(_1493581, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1493581), c_fimplies), _1493583)), _1493585)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1493581, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1493581, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1493581), _1493583))), hAPP(c_Set_OCollect(_1493581), _1493585)))], (6276 ^ _779203) ^ [_880226, _880228] : [class_Orderings_Opreorder(_880226), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880226), _880228), _880228)))], (37307 ^ _779203) ^ [_1484228, _1484230, _1484232, _1484234, _1484236] : [c_Fun_Oinj__on(_1484228, _1484230, _1484232, c_Orderings_Otop__class_Otop(tc_fun(_1484228, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484230, tc_HOL_Obool)), _1484234), hAPP(c_Set_Oimage(_1484228, _1484230, _1484232), _1484236))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484228, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1484228, _1484230, _1484232), _1484234)), _1484236)))], (1590 ^ _779203) ^ [_802038, _802040] : [-(class_Groups_Oordered__ab__semigroup__add(_802038)), _802040 = _802038, class_Groups_Oordered__ab__semigroup__add(_802040)], (27212 ^ _779203) ^ [_1258262, _1258264] : [class_Orderings_Olinorder(_1258262), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1258262, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1258262), _1258264)) = hAPP(c_SetInterval_Oord__class_OatMost(_1258262), _1258264))], (44664 ^ _779203) ^ [_1673964, _1673966, _1673968, _1673970] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673964)), _1673966) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673968)), _1673970), -(hAPP(hAPP(c_List_Omap(tc_prod(_1673964, _1673968), _1673964), c_Product__Type_Ofst(_1673964, _1673968)), hAPP(hAPP(c_List_Ozip(_1673964, _1673968), _1673966), _1673970)) = _1673966)], (4732 ^ _779203) ^ [_851181, _851183, _851185, _851187] : [-(c_Complete__Lattice_OSup__class_OSup(_851187, _851183) = c_Complete__Lattice_OSup__class_OSup(_851185, _851181)), _851187 = _851185, _851183 = _851181], (8456 ^ _779203) ^ [_920859, _920861, _920863] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_920859), _920861)), hBOOL(hAPP(hAPP(c_member(_920859), _920863), _920861)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_920859), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920859, tc_HOL_Obool)), _920861), hAPP(hAPP(c_Set_Oinsert(_920859), _920863), c_Orderings_Obot__class_Obot(tc_fun(_920859, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_920859), _920861))], (20877 ^ _779203) ^ [_1147564] : [class_Groups_Osgn__if(_1147564), -(c_Groups_Osgn__class_Osgn(_1147564, c_Groups_Ozero__class_Ozero(_1147564)) = c_Groups_Ozero__class_Ozero(_1147564))], (26366 ^ _779203) ^ [_1242925, _1242927] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1242925, _1242927)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1242927), hAPP(c_Nat_OSuc, _1242925)))], (29982 ^ _779203) ^ [_1312979, _1312981, _1312983] : [class_Orderings_Oorder(_1312979), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312979, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1312979, _1312981, _1312983)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1312979), _1312983)) = c_Orderings_Obot__class_Obot(tc_fun(_1312979, tc_HOL_Obool)))], (21215 ^ _779203) ^ [_1153307] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1153307))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1153307)))))], (31997 ^ _779203) ^ [_1356182, _1356184, _1356186, _1356188, _1356190] : [class_Fields_Ofield__inverse__zero(_1356182), hBOOL(hAPP(c_Finite__Set_Ofinite(_1356184), _1356186)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1356184, _1356182), hAPP(hAPP(c_COMBS(_1356184, _1356182, _1356182), hAPP(hAPP(c_COMBB(_1356182, tc_fun(_1356182, _1356182), _1356184), c_Rings_Oinverse__class_Odivide(_1356182)), _1356188)), _1356190)), _1356186) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356182), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1356184, _1356182), _1356188), _1356186)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1356184, _1356182), _1356190), _1356186)))], (45632 ^ _779203) ^ [_1696119, _1696121, _1696123] : [hBOOL(hAPP(c_List_Odistinct(_1696119), _1696121)), -(hBOOL(hAPP(c_List_Odistinct(_1696119), hAPP(c_List_Ofilter(_1696119, _1696123), _1696121))))], (23665 ^ _779203) ^ [_1195660] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1195660)))), -(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), _1195660)) = 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), _1195660))))], (21321 ^ _779203) ^ [] : [-(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)))))], (25702 ^ _779203) ^ [_1231651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231651), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1231651)), c_Int_OMin)))], (17370 ^ _779203) ^ [_1085461, _1085463, _1085465] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085461), _1085463)), _1085465) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085461), _1085465)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085463), _1085465)))], (48802 ^ _779203) ^ [_1764854, _1764856] : [-(c_Relation_Otrans(_1764854, c_Transitive__Closure_Ortrancl(_1764854, _1764856)))], (18812 ^ _779203) ^ [_1110700] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1110700), 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), _1110700)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1110700)))], (40789 ^ _779203) ^ [_1579027, _1579029, _1579031, _1579033] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579027, _1579027)), hAPP(hAPP(c_Product__Type_OPair(_1579027, _1579027), _1579029), _1579031)), c_Transitive__Closure_Ortrancl(_1579027, _1579033))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579027, _1579027)), hAPP(hAPP(c_Product__Type_OPair(_1579027, _1579027), _1579031), _1579029)), c_Transitive__Closure_Ortrancl(_1579027, hAPP(c_Relation_Oconverse(_1579027, _1579027), _1579033)))))], (45344 ^ _779203) ^ [_1689497, _1689499] : [c_List_Oremdups(_1689497, _1689499) = _1689499, -(hBOOL(hAPP(c_List_Odistinct(_1689497), _1689499)))], (32877 ^ _779203) ^ [_1381317, _1381319, _1381321, _1381323, _1381325, _1381327] : [hAPP(hAPP(c_Product__Type_OPair(_1381317, _1381319), _1381321), _1381323) = hAPP(hAPP(c_Product__Type_OPair(_1381317, _1381319), _1381325), _1381327), 32880 ^ _779203 : [(32883 ^ _779203) ^ [] : [-(_1381323 = _1381327)], (32881 ^ _779203) ^ [] : [-(_1381321 = _1381325)]]], (4116 ^ _779203) ^ [_841515, _841517, _841519, _841521, _841523, _841525] : [-(c_Predicate_Oconversep(_841525, _841521, _841517) = c_Predicate_Oconversep(_841523, _841519, _841515)), _841525 = _841523, _841521 = _841519, _841517 = _841515], (21505 ^ _779203) ^ [_1157830, _1157832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1157830), _1157832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1157830)), c_Int_OBit0(_1157832))))], (30771 ^ _779203) ^ [_1329302, _1329304, _1329306, _1329308, _1329310] : [class_Groups_Ocomm__monoid__mult(_1329302), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329304), _1329306)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1329304), _1329308)), 30785 ^ _779203 : [(30788 ^ _779203) ^ [] : [hAPP(_1329310, 30784 ^ [_1329302, _1329304, _1329306, _1329308, _1329310]) = c_Groups_Oone__class_Oone(_1329302)], (30786 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1329304), 30784 ^ [_1329302, _1329304, _1329306, _1329308, _1329310]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1329304, tc_HOL_Obool)), _1329306), _1329308))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1329304, _1329302), _1329310), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1329304, tc_HOL_Obool)), _1329306), _1329308)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329302), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1329304, _1329302), _1329310), _1329306)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1329304, _1329302), _1329310), _1329308)))], (38564 ^ _779203) ^ [_1525870, _1525872, _1525874] : [c_Relation_Orefl__on(_1525870, _1525872, _1525874), 38567 ^ _779203 : [(38570 ^ _779203) ^ [_1526052] : [hBOOL(hAPP(hAPP(c_member(_1525870), _1526052), _1525872)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1525870, _1525870)), hAPP(hAPP(c_Product__Type_OPair(_1525870, _1525870), _1526052), _1526052)), _1525874)))], (38568 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1525870, _1525870), tc_HOL_Obool)), _1525874), hAPP(hAPP(c_Product__Type_OSigma(_1525870, _1525870), _1525872), hAPP(c_COMBK(tc_fun(_1525870, tc_HOL_Obool), _1525870), _1525872)))))]]], (33739 ^ _779203) ^ [_1396895] : [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), _1396895))), -(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), _1396895)) = 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), _1396895))))], (47909 ^ _779203) ^ [_1744541, _1744543, _1744545] : [c_List_Olist__all(_1744541, _1744543, _1744545), 47912 ^ _779203 : [(47913 ^ _779203) ^ [_1744622] : [hBOOL(hAPP(hAPP(c_member(_1744541), _1744622), hAPP(c_List_Oset(_1744541), _1744545))), -(hBOOL(hAPP(_1744543, _1744622)))]]], (44750 ^ _779203) ^ [_1675786, _1675788, _1675790] : [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, _1675786), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1675786)), _1675788)))), -(hBOOL(hAPP(hAPP(c_member(_1675786), hAPP(c_Product__Type_Ofst(_1675786, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1675786, _1675788), _1675790))), hAPP(c_List_Oset(_1675786), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1675786), _1675786), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1675786)), _1675788)))))], (43766 ^ _779203) ^ [_1654734] : [-(c_List_Orotate(_1654734, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1654734)))], (52473 ^ _779203) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (35537 ^ _779203) ^ [] : [-(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))))))], (23066 ^ _779203) ^ [_1185242, _1185244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185244)), 23073 ^ _779203 : [(23080 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1185242), _1185244)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1185242)), hAPP(c_Int_Onat, _1185244))))], (23074 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1185242)), hAPP(c_Int_Onat, _1185244))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1185242), _1185244)))]]], (2634 ^ _779203) ^ [_818002, _818004, _818006, _818008, _818010, _818012, _818014, _818016] : [-(c_Recdef_Osame__fst(_818016, _818012, _818008, _818004) = c_Recdef_Osame__fst(_818014, _818010, _818006, _818002)), _818016 = _818014, _818012 = _818010, _818008 = _818006, _818004 = _818002], (52339 ^ _779203) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (42704 ^ _779203) ^ [_1630407, _1630409] : [hAPP(c_List_Oset(_1630407), _1630409) = c_Orderings_Obot__class_Obot(tc_fun(_1630407, tc_HOL_Obool)), -(_1630409 = c_List_Olist_ONil(_1630407))], (43658 ^ _779203) ^ [_1652568, _1652570, _1652572, _1652574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1652568), _1652570)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652572)), _1652574))), -(hAPP(hAPP(c_List_Otake(_1652572), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1652568), _1652570)), _1652574) = hAPP(hAPP(c_List_Oappend(_1652572), hAPP(hAPP(c_List_Otake(_1652572), _1652568), _1652574)), hAPP(hAPP(c_List_Otake(_1652572), _1652570), hAPP(hAPP(c_List_Odrop(_1652572), _1652568), _1652574))))], (41204 ^ _779203) ^ [_1590295, _1590297, _1590299, _1590301] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590295, _1590295)), hAPP(hAPP(c_Product__Type_OPair(_1590295, _1590295), _1590297), _1590299)), c_Transitive__Closure_Otrancl(_1590295, _1590301))), 41208 ^ _779203 : [(41211 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590295, _1590295)), hAPP(hAPP(c_Product__Type_OPair(_1590295, _1590295), 41207 ^ [_1590295, _1590297, _1590299, _1590301]), _1590299)), _1590301)))], (41209 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590295, _1590295)), hAPP(hAPP(c_Product__Type_OPair(_1590295, _1590295), _1590297), 41207 ^ [_1590295, _1590297, _1590299, _1590301])), c_Transitive__Closure_Ortrancl(_1590295, _1590301))))]]], (44339 ^ _779203) ^ [_1666557, _1666559, _1666561] : [-(hAPP(hAPP(c_List_Omap(_1666557, _1666559), _1666561), c_List_Olist_ONil(_1666557)) = c_List_Olist_ONil(_1666559))], (44893 ^ _779203) ^ [_1678716, _1678718, _1678720, _1678722] : [-(c_List_Opartition(_1678716, _1678718, hAPP(hAPP(c_List_Olist_OCons(_1678716), _1678720), _1678722)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1678716), tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1678716), tc_fun(tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716))), tc_fun(tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1678716), tc_fun(tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)))), tc_fun(tc_fun(tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716))), tc_fun(tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)))), tc_List_Olist(_1678716)), c_COMBS(tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716))), tc_fun(tc_List_Olist(_1678716), tc_fun(tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)))), tc_List_Olist(_1678716)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)), tc_fun(tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716))), tc_List_Olist(_1678716)), hAPP(c_If(tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716))), hAPP(_1678718, _1678720)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1678716), tc_fun(tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716))), tc_List_Olist(_1678716)), c_Product__Type_OPair(tc_List_Olist(_1678716), tc_List_Olist(_1678716))), hAPP(c_List_Olist_OCons(_1678716), _1678720))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1678716), tc_fun(tc_List_Olist(_1678716), tc_List_Olist(_1678716)), tc_fun(tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716))), tc_fun(tc_fun(tc_List_Olist(_1678716), tc_List_Olist(_1678716)), tc_fun(tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)))), tc_List_Olist(_1678716)), c_COMBB(tc_List_Olist(_1678716), tc_prod(tc_List_Olist(_1678716), tc_List_Olist(_1678716)), tc_List_Olist(_1678716))), c_Product__Type_OPair(tc_List_Olist(_1678716), tc_List_Olist(_1678716)))), hAPP(c_List_Olist_OCons(_1678716), _1678720)))), c_List_Opartition(_1678716, _1678718, _1678722)))], (43644 ^ _779203) ^ [_1652275, _1652277, _1652279, _1652281] : [-(hAPP(c_List_Orotate1(_1652277), hAPP(hAPP(c_List_Olist_OCons(_1652277), _1652279), _1652281)) = hAPP(hAPP(c_List_Oappend(_1652277), _1652281), hAPP(hAPP(c_List_Olist_OCons(_1652277), _1652279), c_List_Olist_ONil(_1652277))))], (6104 ^ _779203) ^ [_876577, _876579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_876577, tc_HOL_Obool)), _876579), c_Orderings_Obot__class_Obot(tc_fun(_876577, tc_HOL_Obool)))), -(_876579 = c_Orderings_Obot__class_Obot(tc_fun(_876577, tc_HOL_Obool)))], (40538 ^ _779203) ^ [_1573227] : [-(hAPP(c_Relation_ORange(_1573227, _1573227), c_Relation_OId(_1573227)) = c_Orderings_Otop__class_Otop(tc_fun(_1573227, tc_HOL_Obool)))], (26508 ^ _779203) ^ [_1245510, _1245512] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1245510, _1245512)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1245512)), _1245510))], (2786 ^ _779203) ^ [_820422, _820424, _820426, _820428] : [-(c_Relation_ORange(_820428, _820424) = c_Relation_ORange(_820426, _820422)), _820428 = _820426, _820424 = _820422], (39308 ^ _779203) ^ [_1543176, _1543178] : [class_Complete__Lattice_Ocomplete__lattice(_1543176), -(c_Complete__Lattice_OInf__class_OInf(_1543176, _1543178) = c_Complete__Lattice_OSup__class_OSup(_1543176, hAPP(c_Set_OCollect(_1543176), hAPP(hAPP(c_COMBB(tc_fun(_1543176, tc_HOL_Obool), tc_HOL_Obool, _1543176), c_HOL_OAll(_1543176)), hAPP(hAPP(c_COMBB(tc_fun(_1543176, tc_HOL_Obool), tc_fun(_1543176, tc_HOL_Obool), _1543176), hAPP(c_COMBS(_1543176, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543176), c_fimplies), hAPP(hAPP(c_COMBC(_1543176, tc_fun(_1543176, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543176)), _1543178)))), c_Orderings_Oord__class_Oless__eq(_1543176))))))], (28018 ^ _779203) ^ [_1273844, _1273846, _1273848] : [class_Orderings_Olinorder(_1273844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1273844), _1273846), _1273848)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273844, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1273844, _1273846, _1273848)), hAPP(c_SetInterval_Oord__class_OatLeast(_1273844), _1273848)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1273844), _1273846))], (41335 ^ _779203) ^ [_1593472, _1593474] : [-(c_List_Olenlex(_1593472, _1593474) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1593472), tc_List_Olist(_1593472))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1593472), tc_List_Olist(_1593472), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1593472), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593472), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool)), tc_List_Olist(_1593472)), c_COMBS(tc_List_Olist(_1593472), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593472), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1593472)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1593472)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593472), tc_fun(tc_List_Olist(_1593472), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1593472), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool)), tc_List_Olist(_1593472)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1593472))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593472)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1593472))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1593472)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1593472), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593472), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool)), tc_List_Olist(_1593472)), c_COMBS(tc_List_Olist(_1593472), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593472), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1593472)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1593472)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593472), tc_fun(tc_List_Olist(_1593472), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1593472), tc_Nat_Onat), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool)), tc_List_Olist(_1593472)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1593472))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1593472)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1593472))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1593472)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1593472), tc_fun(tc_prod(tc_List_Olist(_1593472), tc_List_Olist(_1593472)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593472), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593472), tc_List_Olist(_1593472)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593472), tc_List_Olist(_1593472)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1593472), tc_HOL_Obool)), tc_List_Olist(_1593472)), c_COMBC(tc_List_Olist(_1593472), tc_fun(tc_prod(tc_List_Olist(_1593472), tc_List_Olist(_1593472)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1593472), tc_prod(tc_List_Olist(_1593472), tc_List_Olist(_1593472))), tc_fun(tc_List_Olist(_1593472), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593472), tc_List_Olist(_1593472)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1593472)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1593472), tc_List_Olist(_1593472)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1593472), tc_List_Olist(_1593472)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1593472)), c_member(tc_prod(tc_List_Olist(_1593472), tc_List_Olist(_1593472))))), c_Product__Type_OPair(tc_List_Olist(_1593472), tc_List_Olist(_1593472))))), c_List_Olex(_1593472, _1593474)))))))], (23707 ^ _779203) ^ [_1196566] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1196566), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1196566)], (49869 ^ _779203) ^ [_1787760, _1787762] : [-(c_Fun_Obij__betw(_1787760, _1787760, c_Fun_Oid(_1787760), _1787762, _1787762))], (3862 ^ _779203) ^ [_837294, _837296, _837298, _837300, _837302, _837304, _837306, _837308, _837310, _837312, _837314, _837316, _837318, _837320] : [-(c_New__Random__Sequence_Opos__decr__bind(_837320, _837316, _837312, _837308, _837304, _837300, _837296) = c_New__Random__Sequence_Opos__decr__bind(_837318, _837314, _837310, _837306, _837302, _837298, _837294)), _837320 = _837318, _837316 = _837314, _837312 = _837310, _837308 = _837306, _837304 = _837302, _837300 = _837298, _837296 = _837294], (46548 ^ _779203) ^ [_1715201, _1715203] : [hBOOL(hAPP(c_List_Odistinct(_1715201), hAPP(c_List_Orev(_1715201), _1715203))), -(hBOOL(hAPP(c_List_Odistinct(_1715201), _1715203)))], (44440 ^ _779203) ^ [_1669123, _1669125, _1669127, _1669129, _1669131] : [-(hAPP(hAPP(c_List_Otake(_1669123), _1669125), hAPP(hAPP(c_List_Omap(_1669127, _1669123), _1669129), _1669131)) = hAPP(hAPP(c_List_Omap(_1669127, _1669123), _1669129), hAPP(hAPP(c_List_Otake(_1669127), _1669125), _1669131)))], (48688 ^ _779203) ^ [_1761630, _1761632, _1761634] : [48690 ^ _779203 : [(48693 ^ _779203) ^ [] : [hBOOL(hAPP(_1761630, 48689 ^ [_1761630, _1761632, _1761634]))], (48691 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 48689 ^ [_1761630, _1761632, _1761634]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1761632, _1761634))))]], -(c_List_Oall__interval__int(_1761630, _1761632, _1761634))], (10537 ^ _779203) ^ [_961425, _961427, _961429] : [class_Groups_Oab__semigroup__mult(_961425), -(_961427 = c_Orderings_Obot__class_Obot(tc_fun(_961425, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_961425), _961427)), -(hBOOL(hAPP(hAPP(c_member(_961425), _961429), _961427))), -(hAPP(c_Finite__Set_Ofold1(_961425, c_Groups_Otimes__class_Otimes(_961425)), hAPP(hAPP(c_Set_Oinsert(_961425), _961429), _961427)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961425), _961429), hAPP(c_Finite__Set_Ofold1(_961425, c_Groups_Otimes__class_Otimes(_961425)), _961427)))], (27454 ^ _779203) ^ [_1262910, _1262912, _1262914, _1262916] : [class_Lattices_Osemilattice__sup(_1262910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262910), _1262912), _1262914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262910), _1262912), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262910), _1262914), _1262916))))], (40330 ^ _779203) ^ [_1568170, _1568172] : [-(c_Transitive__Closure_Otrancl(_1568170, c_Transitive__Closure_Ortrancl(_1568170, _1568172)) = c_Transitive__Closure_Ortrancl(_1568170, _1568172))], (3802 ^ _779203) ^ [_836234, _836236] : [_836236 = _836234, -(c_Nat_Osemiring__1__class_Oof__nat(_836236) = c_Nat_Osemiring__1__class_Oof__nat(_836234))], (21831 ^ _779203) ^ [] : [-(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))))))], (13071 ^ _779203) ^ [_1005293, _1005295, _1005297] : [13072 ^ _779203 : [(13075 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005295), _1005297))], (13073 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005293)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005293), _1005295)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005293), _1005297))))], (3084 ^ _779203) ^ [_825015, _825017, _825019, _825021] : [-(c_Finite__Set_Ofold1(_825021, _825017) = c_Finite__Set_Ofold1(_825019, _825015)), _825021 = _825019, _825017 = _825015], (50479 ^ _779203) ^ [_1802091, _1802093, _1802095] : [-(c_Lazy__Sequence_Oflat(_1802091, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1802091), _1802093, _1802095)) = c_Lazy__Sequence_Oappend(_1802091, _1802093, c_Lazy__Sequence_Oflat(_1802091, _1802095)))], (43450 ^ _779203) ^ [_1647559, _1647561] : [-(hAPP(c_List_Orotate1(_1647559), _1647561) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1647559), _1647559, c_List_Olist_ONil(_1647559), hAPP(hAPP(c_COMBB(tc_List_Olist(_1647559), tc_fun(tc_List_Olist(_1647559), tc_List_Olist(_1647559)), _1647559), hAPP(c_COMBC(tc_List_Olist(_1647559), tc_List_Olist(_1647559), tc_List_Olist(_1647559)), c_List_Oappend(_1647559))), hAPP(hAPP(c_COMBC(_1647559, tc_List_Olist(_1647559), tc_List_Olist(_1647559)), c_List_Olist_OCons(_1647559)), c_List_Olist_ONil(_1647559)))), _1647561))], (22035 ^ _779203) ^ [_1167865, _1167867, _1167869, _1167871] : [class_Divides_Osemiring__div(_1167865), -(c_Divides_Odiv__class_Omod(_1167865, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167865), _1167867), _1167869), _1167871) = c_Divides_Odiv__class_Omod(_1167865, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167865), c_Divides_Odiv__class_Omod(_1167865, _1167867, _1167871)), c_Divides_Odiv__class_Omod(_1167865, _1167869, _1167871)), _1167871))], (24520 ^ _779203) ^ [_1211147, _1211149, _1211151] : [class_Rings_Olinordered__semidom(_1211147), hAPP(hAPP(c_Power_Opower__class_Opower(_1211147), _1211149), 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(_1211147), _1211151), 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(_1211147), c_Groups_Ozero__class_Ozero(_1211147)), _1211149)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1211147), c_Groups_Ozero__class_Ozero(_1211147)), _1211151)), -(_1211149 = _1211151)], (49040 ^ _779203) ^ [_1771139, _1771141] : [c_Equiv__Relations_Oequivp(_1771139, _1771141), 49043 ^ _779203 : [(49048 ^ _779203) ^ [] : [-(c_Predicate_Otransp(_1771139, _1771141))], (49046 ^ _779203) ^ [] : [-(c_Predicate_Osymp(_1771139, _1771141))], (49044 ^ _779203) ^ [] : [-(c_Predicate_Oreflp(_1771139, _1771141))]]], (51047 ^ _779203) ^ [_1812503, _1812505, _1812507, _1812509] : [class_Rings_Ocomm__ring__1(_1812503), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812503), _1812505), _1812507)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812503), _1812505), _1812509)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812503), _1812505), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1812503), _1812507), _1812509))))], (48034 ^ _779203) ^ [_1747171, _1747173] : [-(hAPP(c_New__DSequence_Opos__empty(_1747171), _1747173) = c_Lazy__Sequence_Oempty(_1747171))], (17270 ^ _779203) ^ [_1083834, _1083836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083834)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083836))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1083834), _1083836)))], (3528 ^ _779203) ^ [_831965, _831967, _831969, _831971] : [-(c_List_Olinorder__class_Osorted__list__of__set(_831971, _831967) = c_List_Olinorder__class_Osorted__list__of__set(_831969, _831965)), _831971 = _831969, _831967 = _831965], (29502 ^ _779203) ^ [_1302668, _1302670, _1302672] : [class_Lattices_Osemilattice__inf(_1302668), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1302668), _1302670), _1302672)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1302668), _1302672), _1302670) = _1302670)], (41515 ^ _779203) ^ [_1599788, _1599790, _1599792, _1599794] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599788), tc_List_Olist(_1599788))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599788), tc_List_Olist(_1599788)), _1599790), _1599792)), c_List_Olistrel1(_1599788, hAPP(c_Relation_Oconverse(_1599788, _1599788), _1599794)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599788), tc_List_Olist(_1599788))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599788), tc_List_Olist(_1599788)), _1599790), _1599792)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1599788), tc_List_Olist(_1599788)), c_List_Olistrel1(_1599788, _1599794)))))], (49871 ^ _779203) ^ [_1787790, _1787792, _1787794, _1787796, _1787798] : [c_Fun_Obij__betw(_1787790, _1787792, _1787794, _1787796, _1787798), -(c_Fun_Obij__betw(_1787792, _1787790, c_Hilbert__Choice_Oinv__into(_1787790, _1787792, _1787796, _1787794), _1787798, _1787796))], (44145 ^ _779203) ^ [_1662637, _1662639, _1662641, _1662643] : [-(_1662637 = c_List_Olist_ONil(_1662639)), 44148 ^ _779203 : [(44155 ^ _779203) ^ [] : [-(_1662641 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662639)), _1662637)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1662639, hAPP(hAPP(c_List_Olist__update(_1662639, _1662637), _1662641), _1662643)) = c_List_Olast(_1662639, _1662637))], (44149 ^ _779203) ^ [] : [_1662641 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662639)), _1662637)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1662639, hAPP(hAPP(c_List_Olist__update(_1662639, _1662637), _1662641), _1662643)) = _1662643)]]], (31384 ^ _779203) ^ [_1341899, _1341901, _1341903] : [class_Complete__Lattice_Ocomplete__lattice(_1341899), 31387 ^ _779203 : [(31388 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341899), _1341901), c_Complete__Lattice_OInf__class_OInf(_1341899, _1341903))), 31391 ^ _779203 : [(31392 ^ _779203) ^ [_1342057] : [hBOOL(hAPP(hAPP(c_member(_1341899), _1342057), _1341903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341899), _1341901), _1342057)))]]], (31398 ^ _779203) ^ [] : [31400 ^ _779203 : [(31403 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341899), _1341901), 31399 ^ [_1341899, _1341901, _1341903]))], (31401 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1341899), 31399 ^ [_1341899, _1341901, _1341903]), _1341903)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341899), _1341901), c_Complete__Lattice_OInf__class_OInf(_1341899, _1341903))))]]], (31691 ^ _779203) ^ [_1348150, _1348152, _1348154] : [-(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), _1348150)), 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))), _1348152))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1348154))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1348154)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1348150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1348150), 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), _1348154), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1348152)))))], (20048 ^ _779203) ^ [_1132723, _1132725, _1132727] : [-(hBOOL(hAPP(hAPP(c_member(_1132723), _1132725), _1132727))), -(hBOOL(hAPP(hAPP(c_member(_1132723), _1132725), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1132723, tc_HOL_Obool)), _1132727))))], (38750 ^ _779203) ^ [_1529388, _1529390] : [hAPP(hAPP(c_Relation_Orel__comp(_1529388, _1529388, _1529388), _1529390), _1529390) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1529388, _1529388), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1529388, _1529390))], (49314 ^ _779203) ^ [_1776368, _1776370] : [c_Relation_Osym(_1776368, _1776370), -(c_Relation_Osym(_1776368, hAPP(c_Relation_Oconverse(_1776368, _1776368), _1776370)))], (32936 ^ _779203) ^ [_1382626, _1382628] : [32937 ^ _779203 : [(32940 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1382628), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (32938 ^ _779203) ^ [] : [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), _1382626), _1382628)))]], -(c_Divides_OnegDivAlg(_1382626, _1382628) = 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), _1382626), _1382628)))], (27954 ^ _779203) ^ [_1272590, _1272592, _1272594, _1272596] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272590, tc_HOL_Obool)), _1272592), hAPP(hAPP(c_Set_Oinsert(_1272590), _1272594), _1272596)) = hAPP(hAPP(c_Set_Oinsert(_1272590), _1272594), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272590, tc_HOL_Obool)), _1272592), _1272596)))], (52187 ^ _779203) ^ [_1831822, _1831824] : [class_Orderings_Otop(_1831822), -(class_Orderings_Otop(tc_fun(_1831824, _1831822)))], (8160 ^ _779203) ^ [_914760, _914762, _914764, _914766, _914768, _914770] : [-(c_Fun_Ofun__upd(_914760, _914762, c_Fun_Ofun__upd(_914760, _914762, _914764, _914766, _914768), _914766, _914770) = c_Fun_Ofun__upd(_914760, _914762, _914764, _914766, _914770))], (42806 ^ _779203) ^ [_1632396, _1632398, _1632400, _1632402] : [-(hAPP(hAPP(c_List_Otake(_1632396), _1632398), hAPP(hAPP(c_List_Olist_OCons(_1632396), _1632400), _1632402)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1632396), c_List_Olist_ONil(_1632396), hAPP(hAPP(c_COMBB(tc_List_Olist(_1632396), tc_List_Olist(_1632396), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1632396), _1632400)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1632396), tc_List_Olist(_1632396)), c_List_Otake(_1632396)), _1632402)), _1632398))], (16058 ^ _779203) ^ [_1061198, _1061200, _1061202, _1061204] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061198), hAPP(c_Int_Onumber__class_Onumber__of(_1061198), _1061200)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1061198), _1061202), _1061204)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1061198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061198), hAPP(c_Int_Onumber__class_Onumber__of(_1061198), _1061200)), _1061202)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1061198), hAPP(c_Int_Onumber__class_Onumber__of(_1061198), _1061200)), _1061204))), class_Int_Onumber(_1061198), class_Rings_Oring(_1061198)], (52729 ^ _779203) ^ [_1837432, _1837434] : [hBOOL(hAPP(hAPP(c_fconj, _1837432), _1837434)), -(hBOOL(_1837432))], (15634 ^ _779203) ^ [_1053286, _1053288, _1053290, _1053292] : [class_Orderings_Olinorder(_1053286), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053286), _1053288), _1053290)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053286), _1053288), _1053292)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053286), _1053288), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1053286), _1053290), _1053292))))], (44422 ^ _779203) ^ [_1668794, _1668796, _1668798, _1668800, _1668802] : [c_Fun_Oinj__on(_1668794, _1668796, _1668798, c_Orderings_Otop__class_Otop(tc_fun(_1668794, tc_HOL_Obool))), 44425 ^ _779203 : [(44432 ^ _779203) ^ [] : [_1668800 = _1668802, -(hAPP(hAPP(c_List_Omap(_1668794, _1668796), _1668798), _1668800) = hAPP(hAPP(c_List_Omap(_1668794, _1668796), _1668798), _1668802))], (44426 ^ _779203) ^ [] : [hAPP(hAPP(c_List_Omap(_1668794, _1668796), _1668798), _1668800) = hAPP(hAPP(c_List_Omap(_1668794, _1668796), _1668798), _1668802), -(_1668800 = _1668802)]]], (37142 ^ _779203) ^ [_1480238, _1480240, _1480242, _1480244] : [c_Fun_Oinj__on(_1480238, _1480240, _1480242, c_Orderings_Otop__class_Otop(tc_fun(_1480238, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1480238, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1480238, _1480240, _1480242), hAPP(hAPP(c_Set_Oinsert(_1480240), _1480244), c_Orderings_Obot__class_Obot(tc_fun(_1480240, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1480238), c_HOL_OThe(_1480238, hAPP(hAPP(c_COMBC(_1480238, _1480240, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1480240, tc_fun(_1480240, tc_HOL_Obool), _1480238), c_fequal), _1480242)), _1480244))), c_Orderings_Obot__class_Obot(tc_fun(_1480238, tc_HOL_Obool))))))], (39145 ^ _779203) ^ [_1538897, _1538899] : [-(c_HOL_OThe(_1538897, hAPP(hAPP(c_COMBC(_1538897, _1538897, tc_HOL_Obool), c_fequal), _1538899)) = _1538899)], (3952 ^ _779203) ^ [_838871, _838873, _838875, _838877, _838879, _838881, _838883, _838885] : [-(c_New__DSequence_Oneg__bind(_838885, _838881, _838877, _838873) = c_New__DSequence_Oneg__bind(_838883, _838879, _838875, _838871)), _838885 = _838883, _838881 = _838879, _838877 = _838875, _838873 = _838871], (9267 ^ _779203) ^ [_937356, _937358] : [hAPP(c_Nat_OSuc, _937356) = hAPP(c_Nat_OSuc, _937358), -(_937356 = _937358)], (34310 ^ _779203) ^ [_1409658, _1409660, _1409662, _1409664, _1409666] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409658, tc_HOL_Obool)), _1409660), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409662, tc_fun(_1409658, tc_HOL_Obool)), _1409664), _1409666)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409662, tc_fun(_1409658, tc_HOL_Obool)), _1409664), hAPP(hAPP(c_COMBB(tc_fun(_1409658, tc_HOL_Obool), tc_fun(_1409658, tc_HOL_Obool), _1409662), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409658, tc_HOL_Obool)), _1409660)), _1409666)))], (39189 ^ _779203) ^ [_1539550, _1539552] : [c_Nitpick_Owf_H(_1539550, _1539552), 39192 ^ _779203 : [(39195 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1539550, _1539550)), _1539552))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (39193 ^ _779203) ^ [] : [-(c_Wellfounded_Oacyclic(_1539550, _1539552))]]], (40074 ^ _779203) ^ [_1561238, _1561240, _1561242, _1561244, _1561246, _1561248, _1561250, _1561252] : [class_Groups_Ocomm__monoid__add(_1561238), c_Fun_Oinj__on(_1561240, _1561242, _1561244, _1561246), _1561248 = hAPP(c_Set_Oimage(_1561240, _1561242, _1561244), _1561246), 40088 ^ _779203 : [(40091 ^ _779203) ^ [] : [hAPP(_1561250, 40087 ^ [_1561238, _1561240, _1561242, _1561244, _1561246, _1561248, _1561250, _1561252]) = hAPP(_1561252, hAPP(_1561244, 40087 ^ [_1561238, _1561240, _1561242, _1561244, _1561246, _1561248, _1561250, _1561252]))], (40089 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561240), 40087 ^ [_1561238, _1561240, _1561242, _1561244, _1561246, _1561248, _1561250, _1561252]), _1561246)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561242, _1561238), _1561252), _1561248) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561240, _1561238), _1561250), _1561246))], (3632 ^ _779203) ^ [_833575, _833577] : [_833577 = _833575, -(c_List_Omonoid__add__class_Olistsum(_833577) = c_List_Omonoid__add__class_Olistsum(_833575))], (49925 ^ _779203) ^ [_1788964, _1788966, _1788968, _1788970, _1788972, _1788974, _1788976, _1788978] : [c_Fun_Obij__betw(_1788964, _1788966, _1788968, _1788970, _1788972), c_Fun_Obij__betw(_1788966, _1788974, _1788976, _1788972, _1788978), -(c_Fun_Obij__betw(_1788964, _1788974, hAPP(c_Fun_Ocomp(_1788966, _1788974, _1788964, _1788976), _1788968), _1788970, _1788978))], (41304 ^ _779203) ^ [_1592804] : [-(c_Nitpick_Onum(_1592804) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1592804, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1592804)))], (46001 ^ _779203) ^ [_1704705, _1704707] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1704705, _1704707) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1704705), _1704707)))], (1270 ^ _779203) ^ [_798038, _798040] : [-(class_Rings_Ocomm__ring__1(_798038)), _798040 = _798038, class_Rings_Ocomm__ring__1(_798040)], (39560 ^ _779203) ^ [_1549275, _1549277, _1549279, _1549281, _1549283, _1549285, _1549287] : [hAPP(c_Fun_Ocomp(_1549275, _1549277, _1549279, _1549281), _1549283) = hAPP(c_Fun_Ocomp(_1549277, _1549277, _1549279, c_Fun_Oid(_1549277)), _1549285), -(hAPP(_1549281, hAPP(_1549283, _1549287)) = hAPP(_1549285, _1549287))], (15442 ^ _779203) ^ [_1049921, _1049923, _1049925, _1049927] : [class_Orderings_Olinorder(_1049921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049921), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1049921), _1049923), _1049925)), _1049927)), 15449 ^ _779203 : [(15452 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049921), _1049925), _1049927)))], (15450 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049921), _1049923), _1049927)))]]], (37559 ^ _779203) ^ [_1491002, _1491004, _1491006, _1491008] : [-(hBOOL(hAPP(hAPP(c_member(_1491002), _1491004), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491002, tc_HOL_Obool)), _1491006), hAPP(c_Set_OCollect(_1491002), _1491008))))), hBOOL(hAPP(hAPP(c_member(_1491002), _1491004), _1491006)), hBOOL(hAPP(_1491008, _1491004))], (10017 ^ _779203) ^ [_950375, _950377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950375), _950377)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _950375), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _950377), _950375)) = _950377)], (22309 ^ _779203) ^ [_1172945, _1172947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172945)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172947)), 22316 ^ _779203 : [(22323 ^ _779203) ^ [] : [_1172945 = _1172947, -(hAPP(c_Int_Onat, _1172945) = hAPP(c_Int_Onat, _1172947))], (22317 ^ _779203) ^ [] : [hAPP(c_Int_Onat, _1172945) = hAPP(c_Int_Onat, _1172947), -(_1172945 = _1172947)]]], (34769 ^ _779203) ^ [_1423865, _1423867, _1423869, _1423871] : [class_Complete__Lattice_Ocomplete__lattice(_1423865), -(_1423867 = c_Orderings_Obot__class_Obot(tc_fun(_1423869, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1423869, _1423865), _1423867), hAPP(c_COMBK(_1423865, _1423869), _1423871)) = _1423871)], (43522 ^ _779203) ^ [_1649302, _1649304] : [_1649304 = c_List_Olist_ONil(_1649302), -(hAPP(c_List_Orotate1(_1649302), _1649304) = c_List_Olist_ONil(_1649302))], (52551 ^ _779203) ^ [_1835424, _1835426] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1835424, _1835426)))], (1830 ^ _779203) ^ [_805038, _805040] : [-(class_Rings_Osemiring__1(_805038)), _805040 = _805038, class_Rings_Osemiring__1(_805040)], (16892 ^ _779203) ^ [_1076460, _1076462, _1076464, _1076466] : [class_Fields_Olinordered__field__inverse__zero(_1076460), class_Int_Onumber(_1076460), 16899 ^ _779203 : [(16900 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076460), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1076460), _1076462), _1076464)), hAPP(c_Int_Onumber__class_Onumber__of(_1076460), _1076466))), 16903 ^ _779203 : [(16910 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076460), c_Groups_Ozero__class_Ozero(_1076460)), _1076464))), 16913 ^ _779203 : [(16920 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076460), _1076464), c_Groups_Ozero__class_Ozero(_1076460)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076460), c_Groups_Ozero__class_Ozero(_1076460)), hAPP(c_Int_Onumber__class_Onumber__of(_1076460), _1076466))))], (16914 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076460), _1076464), c_Groups_Ozero__class_Ozero(_1076460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076460), hAPP(c_Int_Onumber__class_Onumber__of(_1076460), _1076466)), _1076464)), _1076462)))]]], (16904 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076460), c_Groups_Ozero__class_Ozero(_1076460)), _1076464)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076460), _1076462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076460), hAPP(c_Int_Onumber__class_Onumber__of(_1076460), _1076466)), _1076464))))]]], (16926 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076460), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1076460), _1076462), _1076464)), hAPP(c_Int_Onumber__class_Onumber__of(_1076460), _1076466)))), 16929 ^ _779203 : [(16932 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076460), _1076462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076460), hAPP(c_Int_Onumber__class_Onumber__of(_1076460), _1076466)), _1076464)))], (16930 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076460), c_Groups_Ozero__class_Ozero(_1076460)), _1076464)))]], 16933 ^ _779203 : [(16936 ^ _779203) ^ [] : [16937 ^ _779203 : [(16940 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076460), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076460), hAPP(c_Int_Onumber__class_Onumber__of(_1076460), _1076466)), _1076464)), _1076462))], (16938 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076460), _1076464), c_Groups_Ozero__class_Ozero(_1076460))))]], 16941 ^ _779203 : [(16944 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1076460), c_Groups_Ozero__class_Ozero(_1076460)), hAPP(c_Int_Onumber__class_Onumber__of(_1076460), _1076466)))], (16942 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076460), _1076464), c_Groups_Ozero__class_Ozero(_1076460)))]]], (16934 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1076460), c_Groups_Ozero__class_Ozero(_1076460)), _1076464))]]]]], (37827 ^ _779203) ^ [_1498820, _1498822, _1498824, _1498826] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1498820, _1498822), _1498824), _1498826) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1498820, tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool)), _1498824), hAPP(hAPP(c_COMBS(_1498820, tc_fun(_1498822, tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool)), tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498822, tc_HOL_Obool), tc_fun(tc_fun(_1498822, tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool)), tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool)), _1498820), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1498822, tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool))), _1498826)), hAPP(hAPP(c_COMBC(_1498820, tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool), tc_fun(_1498822, tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1498822, tc_fun(tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool), tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool), tc_fun(_1498822, tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool))), _1498820), c_COMBC(_1498822, tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool), tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1498822, tc_prod(_1498820, _1498822)), tc_fun(_1498822, tc_fun(tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool), tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool))), _1498820), hAPP(c_COMBB(tc_prod(_1498820, _1498822), tc_fun(tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool), tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool)), _1498822), c_Set_Oinsert(tc_prod(_1498820, _1498822)))), c_Product__Type_OPair(_1498820, _1498822)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1498820, _1498822), tc_HOL_Obool))))))], (27950 ^ _779203) ^ [] : [-(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)))], (43963 ^ _779203) ^ [_1658894, _1658896, _1658898, _1658900] : [class_Complete__Lattice_Ocomplete__lattice(_1658894), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1658896, _1658894), hAPP(c_List_Oset(_1658896), _1658898)), _1658900) = hAPP(c_List_Ofoldl(_1658894, _1658896, hAPP(c_COMBC(_1658896, _1658894, _1658894), hAPP(hAPP(c_COMBB(_1658894, tc_fun(_1658894, _1658894), _1658896), c_Lattices_Osemilattice__inf__class_Oinf(_1658894)), _1658900)), c_Orderings_Otop__class_Otop(_1658894)), _1658898))], (22894 ^ _779203) ^ [_1182441, _1182443] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1182441) = _1182443), _1182441 = hAPP(c_Int_Onat, _1182443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182443))], (37223 ^ _779203) ^ [_1482260, _1482262, _1482264, _1482266, _1482268] : [hBOOL(hAPP(hAPP(c_member(_1482264), hAPP(_1482266, _1482262)), _1482268)), -(hBOOL(hAPP(hAPP(c_member(_1482260), _1482262), hAPP(c_Set_Ovimage(_1482260, _1482264, _1482266), _1482268))))], (28114 ^ _779203) ^ [_1275863, _1275865, _1275867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1275863, tc_HOL_Obool)), _1275865), _1275867)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275863, tc_HOL_Obool)), _1275865), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1275863, tc_HOL_Obool)), _1275867), _1275865)) = _1275867)], (22273 ^ _779203) ^ [_1172401, _1172403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172401)), 22276 ^ _779203 : [(22283 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1172403), 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), _1172403), _1172401)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (22277 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1172403), _1172401)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1172403), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (38707 ^ _779203) ^ [_1528600, _1528602, _1528604] : [c_Wellfounded_Owf(_1528600, _1528602), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528600, _1528600)), hAPP(hAPP(c_Product__Type_OPair(_1528600, _1528600), _1528604), _1528604)), _1528602))], (45693 ^ _779203) ^ [_1697402, _1697404] : [-(hAPP(c_List_Ofilter(_1697402, _1697404), c_List_Olist_ONil(_1697402)) = c_List_Olist_ONil(_1697402))], (3202 ^ _779203) ^ [_826892, _826894, _826896, _826898, _826900, _826902] : [-(c_List_Olist_Olist__size(_826902, _826898, _826894) = c_List_Olist_Olist__size(_826900, _826896, _826892)), _826902 = _826900, _826898 = _826896, _826894 = _826892], (52321 ^ _779203) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (11013 ^ _779203) ^ [_969104, _969106] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969104), _969106) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 11016 ^ _779203 : [(11019 ^ _779203) ^ [] : [-(_969106 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11017 ^ _779203) ^ [] : [-(_969104 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (40980 ^ _779203) ^ [_1583987, _1583989, _1583991, _1583993] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583987, _1583987)), hAPP(hAPP(c_Product__Type_OPair(_1583987, _1583987), _1583989), _1583991)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583987, _1583987), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1583993))), -(_1583989 = _1583991)], (30729 ^ _779203) ^ [_1328311, _1328313, _1328315, _1328317, _1328319] : [class_Fields_Ofield(_1328311), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328313), _1328315)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1328313), _1328317)), 30743 ^ _779203 : [(30746 ^ _779203) ^ [] : [-(hAPP(_1328319, 30742 ^ [_1328311, _1328313, _1328315, _1328317, _1328319]) = c_Groups_Ozero__class_Ozero(_1328311))], (30744 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1328313), 30742 ^ [_1328311, _1328313, _1328315, _1328317, _1328319]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328313, tc_HOL_Obool)), _1328315), _1328317))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1328313, _1328311), _1328319), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328313, tc_HOL_Obool)), _1328315), _1328317)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328311), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328311), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1328313, _1328311), _1328319), _1328315)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1328313, _1328311), _1328319), _1328317))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1328313, _1328311), _1328319), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1328313, tc_HOL_Obool)), _1328315), _1328317))))], (49731 ^ _779203) ^ [_1784498, _1784500, _1784502, _1784504, _1784506] : [c_Fun_Oinj__on(_1784498, _1784500, _1784502, c_Orderings_Otop__class_Otop(tc_fun(_1784498, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1784500, _1784504, _1784498, hAPP(c_Fun_Ocomp(_1784498, _1784504, _1784500, _1784506), c_Hilbert__Choice_Oinv__into(_1784498, _1784500, c_Orderings_Otop__class_Otop(tc_fun(_1784498, tc_HOL_Obool)), _1784502))), _1784502) = _1784506)], (44323 ^ _779203) ^ [_1666001, _1666003, _1666005, _1666007, _1666009, _1666011, _1666013, _1666015] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1666001, _1666003), _1666005), _1666007), hAPP(hAPP(c_List_Ozip(_1666001, _1666003), _1666009), hAPP(hAPP(c_List_Omap(_1666011, _1666003), _1666013), _1666015))) = hAPP(hAPP(c_List_Omap(tc_prod(_1666001, _1666011), _1666005), hAPP(c_Product__Type_Oprod_Oprod__case(_1666001, _1666011, _1666005), hAPP(hAPP(c_COMBB(tc_fun(_1666011, tc_prod(_1666001, _1666003)), tc_fun(_1666011, _1666005), _1666001), hAPP(c_COMBB(tc_prod(_1666001, _1666003), _1666005, _1666011), _1666007)), hAPP(hAPP(c_COMBC(_1666001, tc_fun(_1666011, _1666003), tc_fun(_1666011, tc_prod(_1666001, _1666003))), hAPP(hAPP(c_COMBB(tc_fun(_1666003, tc_prod(_1666001, _1666003)), tc_fun(tc_fun(_1666011, _1666003), tc_fun(_1666011, tc_prod(_1666001, _1666003))), _1666001), c_COMBB(_1666003, tc_prod(_1666001, _1666003), _1666011)), c_Product__Type_OPair(_1666001, _1666003))), _1666013)))), hAPP(hAPP(c_List_Ozip(_1666001, _1666011), _1666009), _1666015)))], (42299 ^ _779203) ^ [_1621853, _1621855, _1621857, _1621859, _1621861] : [-(hAPP(hAPP(c_List_Olist__update(_1621853, hAPP(hAPP(c_List_Olist_OCons(_1621853), _1621855), _1621857)), hAPP(c_Nat_OSuc, _1621859)), _1621861) = hAPP(hAPP(c_List_Olist_OCons(_1621853), _1621855), hAPP(hAPP(c_List_Olist__update(_1621853, _1621857), _1621859), _1621861)))], (52629 ^ _779203) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (1720 ^ _779203) ^ [_803663, _803665] : [-(class_Groups_Ocomm__monoid__add(_803663)), _803665 = _803663, class_Groups_Ocomm__monoid__add(_803665)], (5526 ^ _779203) ^ [_863672, _863674] : [_863674 = _863672, -(c_COMBI(_863674) = c_COMBI(_863672))], (44823 ^ _779203) ^ [_1677343] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677343)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (36959 ^ _779203) ^ [_1475634, _1475636, _1475638] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1475634, hAPP(hAPP(c_COMBC(_1475634, tc_fun(tc_prod(_1475634, _1475634), tc_HOL_Obool), tc_fun(_1475634, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1475634, tc_fun(tc_fun(tc_prod(_1475634, _1475634), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1475634, _1475634), tc_HOL_Obool), tc_fun(_1475634, tc_HOL_Obool)), _1475634), c_COMBC(_1475634, tc_fun(tc_prod(_1475634, _1475634), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1475634, tc_prod(_1475634, _1475634)), tc_fun(_1475634, tc_fun(tc_fun(tc_prod(_1475634, _1475634), tc_HOL_Obool), tc_HOL_Obool)), _1475634), hAPP(c_COMBB(tc_prod(_1475634, _1475634), tc_fun(tc_fun(tc_prod(_1475634, _1475634), tc_HOL_Obool), tc_HOL_Obool), _1475634), c_member(tc_prod(_1475634, _1475634)))), c_Product__Type_OPair(_1475634, _1475634)))), _1475636)), _1475638)), -(hBOOL(hAPP(hAPP(c_member(_1475634), _1475638), c_Wellfounded_Oacc(_1475634, _1475636))))], (43343 ^ _779203) ^ [_1644502, _1644504, _1644506, _1644508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644502), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644504)), _1644506))), -(hAPP(hAPP(c_List_Onth(_1644504), hAPP(hAPP(c_List_Oappend(_1644504), _1644506), _1644508)), _1644502) = hAPP(hAPP(c_List_Onth(_1644504), _1644506), _1644502))], (21201 ^ _779203) ^ [_1153065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1153065), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1153065)), c_Int_OPls)))], (29880 ^ _779203) ^ [_1310680, _1310682, _1310684] : [class_Orderings_Oorder(_1310680), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310680, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1310680), _1310682)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1310680, _1310682), _1310684)) = c_Orderings_Obot__class_Obot(tc_fun(_1310680, tc_HOL_Obool)))], (50353 ^ _779203) ^ [_1797396, _1797398, _1797400, _1797402, _1797404] : [hBOOL(hAPP(hAPP(c_member(_1797396), _1797398), _1797400)), -(hAPP(c_Quotient_OBabs(_1797396, _1797402, _1797400, _1797404), _1797398) = hAPP(_1797404, _1797398))], (34424 ^ _779203) ^ [_1413228, _1413230, _1413232, _1413234, _1413236] : [34426 ^ _779203 : [(34429 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413228, tc_HOL_Obool)), _1413230), hAPP(_1413236, 34425 ^ [_1413228, _1413230, _1413232, _1413234, _1413236])))], (34427 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1413232), 34425 ^ [_1413228, _1413230, _1413232, _1413234, _1413236]), _1413234)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1413228, tc_HOL_Obool)), _1413230), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1413232, tc_fun(_1413228, tc_HOL_Obool)), _1413234), _1413236))))], (48346 ^ _779203) ^ [_1753987, _1753989, _1753991] : [-(_1753987 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1753989), c_List_Oreplicate(_1753989, _1753987, _1753991)) = hAPP(hAPP(c_Set_Oinsert(_1753989), _1753991), c_Orderings_Obot__class_Obot(tc_fun(_1753989, tc_HOL_Obool))))], (48072 ^ _779203) ^ [_1748234, _1748236] : [c_Wellfounded_Oacyclic(_1748234, hAPP(c_Set_OCollect(tc_prod(_1748234, _1748234)), hAPP(c_Product__Type_Oprod_Oprod__case(_1748234, _1748234, tc_HOL_Obool), _1748236))), -(c_Wellfounded_Oacyclic(_1748234, hAPP(c_Set_OCollect(tc_prod(_1748234, _1748234)), hAPP(c_Product__Type_Oprod_Oprod__case(_1748234, _1748234, tc_HOL_Obool), c_Predicate_Oconversep(_1748234, _1748234, _1748236)))))], (7649 ^ _779203) ^ [_905433, _905435, _905437] : [class_Orderings_Oorder(_905433), 7652 ^ _779203 : [(7653 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905433), _905435), _905437)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905433), _905435), _905437))), -(_905435 = _905437)], (7663 ^ _779203) ^ [] : [7664 ^ _779203 : [(7667 ^ _779203) ^ [] : [_905435 = _905437], (7665 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_905433), _905435), _905437))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_905433), _905435), _905437)))]]], (39043 ^ _779203) ^ [_1536416, _1536418, _1536420] : [c_Wellfounded_Owf(_1536416, _1536418), -(c_Wellfounded_Owf(tc_List_Olist(_1536416), hAPP(c_List_Olexn(_1536416, _1536418), _1536420)))], (10483 ^ _779203) ^ [_960306, _960308, _960310, _960312] : [class_Rings_Ocomm__semiring__1(_960306), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960306), _960308), _960310)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960306), _960312), _960310)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960306), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960306), _960308), _960312)), _960310))], (6981 ^ _779203) ^ [_893757, _893759, _893761, _893763] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893757, tc_HOL_Obool)), _893759), hAPP(hAPP(c_Set_Oinsert(_893757), _893761), _893763)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893757, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893757, tc_HOL_Obool)), _893759), hAPP(hAPP(c_Set_Oinsert(_893757), _893761), c_Orderings_Obot__class_Obot(tc_fun(_893757, tc_HOL_Obool))))), _893763))], (40976 ^ _779203) ^ [_1583890, _1583892] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583890, _1583890), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1583892) = c_Relation_OId(_1583890))], (23703 ^ _779203) ^ [_1196460, _1196462, _1196464] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196460), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1196462, _1196464)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196460), _1196462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196460), _1196464)))], (45206 ^ _779203) ^ [_1686267, _1686269, _1686271, _1686273, _1686275, _1686277] : [c_List_Olist__all2(_1686267, _1686269, _1686271, _1686273, _1686275), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686277), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686269)), _1686275))), -(hBOOL(hAPP(hAPP(_1686271, hAPP(hAPP(c_List_Onth(_1686267), _1686273), _1686277)), hAPP(hAPP(c_List_Onth(_1686269), _1686275), _1686277))))], (42024 ^ _779203) ^ [_1613848, _1613850, _1613852] : [hBOOL(hAPP(hAPP(c_member(_1613848), _1613850), hAPP(c_List_Oset(_1613848), _1613852))), -(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(_1613848)), _1613852))))], (52515 ^ _779203) ^ [_1834965, _1834967] : [-(class_Finite__Set_Ofinite(tc_sum(_1834965, _1834967))), class_Finite__Set_Ofinite(_1834965), class_Finite__Set_Ofinite(_1834967)], (19390 ^ _779203) ^ [_1120958, _1120960, _1120962, _1120964, _1120966] : [class_Groups_Oordered__ab__group__add__abs(_1120958), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120958), hAPP(c_Groups_Oabs__class_Oabs(_1120958), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1120958), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120958), _1120960), _1120962)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120958), _1120964), _1120966)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120958), hAPP(c_Groups_Oabs__class_Oabs(_1120958), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1120958), _1120960), _1120964))), hAPP(c_Groups_Oabs__class_Oabs(_1120958), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1120958), _1120962), _1120966))))))], (45071 ^ _779203) ^ [_1683442, _1683444, _1683446, _1683448, _1683450, _1683452, _1683454] : [c_List_Olist__all2(_1683442, _1683444, _1683446, _1683448, _1683450), c_List_Olist__all2(_1683442, _1683444, _1683446, _1683452, _1683454), -(c_List_Olist__all2(_1683442, _1683444, _1683446, hAPP(hAPP(c_List_Oappend(_1683442), _1683448), _1683452), hAPP(hAPP(c_List_Oappend(_1683444), _1683450), _1683454)))], (6803 ^ _779203) ^ [_889818, _889820, _889822, _889824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889818, tc_HOL_Obool)), _889820), hAPP(hAPP(c_Set_Oinsert(_889818), _889822), _889824))), 6806 ^ _779203 : [(6813 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889818), _889822), _889820))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889818, tc_HOL_Obool)), _889820), _889824)))], (6807 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889818), _889822), _889820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889818, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889818, tc_HOL_Obool)), _889820), hAPP(hAPP(c_Set_Oinsert(_889818), _889822), c_Orderings_Obot__class_Obot(tc_fun(_889818, tc_HOL_Obool))))), _889824)))]]], (40388 ^ _779203) ^ [_1569622, _1569624, _1569626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569622, _1569622), tc_HOL_Obool)), _1569624), _1569626)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569622, _1569622), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1569622, _1569624)), c_Transitive__Closure_Ortrancl(_1569622, _1569626))))], (49250 ^ _779203) ^ [_1775102, _1775104] : [c_Relation_Osym(_1775102, _1775104), 49253 ^ _779203 : [(49254 ^ _779203) ^ [_1775208, _1775210] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775102, _1775102)), hAPP(hAPP(c_Product__Type_OPair(_1775102, _1775102), _1775210), _1775208)), _1775104)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775102, _1775102)), hAPP(hAPP(c_Product__Type_OPair(_1775102, _1775102), _1775208), _1775210)), _1775104)))]]], (9201 ^ _779203) ^ [_936152, _936154, _936156] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936152), _936154)), _936156) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936152), _936156)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936154), _936156)))], (30618 ^ _779203) ^ [_1326174, _1326176, _1326178] : [class_Complete__Lattice_Ocomplete__lattice(_1326174), 30621 ^ _779203 : [(30622 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326174), c_Complete__Lattice_OSup__class_OSup(_1326174, _1326176)), _1326178)), 30625 ^ _779203 : [(30626 ^ _779203) ^ [_1326332] : [hBOOL(hAPP(hAPP(c_member(_1326174), _1326332), _1326176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326174), _1326332), _1326178)))]]], (30632 ^ _779203) ^ [] : [30634 ^ _779203 : [(30637 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326174), 30633 ^ [_1326174, _1326176, _1326178]), _1326178))], (30635 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1326174), 30633 ^ [_1326174, _1326176, _1326178]), _1326176)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326174), c_Complete__Lattice_OSup__class_OSup(_1326174, _1326176)), _1326178)))]]], (44930 ^ _779203) ^ [_1680035, _1680037, _1680039, _1680041] : [hBOOL(hAPP(c_List_Olistsp(_1680035, hAPP(hAPP(c_COMBS(_1680035, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1680035), c_fconj), _1680037)), _1680039)), _1680041)), 44933 ^ _779203 : [(44936 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1680035, _1680039), _1680041)))], (44934 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1680035, _1680037), _1680041)))]]], (32863 ^ _779203) ^ [_1381006, _1381008, _1381010, _1381012, _1381014, _1381016] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1381006, tc_fun(_1381008, tc_HOL_Obool))), _1381010), _1381012), _1381014), _1381016)), -(hBOOL(hAPP(hAPP(_1381010, _1381014), _1381016)))], (5144 ^ _779203) ^ [_857649, _857651, _857653, _857655, _857657, _857659, _857661, _857663] : [-(c_Fun_Ocomp(_857663, _857659, _857655, _857651) = c_Fun_Ocomp(_857661, _857657, _857653, _857649)), _857663 = _857661, _857659 = _857657, _857655 = _857653, _857651 = _857649], (31675 ^ _779203) ^ [_1347841, _1347843, _1347845, _1347847, _1347849, _1347851] : [-(c_Nitpick_Opair__box_OPairBox(_1347841, _1347843, _1347845, _1347847) = c_Nitpick_Opair__box_OPairBox(_1347841, _1347843, _1347849, _1347851)), _1347845 = _1347849, _1347847 = _1347851], (11894 ^ _779203) ^ [_984535, _984537, _984539] : [class_Rings_Olinordered__semiring__strict(_984535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984535), c_Groups_Ozero__class_Ozero(_984535)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984535), _984537), _984539))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984535), c_Groups_Ozero__class_Ozero(_984535)), _984539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984535), c_Groups_Ozero__class_Ozero(_984535)), _984537)))], (21311 ^ _779203) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (36850 ^ _779203) ^ [_1473667, _1473669, _1473671, _1473673, _1473675] : [c_Fun_Oinj__on(_1473667, _1473669, _1473671, _1473673), hBOOL(hAPP(hAPP(c_member(_1473669), _1473675), hAPP(c_Set_Oimage(_1473667, _1473669, _1473671), _1473673))), -(hAPP(_1473671, hAPP(c_Fun_Othe__inv__into(_1473667, _1473669, _1473673, _1473671), _1473675)) = _1473675)], (48942 ^ _779203) ^ [_1767667, _1767669, _1767671] : [c_List_Olist__ex(_1767667, _1767669, _1767671), 48946 ^ _779203 : [(48949 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1767669, 48945 ^ [_1767667, _1767669, _1767671])))], (48947 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767667), 48945 ^ [_1767667, _1767669, _1767671]), hAPP(c_List_Oset(_1767667), _1767671))))]]], (18447 ^ _779203) ^ [_1104569, _1104571, _1104573] : [class_Rings_Osemiring__1(_1104569), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1104571), _1104573)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1104569), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104569), _1104571)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104569), _1104573)))], (52385 ^ _779203) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (50099 ^ _779203) ^ [_1792449, _1792451, _1792453, _1792455, _1792457] : [c_Fun_Obij__betw(_1792449, _1792451, _1792453, _1792455, _1792457), 50102 ^ _779203 : [(50109 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792451), _1792457)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1792449), _1792455)))], (50103 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1792449), _1792455)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1792451), _1792457)))]]], (23597 ^ _779203) ^ [_1194628, _1194630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194628), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1194628), _1194630)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1194628))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1194630))))], (28374 ^ _779203) ^ [_1281044, _1281046, _1281048] : [class_Groups_Ocomm__monoid__add(_1281044), hAPP(_1281046, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1281044), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1281044), _1281046), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1281048)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1281044), _1281046), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1281048)))], (52573 ^ _779203) ^ [_1835709, _1835711] : [-(class_Enum_Oenum(tc_prod(_1835709, _1835711))), class_Enum_Oenum(_1835709), class_Enum_Oenum(_1835711)], (34957 ^ _779203) ^ [] : [-(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)))], (12374 ^ _779203) ^ [_992600, _992602, _992604] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992600), _992602)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992604), _992602)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _992600), _992604))], (39012 ^ _779203) ^ [_1535778, _1535780, _1535782, _1535784] : [39013 ^ _779203 : [(39014 ^ _779203) ^ [_1535832] : [hBOOL(hAPP(hAPP(_1535782, _1535784), _1535832))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1535778, _1535780, _1535782), _1535784)))], (44297 ^ _779203) ^ [_1665112, _1665114, _1665116] : [c_Fun_Oinj__on(_1665112, _1665114, _1665116, c_Orderings_Otop__class_Otop(tc_fun(_1665112, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1665112), tc_List_Olist(_1665114), hAPP(c_List_Omap(_1665112, _1665114), _1665116), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1665112), tc_HOL_Obool))))], (43203 ^ _779203) ^ [_1641342, _1641344, _1641346] : [_1641342 = hAPP(hAPP(c_List_Oappend(_1641344), _1641346), _1641342), -(_1641346 = c_List_Olist_ONil(_1641344))], (11880 ^ _779203) ^ [_984280, _984282, _984284] : [class_Rings_Olinordered__semiring__strict(_984280), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984280), c_Groups_Ozero__class_Ozero(_984280)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984280), _984282), _984284))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984280), c_Groups_Ozero__class_Ozero(_984280)), _984282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984280), c_Groups_Ozero__class_Ozero(_984280)), _984284)))], (21417 ^ _779203) ^ [_1156426, _1156428] : [class_Int_Onumber__ring(_1156426), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156426), c_Groups_Oone__class_Oone(_1156426)), hAPP(c_Int_Onumber__class_Onumber__of(_1156426), _1156428)) = hAPP(c_Int_Onumber__class_Onumber__of(_1156426), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1156428)))], (43830 ^ _779203) ^ [_1656010, _1656012, _1656014] : [-(hAPP(c_List_Orotate(_1656010, _1656012), _1656014) = hAPP(hAPP(c_List_Oappend(_1656010), hAPP(hAPP(c_List_Odrop(_1656010), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1656012, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656010)), _1656014))), _1656014)), hAPP(hAPP(c_List_Otake(_1656010), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1656012, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656010)), _1656014))), _1656014)))], (51757 ^ _779203) ^ [_1824565, _1824567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1824565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1824565), _1824567)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824567), _1824565))], (45943 ^ _779203) ^ [_1703620, _1703622] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1703620, _1703622)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1703622), _1703620))], (21781 ^ _779203) ^ [_1162650, _1162652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1162650), _1162652)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1162650)), c_Int_OBit1(_1162652))))], (15926 ^ _779203) ^ [_1058309, _1058311, _1058313, _1058315] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1058309), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058309), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1058309), _1058311), _1058313)), _1058315) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1058309), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058309), _1058311), _1058315)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1058309), _1058313), _1058315)))], (43728 ^ _779203) ^ [_1654065, _1654067] : [-(_1654065 = c_List_Olist_ONil(_1654067)), -(hAPP(c_List_Orotate1(_1654067), _1654065) = hAPP(hAPP(c_List_Oappend(_1654067), hAPP(c_List_Otl(_1654067), _1654065)), hAPP(hAPP(c_List_Olist_OCons(_1654067), hAPP(c_List_Ohd(_1654067), _1654065)), c_List_Olist_ONil(_1654067))))], (52785 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), v_U)))], (962 ^ _779203) ^ [_793592, _793594, _793596, _793598] : [-(c_Wellfounded_Owf(_793596, _793592)), c_Wellfounded_Owf(_793598, _793594), _793598 = _793596, _793594 = _793592], (18461 ^ _779203) ^ [_1104809, _1104811] : [class_Rings_Oring__1(_1104809), -(hBOOL(hAPP(hAPP(c_member(_1104809), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104809), _1104811)), c_Int_Oring__1__class_OInts(_1104809))))], (28930 ^ _779203) ^ [_1291051, _1291053, _1291055] : [class_Lattices_Olattice(_1291051), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291051), _1291053)), -(_1291053 = c_Orderings_Obot__class_Obot(tc_fun(_1291051, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1291051, hAPP(hAPP(c_Set_Oinsert(_1291051), _1291055), _1291053)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1291051), _1291055), c_Big__Operators_Olattice__class_OSup__fin(_1291051, _1291053)))], (38975 ^ _779203) ^ [_1534653, _1534655, _1534657, _1534659] : [hBOOL(hAPP(c_Predicate_ODomainP(_1534653, _1534655, hAPP(hAPP(c_COMBC(_1534653, tc_fun(tc_prod(_1534653, _1534655), tc_HOL_Obool), tc_fun(_1534655, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534655, tc_fun(tc_fun(tc_prod(_1534653, _1534655), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534653, _1534655), tc_HOL_Obool), tc_fun(_1534655, tc_HOL_Obool)), _1534653), c_COMBC(_1534655, tc_fun(tc_prod(_1534653, _1534655), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534655, tc_prod(_1534653, _1534655)), tc_fun(_1534655, tc_fun(tc_fun(tc_prod(_1534653, _1534655), tc_HOL_Obool), tc_HOL_Obool)), _1534653), hAPP(c_COMBB(tc_prod(_1534653, _1534655), tc_fun(tc_fun(tc_prod(_1534653, _1534655), tc_HOL_Obool), tc_HOL_Obool), _1534655), c_member(tc_prod(_1534653, _1534655)))), c_Product__Type_OPair(_1534653, _1534655)))), _1534657)), _1534659)), -(hBOOL(hAPP(hAPP(c_member(_1534653), _1534659), hAPP(c_Relation_ODomain(_1534653, _1534655), _1534657))))], (52359 ^ _779203) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (38544 ^ _779203) ^ [_1525411, _1525413, _1525415, _1525417, _1525419, _1525421, _1525423] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1525411, _1525413, _1525415, _1525417, _1525419), _1525421), _1525423))), 38545 ^ _779203 : [(38546 ^ _779203) ^ [_1525482] : [hBOOL(hAPP(hAPP(_1525417, _1525421), _1525482)), hBOOL(hAPP(hAPP(_1525419, _1525482), _1525423))]]], (48469 ^ _779203) ^ [_1756845, _1756847, _1756849] : [hBOOL(hAPP(hAPP(c_List_Omember(_1756845), _1756847), _1756849)), -(hBOOL(hAPP(hAPP(c_member(_1756845), _1756849), hAPP(c_List_Oset(_1756845), _1756847))))], (31725 ^ _779203) ^ [_1348991, _1348993, _1348995, _1348997, _1348999] : [class_Lattices_Olattice(_1348991), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1348993, _1348991)), _1348995), _1348997), _1348999) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1348991), hAPP(_1348995, _1348999)), hAPP(_1348997, _1348999)))], (43464 ^ _779203) ^ [_1647996, _1647998, _1648000, _1648002, _1648004] : [hAPP(hAPP(c_List_Odrop(_1647996), _1647998), _1648000) = hAPP(hAPP(c_List_Olist_OCons(_1647996), _1648002), _1648004), -(hAPP(hAPP(c_List_Onth(_1647996), _1648000), _1647998) = _1648002)], (28536 ^ _779203) ^ [_1283847, _1283849] : [class_Orderings_Olinorder(_1283847), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1283847, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1283847), _1283849)), hAPP(hAPP(c_Set_Oinsert(_1283847), _1283849), c_Orderings_Obot__class_Obot(tc_fun(_1283847, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1283847), _1283849))], (32083 ^ _779203) ^ [_1358436, _1358438, _1358440, _1358442, _1358444] : [class_Groups_Ocomm__monoid__mult(_1358436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358438), _1358440)), 32090 ^ _779203 : [(32097 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358438), _1358442), _1358440))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358438, _1358436), hAPP(hAPP(c_COMBC(_1358438, _1358436, _1358436), hAPP(hAPP(c_COMBS(_1358438, _1358436, tc_fun(_1358436, _1358436)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1358436, tc_fun(_1358436, _1358436)), _1358438), c_If(_1358436)), hAPP(c_fequal, _1358442))), _1358444)), c_Groups_Oone__class_Oone(_1358436))), _1358440) = c_Groups_Oone__class_Oone(_1358436))], (32091 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1358438), _1358442), _1358440)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358438, _1358436), hAPP(hAPP(c_COMBC(_1358438, _1358436, _1358436), hAPP(hAPP(c_COMBS(_1358438, _1358436, tc_fun(_1358436, _1358436)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1358436, tc_fun(_1358436, _1358436)), _1358438), c_If(_1358436)), hAPP(c_fequal, _1358442))), _1358444)), c_Groups_Oone__class_Oone(_1358436))), _1358440) = hAPP(_1358444, _1358442))]]], (6088 ^ _779203) ^ [_876229, _876231, _876233] : [hAPP(hAPP(c_Set_Oinsert(_876229), _876231), _876233) = c_Orderings_Obot__class_Obot(tc_fun(_876229, tc_HOL_Obool))], (52421 ^ _779203) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (12466 ^ _779203) ^ [_994211, _994213] : [class_Orderings_Olinorder(_994211), -(c_Big__Operators_Olinorder__class_OMin(_994211, hAPP(hAPP(c_Set_Oinsert(_994211), _994213), c_Orderings_Obot__class_Obot(tc_fun(_994211, tc_HOL_Obool)))) = _994213)], (20204 ^ _779203) ^ [_1135625, _1135627] : [class_Groups_Oordered__ab__group__add(_1135625), 20207 ^ _779203 : [(20214 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135625), _1135627), c_Groups_Ozero__class_Ozero(_1135625))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135625), c_Groups_Ozero__class_Ozero(_1135625)), hAPP(c_Groups_Ouminus__class_Ouminus(_1135625), _1135627))))], (20208 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135625), c_Groups_Ozero__class_Ozero(_1135625)), hAPP(c_Groups_Ouminus__class_Ouminus(_1135625), _1135627))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135625), _1135627), c_Groups_Ozero__class_Ozero(_1135625))))]]], (51243 ^ _779203) ^ [_1815870, _1815872] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815870), _1815872)), 51246 ^ _779203 : [(51253 ^ _779203) ^ [] : [_1815872 = _1815870, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815872), _1815870)))], (51247 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815872), _1815870)), -(_1815872 = _1815870)]]], (43652 ^ _779203) ^ [_1652487, _1652489, _1652491, _1652493] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652487) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1652489), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652487)), hAPP(hAPP(c_List_Olist_OCons(_1652489), _1652491), _1652493)) = hAPP(hAPP(c_List_Odrop(_1652489), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652487)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1652493))], (15196 ^ _779203) ^ [_1045000, _1045002, _1045004] : [class_Int_Onumber(_1045000), class_Orderings_Oord(_1045000), 15203 ^ _779203 : [(15210 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045000), hAPP(c_Int_Onumber__class_Onumber__of(_1045000), _1045002)), hAPP(c_Int_Onumber__class_Onumber__of(_1045000), _1045004)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045000), hAPP(c_Int_Onumber__class_Onumber__of(_1045000), _1045002)), hAPP(c_Int_Onumber__class_Onumber__of(_1045000), _1045004)) = hAPP(c_Int_Onumber__class_Onumber__of(_1045000), _1045004))], (15204 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1045000), hAPP(c_Int_Onumber__class_Onumber__of(_1045000), _1045002)), hAPP(c_Int_Onumber__class_Onumber__of(_1045000), _1045004))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1045000), hAPP(c_Int_Onumber__class_Onumber__of(_1045000), _1045002)), hAPP(c_Int_Onumber__class_Onumber__of(_1045000), _1045004)) = hAPP(c_Int_Onumber__class_Onumber__of(_1045000), _1045002))]]], (52633 ^ _779203) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (35592 ^ _779203) ^ [_1445627] : [-(hAPP(c_Relation_OField(_1445627), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1445627, _1445627), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1445627, tc_HOL_Obool)))], (20110 ^ _779203) ^ [_1134026, _1134028] : [class_Groups_Oordered__ab__group__add__abs(_1134026), -(hAPP(c_Groups_Oabs__class_Oabs(_1134026), hAPP(c_Groups_Ouminus__class_Ouminus(_1134026), _1134028)) = hAPP(c_Groups_Oabs__class_Oabs(_1134026), _1134028))], (36838 ^ _779203) ^ [_1473431, _1473433, _1473435, _1473437] : [c_Fun_Oinj__on(_1473431, _1473433, _1473435, _1473437), -(hAPP(c_Set_Oimage(_1473433, _1473431, c_Fun_Othe__inv__into(_1473431, _1473433, _1473437, _1473435)), hAPP(c_Set_Oimage(_1473431, _1473433, _1473435), _1473437)) = _1473437)], (6373 ^ _779203) ^ [_881935, _881937, _881939, _881941] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_881935), _881937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881935, tc_HOL_Obool)), _881937), _881939)), hBOOL(hAPP(_881941, c_Orderings_Obot__class_Obot(tc_fun(_881935, tc_HOL_Obool)))), 6388 ^ _779203 : [(6389 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_881935), 6387 ^ [_881935, _881937, _881939, _881941])))], (6393 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_881935), 6386 ^ [_881935, _881937, _881939, _881941]), 6387 ^ [_881935, _881937, _881939, _881941]))], (6397 ^ _779203) ^ [] : [hBOOL(hAPP(_881941, hAPP(hAPP(c_Set_Oinsert(_881935), 6386 ^ [_881935, _881937, _881939, _881941]), 6387 ^ [_881935, _881937, _881939, _881941])))], (6395 ^ _779203) ^ [] : [-(hBOOL(hAPP(_881941, 6387 ^ [_881935, _881937, _881939, _881941])))], (6391 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_881935), 6386 ^ [_881935, _881937, _881939, _881941]), _881939)))]], -(hBOOL(hAPP(_881941, _881937)))], (9397 ^ _779203) ^ [_939472] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939472), _939472)))], (38713 ^ _779203) ^ [_1528718] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1528718)))], (35577 ^ _779203) ^ [_1445351, _1445353] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1445351, _1445351)), hAPP(hAPP(c_Product__Type_OPair(_1445351, _1445351), 35578 ^ [_1445351, _1445353]), 35578 ^ [_1445351, _1445353])), _1445353))), -(c_Relation_Oirrefl(_1445351, _1445353))], (35458 ^ _779203) ^ [_1441903, _1441905, _1441907, _1441909, _1441911, _1441913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1441903, _1441905), tc_HOL_Obool)), _1441907), _1441909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1441903, tc_HOL_Obool)), _1441911), _1441913)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1441905, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1441903, _1441905, _1441907), _1441911)), hAPP(c_Relation_OImage(_1441903, _1441905, _1441909), _1441913))))], (31979 ^ _779203) ^ [_1355629, _1355631, _1355633, _1355635] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1355629, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1355629, tc_fun(_1355629, tc_HOL_Obool), tc_HOL_Obool), c_member(_1355629)), _1355631)), hAPP(hAPP(c_COMBC(_1355629, tc_fun(_1355629, tc_HOL_Obool), tc_HOL_Obool), c_member(_1355629)), _1355633)), _1355635)), -(hBOOL(hAPP(hAPP(c_member(_1355629), _1355635), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1355629, tc_HOL_Obool)), _1355631), _1355633))))], (34306 ^ _779203) ^ [_1409346, _1409348, _1409350, _1409352, _1409354, _1409356, _1409358] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409346, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409348, tc_fun(_1409346, tc_HOL_Obool)), _1409350), _1409352)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409354, tc_fun(_1409346, tc_HOL_Obool)), _1409356), _1409358)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409348, tc_fun(_1409346, tc_HOL_Obool)), _1409350), hAPP(hAPP(c_COMBB(tc_fun(_1409354, tc_fun(_1409346, tc_HOL_Obool)), tc_fun(_1409346, tc_HOL_Obool), _1409348), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409354, tc_fun(_1409346, tc_HOL_Obool)), _1409356)), hAPP(hAPP(c_COMBC(_1409348, tc_fun(_1409354, tc_fun(_1409346, tc_HOL_Obool)), tc_fun(_1409354, tc_fun(_1409346, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1409346, tc_HOL_Obool), tc_fun(_1409346, tc_HOL_Obool)), tc_fun(tc_fun(_1409354, tc_fun(_1409346, tc_HOL_Obool)), tc_fun(_1409354, tc_fun(_1409346, tc_HOL_Obool))), _1409348), c_COMBB(tc_fun(_1409346, tc_HOL_Obool), tc_fun(_1409346, tc_HOL_Obool), _1409354)), hAPP(hAPP(c_COMBB(tc_fun(_1409346, tc_HOL_Obool), tc_fun(tc_fun(_1409346, tc_HOL_Obool), tc_fun(_1409346, tc_HOL_Obool)), _1409348), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409346, tc_HOL_Obool))), _1409352))), _1409358))))], (44355 ^ _779203) ^ [_1666926, _1666928, _1666930, _1666932, _1666934] : [hAPP(hAPP(c_List_Omap(_1666926, _1666928), _1666930), _1666932) = hAPP(hAPP(c_List_Omap(_1666926, _1666928), _1666934), _1666932), 44358 ^ _779203 : [(44359 ^ _779203) ^ [_1667049] : [hBOOL(hAPP(hAPP(c_member(_1666926), _1667049), hAPP(c_List_Oset(_1666926), _1666932))), -(hAPP(_1666930, _1667049) = hAPP(_1666934, _1667049))]]], (26302 ^ _779203) ^ [_1241739, _1241741, _1241743] : [class_Groups_Oordered__ab__group__add(_1241739), -(hAPP(c_Set_Oimage(_1241739, _1241739, c_Groups_Ouminus__class_Ouminus(_1241739)), c_SetInterval_Oord__class_OatLeastAtMost(_1241739, _1241741, _1241743)) = c_SetInterval_Oord__class_OatLeastAtMost(_1241739, hAPP(c_Groups_Ouminus__class_Ouminus(_1241739), _1241743), hAPP(c_Groups_Ouminus__class_Ouminus(_1241739), _1241741)))], (9899 ^ _779203) ^ [_948161, _948163, _948165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948161), _948163)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948161), _948165)), _948163)))], (20188 ^ _779203) ^ [_1135357, _1135359] : [class_Rings_Olinordered__idom(_1135357), 20191 ^ _779203 : [(20198 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135357), _1135359), c_Groups_Ozero__class_Ozero(_1135357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135357), _1135359), hAPP(c_Groups_Ouminus__class_Ouminus(_1135357), _1135359))))], (20192 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135357), _1135359), hAPP(c_Groups_Ouminus__class_Ouminus(_1135357), _1135359))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135357), _1135359), c_Groups_Ozero__class_Ozero(_1135357))))]]], (46730 ^ _779203) ^ [_1719029, _1719031, _1719033, _1719035] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719029), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719031)), _1719033))), -(hAPP(c_List_Orev(_1719031), hAPP(hAPP(c_List_Olist__update(_1719031, _1719033), _1719029), _1719035)) = hAPP(hAPP(c_List_Olist__update(_1719031, hAPP(c_List_Orev(_1719031), _1719033)), 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(_1719031)), _1719033)), _1719029)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1719035))], (48048 ^ _779203) ^ [_1747653, _1747655, _1747657] : [-(hAPP(c_New__DSequence_Oneg__single(_1747653, _1747655), _1747657) = c_Lazy__Sequence_Ohb__single(_1747653, _1747655))], (48056 ^ _779203) ^ [_1747858, _1747860, _1747862, _1747864, _1747866] : [-(c_List_Osplice(_1747858, hAPP(hAPP(c_List_Olist_OCons(_1747858), _1747860), _1747862), hAPP(hAPP(c_List_Olist_OCons(_1747858), _1747864), _1747866)) = hAPP(hAPP(c_List_Olist_OCons(_1747858), _1747860), hAPP(hAPP(c_List_Olist_OCons(_1747858), _1747864), c_List_Osplice(_1747858, _1747862, _1747866))))], (29744 ^ _779203) ^ [_1307319, _1307321, _1307323, _1307325] : [hBOOL(hAPP(hAPP(c_member(_1307319), _1307321), _1307323)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307319, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1307319), _1307321), _1307325)), _1307323) = hAPP(hAPP(c_Set_Oinsert(_1307319), _1307321), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307319, tc_HOL_Obool)), _1307325), _1307323)))], (31470 ^ _779203) ^ [_1343560] : [class_Complete__Lattice_Ocomplete__lattice(_1343560), -(c_Complete__Lattice_OInf__class_OInf(_1343560, c_Orderings_Obot__class_Obot(tc_fun(_1343560, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1343560))], (15724 ^ _779203) ^ [_1054844, _1054846, _1054848] : [class_Orderings_Olinorder(_1054844), 15727 ^ _779203 : [(15734 ^ _779203) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1054844), _1054846), _1054848) = _1054846, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054844), _1054846), _1054848)))], (15728 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1054844), _1054846), _1054848)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1054844), _1054846), _1054848) = _1054846)]]], (48713 ^ _779203) ^ [_1762410, _1762412, _1762414] : [-(c_Random__Sequence_Oempty(_1762410, _1762412, _1762414) = 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(_1762410)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1762410)))], (25684 ^ _779203) ^ [_1231372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1231372))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1231372)))], (30405 ^ _779203) ^ [_1321819, _1321821, _1321823] : [class_Orderings_Olinorder(_1321819), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321819), _1321821)), -(_1321821 = c_Orderings_Obot__class_Obot(tc_fun(_1321819, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321819), _1321823)), -(_1321823 = c_Orderings_Obot__class_Obot(tc_fun(_1321819, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1321819, tc_HOL_Obool)), _1321821), _1321823) = c_Orderings_Obot__class_Obot(tc_fun(_1321819, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1321819, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321819, tc_HOL_Obool)), _1321821), _1321823)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321819), c_Big__Operators_Olinorder__class_OMin(_1321819, _1321821)), c_Big__Operators_Olinorder__class_OMin(_1321819, _1321823)))], (38619 ^ _779203) ^ [_1527097, _1527099] : [c_Wellfounded_Owf(_1527097, _1527099), -(c_Wellfounded_Owf(_1527097, hAPP(hAPP(c_Relation_Orel__comp(_1527097, _1527097, _1527097), _1527099), _1527099)))], (27818 ^ _779203) ^ [_1269724, _1269726] : [class_Lattices_Obounded__lattice__top(_1269724), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269724), _1269726), c_Orderings_Otop__class_Otop(_1269724)) = c_Orderings_Otop__class_Otop(_1269724))], (11928 ^ _779203) ^ [_985171, _985173, _985175] : [class_Rings_Olinordered__semiring__strict(_985171), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985171), _985173), c_Groups_Ozero__class_Ozero(_985171))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985171), c_Groups_Ozero__class_Ozero(_985171)), _985175)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985171), _985173), _985175)), c_Groups_Ozero__class_Ozero(_985171))))], (48749 ^ _779203) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (23653 ^ _779203) ^ [_1195511, _1195513] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195511))), -(c_SMT_Oz3mod(_1195513, _1195511) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1195513, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195511)))], (43642 ^ _779203) ^ [_1652240, _1652242, _1652244, _1652246] : [-(hAPP(c_List_Orotate1(_1652240), c_List_Olist_ONil(_1652240)) = c_List_Olist_ONil(_1652240))], (52247 ^ _779203) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (40283 ^ _779203) ^ [_1566299, _1566301] : [-(c_Transitive__Closure_Otrancl(_1566299, _1566301) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566299, _1566299), tc_HOL_Obool)), _1566301), hAPP(hAPP(c_Relation_Orel__comp(_1566299, _1566299, _1566299), c_Transitive__Closure_Otrancl(_1566299, _1566301)), _1566301)))], (38220 ^ _779203) ^ [_1514702, _1514704] : [-(c_Product__Type_Oapfst(_1514702, _1514702, _1514704, c_Fun_Oid(_1514702)) = c_Fun_Oid(tc_prod(_1514702, _1514704)))], (1610 ^ _779203) ^ [_802288, _802290] : [-(class_Groups_Ocancel__ab__semigroup__add(_802288)), _802290 = _802288, class_Groups_Ocancel__ab__semigroup__add(_802290)], (35515 ^ _779203) ^ [_1443532, _1443534, _1443536, _1443538, _1443540] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1443536, _1443532)), hAPP(hAPP(c_Product__Type_OPair(_1443536, _1443532), _1443540), _1443534)), _1443538)), -(hBOOL(hAPP(hAPP(c_member(_1443532), _1443534), hAPP(c_Relation_OImage(_1443536, _1443532, _1443538), hAPP(hAPP(c_Set_Oinsert(_1443536), _1443540), c_Orderings_Obot__class_Obot(tc_fun(_1443536, tc_HOL_Obool)))))))], (40184 ^ _779203) ^ [_1563957, _1563959] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563957, _1563957)), hAPP(hAPP(c_Product__Type_OPair(_1563957, _1563957), 40185 ^ [_1563957, _1563959]), 40185 ^ [_1563957, _1563959])), c_Transitive__Closure_Otrancl(_1563957, _1563959)))), -(c_Wellfounded_Oacyclic(_1563957, _1563959))], (29696 ^ _779203) ^ [_1306345, _1306347, _1306349] : [class_Lattices_Oboolean__algebra(_1306345), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1306345), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1306345), _1306347), _1306349)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1306345), hAPP(c_Groups_Ouminus__class_Ouminus(_1306345), _1306347)), hAPP(c_Groups_Ouminus__class_Ouminus(_1306345), _1306349)))], (15870 ^ _779203) ^ [_1057309, _1057311, _1057313, _1057315] : [class_Orderings_Olinorder(_1057309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057309), _1057311), _1057313)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057309), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1057309), _1057315), _1057311)), _1057313)))], (8415 ^ _779203) ^ [_919964, _919966, _919968] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_919964), _919966)), 8418 ^ _779203 : [(8425 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_919964), _919968), _919966))), -(hAPP(c_Finite__Set_Ocard(_919964), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919964, tc_HOL_Obool)), _919966), hAPP(hAPP(c_Set_Oinsert(_919964), _919968), c_Orderings_Obot__class_Obot(tc_fun(_919964, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_919964), _919966))], (8419 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_919964), _919968), _919966)), -(hAPP(c_Finite__Set_Ocard(_919964), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_919964, tc_HOL_Obool)), _919966), hAPP(hAPP(c_Set_Oinsert(_919964), _919968), c_Orderings_Obot__class_Obot(tc_fun(_919964, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_919964), _919966)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (13127 ^ _779203) ^ [_1006322, _1006324, _1006326] : [class_Orderings_Olinorder(_1006322), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006322), _1006324)), hBOOL(hAPP(hAPP(c_member(_1006322), _1006326), _1006324)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006322), _1006326), c_Big__Operators_Olinorder__class_OMax(_1006322, _1006324))))], (812 ^ _779203) ^ [_791367, _791369, _791371, _791373] : [-(c_Relation_Otrans(_791371, _791367)), c_Relation_Otrans(_791373, _791369), _791373 = _791371, _791369 = _791367], (38408 ^ _779203) ^ [_1520175, _1520177, _1520179] : [-(hAPP(c_Relation_ORange(_1520175, _1520177), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1520175, _1520177), tc_HOL_Obool), _1520179)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1520175, _1520177), tc_HOL_Obool), tc_fun(_1520177, tc_HOL_Obool)), _1520179), c_Relation_ORange(_1520175, _1520177)))], (52377 ^ _779203) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (42177 ^ _779203) ^ [_1619282, _1619284] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1619282, _1619284) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1619282), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1619284), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (440 ^ _779203) ^ [_785801, _785803, _785805, _785807, _785809, _785811] : [-(c_Relation_Osingle__valued(_785809, _785805, _785801)), c_Relation_Osingle__valued(_785811, _785807, _785803), _785811 = _785809, _785807 = _785805, _785803 = _785801], (3610 ^ _779203) ^ [_833256, _833258, _833260, _833262] : [-(c_List_Obutlast(_833262, _833258) = c_List_Obutlast(_833260, _833256)), _833262 = _833260, _833258 = _833256], (22397 ^ _779203) ^ [_1174316, _1174318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1174316)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1174318, _1174316)), _1174316)))], (22596 ^ _779203) ^ [_1177683] : [hAPP(c_Int_Onat, _1177683) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177683), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (50653 ^ _779203) ^ [_1805242, _1805244, _1805246, _1805248] : [class_Rings_Oidom(_1805242), 50656 ^ _779203 : [(50657 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805242), _1805244), _1805246)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805242), _1805248), _1805246))), -(_1805246 = c_Groups_Ozero__class_Ozero(_1805242)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805242), _1805244), _1805248)))], (50667 ^ _779203) ^ [] : [50668 ^ _779203 : [(50671 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805242), _1805244), _1805248))], (50669 ^ _779203) ^ [] : [_1805246 = c_Groups_Ozero__class_Ozero(_1805242)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1805242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805242), _1805244), _1805246)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1805242), _1805248), _1805246))))]]], (18310 ^ _779203) ^ [_1102229, _1102231] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1102229)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1102231)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1102229), _1102231)))], (18245 ^ _779203) ^ [_1100982] : [18246 ^ _779203 : [(18247 ^ _779203) ^ [_1101039] : [hBOOL(hAPP(_1100982, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101039)))]], 18249 ^ _779203 : [(18252 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1100982, 18248 ^ [_1100982])))], (18250 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 18248 ^ [_1100982])))]]], (40831 ^ _779203) ^ [_1580326, _1580328, _1580330] : [hAPP(hAPP(c_Relation_Orel__comp(_1580326, _1580326, _1580326), hAPP(c_Relation_Oconverse(_1580326, _1580326), _1580328)), _1580328) = _1580328, hAPP(c_Relation_ODomain(_1580326, _1580326), _1580328) = _1580330, -(c_Equiv__Relations_Oequiv(_1580326, _1580330, _1580328))], (3390 ^ _779203) ^ [_829758, _829760, _829762, _829764, _829766, _829768, _829770, _829772] : [-(c_List_Olist_Olist__case(_829772, _829768, _829764, _829760) = c_List_Olist_Olist__case(_829770, _829766, _829762, _829758)), _829772 = _829770, _829768 = _829766, _829764 = _829762, _829760 = _829758], (25542 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (52153 ^ _779203) ^ [_1831377, _1831379] : [class_Lattices_Oboolean__algebra(_1831377), -(class_Lattices_Oboolean__algebra(tc_fun(_1831379, _1831377)))], (42588 ^ _779203) ^ [_1628447, _1628449, _1628451] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628447), tc_List_Olist(_1628447))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628447), tc_List_Olist(_1628447)), c_List_Olist_ONil(_1628447)), _1628449)), c_List_Olistrel(_1628447, _1628451))), -(_1628449 = c_List_Olist_ONil(_1628447))], (43764 ^ _779203) ^ [_1654681, _1654683, _1654685, _1654687] : [-(hAPP(c_List_Orotate(_1654681, _1654683), hAPP(c_List_Orotate(_1654681, _1654685), _1654687)) = hAPP(c_List_Orotate(_1654681, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1654683), _1654685)), _1654687))], (15558 ^ _779203) ^ [_1051973, _1051975, _1051977] : [class_Orderings_Olinorder(_1051973), 15561 ^ _779203 : [(15568 ^ _779203) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1051973), _1051975), _1051977) = _1051977, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051973), _1051975), _1051977)))], (15562 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051973), _1051975), _1051977)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1051973), _1051975), _1051977) = _1051977)]]], (48654 ^ _779203) ^ [_1761099, _1761101, _1761103] : [c_List_Olist__all(tc_Int_Oint, _1761099, c_List_Oupto(_1761101, _1761103)), -(c_List_Oall__interval__int(_1761099, _1761101, _1761103))], (48330 ^ _779203) ^ [_1753706, _1753708, _1753710] : [-(hAPP(hAPP(c_List_Oappend(_1753706), c_List_Oreplicate(_1753706, _1753708, _1753710)), hAPP(hAPP(c_List_Olist_OCons(_1753706), _1753710), c_List_Olist_ONil(_1753706))) = hAPP(hAPP(c_List_Olist_OCons(_1753706), _1753710), c_List_Oreplicate(_1753706, _1753708, _1753710)))], (52417 ^ _779203) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (21323 ^ _779203) ^ [] : [-(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)))], (49578 ^ _779203) ^ [_1781042, _1781044, _1781046] : [hAPP(c_Fun_Ocomp(_1781044, _1781042, _1781042, c_Hilbert__Choice_Oinv__into(_1781042, _1781044, c_Orderings_Otop__class_Otop(tc_fun(_1781042, tc_HOL_Obool)), _1781046)), _1781046) = c_Fun_Oid(_1781042), -(c_Fun_Oinj__on(_1781042, _1781044, _1781046, c_Orderings_Otop__class_Otop(tc_fun(_1781042, tc_HOL_Obool))))], (39486 ^ _779203) ^ [_1547496, _1547498] : [39487 ^ _779203 : [(39488 ^ _779203) ^ [_1547542] : [hBOOL(hAPP(_1547496, _1547542))]], -(hBOOL(hAPP(_1547496, c_Hilbert__Choice_OEps(_1547498, _1547496))))], (122 ^ _779203) ^ [_780970, _780972, _780974, _780976] : [-(c_Int_Oiszero(_780974, _780970)), c_Int_Oiszero(_780976, _780972), _780976 = _780974, _780972 = _780970], (17518 ^ _779203) ^ [_1088040] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1088040), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1088040)], (5426 ^ _779203) ^ [_862226, _862228] : [_862228 = _862226, -(c_Int_Onumber__class_Onumber__of(_862228) = c_Int_Onumber__class_Onumber__of(_862226))], (34085 ^ _779203) ^ [_1404361, _1404363, _1404365] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1404361, tc_HOL_Obool), tc_fun(_1404361, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1404361, tc_HOL_Obool), tc_fun(_1404361, tc_HOL_Obool)), _1404363), _1404365)), c_Wellfounded_Ofinite__psubset(_1404361)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1404361, tc_HOL_Obool)), _1404363), _1404365)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1404361), _1404365))], (35722 ^ _779203) ^ [] : [-(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))], (24742 ^ _779203) ^ [_1215221, _1215223] : [class_Rings_Oring__1(_1215221), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1215221), hAPP(c_Groups_Ouminus__class_Ouminus(_1215221), c_Groups_Oone__class_Oone(_1215221))), 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)))), _1215223)) = c_Groups_Oone__class_Oone(_1215221))], (48921 ^ _779203) ^ [_1767153, _1767155] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1767153, tc_HOL_Obool), _1767155) = hAPP(c_Set_OCollect(_1767153), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767153, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1767153), c_HOL_OEx(tc_fun(_1767153, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1767153, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1767153, tc_HOL_Obool), tc_HOL_Obool), _1767153), hAPP(c_COMBS(tc_fun(_1767153, 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(_1767153, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1767153, tc_HOL_Obool), tc_fun(tc_fun(_1767153, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1767153, tc_HOL_Obool))), _1767155)))), c_member(_1767153)))))], (12161 ^ _779203) ^ [_989256] : [12162 ^ _779203 : [(12163 ^ _779203) ^ [_989298] : [_989256 = hAPP(c_Nat_OSuc, _989298)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _989256)))], (17390 ^ _779203) ^ [_1085887, _1085889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085887), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1085889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1085887), _1085889)))], (51015 ^ _779203) ^ [_1811967, _1811969, _1811971] : [class_Rings_Ocomm__ring__1(_1811967), 51018 ^ _779203 : [(51025 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811967), _1811969), _1811971)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811967), _1811969), hAPP(c_Groups_Ouminus__class_Ouminus(_1811967), _1811971))))], (51019 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811967), _1811969), hAPP(c_Groups_Ouminus__class_Ouminus(_1811967), _1811971))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1811967), _1811969), _1811971)))]]], (9999 ^ _779203) ^ [_950008, _950010, _950012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _950008), _950010)), _950012)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950008), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _950012), _950010))))], (9103 ^ _779203) ^ [_933985, _933987, _933989, _933991, _933993, _933995] : [class_Rings_Oordered__ring(_933985), 9106 ^ _779203 : [(9113 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933985), _933991), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933985), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933985), _933993), _933987)), _933989)), _933995))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933985), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933985), _933987), _933989)), _933991)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933985), _933993), _933989)), _933995))))], (9107 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933985), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933985), _933987), _933989)), _933991)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933985), _933993), _933989)), _933995))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933985), _933991), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933985), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933985), _933993), _933987)), _933989)), _933995))))]]], (23792 ^ _779203) ^ [_1197906, _1197908] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197906), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197908)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197906, _1197908)))], (38649 ^ _779203) ^ [_1527555, _1527557] : [-(c_Relation_Orefl__on(_1527555, _1527557, c_Relation_OId__on(_1527555, _1527557)))], (12891 ^ _779203) ^ [_1002087, _1002089, _1002091] : [class_Rings_Olinordered__idom(_1002087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002087), c_Groups_Ozero__class_Ozero(_1002087)), _1002089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002087), c_Groups_Ozero__class_Ozero(_1002087)), _1002091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002087), _1002091), c_Groups_Oone__class_Oone(_1002087))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002087), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1002087), _1002089), _1002091)), _1002089)))], (5200 ^ _779203) ^ [_858541, _858543] : [_858543 = _858541, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_858543) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_858541))], (14587 ^ _779203) ^ [_1033250, _1033252, _1033254, _1033256] : [class_Fields_Olinordered__field(_1033250), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033250), _1033252), c_Groups_Ozero__class_Ozero(_1033250))), 14594 ^ _779203 : [(14601 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033250), _1033256), _1033252)), _1033254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033250), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033250), _1033254), _1033252)), _1033256)))], (14595 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033250), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033250), _1033254), _1033252)), _1033256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033250), _1033256), _1033252)), _1033254)))]]], (41136 ^ _779203) ^ [_1587985, _1587987, _1587989, _1587991, _1587993] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587985, _1587985)), hAPP(hAPP(c_Product__Type_OPair(_1587985, _1587985), _1587987), _1587989)), c_Transitive__Closure_Ortrancl(_1587985, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587985, _1587985), tc_HOL_Obool)), _1587991), _1587993)))), 41142 ^ _779203 : [(41148 ^ _779203) ^ [] : [41144 ^ [_1587985, _1587987, _1587989, _1587991, _1587993] = 41141 ^ [_1587985, _1587987, _1587989, _1587991, _1587993]], (41146 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587985, _1587985)), hAPP(hAPP(c_Product__Type_OPair(_1587985, _1587985), 41144 ^ [_1587985, _1587987, _1587989, _1587991, _1587993]), 41141 ^ [_1587985, _1587987, _1587989, _1587991, _1587993])), _1587993)))], (41143 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587985, _1587985)), hAPP(hAPP(c_Product__Type_OPair(_1587985, _1587985), 41141 ^ [_1587985, _1587987, _1587989, _1587991, _1587993]), _1587989)), c_Transitive__Closure_Ortrancl(_1587985, _1587991))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587985, _1587985)), hAPP(hAPP(c_Product__Type_OPair(_1587985, _1587985), _1587987), _1587989)), c_Transitive__Closure_Ortrancl(_1587985, _1587991))))], (3242 ^ _779203) ^ [_827496, _827498] : [_827498 = _827496, -(c_Lazy__Sequence_Ohb__not__seq(_827498) = c_Lazy__Sequence_Ohb__not__seq(_827496))], (2038 ^ _779203) ^ [_808582, _808584] : [_808584 = _808582, -(c_Int_Osucc(_808584) = c_Int_Osucc(_808582))], (50491 ^ _779203) ^ [_1802339, _1802341, _1802343] : [50493 ^ _779203 : [(50496 ^ _779203) ^ [] : [hBOOL(hAPP(_1802339, 50492 ^ [_1802339, _1802341, _1802343]))], (50494 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 50492 ^ [_1802339, _1802341, _1802343]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1802341), _1802343))))]], -(c_List_Oall__interval__nat(_1802339, _1802341, _1802343))], (27758 ^ _779203) ^ [_1268554, _1268556, _1268558, _1268560] : [class_Lattices_Olattice(_1268554), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268554), _1268556), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268554), _1268558), _1268560)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268554), _1268558), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268554), _1268556), _1268560)))], (12981 ^ _779203) ^ [_1003633, _1003635, _1003637] : [hBOOL(hAPP(_1003633, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003635), _1003637))), 12984 ^ _779203 : [(12991 ^ _779203) ^ [_1003818] : [_1003635 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003637), _1003818), -(hBOOL(hAPP(_1003633, _1003818)))], (12985 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003635), _1003637)), -(hBOOL(hAPP(_1003633, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (4844 ^ _779203) ^ [_852951, _852953, _852955, _852957] : [-(c_Hilbert__Choice_OEps(_852957, _852953) = c_Hilbert__Choice_OEps(_852955, _852951)), _852957 = _852955, _852953 = _852951], (33073 ^ _779203) ^ [_1385143, _1385145] : [33074 ^ _779203 : [(33077 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1385145), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33075 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1385143), _1385145))]], -(c_Divides_OposDivAlg(_1385143, _1385145) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385143))], (18198 ^ _779203) ^ [_1100234] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1100234) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1100234 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11434 ^ _779203) ^ [_976151, _976153, _976155, _976157, _976159] : [class_Rings_Oordered__semiring(_976151), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976151), _976153), _976155)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976151), _976157), _976159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976151), c_Groups_Ozero__class_Ozero(_976151)), _976153)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976151), c_Groups_Ozero__class_Ozero(_976151)), _976157)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976151), _976153), _976157)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976151), _976155), _976159))))], (35003 ^ _779203) ^ [_1429615, _1429617, _1429619, _1429621, _1429623] : [_1429615 = c_Orderings_Obot__class_Obot(tc_fun(_1429617, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429617, tc_fun(_1429619, tc_HOL_Obool)), _1429615), hAPP(hAPP(c_COMBC(_1429617, tc_fun(_1429619, tc_HOL_Obool), tc_fun(_1429619, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429619, tc_HOL_Obool), tc_fun(tc_fun(_1429619, tc_HOL_Obool), tc_fun(_1429619, tc_HOL_Obool)), _1429617), c_Groups_Ominus__class_Ominus(tc_fun(_1429619, tc_HOL_Obool))), _1429621)), _1429623)) = c_Orderings_Otop__class_Otop(tc_fun(_1429619, tc_HOL_Obool)))], (9889 ^ _779203) ^ [_947974, _947976, _947978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947974), _947976)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947974), _947978)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947978), _947976)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _947978), _947974))))], (38436 ^ _779203) ^ [_1520963, _1520965, _1520967] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1520963, _1520965)), _1520967)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1520965), hAPP(c_Relation_ORange(_1520963, _1520965), _1520967))))], (29794 ^ _779203) ^ [_1308811, _1308813, _1308815] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308811, tc_HOL_Obool)), _1308813), _1308815) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308811, tc_HOL_Obool)), _1308813), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308811, tc_HOL_Obool)), _1308815)))], (38611 ^ _779203) ^ [_1526905, _1526907] : [-(c_Wellfounded_Owf(_1526905, hAPP(c_Wellfounded_Omeasure(_1526905), _1526907)))], (37879 ^ _779203) ^ [_1500593, _1500595, _1500597, _1500599, _1500601, _1500603] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1500593), _1500595)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1500597), _1500599)), 37889 ^ _779203 : [(37892 ^ _779203) ^ [] : [hAPP(c_Finite__Set_Ocard(_1500593), hAPP(c_Set_OCollect(_1500593), hAPP(hAPP(c_COMBS(_1500593, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1500593), c_fconj), hAPP(hAPP(c_COMBC(_1500593, tc_fun(_1500593, tc_HOL_Obool), tc_HOL_Obool), c_member(_1500593)), _1500595))), hAPP(hAPP(c_COMBC(_1500593, _1500597, tc_HOL_Obool), _1500601), 37888 ^ [_1500593, _1500595, _1500597, _1500599, _1500601, _1500603])))) = _1500603], (37890 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1500597), 37888 ^ [_1500593, _1500595, _1500597, _1500599, _1500601, _1500603]), _1500599)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1500593, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1500597, tc_HOL_Obool), tc_Nat_Onat, _1500593), c_Finite__Set_Ocard(_1500597)), hAPP(hAPP(c_COMBB(tc_fun(_1500597, tc_HOL_Obool), tc_fun(_1500597, tc_HOL_Obool), _1500593), c_Set_OCollect(_1500597)), hAPP(hAPP(c_COMBB(tc_fun(_1500597, tc_HOL_Obool), tc_fun(_1500597, tc_HOL_Obool), _1500593), hAPP(c_COMBS(_1500597, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1500597), c_fconj), hAPP(hAPP(c_COMBC(_1500597, tc_fun(_1500597, tc_HOL_Obool), tc_HOL_Obool), c_member(_1500597)), _1500599)))), _1500601)))), _1500595) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1500603), hAPP(c_Finite__Set_Ocard(_1500597), _1500599)))], (18983 ^ _779203) ^ [_1113617, _1113619, _1113621] : [class_Rings_Osemiring__1(_1113617), hBOOL(hAPP(hAPP(c_member(_1113617), _1113619), c_Nat_Osemiring__1__class_ONats(_1113617))), hBOOL(hAPP(hAPP(c_member(_1113617), _1113621), c_Nat_Osemiring__1__class_ONats(_1113617))), -(hBOOL(hAPP(hAPP(c_member(_1113617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1113617), _1113619), _1113621)), c_Nat_Osemiring__1__class_ONats(_1113617))))], (37505 ^ _779203) ^ [_1489323, _1489325, _1489327] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1489323, _1489325), c_Orderings_Obot__class_Obot(tc_fun(_1489323, tc_HOL_Obool))), _1489327) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489323, _1489325), tc_HOL_Obool)))], (3724 ^ _779203) ^ [_835015, _835017, _835019, _835021, _835023, _835025, _835027, _835029] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_835029, _835025, _835021, _835017) = c_New__Random__Sequence_Opos__not__random__dseq(_835027, _835023, _835019, _835015)), _835029 = _835027, _835025 = _835023, _835021 = _835019, _835017 = _835015], (15402 ^ _779203) ^ [_1049217, _1049219, _1049221, _1049223] : [class_Orderings_Olinorder(_1049217), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049217), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1049217), _1049219), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049217), _1049221), _1049223))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049217), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1049217), _1049219), _1049221)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1049217), _1049219), _1049223)))))], (3094 ^ _779203) ^ [_825164, _825166, _825168, _825170] : [-(c_Big__Operators_Olattice__class_OSup__fin(_825170, _825166) = c_Big__Operators_Olattice__class_OSup__fin(_825168, _825164)), _825170 = _825168, _825166 = _825164], (35547 ^ _779203) ^ [_1444409, _1444411, _1444413, _1444415] : [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), _1444409), _1444411)), 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), _1444413), _1444415)), 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), _1444409), _1444415)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1444413), _1444411))))], (46754 ^ _779203) ^ [_1719565, _1719567, _1719569] : [class_Orderings_Olinorder(_1719565), c_List_Olinorder__class_Osorted(_1719565, hAPP(c_List_Orev(_1719565), _1719567)), 46761 ^ _779203 : [(46768 ^ _779203) ^ [] : [-(_1719567 = c_List_Olist_ONil(_1719565)), -(c_List_Ofoldr(_1719565, _1719565, c_Orderings_Oord__class_Omax(_1719565), _1719567, _1719569) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1719565), hAPP(hAPP(c_List_Onth(_1719565), _1719567), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1719569))], (46762 ^ _779203) ^ [] : [_1719567 = c_List_Olist_ONil(_1719565), -(c_List_Ofoldr(_1719565, _1719565, c_Orderings_Oord__class_Omax(_1719565), _1719567, _1719569) = _1719569)]]], (5751 ^ _779203) ^ [_870153, _870155, _870157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870153, tc_HOL_Obool)), _870155), _870157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_870153, tc_HOL_Obool)), _870157), _870155)), -(_870155 = _870157)], (52111 ^ _779203) ^ [_1830824, _1830826] : [class_Lattices_Obounded__lattice(_1830824), -(class_Lattices_Obounded__lattice(tc_fun(_1830826, _1830824)))], (4818 ^ _779203) ^ [_852568, _852570, _852572, _852574] : [-(c_Relation_Oconverse(_852574, _852570) = c_Relation_Oconverse(_852572, _852568)), _852574 = _852572, _852570 = _852568], (6274 ^ _779203) ^ [_880185, _880187] : [-(c_Set_Othe__elem(_880185, hAPP(hAPP(c_Set_Oinsert(_880185), _880187), c_Orderings_Obot__class_Obot(tc_fun(_880185, tc_HOL_Obool)))) = _880187)], (38951 ^ _779203) ^ [_1534127, _1534129, _1534131, _1534133] : [c_Wellfounded_Owf(_1534127, _1534129), c_Fun_Oinj__on(_1534127, _1534131, _1534133, c_Orderings_Otop__class_Otop(tc_fun(_1534127, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1534131, hAPP(c_Set_Oimage(tc_prod(_1534127, _1534127), tc_prod(_1534131, _1534131), c_Product__Type_Omap__pair(_1534127, _1534131, _1534127, _1534131, _1534133, _1534133)), _1534129)))], (51773 ^ _779203) ^ [_1824835, _1824837] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824835), _1824837)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1824835), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824837))))], (32371 ^ _779203) ^ [_1365288, _1365290] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365288)), hAPP(c_Nat_OSuc, _1365290))), -(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(_1365288))), 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)), _1365290)))))], (17266 ^ _779203) ^ [_1083727, _1083729] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083727)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1083729)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1083727), _1083729)))], (52349 ^ _779203) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (28172 ^ _779203) ^ [_1277024, _1277026] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1277024, tc_HOL_Obool)), _1277026) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277024, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1277024, tc_HOL_Obool))), _1277026))], (38442 ^ _779203) ^ [_1521076, _1521078, _1521080] : [-(hAPP(c_Set_Oimage(tc_prod(_1521076, _1521078), _1521078, c_Product__Type_Osnd(_1521076, _1521078)), _1521080) = hAPP(c_Relation_ORange(_1521076, _1521078), _1521080))], (26126 ^ _779203) ^ [_1238565, _1238567] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1238565, _1238567))))], (48483 ^ _779203) ^ [_1757123] : [-(c_List_Omember(_1757123) = c_List_Oset(_1757123))], (25142 ^ _779203) ^ [_1222444, _1222446, _1222448, _1222450] : [class_Rings_Olinordered__semidom(_1222444), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222444), hAPP(hAPP(c_Power_Opower__class_Opower(_1222444), _1222446), _1222448)), hAPP(hAPP(c_Power_Opower__class_Opower(_1222444), _1222450), _1222448))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222444), c_Groups_Ozero__class_Ozero(_1222444)), _1222450)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1222444), _1222446), _1222450)))], (25802 ^ _779203) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (7091 ^ _779203) ^ [_896289, _896291, _896293, _896295, _896297, _896299] : [c_Finite__Set_Ofun__left__comm(_896289, _896291, _896293), hBOOL(hAPP(c_Finite__Set_Ofinite(_896289), _896295)), -(hBOOL(hAPP(hAPP(c_member(_896289), _896297), _896295))), -(hAPP(hAPP(c_Finite__Set_Ofold(_896289, _896291, _896293), _896299), hAPP(hAPP(c_Set_Oinsert(_896289), _896297), _896295)) = hAPP(hAPP(c_Finite__Set_Ofold(_896289, _896291, _896293), hAPP(hAPP(_896293, _896297), _896299)), _896295))], (52345 ^ _779203) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (33867 ^ _779203) ^ [_1399623, _1399625, _1399627, _1399629, _1399631] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1399623, _1399625, _1399627), _1399629), _1399631) = hAPP(hAPP(_1399629, hAPP(c_Product__Type_Ofst(_1399623, _1399625), _1399631)), hAPP(c_Product__Type_Osnd(_1399623, _1399625), _1399631)))], (46644 ^ _779203) ^ [_1717221, _1717223, _1717225, _1717227, _1717229] : [c_List_Olist__all2(_1717221, _1717223, _1717225, _1717227, _1717229), -(c_List_Olist__all2(_1717221, _1717223, _1717225, hAPP(c_List_Orev(_1717221), _1717227), hAPP(c_List_Orev(_1717223), _1717229)))], (30915 ^ _779203) ^ [_1332280, _1332282, _1332284] : [class_Lattices_Olattice(_1332280), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332280), _1332282)), 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[hBOOL(hAPP(hAPP(c_member(_1484472), _1484474), _1484476)), 37320 ^ _779203 : [(37327 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484472), _1484478), _1484476))), -(hAPP(c_Set_Ovimage(_1484480, _1484472, hAPP(hAPP(c_COMBC(_1484480, _1484472, _1484472), hAPP(hAPP(c_COMBC(_1484480, _1484472, tc_fun(_1484472, _1484472)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1484472, tc_fun(_1484472, _1484472)), _1484480), c_If(_1484472)), hAPP(hAPP(c_COMBC(_1484480, tc_fun(_1484480, tc_HOL_Obool), tc_HOL_Obool), c_member(_1484480)), _1484482))), _1484474)), _1484478)), _1484476) = _1484482)], (37321 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1484472), _1484478), _1484476)), -(hAPP(c_Set_Ovimage(_1484480, _1484472, hAPP(hAPP(c_COMBC(_1484480, _1484472, _1484472), hAPP(hAPP(c_COMBC(_1484480, _1484472, tc_fun(_1484472, _1484472)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1484472, tc_fun(_1484472, _1484472)), _1484480), c_If(_1484472)), hAPP(hAPP(c_COMBC(_1484480, tc_fun(_1484480, tc_HOL_Obool), tc_HOL_Obool), c_member(_1484480)), _1484482))), _1484474)), _1484478)), _1484476) = c_Orderings_Otop__class_Otop(tc_fun(_1484480, tc_HOL_Obool)))]]], (39096 ^ _779203) ^ [_1537669, _1537671] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1537669, _1537671), 39097 ^ [_1537669, _1537671])), -(c_Wellfounded_OwfP(_1537669, _1537671))], (46290 ^ _779203) ^ [_1709841, _1709843, _1709845, _1709847, _1709849] : [class_Orderings_Olinorder(_1709841), -(c_List_Olinorder__class_Osorted(_1709841, hAPP(hAPP(c_List_Omap(_1709843, _1709841), _1709845), hAPP(c_List_Ofilter(_1709843, hAPP(hAPP(c_COMBC(_1709843, _1709841, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1709841, tc_fun(_1709841, tc_HOL_Obool), _1709843), c_fequal), _1709845)), hAPP(_1709847, _1709849))), _1709849))))], (52297 ^ _779203) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (48046 ^ _779203) ^ [_1747536, _1747538, _1747540, _1747542, _1747544, _1747546, _1747548] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1747536, _1747538, _1747540, _1747542), _1747544), _1747546), _1747548) = c_New__DSequence_Opos__bind(_1747536, _1747538, hAPP(hAPP(hAPP(_1747540, _1747544), _1747546), _1747548), hAPP(hAPP(c_COMBC(_1747536, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1747538))), hAPP(hAPP(c_COMBC(_1747536, 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(_1747538)))), hAPP(hAPP(c_COMBC(_1747536, 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(_1747538))))), _1747542), _1747544)), _1747546)), _1747548)))], (22886 ^ _779203) ^ [_1182326, _1182328] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1182326) = _1182328, 22889 ^ _779203 : [(22892 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182328)))], (22890 ^ _779203) ^ [] : [-(_1182326 = hAPP(c_Int_Onat, _1182328))]]], (36866 ^ _779203) ^ [_1473975, _1473977, _1473979, _1473981, _1473983] : [c_Typedef_Otype__definition(_1473975, _1473977, _1473979, _1473981, _1473983), -(hAPP(c_Set_Oimage(_1473975, _1473977, _1473979), c_Orderings_Otop__class_Otop(tc_fun(_1473975, tc_HOL_Obool))) = _1473983)], (8204 ^ _779203) ^ [_915437, _915439, _915441, _915443, _915445] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_915437, _915439, _915441, _915443, c_Orderings_Obot__class_Obot(tc_fun(_915437, tc_HOL_Obool))), _915445)), -(_915445 = _915443)], (46933 ^ _779203) ^ [_1723204] : [-(c_List_Oembed__list(_1723204) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1723204))], (42710 ^ _779203) ^ [_1630504, _1630506] : [_1630506 = c_List_Olist_ONil(_1630504), -(hAPP(c_List_Oset(_1630504), _1630506) = c_Orderings_Obot__class_Obot(tc_fun(_1630504, tc_HOL_Obool)))], (21689 ^ _779203) ^ [_1161013, _1161015] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1161013)), c_Int_OBit0(_1161015)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1161013), _1161015)))], (35314 ^ _779203) ^ [_1437234] : [-(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)), _1437234), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (25228 ^ _779203) ^ [_1224005, _1224007, _1224009] : [class_Rings_Olinordered__semidom(_1224005), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224005), c_Groups_Oone__class_Oone(_1224005)), _1224007)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224005), c_Groups_Oone__class_Oone(_1224005)), hAPP(hAPP(c_Power_Opower__class_Opower(_1224005), _1224007), hAPP(c_Nat_OSuc, _1224009)))))], (22464 ^ _779203) ^ [_1175391, _1175393, _1175395] : [class_Divides_Osemiring__div(_1175391), -(_1175393 = c_Groups_Ozero__class_Ozero(_1175391)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1175391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175391), _1175395), _1175393)), _1175393) = _1175395)], (37533 ^ _779203) ^ [_1490064, _1490066, _1490068] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1490064, _1490066), _1490068), hAPP(c_COMBK(tc_fun(_1490066, tc_HOL_Obool), _1490064), c_Orderings_Obot__class_Obot(tc_fun(_1490066, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1490064, _1490066), tc_HOL_Obool)))], (38410 ^ _779203) ^ [_1520256, _1520258, _1520260] : [hAPP(c_Relation_ORange(_1520256, _1520258), _1520260) = c_Orderings_Obot__class_Obot(tc_fun(_1520258, tc_HOL_Obool)), -(_1520260 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1520256, _1520258), tc_HOL_Obool)))], (45869 ^ _779203) ^ [_1702428, _1702430] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702428), _1702430))), -(c_List_Oupt(_1702428, hAPP(c_Nat_OSuc, _1702430)) = c_List_Olist_ONil(tc_Nat_Onat))], (29376 ^ _779203) ^ [_1300122, _1300124] : [class_Lattices_Obounded__lattice__bot(_1300122), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1300122), _1300124), c_Orderings_Obot__class_Obot(_1300122)) = c_Orderings_Obot__class_Obot(_1300122))], (45618 ^ _779203) ^ [_1695450, _1695452, _1695454] : [-(c_Enum_On__lists(_1695450, hAPP(c_Nat_OSuc, _1695452), _1695454) = c_List_Oconcat(tc_List_Olist(_1695450), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695450), tc_List_Olist(tc_List_Olist(_1695450))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1695450), tc_List_Olist(_1695450), tc_List_Olist(tc_List_Olist(_1695450))), hAPP(hAPP(c_COMBB(tc_fun(_1695450, tc_List_Olist(_1695450)), tc_fun(tc_List_Olist(_1695450), tc_List_Olist(tc_List_Olist(_1695450))), tc_List_Olist(_1695450)), c_List_Omap(_1695450, tc_List_Olist(_1695450))), hAPP(c_COMBC(_1695450, tc_List_Olist(_1695450), tc_List_Olist(_1695450)), c_List_Olist_OCons(_1695450)))), _1695454)), c_Enum_On__lists(_1695450, _1695452, _1695454))))], (16530 ^ _779203) ^ [_1069836, _1069838, _1069840, _1069842] : [class_Orderings_Olinorder(_1069836), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069836), _1069838)), hBOOL(hAPP(hAPP(c_member(_1069836), _1069840), _1069838)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1069836), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1069836), _1069840), _1069842)), hAPP(hAPP(c_Finite__Set_Ofold(_1069836, _1069836, c_Orderings_Oord__class_Omax(_1069836)), _1069842), _1069838))))], (29760 ^ _779203) ^ [_1307782, _1307784, _1307786, _1307788] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307782, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307782, tc_HOL_Obool)), _1307784), _1307786)), _1307788) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307782, tc_HOL_Obool)), _1307784), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307782, tc_HOL_Obool)), _1307786), _1307788)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307782, tc_HOL_Obool)), _1307788), _1307784)))], (22422 ^ _779203) ^ [_1174763, _1174765] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1174763, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1174765)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1174763, _1174765) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (41483 ^ _779203) ^ [_1598731, _1598733] : [-(c_List_Olistrel1(_1598731, hAPP(c_Relation_Oconverse(_1598731, _1598731), _1598733)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1598731), tc_List_Olist(_1598731)), c_List_Olistrel1(_1598731, _1598733)))], (44809 ^ _779203) ^ [] : [-(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))))], (40996 ^ _779203) ^ [_1584443, _1584445, _1584447, _1584449, _1584451, _1584453] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584443, _1584443)), hAPP(hAPP(c_Product__Type_OPair(_1584443, _1584443), _1584445), _1584447)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584443, _1584443), tc_HOL_Obool), _1584449), _1584451))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584443, _1584443)), hAPP(hAPP(c_Product__Type_OPair(_1584443, _1584443), _1584447), _1584453)), _1584451)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584443, _1584443)), hAPP(hAPP(c_Product__Type_OPair(_1584443, _1584443), _1584445), _1584453)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1584443, _1584443), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1584449)), _1584451))))], (27670 ^ _779203) ^ [_1266872, _1266874, _1266876] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266872, tc_HOL_Obool)), _1266874), _1266876) = c_Orderings_Obot__class_Obot(tc_fun(_1266872, tc_HOL_Obool)), 27673 ^ _779203 : [(27676 ^ _779203) ^ [] : [-(_1266876 = c_Orderings_Obot__class_Obot(tc_fun(_1266872, tc_HOL_Obool)))], (27674 ^ _779203) ^ [] : [-(_1266874 = c_Orderings_Obot__class_Obot(tc_fun(_1266872, tc_HOL_Obool)))]]], (44456 ^ _779203) ^ [_1669498, _1669500, _1669502, _1669504, _1669506] : [-(hAPP(hAPP(c_List_Odrop(_1669498), _1669500), hAPP(hAPP(c_List_Omap(_1669502, _1669498), _1669504), _1669506)) = hAPP(hAPP(c_List_Omap(_1669502, _1669498), _1669504), hAPP(hAPP(c_List_Odrop(_1669502), _1669500), _1669506)))], (52329 ^ _779203) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (48282 ^ _779203) ^ [_1752852, _1752854] : [-(c_List_Oconcat(_1752852, c_List_Oreplicate(tc_List_Olist(_1752852), _1752854, c_List_Olist_ONil(_1752852))) = c_List_Olist_ONil(_1752852))], (11037 ^ _779203) ^ [_969450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _969450), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_969450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15990 ^ _779203) ^ [_1059854] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1059854), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38655 ^ _779203) ^ [_1527646, _1527648] : [c_Wellfounded_Owf(_1527646, _1527648), -(c_Wellfounded_Owf(tc_fun(_1527646, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1527646, _1527648)))], (37537 ^ _779203) ^ [_1490214, _1490216, _1490218] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1490214, _1490216), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1490214, _1490216), c_Orderings_Otop__class_Otop(tc_fun(_1490214, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1490216, tc_HOL_Obool), _1490214), _1490218))) = hAPP(hAPP(c_Product__Type_OSigma(_1490214, _1490216), c_Orderings_Otop__class_Otop(tc_fun(_1490214, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1490216, tc_HOL_Obool), _1490214), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1490216, tc_HOL_Obool)), _1490218))))], (39558 ^ _779203) ^ [_1549180, _1549182, _1549184, _1549186, _1549188, _1549190, _1549192, _1549194, _1549196, _1549198] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1549180, _1549182), tc_prod(_1549184, _1549186), tc_prod(_1549188, _1549190), c_Product__Type_Omap__pair(_1549180, _1549184, _1549182, _1549186, _1549192, _1549194)), c_Product__Type_Omap__pair(_1549188, _1549180, _1549190, _1549182, _1549196, _1549198)) = c_Product__Type_Omap__pair(_1549188, _1549184, _1549190, _1549186, hAPP(c_Fun_Ocomp(_1549180, _1549184, _1549188, _1549192), _1549196), hAPP(c_Fun_Ocomp(_1549182, _1549186, _1549190, _1549194), _1549198)))], (46166 ^ _779203) ^ [_1707715, _1707717, _1707719, _1707721] : [class_Orderings_Olinorder(_1707715), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707715), _1707717), _1707719)), c_List_Olinorder__class_Osorted(_1707715, hAPP(hAPP(c_List_Olist_OCons(_1707715), _1707719), _1707721)), -(c_List_Olinorder__class_Osorted(_1707715, hAPP(hAPP(c_List_Olist_OCons(_1707715), _1707717), hAPP(hAPP(c_List_Olist_OCons(_1707715), _1707719), _1707721))))], (1986 ^ _779203) ^ [_807816, _807818] : [_807818 = _807816, -(c_Com_Obody(_807818) = c_Com_Obody(_807816))], (34162 ^ _779203) ^ [_1406157, _1406159, _1406161, _1406163, _1406165, _1406167] : [hAPP(_1406163, hAPP(c_Product__Type_Ofst(_1406157, _1406161), _1406165)) = hAPP(_1406167, hAPP(c_Product__Type_Ofst(_1406157, _1406161), _1406165)), -(hAPP(c_Product__Type_Oapfst(_1406157, _1406159, _1406161, _1406163), _1406165) = hAPP(c_Product__Type_Oapfst(_1406157, _1406159, _1406161, _1406167), _1406165))], (29460 ^ _779203) ^ [_1301899, _1301901, _1301903, _1301905, _1301907] : [class_Lattices_Osemilattice__inf(_1301899), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301899), _1301901), _1301903)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301899), _1301905), _1301907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1301899), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1301899), _1301901), _1301905)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1301899), _1301903), _1301907))))], (34358 ^ _779203) ^ [_1411604, _1411606, _1411608, _1411610] : [34360 ^ _779203 : [(34363 ^ _779203) ^ [] : [hAPP(_1411610, 34359 ^ [_1411604, _1411606, _1411608, _1411610]) = c_Orderings_Obot__class_Obot(tc_fun(_1411604, tc_HOL_Obool))], (34361 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1411606), 34359 ^ [_1411604, _1411606, _1411608, _1411610]), _1411608)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_1411604, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411606, tc_fun(_1411604, tc_HOL_Obool)), _1411608), _1411610))], (50949 ^ _779203) ^ [_1810844, _1810846] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810844), _1810846)), -(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)))), _1810846, _1810844) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (24233 ^ _779203) ^ [_1206093, _1206095, _1206097, _1206099] : [class_Rings_Ocomm__semiring__1(_1206093), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1206093), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206093), _1206095), _1206097)), _1206099) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206093), hAPP(hAPP(c_Power_Opower__class_Opower(_1206093), _1206095), _1206099)), hAPP(hAPP(c_Power_Opower__class_Opower(_1206093), _1206097), _1206099)))], (47766 ^ _779203) ^ [_1741779, _1741781, _1741783] : [-(hBOOL(hAPP(hAPP(c_member(_1741779), _1741781), hAPP(c_List_Oset(_1741779), _1741783)))), 47767 ^ _779203 : [(47768 ^ _779203) ^ [_1741868, _1741870] : [_1741783 = hAPP(hAPP(c_List_Oappend(_1741779), _1741870), hAPP(hAPP(c_List_Olist_OCons(_1741779), _1741781), _1741868)), -(hBOOL(hAPP(hAPP(c_member(_1741779), _1741781), hAPP(c_List_Oset(_1741779), _1741868))))]]], (41585 ^ _779203) ^ [_1601960, _1601962, _1601964] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601960), tc_List_Olist(_1601960))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601960), tc_List_Olist(_1601960)), _1601962), _1601962)), c_List_Olistrel(_1601960, c_Transitive__Closure_Ortrancl(_1601960, _1601964)))))], (12591 ^ _779203) ^ [_996383, _996385, _996387] : [class_Groups_Oordered__comm__monoid__add(_996383), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_996383), _996385), c_Groups_Ozero__class_Ozero(_996383))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996383), _996387), c_Groups_Ozero__class_Ozero(_996383))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996383), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_996383), _996385), _996387)), c_Groups_Ozero__class_Ozero(_996383))))], (9480 ^ _779203) ^ [_940897, _940899, _940901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940899), _940901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940897), _940899)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940897), _940901))))], (39306 ^ _779203) ^ [_1543011, _1543013, _1543015, _1543017] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1543011, tc_fun(_1543013, tc_HOL_Obool)), _1543015), _1543017) = hAPP(c_Set_OCollect(_1543013), hAPP(hAPP(c_COMBB(tc_fun(_1543011, tc_HOL_Obool), tc_HOL_Obool, _1543013), c_HOL_OAll(_1543011)), hAPP(hAPP(c_COMBB(tc_fun(_1543011, tc_HOL_Obool), tc_fun(_1543011, tc_HOL_Obool), _1543013), hAPP(c_COMBS(_1543011, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543011), c_fimplies), hAPP(hAPP(c_COMBC(_1543011, tc_fun(_1543011, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543011)), _1543015)))), hAPP(hAPP(c_COMBC(_1543013, tc_fun(_1543011, tc_fun(_1543013, tc_HOL_Obool)), tc_fun(_1543011, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1543013, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1543011, tc_fun(_1543013, tc_HOL_Obool)), tc_fun(_1543011, tc_HOL_Obool)), _1543013), c_COMBB(tc_fun(_1543013, tc_HOL_Obool), tc_HOL_Obool, _1543011)), c_member(_1543013))), _1543017)))))], (31781 ^ _779203) ^ [_1350501, _1350503] : [hBOOL(hAPP(hAPP(c_member(_1350501), _1350503), c_Orderings_Obot__class_Obot(tc_fun(_1350501, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1350501, tc_HOL_Obool)), _1350503)))], (43576 ^ _779203) ^ [_1650572, _1650574, _1650576, _1650578] : [_1650572 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1650574), _1650572), hAPP(hAPP(c_List_Olist_OCons(_1650574), _1650576), _1650578)) = hAPP(hAPP(c_List_Olist_OCons(_1650574), _1650576), _1650578))], (19324 ^ _779203) ^ [_1119770, _1119772] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1119770), _1119772)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1119770) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (40332 ^ _779203) ^ [_1568204, _1568206] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568204, _1568204), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1568204, _1568206)), c_Relation_OId(_1568204)) = c_Transitive__Closure_Ortrancl(_1568204, _1568206))], (35529 ^ _779203) ^ [] : [-(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))))))], (46100 ^ _779203) ^ [_1706776, _1706778, _1706780] : [class_Orderings_Olinorder(_1706776), c_List_Olinorder__class_Osorted(_1706776, _1706778), -(c_List_Olinorder__class_Osorted(_1706776, hAPP(hAPP(c_List_Otake(_1706776), _1706780), _1706778)))], (28878 ^ _779203) ^ [_1290164, _1290166] : [-(hBOOL(hAPP(hAPP(c_member(_1290164), _1290166), c_Orderings_Otop__class_Otop(tc_fun(_1290164, tc_HOL_Obool)))))], (33715 ^ _779203) ^ [_1396522, _1396524] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396522, _1396524) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1396522, _1396524)))], (5634 ^ _779203) ^ [_865288, _865290, _865292, _865294, _865296, _865298] : [-(c_Set_Oimage(_865298, _865294, _865290) = c_Set_Oimage(_865296, _865292, _865288)), _865298 = _865296, _865294 = _865292, _865290 = _865288], (7889 ^ _779203) ^ [_908988, _908990, _908992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_908988, tc_HOL_Obool)), _908990), _908992)), 7892 ^ _779203 : [(7895 ^ _779203) ^ [] : [_908990 = _908992], (7893 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_908988, tc_HOL_Obool)), _908990), _908992)))]]], (17798 ^ _779203) ^ [_1093041, _1093043, _1093045] : [class_Orderings_Olinorder(_1093041), hBOOL(hAPP(c_Finite__Set_Ofinite(_1093041), _1093043)), -(hBOOL(hAPP(hAPP(c_member(_1093041), _1093045), _1093043))), -(c_Big__Operators_Olattice_OInf__fin(_1093041, c_Orderings_Oord__class_Omin(_1093041), hAPP(hAPP(c_Set_Oinsert(_1093041), _1093045), _1093043)) = hAPP(hAPP(c_Finite__Set_Ofold(_1093041, _1093041, c_Orderings_Oord__class_Omin(_1093041)), _1093045), _1093043))], (23916 ^ _779203) ^ [_1200183, _1200185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200183)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1200185)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1200183)), hAPP(c_Int_Onat, _1200185)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1200183), _1200185)))], (17372 ^ _779203) ^ [_1085518, _1085520, _1085522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1085518), _1085520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085522), _1085518)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085522), _1085520))))], (1600 ^ _779203) ^ [_802163, _802165] : [-(class_Groups_Oordered__comm__monoid__add(_802163)), _802165 = _802163, class_Groups_Oordered__comm__monoid__add(_802165)], (45825 ^ _779203) ^ [_1701233, _1701235, _1701237, _1701239, _1701241, _1701243] : [-(c_List_Ofoldr(_1701233, _1701235, _1701237, hAPP(hAPP(c_List_Oappend(_1701233), _1701239), _1701241), _1701243) = c_List_Ofoldr(_1701233, _1701235, _1701237, _1701239, c_List_Ofoldr(_1701233, _1701235, _1701237, _1701241, _1701243)))], (37904 ^ _779203) ^ [_1501499, _1501501] : [-(c_Fun_Oinj__on(tc_fun(_1501499, _1501501), tc_fun(tc_prod(_1501499, _1501501), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1501499, _1501501), tc_HOL_Obool), tc_fun(tc_prod(_1501499, _1501501), tc_HOL_Obool), tc_fun(_1501499, _1501501)), c_Set_OCollect(tc_prod(_1501499, _1501501))), hAPP(hAPP(c_COMBB(tc_fun(_1501499, tc_fun(_1501501, tc_HOL_Obool)), tc_fun(tc_prod(_1501499, _1501501), tc_HOL_Obool), tc_fun(_1501499, _1501501)), c_Product__Type_Oprod_Oprod__case(_1501499, _1501501, tc_HOL_Obool)), hAPP(c_COMBB(_1501501, tc_fun(_1501501, tc_HOL_Obool), _1501499), hAPP(c_COMBC(_1501501, _1501501, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1501499, _1501501), tc_HOL_Obool))))], (13141 ^ _779203) ^ [_1006549, _1006551] : [class_Orderings_Olinorder(_1006549), hBOOL(hAPP(c_Finite__Set_Ofinite(_1006549), _1006551)), -(_1006551 = c_Orderings_Obot__class_Obot(tc_fun(_1006549, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1006549), c_Big__Operators_Olinorder__class_OMin(_1006549, _1006551)), _1006551)))], (28690 ^ _779203) ^ [_1286628, _1286630, _1286632] : [class_Orderings_Oorder(_1286628), 28693 ^ _779203 : [(28700 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286628), _1286630), _1286632))), -(c_Orderings_Obot__class_Obot(tc_fun(_1286628, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1286628, _1286630, _1286632))], (28694 ^ _779203) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1286628, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1286628, _1286630, _1286632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286628), _1286630), _1286632))]]], (35201 ^ _779203) ^ [_1434902, _1434904, _1434906, _1434908, _1434910, _1434912, _1434914] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1434902, tc_fun(_1434904, tc_fun(_1434906, tc_HOL_Obool))), _1434908), _1434910), _1434912), _1434914))), 35202 ^ _779203 : [(35203 ^ _779203) ^ [_1434987] : [hBOOL(hAPP(hAPP(c_member(_1434902), _1434987), _1434908)), hBOOL(hAPP(hAPP(hAPP(_1434910, _1434987), _1434912), _1434914))]]], (9536 ^ _779203) ^ [_941988, _941990] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941988), _941990)), _941990) = _941988)], (24506 ^ _779203) ^ [_1210884, _1210886, _1210888] : [class_Rings_Olinordered__semidom(_1210884), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210884), hAPP(hAPP(c_Power_Opower__class_Opower(_1210884), _1210886), 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(_1210884), _1210888), 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(_1210884), c_Groups_Ozero__class_Ozero(_1210884)), _1210888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1210884), _1210886), _1210888)))], (37041 ^ _779203) ^ [_1477879, _1477881, _1477883] : [37043 ^ _779203 : [(37046 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1477879), 37042 ^ [_1477879, _1477881, _1477883]), c_Wellfounded_Oacc(_1477879, _1477883)))], (37044 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1477879, _1477879)), hAPP(hAPP(c_Product__Type_OPair(_1477879, _1477879), 37042 ^ [_1477879, _1477881, _1477883]), _1477881)), _1477883)))]], -(hBOOL(hAPP(hAPP(c_member(_1477879), _1477881), c_Wellfounded_Oacc(_1477879, _1477883))))], (52627 ^ _779203) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (42102 ^ _779203) ^ [_1617221, _1617223, _1617225, _1617227, _1617229, _1617231] : [-(hAPP(hAPP(c_List_Ozip(_1617221, _1617223), hAPP(hAPP(c_List_Olist_OCons(_1617221), _1617225), _1617227)), hAPP(hAPP(c_List_Olist_OCons(_1617223), _1617229), _1617231)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1617221, _1617223)), hAPP(hAPP(c_Product__Type_OPair(_1617221, _1617223), _1617225), _1617229)), hAPP(hAPP(c_List_Ozip(_1617221, _1617223), _1617227), _1617231)))], (21327 ^ _779203) ^ [_1155008] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1155008))) = 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)))), _1155008))], (3454 ^ _779203) ^ [_830748, _830750, _830752, _830754, _830756, _830758] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_830758, _830754, _830750) = c_SetInterval_Oord__class_OgreaterThanAtMost(_830756, _830752, _830748)), _830758 = _830756, _830754 = _830752, _830750 = _830748], (29752 ^ _779203) ^ [_1307574, _1307576, _1307578] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307574, tc_HOL_Obool)), _1307576), _1307578) = c_Orderings_Obot__class_Obot(tc_fun(_1307574, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307574, tc_HOL_Obool)), _1307576), _1307578) = _1307576)], (21653 ^ _779203) ^ [_1160347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160347), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1160347)), c_Int_OPls)))], (20917 ^ _779203) ^ [_1148144, _1148146] : [class_Rings_Olinordered__idom(_1148144), 20920 ^ _779203 : [(20927 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148144), c_Groups_Ozero__class_Ozero(_1148144)), _1148146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148144), c_Groups_Ozero__class_Ozero(_1148144)), c_Groups_Osgn__class_Osgn(_1148144, _1148146))))], (20921 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148144), c_Groups_Ozero__class_Ozero(_1148144)), c_Groups_Osgn__class_Osgn(_1148144, _1148146))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148144), c_Groups_Ozero__class_Ozero(_1148144)), _1148146)))]]], (21569 ^ _779203) ^ [_1158893, _1158895] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1158893)), _1158895) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1158893), _1158895)))], (45807 ^ _779203) ^ [_1700618, _1700620] : [-(c_Random_Oselect__weight(_1700618, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1700618), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1700618, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1700618, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1700618)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1700620)) = c_Random_Oselect__weight(_1700618, _1700620))], (12290 ^ _779203) ^ [_991158, _991160] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991158), _991160) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 12293 ^ _779203 : [(12296 ^ _779203) ^ [] : [-(_991160 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12294 ^ _779203) ^ [] : [-(_991158 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (44825 ^ _779203) ^ [_1677374] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1677374)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1677374))], (14883 ^ _779203) ^ [_1038940, _1038942, _1038944, _1038946, _1038948] : [class_Groups_Ocomm__monoid__mult(_1038940), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038942), _1038944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038942, tc_HOL_Obool)), _1038946), _1038944)), 14897 ^ _779203 : [(14900 ^ _779203) ^ [] : [hAPP(_1038948, 14896 ^ [_1038940, _1038942, _1038944, _1038946, _1038948]) = c_Groups_Oone__class_Oone(_1038940)], (14898 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1038942), 14896 ^ [_1038940, _1038942, _1038944, _1038946, _1038948]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1038942, tc_HOL_Obool)), _1038944), _1038946))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038942, _1038940), _1038948), _1038944) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038942, _1038940), _1038948), _1038946))], (24476 ^ _779203) ^ [_1210325, _1210327, _1210329] : [class_Groups_Omonoid__mult(_1210325), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1210325), _1210327), 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)))), _1210329)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1210325), hAPP(hAPP(c_Power_Opower__class_Opower(_1210325), _1210327), _1210329)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (33873 ^ _779203) ^ [_1399754, _1399756, _1399758, _1399760, _1399762, _1399764] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1399754, _1399756), _1399756, _1399758), hAPP(hAPP(c_COMBB(_1399760, tc_fun(_1399756, _1399758), tc_prod(_1399754, _1399756)), _1399762), hAPP(hAPP(c_COMBB(_1399754, _1399760, tc_prod(_1399754, _1399756)), _1399764), c_Product__Type_Ofst(_1399754, _1399756)))), c_Product__Type_Osnd(_1399754, _1399756)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1399754, _1399756, _1399758), hAPP(hAPP(c_COMBB(_1399760, tc_fun(_1399756, _1399758), _1399754), _1399762), _1399764)))], (18921 ^ _779203) ^ [_1112556, _1112558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1112556), _1112558)), -(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)), _1112556)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1112558))))], (51225 ^ _779203) ^ [_1815592, _1815594] : [-(_1815592 = _1815594), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815592), _1815594)), 51232 ^ _779203 : [(51235 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815594), _1815592))], (51233 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815592), _1815594)))]]], (11236 ^ _779203) ^ [_972618, _972620, _972622, _972624] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_972618, _972622)), c_Sum__Type_OPlus(_972618, _972622, _972620, _972624)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_972618), _972620)), hAPP(c_Finite__Set_Ocard(_972622), _972624))), hBOOL(hAPP(c_Finite__Set_Ofinite(_972618), _972620)), hBOOL(hAPP(c_Finite__Set_Ofinite(_972622), _972624))], (48705 ^ _779203) ^ [_1761999, _1762001, _1762003, _1762005] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1761999), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1762001, _1762003, _1761999, _1762005) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1762001, 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(_1762001)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1762003, _1762005)), 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(_1762001)))), 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(_1762001)))), 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(_1762001)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1762001, 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(_1762001)))), 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(_1762001)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1762001, _1762003, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1761999), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1762005))), 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(_1762001)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1762001))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1762001)))), 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(_1762001)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1762001, 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(_1762001)))), 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(_1762001)))), 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(_1762001))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1762001)))), 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(_1762001)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1762001)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1762001))))), tc_prod(_1762001, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1762001)), hAPP(hAPP(c_COMBB(_1762001, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1762001)))), tc_prod(_1762001, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1762001)), c_Product__Type_Ofst(_1762001, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (32033 ^ _779203) ^ [_1357121, _1357123, _1357125] : [-(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)), _1357121)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1357123), _1357125)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1357123), _1357121)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1357125), _1357121)))], (40364 ^ _779203) ^ [_1569032, _1569034, _1569036] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569032, _1569032), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569032, _1569032), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1569032, _1569034)), c_Transitive__Closure_Ortrancl(_1569032, _1569036))), c_Transitive__Closure_Ortrancl(_1569032, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569032, _1569032), tc_HOL_Obool)), _1569034), _1569036)))))], (15420 ^ _779203) ^ [_1049572, _1049574, _1049576, _1049578] : [class_Orderings_Olinorder(_1049572), 15423 ^ _779203 : [(15424 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049572), _1049574), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1049572), _1049576), _1049578))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049572), _1049574), _1049576))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049572), _1049574), _1049578)))], (15434 ^ _779203) ^ [] : [15435 ^ _779203 : [(15438 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049572), _1049574), _1049578))], (15436 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049572), _1049574), _1049576))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049572), _1049574), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1049572), _1049576), _1049578))))]]], (23695 ^ _779203) ^ [_1196331, _1196333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1196331), _1196333)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1196331, _1196333) = _1196331)], (49672 ^ _779203) ^ [_1783036, _1783038, _1783040, _1783042, _1783044] : [hBOOL(hAPP(hAPP(c_member(_1783036), _1783038), hAPP(c_Set_Oimage(_1783040, _1783036, _1783042), _1783044))), -(hAPP(_1783042, hAPP(c_Hilbert__Choice_Oinv__into(_1783040, _1783036, _1783044, _1783042), _1783038)) = _1783038)], (8579 ^ _779203) ^ [_923767, _923769] : [class_Groups_Oone(_923767), 8582 ^ _779203 : [(8589 ^ _779203) ^ [] : [_923769 = c_Groups_Oone__class_Oone(_923767), -(c_Groups_Oone__class_Oone(_923767) = _923769)], (8583 ^ _779203) ^ [] : [c_Groups_Oone__class_Oone(_923767) = _923769, -(_923769 = c_Groups_Oone__class_Oone(_923767))]]], (45748 ^ _779203) ^ [_1698559, _1698561, _1698563, _1698565] : [-(c_List_Otranspose(_1698559, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698561), tc_List_Olist(_1698559)), hAPP(c_List_Omap(_1698561, _1698559), _1698563)), _1698565)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698561), tc_List_Olist(_1698559)), hAPP(c_List_Omap(_1698561, _1698559), _1698563)), c_List_Otranspose(_1698561, _1698565)))], (4270 ^ _779203) ^ [_843856, _843858, _843860, _843862, _843864, _843866, _843868, _843870] : [-(c_Lazy__Sequence_Oproduct(_843870, _843866, _843862, _843858) = c_Lazy__Sequence_Oproduct(_843868, _843864, _843860, _843856)), _843870 = _843868, _843866 = _843864, _843862 = _843860, _843858 = _843856], (4012 ^ _779203) ^ [_839859, _839861, _839863, _839865, _839867, _839869, _839871, _839873] : [-(c_New__DSequence_Opos__bind(_839873, _839869, _839865, _839861) = c_New__DSequence_Opos__bind(_839871, _839867, _839863, _839859)), _839873 = _839871, _839869 = _839867, _839865 = _839863, _839861 = _839859], (21565 ^ _779203) ^ [_1158819] : [-(c_Int_OBit0(_1158819) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1158819), _1158819))], (25608 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (31901 ^ _779203) ^ [_1353320, _1353322, _1353324, _1353326] : [class_Groups_Oordered__ab__group__add__abs(_1353320), -(hAPP(c_Groups_Oabs__class_Oabs(_1353320), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353322, _1353320), hAPP(hAPP(c_COMBB(_1353320, _1353320, _1353322), c_Groups_Oabs__class_Oabs(_1353320)), _1353324)), _1353326)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353322, _1353320), hAPP(hAPP(c_COMBB(_1353320, _1353320, _1353322), c_Groups_Oabs__class_Oabs(_1353320)), _1353324)), _1353326))], (46702 ^ _779203) ^ [_1718448, _1718450] : [-(_1718448 = c_List_Olist_ONil(_1718450)), -(c_List_Olast(_1718450, hAPP(c_List_Orev(_1718450), _1718448)) = hAPP(c_List_Ohd(_1718450), _1718448))], (33375 ^ _779203) ^ [_1390062, _1390064, _1390066, _1390068] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1390062, _1390064), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1390066), _1390068))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1390062), _1390064) = _1390066)], (50941 ^ _779203) ^ [_1810696, _1810698] : [50942 ^ _779203 : [(50945 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810698), _1810696))], (50943 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810696), _1810698)))]], -(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)))), _1810696, _1810698) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (32181 ^ _779203) ^ [_1360879, _1360881, _1360883] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1360879), _1360881), _1360883) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1360879), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1360879, tc_Int_Oint), _1360881), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1360883))), class_Groups_Ocomm__monoid__add(_1360879), class_Groups_Ocomm__monoid__mult(_1360879)], (27830 ^ _779203) ^ [_1269922, _1269924, _1269926] : [class_Orderings_Otop(_1269922), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1269924, _1269922)), _1269926) = c_Orderings_Otop__class_Otop(_1269922))], (6723 ^ _779203) ^ [_888114, _888116, _888118, _888120, _888122, _888124, _888126, _888128] : [c_Finite__Set_Ofolding__image__simple__idem(_888114, _888116, _888118, _888120, _888122, _888124), hBOOL(hAPP(c_Finite__Set_Ofinite(_888116), _888126)), -(hAPP(_888124, hAPP(hAPP(c_Set_Oinsert(_888116), _888128), _888126)) = hAPP(hAPP(_888118, hAPP(_888122, _888128)), hAPP(_888124, _888126)))], (39914 ^ _779203) ^ [_1557364, _1557366, _1557368, _1557370, _1557372] : [c_Finite__Set_Ofolding__idem(_1557364, _1557366, _1557368, _1557370), -(hAPP(c_Fun_Ocomp(_1557366, _1557366, _1557366, hAPP(_1557368, _1557372)), hAPP(_1557368, _1557372)) = hAPP(_1557368, _1557372))], (46025 ^ _779203) ^ [_1705276, _1705278, _1705280] : [46026 ^ _779203 : [(46029 ^ _779203) ^ [] : [_1705280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (46027 ^ _779203) ^ [] : [-(_1705276 = c_List_Olist_ONil(tc_List_Olist(_1705278)))]], 46033 ^ _779203 : [(46036 ^ _779203) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705278)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1705278)), _1705276), 46032 ^ [_1705276, _1705278, _1705280])) = _1705280], (46034 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46032 ^ [_1705276, _1705278, _1705280]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705278))), _1705276))))]], -(c_List_Otranspose(_1705278, _1705276) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1705278)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1705278)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1705278), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1705278)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1705278)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1705278), hAPP(hAPP(c_COMBB(tc_List_Olist(_1705278), tc_fun(tc_Nat_Onat, _1705278), tc_Nat_Onat), c_List_Onth(_1705278)), hAPP(c_List_Onth(tc_List_Olist(_1705278)), _1705276))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1705278))), _1705276)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1705280)))], (31498 ^ _779203) ^ [_1344162, _1344164, _1344166] : [class_Complete__Lattice_Ocomplete__lattice(_1344162), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344162), _1344164)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1344162), _1344166), c_Complete__Lattice_OInf__class_OInf(_1344162, _1344164)) = hAPP(hAPP(c_Finite__Set_Ofold(_1344162, _1344162, c_Lattices_Osemilattice__inf__class_Oinf(_1344162)), _1344166), _1344164))], (10123 ^ _779203) ^ [_952646, _952648, _952650, _952652, _952654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952646), _952648)), 10126 ^ _779203 : [(10133 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952652), 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), _952648), _952646)), _952650)), _952654))), -(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), _952646), _952650)), _952652)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952648), _952650)), _952654))))], (10127 ^ _779203) ^ [] : [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), _952646), _952650)), _952652)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952648), _952650)), _952654))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952652), 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), _952648), _952646)), _952650)), _952654))))]]], (6961 ^ _779203) ^ [_893284, _893286, _893288, _893290] : [hBOOL(hAPP(hAPP(c_member(_893284), _893286), _893288)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893284, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_893284), _893286), _893290)), _893288) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893284, tc_HOL_Obool)), _893290), _893288))], (794 ^ _779203) ^ [_791098, _791100, _791102, _791104, _791106, _791108] : [-(c_Equiv__Relations_Oequiv(_791106, _791102, _791098)), c_Equiv__Relations_Oequiv(_791108, _791104, _791100), _791108 = _791106, _791104 = _791102, _791100 = _791098], (40107 ^ _779203) ^ [_1562166, _1562168] : [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), _1562166), _1562168)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1562166), _1562168)))], (41955 ^ _779203) ^ [_1612248, _1612250, _1612252] : [-(c_List_Osublist(_1612248, _1612250, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1612252)) = hAPP(hAPP(c_List_Otake(_1612248), _1612252), _1612250))], (24303 ^ _779203) ^ [_1207558, _1207560, _1207562] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1207558), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1207560), _1207562)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1207558), _1207560)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1207558), _1207562)))], (36676 ^ _779203) ^ [_1469721, _1469723, _1469725, _1469727, _1469729] : [-(c_Fun_Oinj__on(_1469721, _1469723, _1469725, hAPP(hAPP(c_Set_Oinsert(_1469721), _1469727), _1469729))), c_Fun_Oinj__on(_1469721, _1469723, _1469725, _1469729), -(hBOOL(hAPP(hAPP(c_member(_1469723), hAPP(_1469725, _1469727)), hAPP(c_Set_Oimage(_1469721, _1469723, _1469725), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469721, tc_HOL_Obool)), _1469729), hAPP(hAPP(c_Set_Oinsert(_1469721), _1469727), c_Orderings_Obot__class_Obot(tc_fun(_1469721, tc_HOL_Obool))))))))], (40524 ^ _779203) ^ [_1572925, _1572927, _1572929, _1572931] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572925, _1572925)), hAPP(hAPP(c_Product__Type_OPair(_1572925, _1572925), _1572927), _1572929)), c_Transitive__Closure_Ortrancl(_1572925, _1572931)))), 40525 ^ _779203 : [(40528 ^ _779203) ^ [] : [-(_1572927 = _1572929), hBOOL(hAPP(hAPP(c_member(tc_prod(_1572925, _1572925)), hAPP(hAPP(c_Product__Type_OPair(_1572925, _1572925), _1572927), _1572929)), c_Transitive__Closure_Otrancl(_1572925, _1572931)))], (40526 ^ _779203) ^ [] : [_1572927 = _1572929]]], (11129 ^ _779203) ^ [_970787, _970789] : [11130 ^ _779203 : [(11133 ^ _779203) ^ [] : [_970789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11131 ^ _779203) ^ [] : [_970787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970787), _970789) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48032 ^ _779203) ^ [_1747110, _1747112, _1747114, _1747116, _1747118] : [-(hAPP(c_New__DSequence_Oneg__bind(_1747110, _1747112, _1747114, _1747116), _1747118) = c_Lazy__Sequence_Ohb__bind(_1747110, _1747112, hAPP(_1747114, _1747118), hAPP(hAPP(c_COMBC(_1747110, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1747112))), _1747116), _1747118)))], (3418 ^ _779203) ^ [_830208, _830210, _830212, _830214] : [-(c_Random_Opick(_830214, _830210) = c_Random_Opick(_830212, _830208)), _830214 = _830212, _830210 = _830208], (31145 ^ _779203) ^ [_1336748, _1336750, _1336752] : [class_Lattices_Olattice(_1336748), hAPP(_1336750, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1336748), 31150 ^ [_1336748, _1336750, _1336752]), 31151 ^ [_1336748, _1336750, _1336752])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1336748), hAPP(_1336750, 31150 ^ [_1336748, _1336750, _1336752])), hAPP(_1336750, 31151 ^ [_1336748, _1336750, _1336752])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336748), _1336752)), -(_1336752 = c_Orderings_Obot__class_Obot(tc_fun(_1336748, tc_HOL_Obool))), -(hAPP(_1336750, c_Big__Operators_Olattice__class_OInf__fin(_1336748, _1336752)) = c_Big__Operators_Olattice__class_OInf__fin(_1336748, hAPP(c_Set_Oimage(_1336748, _1336748, _1336750), _1336752)))], (44678 ^ _779203) ^ [_1674296, _1674298, _1674300] : [-(hAPP(hAPP(c_List_Ozip(_1674296, _1674298), hAPP(hAPP(c_List_Omap(tc_prod(_1674296, _1674298), _1674296), c_Product__Type_Ofst(_1674296, _1674298)), _1674300)), hAPP(hAPP(c_List_Omap(tc_prod(_1674296, _1674298), _1674298), c_Product__Type_Osnd(_1674296, _1674298)), _1674300)) = _1674300)], (40432 ^ _779203) ^ [_1570739, _1570741] : [-(c_Transitive__Closure_Ortrancl(_1570739, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1570739, _1570739), tc_HOL_Obool)), _1570741), c_Relation_OId(_1570739))) = c_Transitive__Closure_Ortrancl(_1570739, _1570741))], (45047 ^ _779203) ^ [_1682738, _1682740, _1682742, _1682744, _1682746, _1682748, _1682750] : [c_List_Olist__all2(_1682744, _1682740, hAPP(hAPP(c_COMBB(_1682738, tc_fun(_1682740, tc_HOL_Obool), _1682744), _1682742), _1682746), _1682748, _1682750), -(c_List_Olist__all2(_1682738, _1682740, _1682742, hAPP(hAPP(c_List_Omap(_1682744, _1682738), _1682746), _1682748), _1682750))], (43295 ^ _779203) ^ [_1643240, _1643242, _1643244] : [-(c_List_Obutlast(_1643240, hAPP(hAPP(c_List_Oappend(_1643240), _1643242), hAPP(hAPP(c_List_Olist_OCons(_1643240), _1643244), c_List_Olist_ONil(_1643240)))) = _1643242)], (49152 ^ _779203) ^ [_1773009, _1773011] : [-(c_Relation_Oantisym(_1773009, c_Relation_OId__on(_1773009, _1773011)))], (6031 ^ _779203) ^ [_875047, _875049, _875051, _875053, _875055] : [hBOOL(hAPP(hAPP(c_member(_875047), _875049), hAPP(c_Set_Oimage(_875051, _875047, _875053), _875055))), 6035 ^ _779203 : [(6038 ^ _779203) ^ [] : [-(_875049 = hAPP(_875053, 6034 ^ [_875047, _875049, _875051, _875053, _875055]))], (6036 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_875051), 6034 ^ [_875047, _875049, _875051, _875053, _875055]), _875055)))]]], (9207 ^ _779203) ^ [_936311, _936313, _936315] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936311), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936313), _936315)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936311), _936313)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936311), _936315)))], (39393 ^ _779203) ^ [_1545498, _1545500, _1545502, _1545504, _1545506, _1545508] : [-(hAPP(c_Set_Ovimage(_1545498, tc_prod(_1545500, _1545502), _1545504), hAPP(hAPP(c_Product__Type_OSigma(_1545500, _1545502), _1545506), hAPP(c_COMBK(tc_fun(_1545502, tc_HOL_Obool), _1545500), _1545508))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545498, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1545498, _1545500, hAPP(c_Fun_Ocomp(tc_prod(_1545500, _1545502), _1545500, _1545498, c_Product__Type_Ofst(_1545500, _1545502)), _1545504)), _1545506)), hAPP(c_Set_Ovimage(_1545498, _1545502, hAPP(c_Fun_Ocomp(tc_prod(_1545500, _1545502), _1545502, _1545498, c_Product__Type_Osnd(_1545500, _1545502)), _1545504)), _1545508)))], (43476 ^ _779203) ^ [_1648241, _1648243] : [hBOOL(hAPP(c_List_Odistinct(_1648241), _1648243)), -(hBOOL(hAPP(c_List_Odistinct(_1648241), hAPP(c_List_Orotate1(_1648241), _1648243))))], (312 ^ _779203) ^ [_783929, _783931, _783933, _783935] : [-(c_FunDef_Oreduction__pair(_783933, _783929)), c_FunDef_Oreduction__pair(_783935, _783931), _783935 = _783933, _783931 = _783929], (25060 ^ _779203) ^ [_1220875, _1220877] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1220875), c_Groups_Ozero__class_Ozero(_1220875)), hAPP(c_Nat_OSuc, _1220877)) = c_Groups_Ozero__class_Ozero(_1220875)), class_Power_Opower(_1220875), class_Rings_Osemiring__0(_1220875)], (32241 ^ _779203) ^ [_1362439, _1362441] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362439), _1362441)), -(hAPP(c_Finite__Set_Ocard(_1362439), _1362441) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1362439, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1362439), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1362441))], (29766 ^ _779203) ^ [_1307967, _1307969, _1307971, _1307973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307967, tc_HOL_Obool)), _1307973), _1307969)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307967, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307967, tc_HOL_Obool)), _1307969), _1307971)), _1307973) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307967, tc_HOL_Obool)), _1307969), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307967, tc_HOL_Obool)), _1307971), _1307973)))], (1650 ^ _779203) ^ [_802788, _802790] : [-(class_Rings_Olinordered__semiring(_802788)), _802790 = _802788, class_Rings_Olinordered__semiring(_802790)], (26158 ^ _779203) ^ [_1239255, _1239257, _1239259] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1239255, tc_HOL_Obool)), _1239257), hAPP(c_Set_OPow(_1239255), _1239259))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239255, tc_HOL_Obool)), _1239257), _1239259)))], (46492 ^ _779203) ^ [_1713820, _1713822, _1713824, _1713826, _1713828] : [class_Orderings_Olinorder(_1713820), c_Fun_Oinj__on(_1713822, _1713820, _1713824, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1713822, tc_HOL_Obool)), hAPP(c_List_Oset(_1713822), _1713826)), hAPP(c_List_Oset(_1713822), _1713828))), c_List_Olinorder__class_Osorted(_1713820, hAPP(hAPP(c_List_Omap(_1713822, _1713820), _1713824), _1713826)), hBOOL(hAPP(c_List_Odistinct(_1713820), hAPP(hAPP(c_List_Omap(_1713822, _1713820), _1713824), _1713826))), c_List_Olinorder__class_Osorted(_1713820, hAPP(hAPP(c_List_Omap(_1713822, _1713820), _1713824), _1713828)), hBOOL(hAPP(c_List_Odistinct(_1713820), hAPP(hAPP(c_List_Omap(_1713822, _1713820), _1713824), _1713828))), hAPP(c_List_Oset(_1713822), _1713826) = hAPP(c_List_Oset(_1713822), _1713828), -(_1713826 = _1713828)], (24255 ^ _779203) ^ [_1206584, _1206586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206584)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1206584), _1206586)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1206584)), _1206586))], (50359 ^ _779203) ^ [_1797515, _1797517, _1797519] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1797515, _1797515)), hAPP(hAPP(c_Product__Type_OPair(_1797515, _1797515), hAPP(_1797517, hAPP(c_Nat_OSuc, 50360 ^ [_1797515, _1797517, _1797519]))), hAPP(_1797517, 50360 ^ [_1797515, _1797517, _1797519]))), c_Transitive__Closure_Ortrancl(_1797515, _1797519))), c_Wellfounded_Owf(_1797515, c_Transitive__Closure_Otrancl(_1797515, _1797519)), 50368 ^ _779203 : [(50369 ^ _779203) ^ [_1797781] : [-(hAPP(_1797517, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 50367 ^ [_1797515, _1797517, _1797519]), _1797781)) = hAPP(_1797517, 50367 ^ [_1797515, _1797517, _1797519]))]]], (1410 ^ _779203) ^ [_799788, _799790] : [-(class_Lattices_Obounded__lattice__top(_799788)), _799790 = _799788, class_Lattices_Obounded__lattice__top(_799790)], (23766 ^ _779203) ^ [_1197502, _1197504] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197502), _1197504))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197502, _1197504) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1197502), _1197504), _1197504))], (24724 ^ _779203) ^ [_1214782, _1214784, _1214786] : [class_Rings_Olinordered__idom(_1214782), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214782), c_Groups_Ozero__class_Ozero(_1214782)), hAPP(hAPP(c_Power_Opower__class_Opower(_1214782), _1214784), 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)))), _1214786)))))], (9047 ^ _779203) ^ [_932528, _932530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _932528), _932530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _932528)), hAPP(c_Nat_OSuc, _932530))))], (35687 ^ _779203) ^ [_1447981, _1447983, _1447985] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1447981), hAPP(hAPP(c_Set_Oinsert(_1447981), _1447983), c_Orderings_Obot__class_Obot(tc_fun(_1447981, tc_HOL_Obool)))), _1447985) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1447981, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1447981, _1447981, _1447985), hAPP(hAPP(c_Set_Oinsert(_1447981), _1447983), c_Orderings_Obot__class_Obot(tc_fun(_1447981, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1447981, tc_HOL_Obool), tc_HOL_Obool))))], (44911 ^ _779203) ^ [_1679626, _1679628, _1679630] : [hBOOL(hAPP(c_List_Olistsp(_1679626, _1679628), _1679630)), 44914 ^ _779203 : [(44915 ^ _779203) ^ [_1679715] : [hBOOL(hAPP(hAPP(c_member(_1679626), _1679715), hAPP(c_List_Oset(_1679626), _1679630))), -(hBOOL(hAPP(_1679628, _1679715)))]]], (46899 ^ _779203) ^ [_1722469, _1722471, _1722473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722469)), c_List_OtakeWhile(_1722469, _1722471, _1722473))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722469)), _1722473))), hBOOL(hAPP(_1722471, hAPP(hAPP(c_List_Onth(_1722469), _1722473), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722469)), c_List_OtakeWhile(_1722469, _1722471, _1722473)))))], (10899 ^ _779203) ^ [_967442, _967444] : [class_Rings_Ocomm__semiring__1(_967442), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967442), c_Groups_Ozero__class_Ozero(_967442)), _967444) = c_Groups_Ozero__class_Ozero(_967442))], (22105 ^ _779203) ^ [_1169408, _1169410, _1169412, _1169414] : [class_Divides_Oring__div(_1169408), c_Divides_Odiv__class_Omod(_1169408, _1169410, _1169412) = c_Divides_Odiv__class_Omod(_1169408, _1169414, _1169412), -(c_Divides_Odiv__class_Omod(_1169408, hAPP(c_Groups_Ouminus__class_Ouminus(_1169408), _1169410), _1169412) = c_Divides_Odiv__class_Omod(_1169408, hAPP(c_Groups_Ouminus__class_Ouminus(_1169408), _1169414), _1169412))], (22818 ^ _779203) ^ [_1181251, _1181253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1181251)), hAPP(c_Int_Onat, _1181253))), 22821 ^ _779203 : [(22824 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181251), _1181253)))], (22822 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181253)))]]], (13695 ^ _779203) ^ [_1017025, _1017027] : [class_Rings_Odivision__ring__inverse__zero(_1017025), 13698 ^ _779203 : [(13705 ^ _779203) ^ [] : [-(_1017027 = c_Groups_Ozero__class_Ozero(_1017025)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017025), _1017027), _1017027) = c_Groups_Oone__class_Oone(_1017025))], (13699 ^ _779203) ^ [] : [_1017027 = c_Groups_Ozero__class_Ozero(_1017025), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017025), _1017027), _1017027) = c_Groups_Ozero__class_Ozero(_1017025))]]], (27392 ^ _779203) ^ [_1261846, _1261848, _1261850] : [class_Lattices_Olattice(_1261846), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1261846), _1261848), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1261846), _1261848), _1261850))))], (22131 ^ _779203) ^ [_1169868, _1169870] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1169868)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1169870)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1169868), _1169870))], (36662 ^ _779203) ^ [_1469303, _1469305, _1469307, _1469309] : [c_Fun_Oinj__on(_1469303, _1469305, _1469307, c_Orderings_Otop__class_Otop(tc_fun(_1469303, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1469305, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469303, _1469305, _1469307), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1469303, tc_HOL_Obool)), _1469309))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1469305, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469303, _1469305, _1469307), _1469309)))))], (46160 ^ _779203) ^ [_1707638] : [class_Orderings_Olinorder(_1707638), -(c_List_Olinorder__class_Osorted(_1707638, c_List_Olist_ONil(_1707638)))], (47234 ^ _779203) ^ [_1729745, _1729747, _1729749, _1729751, _1729753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1729745, _1729747)), hAPP(_1729745, _1729749))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1729751, _1729751)), hAPP(hAPP(c_Product__Type_OPair(_1729751, _1729751), _1729747), _1729749)), c_List_Omeasures(_1729751, _1729753))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729751, _1729751)), hAPP(hAPP(c_Product__Type_OPair(_1729751, _1729751), _1729747), _1729749)), c_List_Omeasures(_1729751, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1729751, tc_Nat_Onat)), _1729745), _1729753)))))], (43482 ^ _779203) ^ [_1648346, _1648348, _1648350] : [hBOOL(hAPP(c_List_Odistinct(_1648346), _1648348)), -(hBOOL(hAPP(c_List_Odistinct(_1648346), hAPP(hAPP(c_List_Odrop(_1648346), _1648350), _1648348))))], (34923 ^ _779203) ^ [_1427635, _1427637, _1427639, _1427641, _1427643] : [_1427635 = c_Orderings_Obot__class_Obot(tc_fun(_1427637, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427639, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427637, tc_fun(_1427639, tc_HOL_Obool)), _1427635), _1427641)), _1427643) = _1427643)], (45685 ^ _779203) ^ [_1697180, _1697182, _1697184] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1697180), tc_List_Olist(_1697180)), c_List_Opartition(_1697180, _1697182, _1697184)) = hAPP(c_List_Ofilter(_1697180, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1697180, c_fNot), _1697182)), _1697184))], (23050 ^ _779203) ^ [_1184983, _1184985] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184983)), 23053 ^ _779203 : [(23060 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184983), _1184985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1184983)), hAPP(c_Int_Onat, _1184985))))], (23054 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1184983)), hAPP(c_Int_Onat, _1184985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1184983), _1184985)))]]], (21687 ^ _779203) ^ [_1160980] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1160980)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1160980)))], (42220 ^ _779203) ^ [_1620118, _1620120] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1620118), _1620120) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1620118, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1620120), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (52669 ^ _779203) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (20220 ^ _779203) ^ [_1135899, _1135901] : [class_Groups_Oordered__ab__group__add(_1135899), 20223 ^ _779203 : [(20230 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135899), c_Groups_Ozero__class_Ozero(_1135899)), _1135901)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135899), hAPP(c_Groups_Ouminus__class_Ouminus(_1135899), _1135901)), c_Groups_Ozero__class_Ozero(_1135899))))], (20224 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135899), hAPP(c_Groups_Ouminus__class_Ouminus(_1135899), _1135901)), c_Groups_Ozero__class_Ozero(_1135899))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1135899), c_Groups_Ozero__class_Ozero(_1135899)), _1135901)))]]], (30103 ^ _779203) ^ [_1315478, _1315480, _1315482, _1315484, _1315486] : [class_Groups_Ocomm__monoid__mult(_1315478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315480), _1315482)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315480), _1315484)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315478), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315480, _1315478), _1315486), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315480, tc_HOL_Obool)), _1315482), _1315484))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315480, _1315478), _1315486), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315480, tc_HOL_Obool)), _1315482), _1315484))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315478), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315480, _1315478), _1315486), _1315482)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315480, _1315478), _1315486), _1315484)))], (45849 ^ _779203) ^ [_1701785, _1701787, _1701789] : [-(c_List_Osublist(_1701785, _1701787, _1701789) = hAPP(hAPP(c_List_Omap(tc_prod(_1701785, tc_Nat_Onat), _1701785), c_Product__Type_Ofst(_1701785, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701785, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701785, 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(_1701785, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1701785, tc_Nat_Onat))), _1701789)), hAPP(hAPP(c_List_Ozip(_1701785, tc_Nat_Onat), _1701787), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701785)), _1701787))))))], (13355 ^ _779203) ^ [_1010564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1010564)), -(_1010564 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1010564), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (15324 ^ _779203) ^ [_1047708, _1047710, _1047712] : [class_Orderings_Olinorder(_1047708), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047708), _1047710), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047708), _1047710), _1047712)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047708), _1047710), _1047712))], (40540 ^ _779203) ^ [_1573263] : [-(c_Relation_Orefl__on(_1573263, c_Orderings_Otop__class_Otop(tc_fun(_1573263, tc_HOL_Obool)), c_Relation_OId(_1573263)))], (17304 ^ _779203) ^ [_1084345, _1084347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1084345), _1084347)), 17307 ^ _779203 : [(17310 ^ _779203) ^ [] : [_1084345 = _1084347], (17308 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084345), _1084347)))]]], (4802 ^ _779203) ^ [_852334, _852336] : [_852336 = _852334, -(c_Relation_OId(_852336) = c_Relation_OId(_852334))], (48646 ^ _779203) ^ [_1760917, _1760919] : [-(c_Lazy__Sequence_Oappend(_1760917, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760917), _1760919) = _1760919)], (37357 ^ _779203) ^ [_1485842, _1485844] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1485842)), 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)), _1485842))), 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, _1485844))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1190 ^ _779203) ^ [_797038, _797040] : [-(class_Rings_Oring__no__zero__divisors(_797038)), _797040 = _797038, class_Rings_Oring__no__zero__divisors(_797040)], (38444 ^ _779203) ^ [_1521143, _1521145, _1521147, _1521149] : [hBOOL(hAPP(hAPP(c_member(_1521143), _1521145), hAPP(c_Relation_ORange(_1521147, _1521143), _1521149))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1521147, _1521143)), hAPP(hAPP(c_Product__Type_OPair(_1521147, _1521143), 38447 ^ [_1521143, _1521145, _1521147, _1521149]), _1521145)), _1521149)))], (37491 ^ _779203) ^ [_1488965, _1488967, _1488969] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1488965), hAPP(c_Set_OCollect(_1488965), hAPP(hAPP(c_COMBS(_1488965, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1488965), c_fdisj), _1488967)), _1488969))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488965), hAPP(c_Set_OCollect(_1488965), _1488967))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1488965), hAPP(c_Set_OCollect(_1488965), _1488969)))], (24083 ^ _779203) ^ [_1203362] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203362), _1203362)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1203362)], (25136 ^ _779203) ^ [_1222305, _1222307, _1222309] : [class_Rings_Olinordered__idom(_1222305), -(hAPP(c_Groups_Oabs__class_Oabs(_1222305), hAPP(hAPP(c_Power_Opower__class_Opower(_1222305), hAPP(c_Groups_Ouminus__class_Ouminus(_1222305), _1222307)), _1222309)) = hAPP(c_Groups_Oabs__class_Oabs(_1222305), hAPP(hAPP(c_Power_Opower__class_Opower(_1222305), _1222307), _1222309)))], (18530 ^ _779203) ^ [_1106026] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106026), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106026), c_Int_OPls)))], (47718 ^ _779203) ^ [_1740691, _1740693, _1740695, _1740697] : [c_List_Olist__ex(_1740691, _1740693, hAPP(hAPP(c_List_Olist_OCons(_1740691), _1740695), _1740697)), -(hBOOL(hAPP(_1740693, _1740695))), -(c_List_Olist__ex(_1740691, _1740693, _1740697))], (44702 ^ _779203) ^ [_1674876, _1674878, _1674880, _1674882, _1674884] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674876)), _1674878) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674880)), _1674882), 44705 ^ _779203 : [(44714 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1674876, _1674880), _1674878), _1674882) = _1674884), hAPP(hAPP(c_List_Omap(tc_prod(_1674876, _1674880), _1674876), c_Product__Type_Ofst(_1674876, _1674880)), _1674884) = _1674878, hAPP(hAPP(c_List_Omap(tc_prod(_1674876, _1674880), _1674880), c_Product__Type_Osnd(_1674876, _1674880)), _1674884) = _1674882], (44706 ^ _779203) ^ [] : [hAPP(hAPP(c_List_Ozip(_1674876, _1674880), _1674878), _1674882) = _1674884, 44709 ^ _779203 : [(44712 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674876, _1674880), _1674880), c_Product__Type_Osnd(_1674876, _1674880)), _1674884) = _1674882)], (44710 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1674876, _1674880), _1674876), c_Product__Type_Ofst(_1674876, _1674880)), _1674884) = _1674878)]]]]], (29176 ^ _779203) ^ [_1295782, _1295784, _1295786, _1295788] : [class_Lattices_Odistrib__lattice(_1295782), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295782), _1295784), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1295782), _1295786), _1295788)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1295782), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295782), _1295784), _1295786)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1295782), _1295784), _1295788)))], (43820 ^ _779203) ^ [_1655828, _1655830] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655828)), hAPP(c_List_Otl(_1655828), _1655830)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655828)), _1655830)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (5669 ^ _779203) ^ [_868650, _868652, _868654] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_868650), _868652)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_868650), hAPP(hAPP(c_Set_Oinsert(_868650), _868654), _868652))))], (28122 ^ _779203) ^ [_1276044, _1276046, _1276048, _1276050, _1276052] : [_1276044 = hAPP(_1276046, _1276048), -(hBOOL(hAPP(hAPP(c_member(_1276050), _1276044), hAPP(c_Set_Oimage(_1276052, _1276050, _1276046), c_Orderings_Otop__class_Otop(tc_fun(_1276052, tc_HOL_Obool))))))], (33777 ^ _779203) ^ [_1397701, _1397703, _1397705] : [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), _1397701), _1397703))), -(hBOOL(hAPP(hAPP(_1397705, _1397701), _1397703))), 33784 ^ _779203 : [(33787 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 33783 ^ [_1397701, _1397703, _1397705]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1397705, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 33782 ^ [_1397701, _1397703, _1397705])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 33783 ^ [_1397701, _1397703, _1397705]))))], (33793 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1397705, 33782 ^ [_1397701, _1397703, _1397705]), 33783 ^ [_1397701, _1397703, _1397705]))], (33785 ^ _779203) ^ [] : [-(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), 33782 ^ [_1397701, _1397703, _1397705]), 33783 ^ [_1397701, _1397703, _1397705]))))]]], (42620 ^ _779203) ^ [_1629021, _1629023, _1629025] : [-(_1629021 = c_List_Olist_ONil(_1629023)), -(c_List_Obutlast(_1629023, hAPP(hAPP(c_List_Olist_OCons(_1629023), _1629025), _1629021)) = hAPP(hAPP(c_List_Olist_OCons(_1629023), _1629025), c_List_Obutlast(_1629023, _1629021)))], (45426 ^ _779203) ^ [_1690912, _1690914, _1690916, _1690918] : [-(c_List_Oremdups(_1690912, hAPP(hAPP(c_List_Omap(_1690914, _1690912), _1690916), c_List_Oremdups(_1690914, _1690918))) = c_List_Oremdups(_1690912, hAPP(hAPP(c_List_Omap(_1690914, _1690912), _1690916), _1690918)))], (45875 ^ _779203) ^ [_1702477, _1702479, _1702481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1702477), _1702479)), -(c_List_Oupt(_1702477, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702479), _1702481)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1702477, _1702479)), c_List_Oupt(_1702479, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1702479), _1702481))))], (26890 ^ _779203) ^ [_1252809] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1252809) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1252809))], (50853 ^ _779203) ^ [_1809293, _1809295] : [_1809293 = _1809295, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809293, _1809295) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1809293), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (13183 ^ _779203) ^ [_1007159, _1007161, _1007163, _1007165, _1007167] : [class_Groups_Ocomm__monoid__mult(_1007159), hBOOL(hAPP(c_Finite__Set_Ofinite(_1007161), _1007163)), -(hBOOL(hAPP(hAPP(c_member(_1007161), _1007165), _1007163))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1007161, _1007159), _1007167), hAPP(hAPP(c_Set_Oinsert(_1007161), _1007165), _1007163)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1007159), hAPP(_1007167, _1007165)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1007161, _1007159), _1007167), _1007163)))], (40677 ^ _779203) ^ [_1576456, _1576458, _1576460, _1576462, _1576464] : [-(hAPP(c_Relation_Oconverse(_1576456, _1576458), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1576460, tc_fun(tc_prod(_1576456, _1576458), tc_HOL_Obool)), _1576462), _1576464)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1576460, tc_fun(tc_prod(_1576458, _1576456), tc_HOL_Obool)), _1576462), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1576456, _1576458), tc_HOL_Obool), tc_fun(tc_prod(_1576458, _1576456), tc_HOL_Obool), _1576460), c_Relation_Oconverse(_1576456, _1576458)), _1576464)))], (24089 ^ _779203) ^ [_1203487, _1203489] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1203487))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203489)) = 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)))), _1203487), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1203489)))], (16724 ^ _779203) ^ [_1073279, _1073281, _1073283] : [class_Orderings_Olinorder(_1073279), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073279), _1073281)), -(_1073283 = c_Orderings_Obot__class_Obot(tc_fun(_1073279, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1073279, tc_HOL_Obool)), _1073283), _1073281)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1073279), c_Big__Operators_Olinorder__class_OMax(_1073279, _1073283)), c_Big__Operators_Olinorder__class_OMax(_1073279, _1073281)) = c_Big__Operators_Olinorder__class_OMax(_1073279, _1073281))], (8278 ^ _779203) ^ [_916880, _916882, _916884] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_916880), _916882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916880, tc_HOL_Obool)), _916884), _916882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_916880), _916884)), hAPP(c_Finite__Set_Ocard(_916880), _916882))))], (25326 ^ _779203) ^ [_1225933, _1225935, _1225937, _1225939] : [class_Rings_Olinordered__semidom(_1225933), hAPP(hAPP(c_Power_Opower__class_Opower(_1225933), _1225935), _1225937) = hAPP(hAPP(c_Power_Opower__class_Opower(_1225933), _1225939), _1225937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225933), c_Groups_Ozero__class_Ozero(_1225933)), _1225935)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1225933), c_Groups_Ozero__class_Ozero(_1225933)), _1225939)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1225937)), -(_1225935 = _1225939)], (44849 ^ _779203) ^ [_1677801] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1677801), 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, _1677801)) = _1677801)], (39349 ^ _779203) ^ [_1544289, _1544291] : [39351 ^ _779203 : [(39354 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1544291), 39350 ^ [_1544289, _1544291]))], (39352 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 39350 ^ [_1544289, _1544291]), _1544289)))]], -(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)), _1544291), _1544289))], (48751 ^ _779203) ^ [_1763511, _1763513, _1763515, _1763517] : [c_Relation_Otrans(_1763511, _1763513), c_Relation_Otrans(_1763515, _1763517), -(c_Relation_Otrans(tc_prod(_1763511, _1763515), c_Wellfounded_Olex__prod(_1763511, _1763515, _1763513, _1763517)))], (10569 ^ _779203) ^ [_962049, _962051, _962053, _962055, _962057, _962059] : [class_Rings_Olinordered__semiring__1__strict(_962049), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962049), _962051), _962053)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962049), _962055), _962053)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962049), c_Groups_Ozero__class_Ozero(_962049)), _962057)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_962049), c_Groups_Ozero__class_Ozero(_962049)), _962059)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962049), _962057), _962059) = c_Groups_Oone__class_Oone(_962049), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_962049), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_962049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962049), _962057), _962051)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_962049), _962059), _962055))), _962053)))], (32869 ^ _779203) ^ [_1381139, _1381141, _1381143, _1381145, _1381147, _1381149] : [hAPP(hAPP(c_Product__Type_OPair(_1381139, _1381141), _1381143), _1381145) = hAPP(hAPP(c_Product__Type_OPair(_1381139, _1381141), _1381147), _1381149), 32872 ^ _779203 : [(32875 ^ _779203) ^ [] : [-(_1381145 = _1381149)], (32873 ^ _779203) ^ [] : [-(_1381143 = _1381147)]]], (37429 ^ _779203) ^ [_1487579, _1487581, _1487583] : [hBOOL(hAPP(hAPP(c_member(_1487579), _1487581), hAPP(c_Set_OCollect(_1487579), _1487583))), -(hBOOL(hAPP(_1487583, _1487581)))], (4792 ^ _779203) ^ [_852185, _852187, _852189, _852191] : [-(c_Relation_OId__on(_852191, _852187) = c_Relation_OId__on(_852189, _852185)), _852191 = _852189, _852187 = _852185], (33533 ^ _779203) ^ [_1392980, _1392982] : [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), _1392980), _1392982))), 33536 ^ _779203 : [(33543 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392982), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 33546 ^ _779203 : [(33555 ^ _779203) ^ [] : [-(c_Nitpick_Onorm__frac(_1392980, _1392982) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1392980), _1392982)), 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), _1392980))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1392982)))), -(_1392980 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1392982 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33547 ^ _779203) ^ [] : [33548 ^ _779203 : [(33551 ^ _779203) ^ [] : [_1392982 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (33549 ^ _779203) ^ [] : [_1392980 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1392980, _1392982) = 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)))]]], (33537 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392982), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1392980, _1392982) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1392980), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1392982)))]]], (49861 ^ _779203) ^ [_1787579, _1787581, _1787583, _1787585, _1787587, _1787589] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1787579, _1787581, _1787583, _1787585), _1787587), _1787589) = hAPP(_1787585, hAPP(hAPP(c_Product__Type_OPair(_1787579, _1787581), _1787587), _1787589)))], (8991 ^ _779203) ^ [_931350, _931352, _931354] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_931350), _931352)), 8994 ^ _779203 : [(9001 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_931350), _931354), _931352))), -(hAPP(c_Finite__Set_Ocard(_931350), hAPP(hAPP(c_Set_Oinsert(_931350), _931354), _931352)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_931350), _931352)))], (8995 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_931350), _931354), _931352)), -(hAPP(c_Finite__Set_Ocard(_931350), hAPP(hAPP(c_Set_Oinsert(_931350), _931354), _931352)) = hAPP(c_Finite__Set_Ocard(_931350), _931352))]]], (45887 ^ _779203) ^ [_1702740, _1702742] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702740), _1702742))), -(c_List_Oupt(_1702740, _1702742) = c_List_Olist_ONil(tc_Nat_Onat))], (32910 ^ _779203) ^ [_1381986, _1381988, _1381990, _1381992, _1381994, _1381996] : [_1381986 = _1381988, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1381990, _1381992, _1381994), _1381996), _1381986) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1381990, _1381992, _1381994), _1381996), _1381988))], (3662 ^ _779203) ^ [_834030, _834032, _834034, _834036, _834038, _834040, _834042, _834044] : [-(c_List_Omaps(_834044, _834040, _834036, _834032) = c_List_Omaps(_834042, _834038, _834034, _834030)), _834044 = _834042, _834040 = _834038, _834036 = _834034, _834032 = _834030], (31665 ^ _779203) ^ [_1347625, _1347627, _1347629, _1347631, _1347633, _1347635] : [-(c_Nitpick_Opair__box_Opair__box__size(_1347625, _1347627, _1347629, _1347631, c_Nitpick_Opair__box_OPairBox(_1347625, _1347627, _1347633, _1347635)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1347629, _1347633)), hAPP(_1347631, _1347635))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24992 ^ _779203) ^ [_1219748, _1219750, _1219752, _1219754] : [class_Rings_Olinordered__semidom(_1219748), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219748), _1219750), _1219752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219748), c_Groups_Ozero__class_Ozero(_1219748)), _1219750)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219748), hAPP(hAPP(c_Power_Opower__class_Opower(_1219748), _1219750), _1219754)), hAPP(hAPP(c_Power_Opower__class_Opower(_1219748), _1219752), _1219754))))], (10977 ^ _779203) ^ [_968660] : [hAPP(c_Nat_OSuc, _968660) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (35976 ^ _779203) ^ [_1454945, _1454947] : [c_Equiv__Relations_Oequivp(_1454945, _1454947), 35979 ^ _779203 : [(35986 ^ _779203) ^ [_1455138, _1455140] : [hAPP(_1454947, _1455140) = hAPP(_1454947, _1455138), -(hBOOL(hAPP(hAPP(_1454947, _1455140), _1455138)))], (35980 ^ _779203) ^ [_1455039, _1455041] : [hBOOL(hAPP(hAPP(_1454947, _1455041), _1455039)), -(hAPP(_1454947, _1455041) = hAPP(_1454947, _1455039))]]], (32157 ^ _779203) ^ [_1360317, _1360319, _1360321, _1360323] : [class_Groups_Ocomm__monoid__mult(_1360317), hBOOL(hAPP(c_Finite__Set_Ofinite(_1360319), _1360321)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1360319, _1360317), hAPP(c_COMBK(_1360317, _1360319), _1360323)), _1360321) = hAPP(hAPP(c_Power_Opower__class_Opower(_1360317), _1360323), hAPP(c_Finite__Set_Ocard(_1360319), _1360321)))], (12192 ^ _779203) ^ [_989731, _989733] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989731), hAPP(c_Nat_OSuc, _989733)))), 12193 ^ _779203 : [(12196 ^ _779203) ^ [_989819] : [_989731 = hAPP(c_Nat_OSuc, _989819), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989819), _989733))], (12194 ^ _779203) ^ [] : [_989731 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (46616 ^ _779203) ^ [_1716564, _1716566, _1716568] : [-(hAPP(c_List_Orev(_1716564), hAPP(c_List_Ofilter(_1716564, _1716566), _1716568)) = hAPP(c_List_Ofilter(_1716564, _1716566), hAPP(c_List_Orev(_1716564), _1716568)))], (36900 ^ _779203) ^ [_1474563, _1474565, _1474567, _1474569, _1474571, _1474573, _1474575] : [c_Typedef_Otype__definition(_1474563, _1474565, _1474567, _1474569, _1474571), hBOOL(hAPP(hAPP(c_member(_1474565), _1474573), _1474571)), hBOOL(hAPP(hAPP(c_member(_1474565), _1474575), _1474571)), 36911 ^ _779203 : [(36918 ^ _779203) ^ [] : [_1474573 = _1474575, -(hAPP(_1474569, _1474573) = hAPP(_1474569, _1474575))], (36912 ^ _779203) ^ [] : [hAPP(_1474569, _1474573) = hAPP(_1474569, _1474575), -(_1474573 = _1474575)]]], (23281 ^ _779203) ^ [_1188797] : [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, _1188797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1188797)))], (23727 ^ _779203) ^ [_1196879] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1196879, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27948 ^ _779203) ^ [_1272482, _1272484] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272482, tc_HOL_Obool)), _1272484), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272482, tc_HOL_Obool)), _1272484)) = c_Orderings_Otop__class_Otop(tc_fun(_1272482, tc_HOL_Obool)))], (47430 ^ _779203) ^ [_1734413, _1734415, _1734417, _1734419] : [47432 ^ _779203 : [(47435 ^ _779203) ^ [] : [hBOOL(hAPP(_1734417, 47431 ^ [_1734413, _1734415, _1734417, _1734419]))], (47433 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734413), 47431 ^ [_1734413, _1734415, _1734417, _1734419]), hAPP(c_List_Oset(_1734413), _1734415))))]], -(c_List_OtakeWhile(_1734413, _1734417, hAPP(hAPP(c_List_Oappend(_1734413), _1734415), _1734419)) = hAPP(hAPP(c_List_Oappend(_1734413), _1734415), c_List_OtakeWhile(_1734413, _1734417, _1734419)))], (32103 ^ _779203) ^ [_1358946, _1358948, _1358950, _1358952, _1358954] : [class_Groups_Ocomm__monoid__mult(_1358946), hBOOL(hAPP(c_Finite__Set_Ofinite(_1358948), _1358950)), 32110 ^ _779203 : [(32117 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1358948), _1358952), _1358950))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358948, _1358946), hAPP(hAPP(c_COMBC(_1358948, _1358946, _1358946), hAPP(hAPP(c_COMBS(_1358948, _1358946, tc_fun(_1358946, _1358946)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1358946, tc_fun(_1358946, _1358946)), _1358948), c_If(_1358946)), hAPP(hAPP(c_COMBC(_1358948, _1358948, tc_HOL_Obool), c_fequal), _1358952))), _1358954)), c_Groups_Oone__class_Oone(_1358946))), _1358950) = c_Groups_Oone__class_Oone(_1358946))], (32111 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1358948), _1358952), _1358950)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1358948, _1358946), hAPP(hAPP(c_COMBC(_1358948, _1358946, _1358946), hAPP(hAPP(c_COMBS(_1358948, _1358946, tc_fun(_1358946, _1358946)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1358946, tc_fun(_1358946, _1358946)), _1358948), c_If(_1358946)), hAPP(hAPP(c_COMBC(_1358948, _1358948, tc_HOL_Obool), c_fequal), _1358952))), _1358954)), c_Groups_Oone__class_Oone(_1358946))), _1358950) = hAPP(_1358954, _1358952))]]], (15860 ^ _779203) ^ [_1057130, _1057132, _1057134, _1057136] : [class_Orderings_Olinorder(_1057130), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057130), _1057132), _1057134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1057130), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1057130), _1057132), _1057136)), _1057134)))], (12458 ^ _779203) ^ [_994094, _994096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994094), _994096)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994094), _994096) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50913 ^ _779203) ^ [_1810211, _1810213] : [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)))), _1810211, _1810213), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810211), _1810213)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810213), _1810211)))], (27404 ^ _779203) ^ [_1262060, _1262062, _1262064] : [class_Lattices_Olattice(_1262060), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1262060), _1262062), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1262060), _1262064), _1262062))))], (40634 ^ _779203) ^ [_1575381, _1575383, _1575385, _1575387, _1575389] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1575381, _1575381)), hAPP(hAPP(c_Product__Type_OPair(_1575381, _1575381), _1575383), _1575385)), c_Transitive__Closure_Ortrancl(_1575381, _1575387))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575381, _1575381), tc_HOL_Obool)), _1575387), hAPP(hAPP(c_Product__Type_OSigma(_1575381, _1575381), _1575389), hAPP(c_COMBK(tc_fun(_1575381, tc_HOL_Obool), _1575381), _1575389)))), -(_1575383 = _1575385), -(hBOOL(hAPP(hAPP(c_member(_1575381), _1575383), _1575389)))], (40350 ^ _779203) ^ [_1568655, _1568657] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1568655, _1568655, _1568655), _1568657), c_Transitive__Closure_Ortrancl(_1568655, _1568657)) = hAPP(hAPP(c_Relation_Orel__comp(_1568655, _1568655, _1568655), c_Transitive__Closure_Ortrancl(_1568655, _1568657)), _1568657))], (2446 ^ _779203) ^ [_815096, _815098, _815100, _815102] : [-(c_FunDef_Orp__inv__image(_815102, _815098) = c_FunDef_Orp__inv__image(_815100, _815096)), _815102 = _815100, _815098 = _815096], (31223 ^ _779203) ^ [_1338215, _1338217, _1338219, _1338221] : [class_Groups_Ocomm__monoid__add(_1338215), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338217), _1338219)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1338217, _1338215), _1338221), _1338219) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1338215, _1338217, c_Groups_Oplus__class_Oplus(_1338215)), _1338221), c_Groups_Ozero__class_Ozero(_1338215)), _1338219))], (5887 ^ _779203) ^ [_872484, _872486, _872488] : [-(_872484 = _872486), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872488, tc_HOL_Obool)), _872484), _872486)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872488, tc_HOL_Obool)), _872486), _872484))], (41481 ^ _779203) ^ [_1598675, _1598677] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1598675), tc_List_Olist(_1598675)), tc_HOL_Obool)), c_List_Olistrel1(_1598675, c_Transitive__Closure_Ortrancl(_1598675, _1598677))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1598675), c_List_Olistrel1(_1598675, _1598677)))))], (21149 ^ _779203) ^ [_1152168, _1152170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152168), _1152170)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1152168)), c_Int_OBit1(_1152170))))], (18467 ^ _779203) ^ [_1104924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1104924)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1104924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48116 ^ _779203) ^ [_1749184, _1749186, _1749188, _1749190, _1749192] : [hBOOL(hAPP(hAPP(_1749188, _1749192), _1749190)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749184, _1749186, _1749188), _1749190), _1749192)))], (29082 ^ _779203) ^ [_1293830, _1293832, _1293834, _1293836] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1293830), _1293832)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1293830), _1293834)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293830, tc_Nat_Onat), _1293836), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1293830, tc_HOL_Obool)), _1293832), _1293834)) = 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(_1293830, tc_Nat_Onat), _1293836), _1293832)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293830, tc_Nat_Onat), _1293836), _1293834))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1293830, tc_Nat_Onat), _1293836), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293830, tc_HOL_Obool)), _1293832), _1293834))))], (51153 ^ _779203) ^ [_1814414, _1814416] : [class_Rings_Ocomm__semiring__1(_1814414), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814414), _1814416), _1814416)))], (43141 ^ _779203) ^ [_1640055, _1640057, _1640059] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640055)), hAPP(hAPP(c_List_Oappend(_1640055), _1640057), _1640059)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640055)), _1640057)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640055)), _1640059)))], (37233 ^ _779203) ^ [_1482520, _1482522, _1482524, _1482526] : [hAPP(c_Set_Oimage(_1482520, _1482522, _1482524), c_Orderings_Otop__class_Otop(tc_fun(_1482520, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1482522, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1482520, _1482522, _1482524), hAPP(c_Set_Ovimage(_1482520, _1482522, _1482524), _1482526)) = _1482526)], (43215 ^ _779203) ^ [_1641556, _1641558, _1641560] : [_1641556 = hAPP(hAPP(c_List_Oappend(_1641558), _1641556), _1641560), -(_1641560 = c_List_Olist_ONil(_1641558))], (39026 ^ _779203) ^ [_1536001, _1536003, _1536005] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1536001, _1536001), tc_HOL_Obool)), _1536003), hAPP(hAPP(c_Product__Type_OSigma(_1536001, _1536001), _1536005), hAPP(c_COMBK(tc_fun(_1536001, tc_HOL_Obool), _1536001), _1536005)))), 39032 ^ _779203 : [(39035 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1536001, _1536001)), hAPP(hAPP(c_Product__Type_OPair(_1536001, _1536001), 39031 ^ [_1536001, _1536003, _1536005]), 39031 ^ [_1536001, _1536003, _1536005])), _1536003))], (39033 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536001), 39031 ^ [_1536001, _1536003, _1536005]), _1536005)))]], -(c_Relation_Orefl__on(_1536001, _1536005, _1536003))], (8130 ^ _779203) ^ [_914177, _914179, _914181] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_914177), _914179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_914177), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914177, tc_HOL_Obool)), _914179), hAPP(hAPP(c_Set_Oinsert(_914177), _914181), c_Orderings_Obot__class_Obot(tc_fun(_914177, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_914177), _914179))))], (37126 ^ _779203) ^ [_1479869, _1479871, _1479873] : [-(hAPP(c_Finite__Set_Ofold1(_1479869, _1479871), _1479873) = c_HOL_OThe(_1479869, c_Finite__Set_Ofold1Set(_1479869, _1479871, _1479873)))], (5484 ^ _779203) ^ [_863055, _863057, _863059, _863061] : [-(tc_sum(_863061, _863057) = tc_sum(_863059, _863055)), _863061 = _863059, _863057 = _863055], (6671 ^ _779203) ^ [_887065, _887067, _887069, _887071, _887073, _887075, _887077, _887079] : [c_Finite__Set_Ofolding__image__simple(_887065, _887067, _887069, _887071, _887073, _887075), hBOOL(hAPP(c_Finite__Set_Ofinite(_887067), _887077)), -(hBOOL(hAPP(hAPP(c_member(_887067), _887079), _887077))), -(hAPP(_887075, hAPP(hAPP(c_Set_Oinsert(_887067), _887079), _887077)) = hAPP(hAPP(_887069, hAPP(_887073, _887079)), hAPP(_887075, _887077)))], (8294 ^ _779203) ^ [_917204, _917206, _917208] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_917204), _917206)), -(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(_917204), _917208)), hAPP(c_Finite__Set_Ocard(_917204), _917206))), hAPP(c_Finite__Set_Ocard(_917204), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917204, tc_HOL_Obool)), _917208), _917206)))))], (12167 ^ _779203) ^ [_989368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989368), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_989368 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27562 ^ _779203) ^ [_1264905, _1264907, _1264909, _1264911] : [hBOOL(hAPP(hAPP(c_member(_1264905), _1264907), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264905, tc_HOL_Obool)), _1264909), _1264911))), -(hBOOL(hAPP(hAPP(c_member(_1264905), _1264907), _1264909))), -(hBOOL(hAPP(hAPP(c_member(_1264905), _1264907), _1264911)))], (42676 ^ _779203) ^ [_1629918, _1629920] : [-(c_List_Olistrelp(_1629918, _1629920, c_List_Olist_ONil(_1629918), c_List_Olist_ONil(_1629918)))], (45941 ^ _779203) ^ [_1703590, _1703592] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1703590, _1703592))))], (32673 ^ _779203) ^ [_1375200, _1375202, _1375204, _1375206] : [hAPP(hAPP(c_COMBC(_1375200, tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_fun(_1375202, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1375202, tc_fun(tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_fun(_1375202, tc_HOL_Obool)), _1375200), c_COMBC(_1375202, tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1375202, tc_prod(_1375200, _1375202)), tc_fun(_1375202, tc_fun(tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_HOL_Obool)), _1375200), hAPP(c_COMBB(tc_prod(_1375200, _1375202), tc_fun(tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_HOL_Obool), _1375202), c_member(tc_prod(_1375200, _1375202)))), c_Product__Type_OPair(_1375200, _1375202)))), _1375204) = hAPP(hAPP(c_COMBC(_1375200, tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_fun(_1375202, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1375202, tc_fun(tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_fun(_1375202, tc_HOL_Obool)), _1375200), c_COMBC(_1375202, tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1375202, tc_prod(_1375200, _1375202)), tc_fun(_1375202, tc_fun(tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_HOL_Obool)), _1375200), hAPP(c_COMBB(tc_prod(_1375200, _1375202), tc_fun(tc_fun(tc_prod(_1375200, _1375202), tc_HOL_Obool), tc_HOL_Obool), _1375202), c_member(tc_prod(_1375200, _1375202)))), c_Product__Type_OPair(_1375200, _1375202)))), _1375206), -(_1375204 = _1375206)], (34905 ^ _779203) ^ [_1427231, _1427233, _1427235, _1427237, _1427239] : [-(_1427231 = c_Orderings_Obot__class_Obot(tc_fun(_1427233, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427233, tc_fun(_1427235, tc_HOL_Obool)), _1427231), hAPP(hAPP(c_COMBC(_1427233, tc_fun(_1427235, tc_HOL_Obool), tc_fun(_1427235, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1427235, tc_HOL_Obool), tc_fun(tc_fun(_1427235, tc_HOL_Obool), tc_fun(_1427235, tc_HOL_Obool)), _1427233), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427235, tc_HOL_Obool))), _1427237)), _1427239)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427235, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427233, tc_fun(_1427235, tc_HOL_Obool)), _1427231), _1427237)), _1427239))], (52301 ^ _779203) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (6090 ^ _779203) ^ [_876284, _876286, _876288] : [c_Orderings_Obot__class_Obot(tc_fun(_876284, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_876284), _876286), _876288)], (39157 ^ _779203) ^ [_1539094, _1539096] : [c_Wellfounded_Owf(_1539094, _1539096), -(c_Wellfounded_Oacyclic(_1539094, _1539096))], (51949 ^ _779203) ^ [_1828099, _1828101, _1828103, _1828105] : [class_Divides_Osemiring__div(_1828099), -(_1828101 = c_Groups_Ozero__class_Ozero(_1828099)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828099), _1828101), _1828103)), 51960 ^ _779203 : [(51967 ^ _779203) ^ [] : [_1828103 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828099), _1828105), _1828101), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1828099), _1828103), _1828101) = _1828105)], (51961 ^ _779203) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1828099), _1828103), _1828101) = _1828105, -(_1828103 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1828099), _1828105), _1828101))]]], (29208 ^ _779203) ^ [_1296488, _1296490, _1296492, _1296494] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296488, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296488, tc_HOL_Obool)), _1296490), _1296492)), _1296494) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296488, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296488, tc_HOL_Obool)), _1296490), _1296494)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296488, tc_HOL_Obool)), _1296492), _1296494)))], (29612 ^ _779203) ^ [_1304737, _1304739, _1304741, _1304743] : [class_Lattices_Osemilattice__inf(_1304737), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304737), _1304739), _1304741)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304737), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1304737), _1304743), _1304739)), _1304741)))], (43361 ^ _779203) ^ [_1644927, _1644929, _1644931, _1644933, _1644935] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644927), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644929)), _1644931)))), -(hAPP(hAPP(c_List_Olist__update(_1644929, hAPP(hAPP(c_List_Oappend(_1644929), _1644931), _1644933)), _1644927), _1644935) = hAPP(hAPP(c_List_Oappend(_1644929), _1644931), hAPP(hAPP(c_List_Olist__update(_1644929, _1644933), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644927), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644929)), _1644931))), _1644935)))], (2734 ^ _779203) ^ [_819586, _819588, _819590, _819592, _819594, _819596, _819598, _819600] : [-(c_Product__Type_Oapsnd(_819600, _819596, _819592, _819588) = c_Product__Type_Oapsnd(_819598, _819594, _819590, _819586)), _819600 = _819598, _819596 = _819594, _819592 = _819590, _819588 = _819586], (40598 ^ _779203) ^ [_1574512, _1574514, _1574516, _1574518] : [c_Wellfounded_Oacyclic(_1574512, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1574512, _1574512)), hAPP(hAPP(c_Product__Type_OPair(_1574512, _1574512), _1574514), _1574516)), _1574518)), 40601 ^ _779203 : [(40604 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574512, _1574512)), hAPP(hAPP(c_Product__Type_OPair(_1574512, _1574512), _1574516), _1574514)), c_Transitive__Closure_Ortrancl(_1574512, _1574518)))], (40602 ^ _779203) ^ [] : [-(c_Wellfounded_Oacyclic(_1574512, _1574518))]]], (22552 ^ _779203) ^ [_1176847, _1176849, _1176851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176847)), 22555 ^ _779203 : [(22556 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1176849, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1176851), _1176847)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176851, _1176847))), 22559 ^ _779203 : [(22560 ^ _779203) ^ [_1177048, _1177050] : [-(hBOOL(hAPP(hAPP(_1176849, _1177050), _1177048))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1177048)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177048), _1176847)), _1176851 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1176847), _1177050)), _1177048)]]], (22574 ^ _779203) ^ [] : [22577 ^ _779203 : [(22580 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 22576 ^ [_1176847, _1176849, _1176851]), _1176847)))], (22582 ^ _779203) ^ [] : [-(_1176851 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1176847), 22575 ^ [_1176847, _1176849, _1176851])), 22576 ^ [_1176847, _1176849, _1176851]))], (22584 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1176849, 22575 ^ [_1176847, _1176849, _1176851]), 22576 ^ [_1176847, _1176849, _1176851]))], (22578 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22576 ^ [_1176847, _1176849, _1176851])))]], -(hBOOL(hAPP(hAPP(_1176849, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1176851), _1176847)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1176851, _1176847))))]]], (11065 ^ _779203) ^ [_969873, _969875, _969877] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969873), _969875) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969877), _969875), -(_969873 = _969877), -(_969875 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4430 ^ _779203) ^ [_846430, _846432] : [_846432 = _846430, -(c_List_Omember(_846432) = c_List_Omember(_846430))], (9139 ^ _779203) ^ [_934893, _934895, _934897, _934899, _934901] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _934893), _934895)), 9142 ^ _779203 : [(9149 ^ _779203) ^ [] : [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), _934895), _934893)), _934897)), _934899)), _934901)), -(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), _934895), _934897)), _934899)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _934893), _934897)), _934901))))], (9143 ^ _779203) ^ [] : [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), _934895), _934897)), _934899)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _934893), _934897)), _934901))), -(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), _934895), _934893)), _934897)), _934899)), _934901)))]]], (39277 ^ _779203) ^ [_1541970] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1541970, tc_HOL_Obool) = c_Set_OBall(_1541970))], (5134 ^ _779203) ^ [_857500, _857502, _857504, _857506] : [-(c_List_Oupt(_857506, _857502) = c_List_Oupt(_857504, _857500)), _857506 = _857504, _857502 = _857500], (5675 ^ _779203) ^ [_868761] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_868761), c_Orderings_Obot__class_Obot(tc_fun(_868761, tc_HOL_Obool)))))], (28080 ^ _779203) ^ [_1275039, _1275041, _1275043] : [-(hAPP(hAPP(c_Set_Oinsert(_1275039), _1275041), _1275043) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1275039, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1275039), _1275041), c_Orderings_Obot__class_Obot(tc_fun(_1275039, tc_HOL_Obool)))), _1275043))], (882 ^ _779203) ^ [_792332, _792334, _792336, _792338, _792340, _792342, _792344, _792346] : [-(c_Fun_Oinj__on(_792344, _792340, _792336, _792332)), c_Fun_Oinj__on(_792346, _792342, _792338, _792334), _792346 = _792344, _792342 = _792340, _792338 = _792336, _792334 = _792332], (6985 ^ _779203) ^ [_893944, _893946, _893948, _893950] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_893944), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893944, tc_HOL_Obool)), _893946), hAPP(hAPP(c_Set_Oinsert(_893944), _893948), _893950)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_893944), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893944, tc_HOL_Obool)), _893946), _893950))))], (43153 ^ _779203) ^ [_1640426, _1640428, _1640430] : [-(hAPP(c_List_Oset(_1640426), hAPP(hAPP(c_List_Oappend(_1640426), _1640428), _1640430)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1640426, tc_HOL_Obool)), hAPP(c_List_Oset(_1640426), _1640428)), hAPP(c_List_Oset(_1640426), _1640430)))], (44317 ^ _779203) ^ [_1665583, _1665585, _1665587, _1665589, _1665591, _1665593, _1665595, _1665597] : [-(hAPP(hAPP(c_List_Ozip(_1665583, _1665585), hAPP(hAPP(c_List_Omap(_1665587, _1665583), _1665589), _1665591)), hAPP(hAPP(c_List_Omap(_1665593, _1665585), _1665595), _1665597)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665587, _1665593), tc_prod(_1665583, _1665585)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665587, _1665593, tc_prod(_1665583, _1665585)), hAPP(hAPP(c_COMBC(_1665587, tc_fun(_1665593, _1665585), tc_fun(_1665593, tc_prod(_1665583, _1665585))), hAPP(hAPP(c_COMBB(tc_fun(_1665585, tc_prod(_1665583, _1665585)), tc_fun(tc_fun(_1665593, _1665585), tc_fun(_1665593, tc_prod(_1665583, _1665585))), _1665587), c_COMBB(_1665585, tc_prod(_1665583, _1665585), _1665593)), hAPP(hAPP(c_COMBB(_1665583, tc_fun(_1665585, tc_prod(_1665583, _1665585)), _1665587), c_Product__Type_OPair(_1665583, _1665585)), _1665589))), _1665595))), hAPP(hAPP(c_List_Ozip(_1665587, _1665593), _1665591), _1665597)))], (29964 ^ _779203) ^ [_1312598, _1312600, _1312602, _1312604] : [class_Orderings_Oorder(_1312598), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312598, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1312598, _1312600, _1312602)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1312598, _1312602, _1312604)) = c_Orderings_Obot__class_Obot(tc_fun(_1312598, tc_HOL_Obool)))], (4808 ^ _779203) ^ [_852419, _852421, _852423, _852425] : [-(c_List_Olistrel(_852425, _852421) = c_List_Olistrel(_852423, _852419)), _852425 = _852423, _852421 = _852419], (32567 ^ _779203) ^ [_1370224, _1370226] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1370224), hAPP(c_Nat_OSuc, _1370226)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1370226), 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)), _1370226)), _1370224))], (42748 ^ _779203) ^ [_1631197, _1631199, _1631201] : [-(hBOOL(hAPP(hAPP(c_member(_1631197), _1631199), hAPP(c_List_Oset(_1631197), _1631201)))), -(c_List_Oremove1(_1631197, _1631199, _1631201) = _1631201)], (31539 ^ _779203) ^ [_1344860, _1344862, _1344864, _1344866, _1344868, _1344870] : [class_Groups_Oab__semigroup__mult(_1344860), hBOOL(hAPP(c_Finite__Set_Ofinite(_1344862), _1344864)), 31549 ^ _779203 : [(31552 ^ _779203) ^ [] : [hAPP(_1344866, 31548 ^ [_1344860, _1344862, _1344864, _1344866, _1344868, _1344870]) = hAPP(_1344868, 31548 ^ [_1344860, _1344862, _1344864, _1344866, _1344868, _1344870])], (31550 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1344862), 31548 ^ [_1344860, _1344862, _1344864, _1344866, _1344868, _1344870]), _1344864)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1344860, _1344862, c_Groups_Otimes__class_Otimes(_1344860)), _1344866), _1344870), _1344864) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1344860, _1344862, c_Groups_Otimes__class_Otimes(_1344860)), _1344868), _1344870), _1344864))], (44847 ^ _779203) ^ [_1677755, _1677757] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1677755), _1677757) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677755)), hAPP(c_Code__Numeral_Onat__of, _1677757))))], (20042 ^ _779203) ^ [_1132605, _1132607, _1132609] : [hBOOL(hAPP(hAPP(c_member(_1132605), _1132607), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1132605, tc_HOL_Obool)), _1132609))), hBOOL(hAPP(hAPP(c_member(_1132605), _1132607), _1132609))], (34474 ^ _779203) ^ [_1414890, _1414892, _1414894, _1414896, _1414898] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414890, tc_fun(_1414892, tc_HOL_Obool)), _1414894), hAPP(hAPP(c_COMBB(tc_fun(_1414892, tc_HOL_Obool), tc_fun(_1414892, tc_HOL_Obool), _1414890), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414892, tc_HOL_Obool)), _1414896)), _1414898)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414892, tc_HOL_Obool)), _1414896), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414890, tc_fun(_1414892, tc_HOL_Obool)), _1414894), _1414898)))], (49356 ^ _779203) ^ [_1777042, _1777044, _1777046] : [c_Equiv__Relations_Oequiv(_1777042, _1777044, _1777046), 49359 ^ _779203 : [(49364 ^ _779203) ^ [] : [-(c_Relation_Otrans(_1777042, _1777046))], (49362 ^ _779203) ^ [] : [-(c_Relation_Osym(_1777042, _1777046))], (49360 ^ _779203) ^ [] : [-(c_Relation_Orefl__on(_1777042, _1777044, _1777046))]]], (7417 ^ _779203) ^ [_901842, _901844, _901846, _901848] : [class_Orderings_Oorder(_901842), _901844 = _901846, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901842), _901848), _901846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901842), _901848), _901844)))], (39429 ^ _779203) ^ [_1546284, _1546286, _1546288, _1546290, _1546292, _1546294] : [c_Fun_Oinj__on(_1546284, _1546286, _1546288, _1546290), c_Fun_Oinj__on(_1546286, _1546292, _1546294, hAPP(c_Set_Oimage(_1546284, _1546286, _1546288), _1546290)), -(c_Fun_Oinj__on(_1546284, _1546292, hAPP(c_Fun_Ocomp(_1546286, _1546292, _1546284, _1546294), _1546288), _1546290))], (27176 ^ _779203) ^ [_1257633] : [-(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)), _1257633))))], (5897 ^ _779203) ^ [_872659, _872661] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872659, tc_HOL_Obool)), _872661), _872661)))], (41697 ^ _779203) ^ [_1605487, _1605489, _1605491, _1605493, _1605495] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605487), tc_List_Olist(_1605487))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605487), tc_List_Olist(_1605487)), _1605489), hAPP(hAPP(c_List_Olist_OCons(_1605487), _1605491), _1605493))), c_List_Olistrel(_1605487, _1605495))), 41702 ^ _779203 : [(41707 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1605487), tc_List_Olist(_1605487))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1605487), tc_List_Olist(_1605487)), 41701 ^ [_1605487, _1605489, _1605491, _1605493, _1605495]), _1605493)), c_List_Olistrel(_1605487, _1605495))))], (41705 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605487, _1605487)), hAPP(hAPP(c_Product__Type_OPair(_1605487, _1605487), 41700 ^ [_1605487, _1605489, _1605491, _1605493, _1605495]), _1605491)), _1605495)))], (41703 ^ _779203) ^ [] : [-(_1605489 = hAPP(hAPP(c_List_Olist_OCons(_1605487), 41700 ^ [_1605487, _1605489, _1605491, _1605493, _1605495]), 41701 ^ [_1605487, _1605489, _1605491, _1605493, _1605495]))]]], (46180 ^ _779203) ^ [_1707968, _1707970, _1707972, _1707974] : [class_Orderings_Olinorder(_1707968), 46183 ^ _779203 : [(46192 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1707968, hAPP(hAPP(c_List_Olist_OCons(_1707968), _1707970), hAPP(hAPP(c_List_Olist_OCons(_1707968), _1707972), _1707974)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707968), _1707970), _1707972)), c_List_Olinorder__class_Osorted(_1707968, hAPP(hAPP(c_List_Olist_OCons(_1707968), _1707972), _1707974))], (46184 ^ _779203) ^ [] : [c_List_Olinorder__class_Osorted(_1707968, hAPP(hAPP(c_List_Olist_OCons(_1707968), _1707970), hAPP(hAPP(c_List_Olist_OCons(_1707968), _1707972), _1707974))), 46187 ^ _779203 : [(46190 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1707968, hAPP(hAPP(c_List_Olist_OCons(_1707968), _1707972), _1707974)))], (46188 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1707968), _1707970), _1707972)))]]]]], (40544 ^ _779203) ^ [_1573311, _1573313, _1573315, _1573317] : [-(hBOOL(hAPP(hAPP(c_member(_1573311), _1573313), hAPP(c_Relation_ODomain(_1573311, _1573311), _1573315)))), 40547 ^ _779203 : [(40554 ^ _779203) ^ [] : [_1573313 = _1573317, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573311, _1573311)), hAPP(hAPP(c_Product__Type_OPair(_1573311, _1573311), _1573313), _1573317)), c_Transitive__Closure_Ortrancl(_1573311, _1573315))))], (40548 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573311, _1573311)), hAPP(hAPP(c_Product__Type_OPair(_1573311, _1573311), _1573313), _1573317)), c_Transitive__Closure_Ortrancl(_1573311, _1573315))), -(_1573313 = _1573317)]]], (6423 ^ _779203) ^ [_882906, _882908, _882910] : [class_Orderings_Oorder(_882906), 6426 ^ _779203 : [(6435 ^ _779203) ^ [] : [-(_882908 = _882910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882906), _882908), _882910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882906), _882910), _882908))], (6427 ^ _779203) ^ [] : [_882908 = _882910, 6430 ^ _779203 : [(6433 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882906), _882910), _882908)))], (6431 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882906), _882908), _882910)))]]]]], (11001 ^ _779203) ^ [_968964] : [-(_968964 = 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)), _968964)))], (25958 ^ _779203) ^ [_1235602, _1235604, _1235606] : [class_Rings_Oring__1(_1235602), -(hAPP(c_Int_Oring__1__class_Oof__int(_1235602), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1235604), _1235606)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1235602), hAPP(c_Int_Oring__1__class_Oof__int(_1235602), _1235604)), hAPP(c_Int_Oring__1__class_Oof__int(_1235602), _1235606)))], (17926 ^ _779203) ^ [_1095259, _1095261, _1095263, _1095265, _1095267] : [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), _1095259), _1095261)), _1095263)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1095259), _1095265)), _1095267))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095267), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095259), _1095267)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1095259), _1095263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1095265), _1095261)))], (16272 ^ _779203) ^ [_1064921, _1064923, _1064925] : [class_Orderings_Olinorder(_1064921), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064921), _1064923)), hBOOL(hAPP(hAPP(c_member(_1064921), _1064925), _1064923)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1064921), _1064925), c_Big__Operators_Olinorder__class_OMin(_1064921, _1064923)) = c_Big__Operators_Olinorder__class_OMin(_1064921, _1064923))], (29412 ^ _779203) ^ [_1300874, _1300876, _1300878, _1300880, _1300882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300874, tc_HOL_Obool)), _1300876), _1300878)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300874, tc_HOL_Obool)), _1300880), _1300882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1300874, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300874, tc_HOL_Obool)), _1300876), _1300880)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300874, tc_HOL_Obool)), _1300878), _1300882))))], (23950 ^ _779203) ^ [_1200813, _1200815, _1200817] : [-(hBOOL(hAPP(_1200813, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1200815, _1200817)))), 23953 ^ _779203 : [(23956 ^ _779203) ^ [] : [hBOOL(hAPP(_1200813, _1200815))], (23954 ^ _779203) ^ [] : [-(_1200817 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 23957 ^ _779203 : [(23962 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 23960 ^ [_1200813, _1200815, _1200817]), _1200817)))], (23964 ^ _779203) ^ [] : [-(_1200815 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1200817), 23959 ^ [_1200813, _1200815, _1200817])), 23960 ^ [_1200813, _1200815, _1200817]))], (23966 ^ _779203) ^ [] : [hBOOL(hAPP(_1200813, 23960 ^ [_1200813, _1200815, _1200817]))], (23958 ^ _779203) ^ [] : [_1200817 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (41905 ^ _779203) ^ [_1611101, _1611103, _1611105, _1611107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1611101), _1611103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1611105, tc_HOL_Obool)), hAPP(c_List_Oset(_1611105), hAPP(hAPP(c_List_Otake(_1611105), _1611101), _1611107))), hAPP(c_List_Oset(_1611105), hAPP(hAPP(c_List_Otake(_1611105), _1611103), _1611107)))))], (37649 ^ _779203) ^ [_1493356, _1493358, _1493360, _1493362, _1493364] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1493356, _1493358), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493356, tc_HOL_Obool)), _1493360), _1493362)), hAPP(c_COMBK(tc_fun(_1493358, tc_HOL_Obool), _1493356), _1493364)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1493356, _1493358), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1493356, _1493358), _1493360), hAPP(c_COMBK(tc_fun(_1493358, tc_HOL_Obool), _1493356), _1493364))), hAPP(hAPP(c_Product__Type_OSigma(_1493356, _1493358), _1493362), hAPP(c_COMBK(tc_fun(_1493358, tc_HOL_Obool), _1493356), _1493364))))], (32021 ^ _779203) ^ [_1356860, _1356862, _1356864, _1356866] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1356860), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1356862, tc_Nat_Onat), _1356864), _1356866)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1356862, _1356860), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1356860, _1356862), c_Nat_Osemiring__1__class_Oof__nat(_1356860)), _1356864)), _1356866)), class_Groups_Ocomm__monoid__mult(_1356860), class_Rings_Osemiring__1(_1356860)], (21371 ^ _779203) ^ [_1155680, _1155682] : [class_Int_Onumber__ring(_1155680), class_Rings_Olinordered__idom(_1155680), 21378 ^ _779203 : [(21385 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1155682), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155680), hAPP(c_Int_Onumber__class_Onumber__of(_1155680), _1155682)), c_Groups_Oone__class_Oone(_1155680))))], (21379 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155680), hAPP(c_Int_Onumber__class_Onumber__of(_1155680), _1155682)), c_Groups_Oone__class_Oone(_1155680))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1155682), c_Int_OBit1(c_Int_OPls))))]]], (50889 ^ _779203) ^ [_1809901, _1809903] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809901, _1809903) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809901), _1809903))], (49168 ^ _779203) ^ [_1773259] : [-(c_Relation_Oantisym(_1773259, c_Relation_OId(_1773259)))], (1810 ^ _779203) ^ [_804788, _804790] : [-(class_Groups_Omonoid__mult(_804788)), _804790 = _804788, class_Groups_Omonoid__mult(_804790)], (4672 ^ _779203) ^ [_850255, _850257, _850259, _850261, _850263, _850265] : [-(c_Relation_OImage(_850265, _850261, _850257) = c_Relation_OImage(_850263, _850259, _850255)), _850265 = _850263, _850261 = _850259, _850257 = _850255], (10728 ^ _779203) ^ [_964831, _964833] : [class_Groups_Ozero(_964831), 10731 ^ _779203 : [(10738 ^ _779203) ^ [] : [_964833 = c_Groups_Ozero__class_Ozero(_964831), -(c_Groups_Ozero__class_Ozero(_964831) = _964833)], (10732 ^ _779203) ^ [] : [c_Groups_Ozero__class_Ozero(_964831) = _964833, -(_964833 = c_Groups_Ozero__class_Ozero(_964831))]]], (36550 ^ _779203) ^ [_1466938, _1466940, _1466942, _1466944, _1466946, _1466948] : [c_Fun_Oinj__on(_1466938, _1466940, _1466942, _1466944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466938, tc_HOL_Obool)), _1466946), _1466944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466938, tc_HOL_Obool)), _1466948), _1466944)), -(hAPP(c_Set_Oimage(_1466938, _1466940, _1466942), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466938, tc_HOL_Obool)), _1466946), _1466948)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1466940, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1466938, _1466940, _1466942), _1466946)), hAPP(c_Set_Oimage(_1466938, _1466940, _1466942), _1466948)))], (17350 ^ _779203) ^ [_1085008, _1085010, _1085012] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085008), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1085010), _1085012)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085008), _1085010)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085008), _1085012)))], (34779 ^ _779203) ^ [_1423999, _1424001, _1424003, _1424005] : [class_Complete__Lattice_Ocomplete__lattice(_1423999), -(_1424001 = c_Orderings_Obot__class_Obot(tc_fun(_1424003, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424003, _1423999), _1424001), hAPP(c_COMBK(_1423999, _1424003), _1424005)) = _1424005)], (29672 ^ _779203) ^ [_1305877, _1305879] : [class_Lattices_Oboolean__algebra(_1305877), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1305877), _1305879), hAPP(c_Groups_Ouminus__class_Ouminus(_1305877), _1305879)) = c_Orderings_Obot__class_Obot(_1305877))], (40970 ^ _779203) ^ [_1583716, _1583718] : [-(c_Relation_Osingle__valued(_1583716, _1583716, c_Relation_OId__on(_1583716, _1583718)))], (52703 ^ _779203) ^ [] : [hBOOL(c_fFalse)], (13051 ^ _779203) ^ [_1004943, _1004945] : [-(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), _1004943), _1004945)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1004943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1004945))], (14447 ^ _779203) ^ [_1030616, _1030618, _1030620, _1030622] : [class_Fields_Olinordered__field__inverse__zero(_1030616), 14450 ^ _779203 : [(14451 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1030616), _1030618), _1030620)), _1030622)), 14454 ^ _779203 : [(14461 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), c_Groups_Ozero__class_Ozero(_1030616)), _1030620))), 14464 ^ _779203 : [(14471 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), _1030620), c_Groups_Ozero__class_Ozero(_1030616)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), c_Groups_Ozero__class_Ozero(_1030616)), _1030622)))], (14465 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), _1030620), c_Groups_Ozero__class_Ozero(_1030616))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030616), _1030622), _1030620)), _1030618)))]]], (14455 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), c_Groups_Ozero__class_Ozero(_1030616)), _1030620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), _1030618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030616), _1030622), _1030620))))]]], (14477 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1030616), _1030618), _1030620)), _1030622))), 14480 ^ _779203 : [(14483 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), _1030618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030616), _1030622), _1030620)))], (14481 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), c_Groups_Ozero__class_Ozero(_1030616)), _1030620)))]], 14484 ^ _779203 : [(14487 ^ _779203) ^ [] : [14488 ^ _779203 : [(14491 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1030616), _1030622), _1030620)), _1030618))], (14489 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), _1030620), c_Groups_Ozero__class_Ozero(_1030616))))]], 14492 ^ _779203 : [(14495 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), c_Groups_Ozero__class_Ozero(_1030616)), _1030622))], (14493 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), _1030620), c_Groups_Ozero__class_Ozero(_1030616)))]]], (14485 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1030616), c_Groups_Ozero__class_Ozero(_1030616)), _1030620))]]]]], (32261 ^ _779203) ^ [_1362848, _1362850] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1362848)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1362850)), hAPP(c_Int_Onat, _1362848)) = hAPP(c_Int_Onat, _1362850))], (20905 ^ _779203) ^ [_1147989] : [class_Rings_Osemiring__1(_1147989), -(c_Int_Oiszero(_1147989, c_Groups_Ozero__class_Ozero(_1147989)))], (32459 ^ _779203) ^ [_1367565, _1367567, _1367569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1367565), _1367567)), -(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)), _1367565)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1367569), _1367567)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1367569), _1367565)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1367567), _1367565)))], (2892 ^ _779203) ^ [_822021, _822023, _822025, _822027] : [-(c_Nitpick_OAbs__Frac(_822027, _822023) = c_Nitpick_OAbs__Frac(_822025, _822021)), _822027 = _822025, _822023 = _822021], (6237 ^ _779203) ^ [_879413, _879415, _879417, _879419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879413, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_879413), _879415), _879417)), _879419)), 6240 ^ _779203 : [(6243 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879413, tc_HOL_Obool)), _879417), _879419)))], (6241 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_879413), _879415), _879419)))]]], (42874 ^ _779203) ^ [_1633713, _1633715] : [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), _1633713), _1633715))), 42877 ^ _779203 : [(42884 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1633713), _1633715))), -(c_List_Oupto(_1633713, _1633715) = c_List_Olist_ONil(tc_Int_Oint))], (42878 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1633713), _1633715)), -(c_List_Oupto(_1633713, _1633715) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1633713), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1633713), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1633715)))]]], (46839 ^ _779203) ^ [_1721300, _1721302, _1721304, _1721306] : [hBOOL(hAPP(hAPP(c_member(_1721300), _1721302), hAPP(c_List_Oset(_1721300), c_List_OtakeWhile(_1721300, _1721304, _1721306)))), 46842 ^ _779203 : [(46845 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1721304, _1721302)))], (46843 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1721300), _1721302), hAPP(c_List_Oset(_1721300), _1721306))))]]], (3638 ^ _779203) ^ [_833660, _833662, _833664, _833666] : [-(c_List_Oremdups(_833666, _833662) = c_List_Oremdups(_833664, _833660)), _833666 = _833664, _833662 = _833660], (34286 ^ _779203) ^ [_1408895, _1408897, _1408899, _1408901, _1408903, _1408905, _1408907, _1408909] : [hBOOL(hAPP(hAPP(c_member(_1408895), _1408897), _1408899)), hBOOL(hAPP(hAPP(hAPP(_1408901, _1408897), _1408903), _1408905)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1408895, tc_fun(_1408907, tc_fun(_1408909, tc_HOL_Obool))), _1408899), _1408901), _1408903), _1408905)))], (34739 ^ _779203) ^ [_1422875, _1422877, _1422879, _1422881, _1422883, _1422885] : [hBOOL(hAPP(hAPP(c_member(_1422875), _1422877), _1422879)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1422875, tc_fun(_1422881, tc_HOL_Obool)), _1422879), hAPP(hAPP(c_COMBB(tc_fun(_1422881, tc_HOL_Obool), tc_fun(_1422881, tc_HOL_Obool), _1422875), hAPP(c_Set_Oinsert(_1422881), _1422883)), _1422885)) = hAPP(hAPP(c_Set_Oinsert(_1422881), _1422883), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1422875, tc_fun(_1422881, tc_HOL_Obool)), _1422879), _1422885)))], (35713 ^ _779203) ^ [_1448722, _1448724, _1448726, _1448728] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1448722, tc_HOL_Obool)), _1448724), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1448722), _1448726), _1448728))), 35717 ^ _779203 : [(35720 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1448722), 35716 ^ [_1448722, _1448724, _1448726, _1448728]), _1448726)))], (35718 ^ _779203) ^ [] : [-(_1448724 = hAPP(c_Relation_OImage(_1448722, _1448722, _1448728), hAPP(hAPP(c_Set_Oinsert(_1448722), 35716 ^ [_1448722, _1448724, _1448726, _1448728]), c_Orderings_Obot__class_Obot(tc_fun(_1448722, tc_HOL_Obool)))))]]], (28130 ^ _779203) ^ [_1276222] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1276222), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (15176 ^ _779203) ^ [_1044608, _1044610, _1044612] : [class_Int_Onumber(_1044608), class_Orderings_Oord(_1044608), 15183 ^ _779203 : [(15190 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044608), hAPP(c_Int_Onumber__class_Onumber__of(_1044608), _1044610)), hAPP(c_Int_Onumber__class_Onumber__of(_1044608), _1044612)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1044608), hAPP(c_Int_Onumber__class_Onumber__of(_1044608), _1044610)), hAPP(c_Int_Onumber__class_Onumber__of(_1044608), _1044612)) = hAPP(c_Int_Onumber__class_Onumber__of(_1044608), _1044610))], (15184 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1044608), hAPP(c_Int_Onumber__class_Onumber__of(_1044608), _1044610)), hAPP(c_Int_Onumber__class_Onumber__of(_1044608), _1044612))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1044608), hAPP(c_Int_Onumber__class_Onumber__of(_1044608), _1044610)), hAPP(c_Int_Onumber__class_Onumber__of(_1044608), _1044612)) = hAPP(c_Int_Onumber__class_Onumber__of(_1044608), _1044612))]]], (9339 ^ _779203) ^ [_938409, _938411, _938413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938409), _938411)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938409), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938413), _938411))))], (43788 ^ _779203) ^ [_1655156, _1655158, _1655160] : [-(hAPP(c_List_Orotate1(_1655156), hAPP(c_List_Orotate(_1655156, _1655158), _1655160)) = hAPP(c_List_Orotate(_1655156, _1655158), hAPP(c_List_Orotate1(_1655156), _1655160)))], (8775 ^ _779203) ^ [_927268, _927270, _927272, _927274] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_927268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927268), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927268), _927270), _927272)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927268), _927270), _927274))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927268), _927272), _927274)))], (21907 ^ _779203) ^ [_1165077, _1165079, _1165081] : [class_Divides_Osemiring__div(_1165077), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165077), c_Divides_Odiv__class_Omod(_1165077, _1165079, _1165081)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165077), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1165077), _1165079), _1165081)), _1165081)) = _1165079)], (24075 ^ _779203) ^ [_1203165, _1203167] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1203165), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1203167)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1203165), 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)))), _1203167)))], (44412 ^ _779203) ^ [_1668603, _1668605, _1668607, _1668609, _1668611] : [hAPP(hAPP(c_List_Omap(_1668603, _1668605), _1668607), _1668609) = hAPP(hAPP(c_List_Omap(_1668603, _1668605), _1668607), _1668611), c_Fun_Oinj__on(_1668603, _1668605, _1668607, c_Orderings_Otop__class_Otop(tc_fun(_1668603, tc_HOL_Obool))), -(_1668609 = _1668611)], (25266 ^ _779203) ^ [_1224724, _1224726, _1224728, _1224730] : [class_Rings_Olinordered__semidom(_1224724), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224724), c_Groups_Oone__class_Oone(_1224724)), _1224726)), 25273 ^ _779203 : [(25280 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1224728), _1224730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224724), hAPP(hAPP(c_Power_Opower__class_Opower(_1224724), _1224726), _1224728)), hAPP(hAPP(c_Power_Opower__class_Opower(_1224724), _1224726), _1224730))))], (25274 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224724), hAPP(hAPP(c_Power_Opower__class_Opower(_1224724), _1224726), _1224728)), hAPP(hAPP(c_Power_Opower__class_Opower(_1224724), _1224726), _1224730))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1224728), _1224730)))]]], (33041 ^ _779203) ^ [_1384576, _1384578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1384576)), 33044 ^ _779203 : [(33051 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384578), _1384576))), -(c_Divides_OposDivAlg(_1384578, _1384576) = hAPP(c_Divides_Oadjust(_1384576), c_Divides_OposDivAlg(_1384578, 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)))), _1384576))))], (33045 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384578), _1384576)), -(c_Divides_OposDivAlg(_1384578, _1384576) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1384578))]]], (36610 ^ _779203) ^ [_1468258, _1468260, _1468262, _1468264, _1468266] : [c_Fun_Oinj__on(_1468258, _1468260, _1468262, c_Orderings_Otop__class_Otop(tc_fun(_1468258, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1468258, _1468260, _1468262), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468258, tc_HOL_Obool)), _1468264), _1468266)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1468260, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1468258, _1468260, _1468262), _1468264)), hAPP(c_Set_Oimage(_1468258, _1468260, _1468262), _1468266)))], (34745 ^ _779203) ^ [_1423080, _1423082, _1423084, _1423086, _1423088] : [hBOOL(hAPP(hAPP(c_member(_1423080), _1423082), _1423084)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1423086, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1423080, tc_fun(_1423086, tc_HOL_Obool)), _1423084), _1423088)), hAPP(_1423088, _1423082))))], (52271 ^ _779203) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (44460 ^ _779203) ^ [_1669598, _1669600, _1669602, _1669604, _1669606, _1669608] : [-(hAPP(hAPP(c_List_Omap(_1669598, _1669600), _1669602), hAPP(hAPP(c_List_Omap(_1669604, _1669598), _1669606), _1669608)) = hAPP(hAPP(c_List_Omap(_1669604, _1669600), hAPP(c_Fun_Ocomp(_1669598, _1669600, _1669604, _1669602), _1669606)), _1669608))], (47201 ^ _779203) ^ [_1728836, _1728838, _1728840, _1728842] : [-(c_List_Oconcat(_1728836, hAPP(hAPP(c_List_Omap(_1728838, tc_List_Olist(_1728836)), _1728840), _1728842)) = c_List_Omaps(_1728838, _1728836, _1728840, _1728842))], (25882 ^ _779203) ^ [_1234409] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234409)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234409))], (9925 ^ _779203) ^ [_948619, _948621, _948623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _948619), _948621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948623), _948621)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948623), _948619))))], (15998 ^ _779203) ^ [_1060001, _1060003, _1060005] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060001), _1060003)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1060005), _1060003)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1060001), _1060005)), _1060003))], (46013 ^ _779203) ^ [_1704970, _1704972, _1704974, _1704976] : [class_Groups_Ocomm__monoid__add(_1704970), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1704970), _1704972), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704974, _1704976))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1704970), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704970), _1704972), c_List_Oupt(_1704974, _1704976))))], (50514 ^ _779203) ^ [_1802763, _1802765, _1802767] : [c_List_Olist__ex(tc_Nat_Onat, _1802763, c_List_Oupt(_1802765, _1802767)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1802763), _1802765, _1802767)], (26492 ^ _779203) ^ [_1245152, _1245154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1245152), hAPP(c_Nat_OSuc, _1245154))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1245152, hAPP(c_Nat_OSuc, _1245154)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1245154)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1245152, _1245154)))], (41509 ^ _779203) ^ [_1599588, _1599590, _1599592, _1599594] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599588), tc_List_Olist(_1599588))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599588), tc_List_Olist(_1599588)), _1599590), _1599592)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1599588), c_List_Olistrel1(_1599588, _1599594)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599588)), _1599590) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599588)), _1599592))], (52363 ^ _779203) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (32637 ^ _779203) ^ [_1372289, _1372291, _1372293, _1372295, _1372297, _1372299] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372289, tc_fun(_1372291, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1372289, tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_fun(_1372291, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372291, tc_fun(tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_fun(_1372291, tc_HOL_Obool)), _1372289), c_COMBC(_1372291, tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372291, tc_prod(_1372289, _1372291)), tc_fun(_1372291, tc_fun(tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_HOL_Obool)), _1372289), hAPP(c_COMBB(tc_prod(_1372289, _1372291), tc_fun(tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_HOL_Obool), _1372291), c_member(tc_prod(_1372289, _1372291)))), c_Product__Type_OPair(_1372289, _1372291)))), _1372293)), hAPP(hAPP(c_COMBC(_1372289, tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_fun(_1372291, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372291, tc_fun(tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_fun(_1372291, tc_HOL_Obool)), _1372289), c_COMBC(_1372291, tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372291, tc_prod(_1372289, _1372291)), tc_fun(_1372291, tc_fun(tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_HOL_Obool)), _1372289), hAPP(c_COMBB(tc_prod(_1372289, _1372291), tc_fun(tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool), tc_HOL_Obool), _1372291), c_member(tc_prod(_1372289, _1372291)))), c_Product__Type_OPair(_1372289, _1372291)))), _1372295)), _1372297), _1372299)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1372289, _1372291)), hAPP(hAPP(c_Product__Type_OPair(_1372289, _1372291), _1372297), _1372299)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1372289, _1372291), tc_HOL_Obool)), _1372293), _1372295))))], (6861 ^ _779203) ^ [_891108, _891110, _891112] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_891108), _891110)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_891108), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891108, tc_HOL_Obool)), _891110), _891112))))], (25470 ^ _779203) ^ [_1228221] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228221)))], (21617 ^ _779203) ^ [_1159726, _1159728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159726), _1159728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1159726)), c_Int_OBit1(_1159728))))], (42674 ^ _779203) ^ [_1629873, _1629875, _1629877, _1629879] : [-(c_List_Oremove1(_1629873, _1629875, c_List_Oremove1(_1629873, _1629877, _1629879)) = c_List_Oremove1(_1629873, _1629877, c_List_Oremove1(_1629873, _1629875, _1629879)))], (21587 ^ _779203) ^ [_1159230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1159230))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1159230)))], (48122 ^ _779203) ^ [_1749297, _1749299, _1749301, _1749303, _1749305] : [hBOOL(hAPP(hAPP(_1749297, _1749299), _1749301)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749303, _1749305, _1749297), _1749301), _1749299)))], (44319 ^ _779203) ^ [_1665754, _1665756, _1665758, _1665760, _1665762, _1665764] : [-(hAPP(hAPP(c_List_Ozip(_1665754, _1665756), hAPP(hAPP(c_List_Omap(_1665758, _1665754), _1665760), _1665762)), _1665764) = hAPP(hAPP(c_List_Omap(tc_prod(_1665758, _1665756), tc_prod(_1665754, _1665756)), hAPP(c_Product__Type_Oprod_Oprod__case(_1665758, _1665756, tc_prod(_1665754, _1665756)), hAPP(hAPP(c_COMBB(_1665754, tc_fun(_1665756, tc_prod(_1665754, _1665756)), _1665758), c_Product__Type_OPair(_1665754, _1665756)), _1665760))), hAPP(hAPP(c_List_Ozip(_1665758, _1665756), _1665762), _1665764)))], (694 ^ _779203) ^ [_789628, _789630, _789632, _789634, _789636, _789638] : [-(c_List_Olist__ex1(_789636, _789632, _789628)), c_List_Olist__ex1(_789638, _789634, _789630), _789638 = _789636, _789634 = _789632, _789630 = _789628], (41972 ^ _779203) ^ [_1612666, _1612668, _1612670] : [41974 ^ _779203 : [(41977 ^ _779203) ^ [] : [hBOOL(hAPP(_1612670, hAPP(hAPP(c_List_Onth(_1612666), _1612668), 41973 ^ [_1612666, _1612668, _1612670])))], (41975 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41973 ^ [_1612666, _1612668, _1612670]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612666)), _1612668))))]], 41978 ^ _779203 : [(41979 ^ _779203) ^ [_1612868] : [hBOOL(hAPP(hAPP(c_member(_1612666), _1612868), hAPP(c_List_Oset(_1612666), _1612668))), -(hBOOL(hAPP(_1612670, _1612868)))]]], (8905 ^ _779203) ^ [_929662, _929664, _929666, _929668, _929670] : [class_Groups_Oordered__cancel__ab__semigroup__add(_929662), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_929662), _929664), _929666)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929662), _929668), _929670)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929662), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929662), _929664), _929668)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929662), _929666), _929670))))], (37181 ^ _779203) ^ [_1481224, _1481226, _1481228, _1481230] : [-(hAPP(c_Set_Ovimage(_1481224, _1481226, _1481228), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1481226, tc_HOL_Obool)), _1481230)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1481224, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1481224, _1481226, _1481228), _1481230)))], (15258 ^ _779203) ^ [_1046087, _1046089, _1046091, _1046093] : [class_Orderings_Olinorder(_1046087), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046087), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046087), _1046089), _1046091)), _1046093) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046087), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046087), _1046089), _1046093)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046087), _1046091), _1046093)))], (52513 ^ _779203) ^ [_1834941] : [-(class_Nat_Osize(tc_List_Olist(_1834941)))], (41100 ^ _779203) ^ [_1587101, _1587103, _1587105, _1587107, _1587109] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1587101, _1587101)), hAPP(hAPP(c_Product__Type_OPair(_1587101, _1587101), _1587103), _1587105)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587101, _1587101), tc_HOL_Obool), _1587107), _1587109))), 41105 ^ _779203 : [(41108 ^ _779203) ^ [] : [-(_1587103 = _1587105)], (41106 ^ _779203) ^ [] : [-(_1587107 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 41111 ^ _779203 : [(41116 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587101, _1587101)), hAPP(hAPP(c_Product__Type_OPair(_1587101, _1587101), 41109 ^ [_1587101, _1587103, _1587105, _1587107, _1587109]), _1587105)), _1587109)))], (41114 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1587101, _1587101)), hAPP(hAPP(c_Product__Type_OPair(_1587101, _1587101), _1587103), 41109 ^ [_1587101, _1587103, _1587105, _1587107, _1587109])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1587101, _1587101), tc_HOL_Obool), 41110 ^ [_1587101, _1587103, _1587105, _1587107, _1587109]), _1587109))))], (41112 ^ _779203) ^ [] : [-(_1587107 = hAPP(c_Nat_OSuc, 41110 ^ [_1587101, _1587103, _1587105, _1587107, _1587109]))]]], (28218 ^ _779203) ^ [_1277885, _1277887, _1277889, _1277891] : [class_Lattices_Osemilattice__sup(_1277885), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277885), _1277887)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1277885, _1277885, c_Lattices_Osemilattice__sup__class_Osup(_1277885)), _1277889), hAPP(hAPP(c_Set_Oinsert(_1277885), _1277891), _1277887)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1277885), _1277891), hAPP(hAPP(c_Finite__Set_Ofold(_1277885, _1277885, c_Lattices_Osemilattice__sup__class_Osup(_1277885)), _1277889), _1277887)))], (7105 ^ _779203) ^ [_896541, _896543, _896545, _896547, _896549, _896551] : [c_Finite__Set_Ofun__left__comm(_896541, _896543, _896545), hBOOL(hAPP(c_Finite__Set_Ofinite(_896541), _896547)), -(hBOOL(hAPP(hAPP(c_member(_896541), _896549), _896547))), -(hAPP(hAPP(c_Finite__Set_Ofold(_896541, _896543, _896545), _896551), hAPP(hAPP(c_Set_Oinsert(_896541), _896549), _896547)) = hAPP(hAPP(_896545, _896549), hAPP(hAPP(c_Finite__Set_Ofold(_896541, _896543, _896545), _896551), _896547)))], (16836 ^ _779203) ^ [_1075391, _1075393, _1075395, _1075397] : [class_Fields_Olinordered__field__inverse__zero(_1075391), class_Int_Onumber(_1075391), 16843 ^ _779203 : [(16844 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075391), hAPP(c_Int_Onumber__class_Onumber__of(_1075391), _1075393)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1075391), _1075395), _1075397))), 16847 ^ _779203 : [(16854 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075391), c_Groups_Ozero__class_Ozero(_1075391)), _1075397))), 16857 ^ _779203 : [(16864 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075391), _1075397), c_Groups_Ozero__class_Ozero(_1075391)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075391), hAPP(c_Int_Onumber__class_Onumber__of(_1075391), _1075393)), c_Groups_Ozero__class_Ozero(_1075391))))], (16858 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075391), _1075397), c_Groups_Ozero__class_Ozero(_1075391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075391), _1075395), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075391), hAPP(c_Int_Onumber__class_Onumber__of(_1075391), _1075393)), _1075397))))]]], (16848 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075391), c_Groups_Ozero__class_Ozero(_1075391)), _1075397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075391), hAPP(c_Int_Onumber__class_Onumber__of(_1075391), _1075393)), _1075397)), _1075395)))]]], (16870 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075391), hAPP(c_Int_Onumber__class_Onumber__of(_1075391), _1075393)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1075391), _1075395), _1075397)))), 16873 ^ _779203 : [(16876 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075391), hAPP(c_Int_Onumber__class_Onumber__of(_1075391), _1075393)), _1075397)), _1075395))], (16874 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075391), c_Groups_Ozero__class_Ozero(_1075391)), _1075397)))]], 16877 ^ _779203 : [(16880 ^ _779203) ^ [] : [16881 ^ _779203 : [(16884 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075391), _1075395), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075391), hAPP(c_Int_Onumber__class_Onumber__of(_1075391), _1075393)), _1075397)))], (16882 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075391), _1075397), c_Groups_Ozero__class_Ozero(_1075391))))]], 16885 ^ _779203 : [(16888 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1075391), hAPP(c_Int_Onumber__class_Onumber__of(_1075391), _1075393)), c_Groups_Ozero__class_Ozero(_1075391)))], (16886 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075391), _1075397), c_Groups_Ozero__class_Ozero(_1075391)))]]], (16878 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1075391), c_Groups_Ozero__class_Ozero(_1075391)), _1075397))]]]]], (7849 ^ _779203) ^ [_908267, _908269, _908271, _908273] : [class_Orderings_Opreorder(_908267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908267), _908269), _908271)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908267), _908271), _908273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908267), _908269), _908273)))], (45286 ^ _779203) ^ [_1688157, _1688159] : [-(_1688157 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1688159, _1688157, c_List_Olist_ONil(_1688159)) = c_List_Olist_ONil(tc_List_Olist(_1688159)))], (33755 ^ _779203) ^ [_1397193, _1397195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397193), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1397195), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397193, _1397195) = 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), _1397193), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1397195)))))], (12803 ^ _779203) ^ [_1000437, _1000439, _1000441, _1000443] : [class_Rings_Olinordered__semiring__strict(_1000437), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000437), _1000439), _1000441)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1000437), _1000439), _1000443))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000437), c_Groups_Ozero__class_Ozero(_1000437)), _1000439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1000437), _1000441), _1000443)))], (36965 ^ _779203) ^ [_1475975, _1475977, _1475979] : [hBOOL(hAPP(hAPP(c_member(_1475975), _1475979), c_Wellfounded_Oacc(_1475975, _1475977))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1475975, hAPP(hAPP(c_COMBC(_1475975, tc_fun(tc_prod(_1475975, _1475975), tc_HOL_Obool), tc_fun(_1475975, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1475975, tc_fun(tc_fun(tc_prod(_1475975, _1475975), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1475975, _1475975), tc_HOL_Obool), tc_fun(_1475975, tc_HOL_Obool)), _1475975), c_COMBC(_1475975, tc_fun(tc_prod(_1475975, _1475975), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1475975, tc_prod(_1475975, _1475975)), tc_fun(_1475975, tc_fun(tc_fun(tc_prod(_1475975, _1475975), tc_HOL_Obool), tc_HOL_Obool)), _1475975), hAPP(c_COMBB(tc_prod(_1475975, _1475975), tc_fun(tc_fun(tc_prod(_1475975, _1475975), tc_HOL_Obool), tc_HOL_Obool), _1475975), c_member(tc_prod(_1475975, _1475975)))), c_Product__Type_OPair(_1475975, _1475975)))), _1475977)), _1475979)))], (45556 ^ _779203) ^ [_1693485, _1693487, _1693489, _1693491] : [-(hAPP(hAPP(c_List_Omap(_1693485, _1693487), _1693489), c_List_Oconcat(_1693485, _1693491)) = c_List_Oconcat(_1693487, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1693485), tc_List_Olist(_1693487)), hAPP(c_List_Omap(_1693485, _1693487), _1693489)), _1693491)))], (49993 ^ _779203) ^ [_1790441, _1790443, _1790445] : [-(c_Fun_Obij__betw(_1790441, _1790443, _1790445, c_Orderings_Otop__class_Otop(tc_fun(_1790441, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790443, tc_HOL_Obool)))), c_Fun_Oinj__on(_1790441, _1790443, _1790445, c_Orderings_Otop__class_Otop(tc_fun(_1790441, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1790441, _1790443, _1790445), c_Orderings_Otop__class_Otop(tc_fun(_1790441, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1790443, tc_HOL_Obool))], (41278 ^ _779203) ^ [_1592262, _1592264] : [-(c_Nitpick_Ouminus__frac(_1592262, _1592264) = c_Nitpick_OAbs__Frac(_1592262, 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(_1592262), _1592264))), hAPP(c_Nitpick_Odenom(_1592262), _1592264))))], (50371 ^ _779203) ^ [_1797840, _1797842, _1797844, _1797846, _1797848, _1797850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797840, tc_HOL_Obool)), _1797842), _1797844)), 50377 ^ _779203 : [(50380 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797846, tc_HOL_Obool)), hAPP(_1797848, 50376 ^ [_1797840, _1797842, _1797844, _1797846, _1797848, _1797850])), hAPP(_1797850, 50376 ^ [_1797840, _1797842, _1797844, _1797846, _1797848, _1797850])))], (50378 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1797840), 50376 ^ [_1797840, _1797842, _1797844, _1797846, _1797848, _1797850]), _1797844)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1797846, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1797840, tc_fun(_1797846, tc_HOL_Obool)), _1797844), _1797848)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1797840, tc_fun(_1797846, tc_HOL_Obool)), _1797844), _1797850))))], (27300 ^ _779203) ^ [_1259784, _1259786, _1259788] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1259784, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1259784, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1259784), _1259786)), hAPP(c_Set_OPow(_1259784), _1259788))), hAPP(c_Set_OPow(_1259784), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1259784, tc_HOL_Obool)), _1259786), _1259788)))))], (33029 ^ _779203) ^ [_1384375] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1384375) = 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)))], (10107 ^ _779203) ^ [_952285, _952287, _952289, _952291, _952293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _952285), _952287)), 10110 ^ _779203 : [(10117 ^ _779203) ^ [] : [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), _952287), _952285)), _952289)), _952291) = _952293, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952287), _952289)), _952291) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952285), _952289)), _952293))], (10111 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952287), _952289)), _952291) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _952285), _952289)), _952293), -(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), _952287), _952285)), _952289)), _952291) = _952293)]]], (35393 ^ _779203) ^ [_1439901, _1439903, _1439905, _1439907] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1439901), _1439907) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1439905), _1439903), -(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), _1439901), _1439903)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1439905), _1439907))), c_Int_Ointrel)))], (42499 ^ _779203) ^ [_1626551, _1626553, _1626555, _1626557] : [hBOOL(hAPP(c_List_Odistinct(_1626551), _1626553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1626555), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626551)), _1626553))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1626557), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1626551)), _1626553))), 42510 ^ _779203 : [(42517 ^ _779203) ^ [] : [_1626555 = _1626557, -(hAPP(hAPP(c_List_Onth(_1626551), _1626553), _1626555) = hAPP(hAPP(c_List_Onth(_1626551), _1626553), _1626557))], (42511 ^ _779203) ^ [] : [hAPP(hAPP(c_List_Onth(_1626551), _1626553), _1626555) = hAPP(hAPP(c_List_Onth(_1626551), _1626553), _1626557), -(_1626555 = _1626557)]]], (40560 ^ _779203) ^ [_1573607, _1573609, _1573611, _1573613] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573607, _1573607)), hAPP(hAPP(c_Product__Type_OPair(_1573607, _1573607), _1573609), _1573611)), c_Transitive__Closure_Ortrancl(_1573607, _1573613))), hBOOL(hAPP(hAPP(c_member(_1573607), _1573611), c_Wellfounded_Oacc(_1573607, _1573613))), -(hBOOL(hAPP(hAPP(c_member(_1573607), _1573609), c_Wellfounded_Oacc(_1573607, _1573613))))], (24273 ^ _779203) ^ [_1206949, _1206951, _1206953] : [class_Rings_Ocomm__semiring__1(_1206949), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1206949), _1206951), hAPP(hAPP(c_Power_Opower__class_Opower(_1206949), _1206951), _1206953)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1206949), _1206951), hAPP(c_Nat_OSuc, _1206953)))], (38216 ^ _779203) ^ [_1514635, _1514637] : [-(c_Product__Type_Oapsnd(_1514635, _1514635, _1514637, c_Fun_Oid(_1514635)) = c_Fun_Oid(tc_prod(_1514637, _1514635)))], (20482 ^ _779203) ^ [_1140464, _1140466] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1140464)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1140466)), _1140464 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1140466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (52351 ^ _779203) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (28900 ^ _779203) ^ [_1290552, _1290554] : [class_Lattices_Olattice(_1290552), -(c_Big__Operators_Olattice__class_OSup__fin(_1290552, hAPP(hAPP(c_Set_Oinsert(_1290552), _1290554), c_Orderings_Obot__class_Obot(tc_fun(_1290552, tc_HOL_Obool)))) = _1290554)], (10045 ^ _779203) ^ [_950912, _950914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950912), _950914)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _950914), _950912)), _950912) = _950914)], (26122 ^ _779203) ^ [_1238486, _1238488, _1238490] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1238486, _1238488, _1238490, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1238488)], (15300 ^ _779203) ^ [_1047136, _1047138, _1047140, _1047142] : [class_Orderings_Olinorder(_1047136), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047136), _1047138), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047136), _1047140), _1047142)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047136), _1047140), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047136), _1047138), _1047142)))], (52251 ^ _779203) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (28394 ^ _779203) ^ [_1281466, _1281468, _1281470] : [class_Lattices_Oab__semigroup__idem__mult(_1281466), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281466), _1281468)), -(_1281468 = c_Orderings_Obot__class_Obot(tc_fun(_1281466, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1281466), _1281470)), -(_1281470 = c_Orderings_Obot__class_Obot(tc_fun(_1281466, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1281466, c_Groups_Otimes__class_Otimes(_1281466)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1281466, tc_HOL_Obool)), _1281468), _1281470)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281466), hAPP(c_Finite__Set_Ofold1(_1281466, c_Groups_Otimes__class_Otimes(_1281466)), _1281468)), hAPP(c_Finite__Set_Ofold1(_1281466, c_Groups_Otimes__class_Otimes(_1281466)), _1281470)))], (2302 ^ _779203) ^ [_812850, _812852, _812854, _812856] : [-(c_Groups_Osgn__class_Osgn(_812856, _812852) = c_Groups_Osgn__class_Osgn(_812854, _812850)), _812856 = _812854, _812852 = _812850], (29206 ^ _779203) ^ [_1296349, _1296351, _1296353, _1296355] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296349, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296349, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296349, tc_HOL_Obool)), _1296351), _1296353)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296349, tc_HOL_Obool)), _1296353), _1296355))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296349, tc_HOL_Obool)), _1296355), _1296351)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296349, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296349, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296349, tc_HOL_Obool)), _1296351), _1296353)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296349, tc_HOL_Obool)), _1296353), _1296355))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1296349, tc_HOL_Obool)), _1296355), _1296351)))], (4686 ^ _779203) ^ [_850476, _850478, _850480, _850482, _850484, _850486, _850488, _850490] : [-(c_Wellfounded_Olex__prod(_850490, _850486, _850482, _850478) = c_Wellfounded_Olex__prod(_850488, _850484, _850480, _850476)), _850490 = _850488, _850486 = _850484, _850482 = _850480, _850478 = _850476], (47667 ^ _779203) ^ [_1739796, _1739798] : [c_List_Olist__ex(_1739796, _1739798, c_List_Olist_ONil(_1739796))], (8607 ^ _779203) ^ [_924174, _924176] : [class_Lattices_Oab__semigroup__idem__mult(_924174), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924174), _924176), _924176) = _924176)], (12282 ^ _779203) ^ [_991069] : [-(hAPP(c_Finite__Set_Ocard(_991069), c_Orderings_Obot__class_Obot(tc_fun(_991069, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20018 ^ _779203) ^ [_1132071, _1132073, _1132075] : [class_Rings_Oring(_1132071), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132071), hAPP(c_Groups_Ouminus__class_Ouminus(_1132071), _1132073)), hAPP(c_Groups_Ouminus__class_Ouminus(_1132071), _1132075)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132071), _1132073), _1132075))], (34186 ^ _779203) ^ [_1406765, _1406767, _1406769, _1406771] : [class_Complete__Lattice_Ocomplete__lattice(_1406765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406767), _1406769)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1406767, _1406765), _1406769), _1406771) = hAPP(hAPP(c_Finite__Set_Ofold(_1406767, _1406765, hAPP(hAPP(c_COMBB(_1406765, tc_fun(_1406765, _1406765), _1406767), c_Lattices_Osemilattice__inf__class_Oinf(_1406765)), _1406771)), c_Orderings_Otop__class_Otop(_1406765)), _1406769))], (43716 ^ _779203) ^ [_1653967, _1653969] : [-(_1653967 = c_List_Olist_ONil(_1653969)), -(hBOOL(hAPP(hAPP(c_member(_1653969), hAPP(c_List_Ohd(_1653969), _1653967)), hAPP(c_List_Oset(_1653969), _1653967))))], (8939 ^ _779203) ^ [_930381, _930383, _930385] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_930381), _930383)), hBOOL(hAPP(hAPP(c_member(_930381), _930385), _930383)), -(hAPP(c_Finite__Set_Ocard(_930381), _930383) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_930381), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930381, tc_HOL_Obool)), _930383), hAPP(hAPP(c_Set_Oinsert(_930381), _930385), c_Orderings_Obot__class_Obot(tc_fun(_930381, tc_HOL_Obool)))))))], (2194 ^ _779203) ^ [_811106, _811108, _811110, _811112, _811114, _811116, _811118, _811120, _811122, _811124] : [-(c_Nitpick_Opair__box_Opair__box__case(_811124, _811120, _811116, _811112, _811108) = c_Nitpick_Opair__box_Opair__box__case(_811122, _811118, _811114, _811110, _811106)), _811124 = _811122, _811120 = _811118, _811116 = _811114, _811112 = _811110, _811108 = _811106], (11202 ^ _779203) ^ [_971970, _971972, _971974, _971976] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_971970, _971972)), c_Sum__Type_OPlus(_971970, _971972, _971974, _971976))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_971970), _971974)))], (36290 ^ _779203) ^ [_1461885, _1461887, _1461889, _1461891] : [36292 ^ _779203 : [(36296 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1461885), 36294 ^ [_1461885, _1461887, _1461889, _1461891]), _1461891)))], (36298 ^ _779203) ^ [] : [-(hAPP(_1461889, 36291 ^ [_1461885, _1461887, _1461889, _1461891]) = hAPP(_1461889, 36294 ^ [_1461885, _1461887, _1461889, _1461891]))], (36300 ^ _779203) ^ [] : [36291 ^ [_1461885, _1461887, _1461889, _1461891] = 36294 ^ [_1461885, _1461887, _1461889, _1461891]], (36293 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1461885), 36291 ^ [_1461885, _1461887, _1461889, _1461891]), _1461891)))]], -(c_Fun_Oinj__on(_1461885, _1461887, _1461889, _1461891))], (25422 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (40648 ^ _779203) ^ [_1575655, _1575657, _1575659] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1575655, _1575655), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1575655, _1575655), _1575657)), c_Transitive__Closure_Ortrancl(_1575655, _1575657)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1575655, _1575655), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1575655, _1575655)), hAPP(hAPP(c_Product__Type_OPair(_1575655, _1575655), _1575659), _1575659)), c_Transitive__Closure_Otrancl(_1575655, _1575657)))], (6887 ^ _779203) ^ [_891676, _891678, _891680, _891682] : [hBOOL(hAPP(hAPP(c_member(_891676), _891678), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891676, tc_HOL_Obool)), _891680), _891682))), 6890 ^ _779203 : [(6893 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_891676), _891678), _891682))], (6891 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_891676), _891678), _891680)))]]], (43500 ^ _779203) ^ [_1648781, _1648783, _1648785, _1648787, _1648789] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1648781, _1648783)), _1648785), hAPP(hAPP(c_List_Ozip(_1648781, _1648783), _1648787), _1648789)) = hAPP(hAPP(c_List_Ozip(_1648781, _1648783), hAPP(hAPP(c_List_Odrop(_1648781), _1648785), _1648787)), hAPP(hAPP(c_List_Odrop(_1648783), _1648785), _1648789)))], (23427 ^ _779203) ^ [] : [-(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)))))], (51767 ^ _779203) ^ [_1824734, _1824736] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1824734), c_SetInterval_Oord_OatMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824736))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1824734), _1824736)))], (44859 ^ _779203) ^ [_1677990, _1677992] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1677990, _1677992) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1677990), hAPP(c_Code__Numeral_Onat__of, _1677992))))], (9053 ^ _779203) ^ [_932637] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _932637), hAPP(c_Nat_OSuc, _932637))))], (8148 ^ _779203) ^ [_914560, _914562, _914564, _914566, _914568] : [c_Fun_Ofun__upd(_914560, _914562, _914564, _914566, _914568) = _914564, -(hAPP(_914564, _914566) = _914568)], (42648 ^ _779203) ^ [_1629462, _1629464] : [-(hAPP(hAPP(c_List_Otake(_1629462), _1629464), c_List_Olist_ONil(_1629462)) = c_List_Olist_ONil(_1629462))], (35407 ^ _779203) ^ [_1440693, _1440695, _1440697, _1440699, _1440701, _1440703] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1440693, _1440693)), hAPP(hAPP(c_Product__Type_OPair(_1440693, _1440693), _1440695), _1440697)), hAPP(hAPP(c_Relation_Oinv__image(_1440699, _1440693), _1440701), _1440703))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1440699, _1440699)), hAPP(hAPP(c_Product__Type_OPair(_1440699, _1440699), hAPP(_1440703, _1440695)), hAPP(_1440703, _1440697))), _1440701)))], (29622 ^ _779203) ^ [_1304916, _1304918, _1304920, _1304922] : [class_Lattices_Osemilattice__inf(_1304916), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304916), _1304918), _1304920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304916), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1304916), _1304918), _1304922)), _1304920)))], (3782 ^ _779203) ^ [_835928, _835930, _835932, _835934, _835936, _835938] : [-(c_List_Olinorder__class_Oinsort__key(_835938, _835934, _835930) = c_List_Olinorder__class_Oinsort__key(_835936, _835932, _835928)), _835938 = _835936, _835934 = _835932, _835930 = _835928], (28724 ^ _779203) ^ [_1287204, _1287206, _1287208] : [hBOOL(hAPP(hAPP(c_member(_1287204), _1287206), hAPP(c_fequal, _1287208))), -(_1287206 = _1287208)], (24626 ^ _779203) ^ [_1212935] : [c_Nat__Transfer_Onat__set(_1212935), 24629 ^ _779203 : [(24636 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1212935))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1212935)))], (24630 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1212935)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1212935))))]]], (780 ^ _779203) ^ [_790905, _790907, _790909, _790911] : [-(c_Relation_Oantisym(_790909, _790905)), c_Relation_Oantisym(_790911, _790907), _790911 = _790909, _790907 = _790905], (27228 ^ _779203) ^ [_1258559, _1258561] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1258559), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1258561) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1258559, _1258561))], (11700 ^ _779203) ^ [_981019, _981021] : [class_Groups_Olinordered__ab__group__add(_981019), 11703 ^ _779203 : [(11710 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981019), _981021), c_Groups_Ozero__class_Ozero(_981019))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981019), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981019), _981021), _981021)), c_Groups_Ozero__class_Ozero(_981019))))], (11704 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981019), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_981019), _981021), _981021)), c_Groups_Ozero__class_Ozero(_981019))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_981019), _981021), c_Groups_Ozero__class_Ozero(_981019))))]]], (18857 ^ _779203) ^ [_1111459] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1111459) = 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)), _1111459)))], (39088 ^ _779203) ^ [_1537524] : [-(c_Wellfounded_OwfP(_1537524, hAPP(c_COMBK(tc_fun(_1537524, tc_HOL_Obool), _1537524), hAPP(c_COMBK(tc_HOL_Obool, _1537524), c_fFalse))))], (9755 ^ _779203) ^ [_945741, _945743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _945743)), _945741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945741), _945743))], (18361 ^ _779203) ^ [_1103145, _1103147] : [class_Int_Onumber__ring(_1103145), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103145), hAPP(c_Int_Onumber__class_Onumber__of(_1103145), c_Int_OPls)), _1103147) = _1103147)], (52403 ^ _779203) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (33171 ^ _779203) ^ [_1386705, _1386707] : [-(_1386705 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 33174 ^ _779203 : [(33181 ^ _779203) ^ [] : [-(_1386707 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1386705, _1386707) = 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, _1386707))), 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, _1386705)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1386707))), c_Divides_Opdivmod(_1386705, _1386707)), 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), _1386707))))), c_Divides_Opdivmod(_1386705, _1386707)))))], (33175 ^ _779203) ^ [] : [_1386707 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1386705, _1386707) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1386705))]]], (43824 ^ _779203) ^ [_1655933, _1655935, _1655937] : [-(_1655933 = c_List_Olist_ONil(_1655935)), -(hAPP(hAPP(c_List_Otake(_1655935), hAPP(c_Nat_OSuc, _1655937)), _1655933) = hAPP(hAPP(c_List_Olist_OCons(_1655935), hAPP(c_List_Ohd(_1655935), _1655933)), hAPP(hAPP(c_List_Otake(_1655935), _1655937), hAPP(c_List_Otl(_1655935), _1655933))))], (9377 ^ _779203) ^ [_939126, _939128, _939130] : [9378 ^ _779203 : [(9381 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_939130, _939128), _939126))], (9379 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _939126), _939128)))]], 9384 ^ _779203 : [(9387 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_939130, _939128), _939126))], (9385 ^ _779203) ^ [] : [-(_939126 = _939128)]], 9390 ^ _779203 : [(9393 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_939130, _939128), _939126))], (9391 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _939128), _939126)))]], -(hBOOL(hAPP(hAPP(_939130, _939128), _939126)))], (10413 ^ _779203) ^ [_958682, _958684, _958686, _958688, _958690] : [class_Rings_Ocomm__semiring__1(_958682), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958682), _958684), _958686)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958682), _958688), _958690)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958682), _958684), _958688)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_958682), _958686), _958690)))], (37535 ^ _779203) ^ [_1490122, _1490124, _1490126] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1490122, _1490124), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1490122, _1490124), _1490126), hAPP(c_COMBK(tc_fun(_1490124, tc_HOL_Obool), _1490122), c_Orderings_Otop__class_Otop(tc_fun(_1490124, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1490122, _1490124), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1490122, tc_HOL_Obool)), _1490126)), hAPP(c_COMBK(tc_fun(_1490124, tc_HOL_Obool), _1490122), c_Orderings_Otop__class_Otop(tc_fun(_1490124, tc_HOL_Obool)))))], (11075 ^ _779203) ^ [_969985, _969987, _969989] : [11076 ^ _779203 : [(11079 ^ _779203) ^ [] : [_969987 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11077 ^ _779203) ^ [] : [_969985 = _969989]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969985), _969987) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _969989), _969987))], (9231 ^ _779203) ^ [_936672] : [hAPP(c_Nat_OSuc, _936672) = _936672], (43798 ^ _779203) ^ [_1655310, _1655312, _1655314] : [-(hAPP(hAPP(c_List_Otake(_1655310), _1655312), hAPP(c_List_Otl(_1655310), _1655314)) = hAPP(c_List_Otl(_1655310), hAPP(hAPP(c_List_Otake(_1655310), hAPP(c_Nat_OSuc, _1655312)), _1655314)))], (36751 ^ _779203) ^ [_1471405, _1471407, _1471409, _1471411] : [c_Fun_Oinj__on(_1471405, tc_fun(tc_fun(_1471405, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1471405, tc_fun(tc_prod(_1471405, _1471405), tc_HOL_Obool), tc_fun(tc_fun(_1471405, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471405, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1471405, _1471405), tc_HOL_Obool), tc_fun(tc_fun(_1471405, tc_HOL_Obool), tc_HOL_Obool)), _1471405), c_Equiv__Relations_Oquotient(_1471405)), hAPP(hAPP(c_COMBC(_1471405, tc_fun(_1471405, tc_HOL_Obool), tc_fun(_1471405, tc_HOL_Obool)), c_Set_Oinsert(_1471405)), c_Orderings_Obot__class_Obot(tc_fun(_1471405, tc_HOL_Obool))))), _1471407), _1471409), hBOOL(hAPP(hAPP(c_member(_1471405), _1471411), _1471409)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471405), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1471405, tc_HOL_Obool)), _1471409), hAPP(hAPP(c_Set_Oinsert(_1471405), _1471411), c_Orderings_Obot__class_Obot(tc_fun(_1471405, tc_HOL_Obool))))), _1471407) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1471405, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471405), _1471409), _1471407)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1471405), hAPP(hAPP(c_Set_Oinsert(_1471405), _1471411), c_Orderings_Obot__class_Obot(tc_fun(_1471405, tc_HOL_Obool)))), _1471407)))], (43275 ^ _779203) ^ [_1642790, _1642792, _1642794, _1642796] : [hBOOL(hAPP(hAPP(c_member(_1642790), _1642792), hAPP(c_List_Oset(_1642790), _1642794))), -(c_List_Oremove1(_1642790, _1642792, hAPP(hAPP(c_List_Oappend(_1642790), _1642794), _1642796)) = hAPP(hAPP(c_List_Oappend(_1642790), c_List_Oremove1(_1642790, _1642792, _1642794)), _1642796))], (6052 ^ _779203) ^ [_875481, _875483, _875485] : [hAPP(hAPP(c_Set_Oinsert(_875481), _875483), c_Orderings_Obot__class_Obot(tc_fun(_875481, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_875481), _875485), c_Orderings_Obot__class_Obot(tc_fun(_875481, tc_HOL_Obool))), -(_875483 = _875485)], (18288 ^ _779203) ^ [_1101781, _1101783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1101781), _1101783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101781)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101783))))], (43498 ^ _779203) ^ [_1648722, _1648724, _1648726, _1648728] : [-(hAPP(hAPP(c_List_Odrop(_1648722), _1648724), hAPP(hAPP(c_List_Odrop(_1648722), _1648726), _1648728)) = hAPP(hAPP(c_List_Odrop(_1648722), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1648724), _1648726)), _1648728))], (34969 ^ _779203) ^ [_1428741, _1428743, _1428745, _1428747, _1428749] : [class_Complete__Lattice_Ocomplete__lattice(_1428741), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1428743, tc_HOL_Obool)), _1428745), _1428747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428741), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428743, _1428741), _1428745), _1428749)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428743, _1428741), _1428747), _1428749))))], (45434 ^ _779203) ^ [_1691079, _1691081, _1691083] : [-(hBOOL(hAPP(hAPP(c_member(_1691079), _1691081), hAPP(c_List_Oset(_1691079), _1691083)))), -(hAPP(c_List_OremoveAll(_1691079, _1691081), _1691083) = _1691083)], (20967 ^ _779203) ^ [_1148977, _1148979] : [class_Rings_Olinordered__idom(_1148977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148977), c_Groups_Ozero__class_Ozero(_1148977)), _1148979)), -(c_Groups_Osgn__class_Osgn(_1148977, _1148979) = c_Groups_Oone__class_Oone(_1148977))], (42319 ^ _779203) ^ [_1622341, _1622343, _1622345, _1622347] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622341, tc_HOL_Obool)), hAPP(c_List_Oset(_1622341), hAPP(hAPP(c_List_Olist__update(_1622341, _1622343), _1622345), _1622347))), hAPP(hAPP(c_Set_Oinsert(_1622341), _1622347), hAPP(c_List_Oset(_1622341), _1622343)))))], (42539 ^ _779203) ^ [_1627409, _1627411] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1627409), _1627411))), -(c_Nitpick_Ocard_H(_1627409, _1627411) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48836 ^ _779203) ^ [_1765352, _1765354, _1765356] : [hBOOL(hAPP(hAPP(c_member(_1765354), _1765352), c_Orderings_Obot__class_Obot(tc_fun(_1765354, tc_HOL_Obool)))), hBOOL(hAPP(_1765356, _1765352))], (5975 ^ _779203) ^ [_873937, _873939, _873941, _873943] : [5976 ^ _779203 : [(5979 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_873937), _873939), _873943))], (5977 ^ _779203) ^ [] : [_873939 = _873941]], -(hBOOL(hAPP(hAPP(c_member(_873937), _873939), hAPP(hAPP(c_Set_Oinsert(_873937), _873941), _873943))))], (21253 ^ _779203) ^ [_1153948] : [class_Int_Onumber__ring(_1153948), -(hAPP(c_Int_Onumber__class_Onumber__of(_1153948), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1153948))], (8354 ^ _779203) ^ [_918620, _918622, _918624, _918626, _918628] : [class_Groups_Oab__group__add(_918620), hBOOL(hAPP(c_Finite__Set_Ofinite(_918622), _918624)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918622, tc_HOL_Obool)), _918626), _918624)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918622, _918620), _918628), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918622, tc_HOL_Obool)), _918624), _918626)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_918620), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918622, _918620), _918628), _918624)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918622, _918620), _918628), _918626)))], (48951 ^ _779203) ^ [_1767821, _1767823, _1767825] : [-(c_List_Olist__ex(_1767821, _1767823, _1767825)), 48952 ^ _779203 : [(48953 ^ _779203) ^ [_1767878] : [hBOOL(hAPP(hAPP(c_member(_1767821), _1767878), hAPP(c_List_Oset(_1767821), _1767825))), hBOOL(hAPP(_1767823, _1767878))]]], (11007 ^ _779203) ^ [_969000, _969002] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _969000), _969002) = _969000, -(_969002 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11908 ^ _779203) ^ [_984790, _984792, _984794, _984796] : [class_Rings_Olinordered__ring__strict(_984790), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984790), _984792), c_Groups_Ozero__class_Ozero(_984790))), 11915 ^ _779203 : [(11922 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984790), _984796), _984794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984790), _984792), _984794)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984790), _984792), _984796))))], (11916 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984790), _984792), _984794)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_984790), _984792), _984796))), 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[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036341), c_Groups_Ozero__class_Ozero(_1036341)), _1036347)))]], 14788 ^ _779203 : [(14791 ^ _779203) ^ [] : [14792 ^ _779203 : [(14795 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036341), _1036345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1036341), _1036343), _1036347)))], (14793 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036341), _1036347), c_Groups_Ozero__class_Ozero(_1036341))))]], 14796 ^ _779203 : [(14799 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1036341), _1036343), c_Groups_Ozero__class_Ozero(_1036341)))], (14797 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036341), _1036347), c_Groups_Ozero__class_Ozero(_1036341)))]]], (14789 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1036341), c_Groups_Ozero__class_Ozero(_1036341)), _1036347))]]]]], (1140 ^ _779203) ^ [_796413, _796415] : 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c_Relation_Oantisym(_1773284, _1773288), -(c_Relation_Oantisym(_1773284, _1773286))], (42375 ^ _779203) ^ [_1623542, _1623544, _1623546, _1623548] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1623542), tc_List_Olist(_1623542))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1623542), tc_List_Olist(_1623542)), _1623544), _1623546)), c_List_Olistrel1(_1623542, _1623548))), 42380 ^ _779203 : [(42385 ^ _779203) ^ [] : [-(_1623546 = hAPP(hAPP(c_List_Olist__update(_1623542, _1623544), 42379 ^ [_1623542, _1623544, _1623546, _1623548]), 42378 ^ [_1623542, _1623544, _1623546, _1623548]))], (42383 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42379 ^ [_1623542, _1623544, _1623546, _1623548]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623542)), _1623544))))], (42381 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1623542, _1623542)), hAPP(hAPP(c_Product__Type_OPair(_1623542, _1623542), hAPP(hAPP(c_List_Onth(_1623542), _1623544), 42379 ^ 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^ _779203) ^ [_1584882, _1584884, _1584886, _1584888, _1584890, _1584892] : [c_Relation_Osingle__valued(_1584882, _1584884, _1584886), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584882, _1584884)), hAPP(hAPP(c_Product__Type_OPair(_1584882, _1584884), _1584888), _1584890)), _1584886)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584882, _1584884)), hAPP(hAPP(c_Product__Type_OPair(_1584882, _1584884), _1584888), _1584892)), _1584886)), -(_1584890 = _1584892)], (29892 ^ _779203) ^ [_1310938, _1310940, _1310942, _1310944] : [class_Orderings_Oorder(_1310938), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310938, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1310938, _1310940, _1310942)), c_SetInterval_Oord__class_OatLeastAtMost(_1310938, _1310942, _1310944)) = c_Orderings_Obot__class_Obot(tc_fun(_1310938, tc_HOL_Obool)))], (24730 ^ _779203) ^ [_1214899, _1214901, _1214903] : [class_Rings_Ocomm__semiring__1(_1214899), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1214899), _1214901), 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)))), _1214903))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214899), _1214901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1214899), hAPP(hAPP(c_Power_Opower__class_Opower(_1214899), _1214901), _1214903)), hAPP(hAPP(c_Power_Opower__class_Opower(_1214899), _1214901), _1214903))))], (47083 ^ _779203) ^ [_1726550, _1726552, _1726554] : [47085 ^ _779203 : [(47088 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1726552, 47084 ^ [_1726550, _1726552, _1726554])))], (47086 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1726550), 47084 ^ [_1726550, _1726552, _1726554]), hAPP(c_List_Oset(_1726550), c_List_OdropWhile(_1726550, _1726552, _1726554)))))]], -(c_List_OtakeWhile(_1726550, _1726552, _1726554) = hAPP(c_List_Ofilter(_1726550, _1726552), _1726554))], (21985 ^ _779203) ^ [_1166764, _1166766, _1166768, _1166770] : [class_Divides_Osemiring__div(_1166764), -(c_Divides_Odiv__class_Omod(_1166764, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166764), _1166766), _1166768), _1166770) = c_Divides_Odiv__class_Omod(_1166764, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166764), c_Divides_Odiv__class_Omod(_1166764, _1166766, _1166770)), _1166768), _1166770))], (20398 ^ _779203) ^ [_1138898, _1138900, _1138902] : [class_Groups_Oordered__ab__group__add__abs(_1138898), 20401 ^ _779203 : [(20410 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138898), hAPP(c_Groups_Oabs__class_Oabs(_1138898), _1138900)), _1138902))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138898), _1138900), _1138902)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138898), hAPP(c_Groups_Ouminus__class_Ouminus(_1138898), _1138900)), _1138902))], (20402 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138898), hAPP(c_Groups_Oabs__class_Oabs(_1138898), _1138900)), _1138902)), 20405 ^ _779203 : [(20408 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138898), hAPP(c_Groups_Ouminus__class_Ouminus(_1138898), _1138900)), _1138902)))], (20406 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138898), _1138900), _1138902)))]]]]], (10843 ^ _779203) ^ [_966653, _966655] : [class_Rings_Omult__zero(_966653), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966653), _966655), c_Groups_Ozero__class_Ozero(_966653)) = c_Groups_Ozero__class_Ozero(_966653))], (32545 ^ _779203) ^ [_1369820, _1369822, _1369824] : [-(hAPP(c_Nat_Onat_Onat__rec(_1369820, _1369822, _1369824), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1369822)], (52753 ^ _779203) ^ [_1837780, _1837782] : [hBOOL(hAPP(hAPP(c_fdisj, _1837780), _1837782)), -(hBOOL(_1837780)), -(hBOOL(_1837782))], (46264 ^ _779203) ^ [_1709347, _1709349, _1709351, _1709353, _1709355] : [class_Orderings_Olinorder(_1709347), 46267 ^ _779203 : [(46274 ^ _779203) ^ [] : [c_List_Olinorder__class_Osorted(_1709347, hAPP(hAPP(c_List_Omap(_1709349, _1709347), _1709351), _1709355)), -(c_List_Olinorder__class_Osorted(_1709347, hAPP(hAPP(c_List_Omap(_1709349, _1709347), _1709351), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1709349, _1709347, _1709351), _1709353), _1709355))))], (46268 ^ _779203) ^ [] : [c_List_Olinorder__class_Osorted(_1709347, hAPP(hAPP(c_List_Omap(_1709349, _1709347), _1709351), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1709349, _1709347, _1709351), _1709353), _1709355))), -(c_List_Olinorder__class_Osorted(_1709347, hAPP(hAPP(c_List_Omap(_1709349, _1709347), _1709351), _1709355)))]]], (46098 ^ _779203) ^ [_1706748, _1706750] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1706748, _1706750)))], (29732 ^ _779203) ^ [_1307071, _1307073, _1307075, _1307077] : [-(hBOOL(hAPP(hAPP(c_member(_1307071), _1307073), _1307075))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307071, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1307071), _1307073), _1307077)), _1307075) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307071, tc_HOL_Obool)), _1307077), _1307075))], (14037 ^ _779203) ^ [_1023413, _1023415, _1023417] : [class_Fields_Olinordered__field(_1023413), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023413), _1023415), c_Groups_Ozero__class_Ozero(_1023413))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023413), _1023417), c_Groups_Ozero__class_Ozero(_1023413))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1023413), c_Groups_Ozero__class_Ozero(_1023413)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1023413), _1023415), _1023417))))], (42461 ^ _779203) ^ [_1625525, _1625527] : [hAPP(c_Finite__Set_Ocard(_1625525), hAPP(c_List_Oset(_1625525), _1625527)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625525)), _1625527), -(hBOOL(hAPP(c_List_Odistinct(_1625525), _1625527)))], (28638 ^ _779203) ^ [_1285827, _1285829] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1285827, tc_HOL_Obool)), _1285829)))], (9596 ^ _779203) ^ [_943075, _943077, _943079, _943081, _943083] : [class_Rings_Osemiring(_943075), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943075), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943075), _943077), _943079)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943075), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943075), _943081), _943079)), _943083)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943075), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_943075), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_943075), _943077), _943081)), _943079)), _943083))], (22135 ^ _779203) ^ [_1169962, _1169964, _1169966] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1169962), _1169964), _1169966) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1169962), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1169964, _1169966)), _1169966))], (18903 ^ _779203) ^ [_1112219] : [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)), _1112219))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1112219)))], (52357 ^ _779203) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (9973 ^ _779203) ^ [_949500, _949502, _949504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949500), _949502)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949500), _949504)), 9980 ^ _779203 : [(9987 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949502), _949504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949502), _949500)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949504), _949500))))], (9981 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949502), _949500)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949504), _949500))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949502), _949504)))]]], (45652 ^ _779203) ^ [_1696573, _1696575, _1696577] : [45654 ^ _779203 : [(45657 ^ _779203) ^ [] : [hBOOL(hAPP(_1696575, 45653 ^ [_1696573, _1696575, _1696577]))], (45655 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1696573), 45653 ^ [_1696573, _1696575, _1696577]), hAPP(c_List_Oset(_1696573), _1696577))))]], -(hAPP(c_List_Ofilter(_1696573, _1696575), _1696577) = _1696577)], (43969 ^ _779203) ^ [_1659065, _1659067] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1659065), hAPP(c_List_Oset(tc_Nat_Onat), _1659067))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1659065), 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)), _1659067))))], (32559 ^ _779203) ^ [_1370065, _1370067, _1370069, _1370071] : [class_Rings_Osemiring__1(_1370065), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1370065, _1370067, hAPP(c_Nat_OSuc, _1370069), _1370071) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1370065, _1370067, _1370069, hAPP(_1370067, _1370071)))], (5965 ^ _779203) ^ [_873803, _873805, _873807, _873809] : [hBOOL(hAPP(hAPP(c_member(_873803), _873805), hAPP(hAPP(c_Set_Oinsert(_873803), _873807), _873809))), -(_873805 = _873807), -(hBOOL(hAPP(hAPP(c_member(_873803), _873805), _873809)))], (34348 ^ _779203) ^ [_1411375, _1411377, _1411379, _1411381] : [c_Orderings_Obot__class_Obot(tc_fun(_1411375, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1411377, tc_fun(_1411375, tc_HOL_Obool)), _1411379), _1411381), 34351 ^ _779203 : [(34352 ^ _779203) ^ [_1411491] : [hBOOL(hAPP(hAPP(c_member(_1411377), _1411491), _1411379)), -(hAPP(_1411381, _1411491) = c_Orderings_Obot__class_Obot(tc_fun(_1411375, tc_HOL_Obool)))]]], (33841 ^ _779203) ^ [_1399086, _1399088, _1399090, _1399092] : [-(_1399086 = _1399088), hAPP(c_Product__Type_Ofst(_1399090, _1399092), _1399086) = hAPP(c_Product__Type_Ofst(_1399090, _1399092), _1399088), hAPP(c_Product__Type_Osnd(_1399090, _1399092), _1399086) = hAPP(c_Product__Type_Osnd(_1399090, _1399092), _1399088)], (46650 ^ _779203) ^ [_1717356, _1717358, _1717360] : [hAPP(c_List_Orev(_1717356), _1717358) = hAPP(c_List_Orev(_1717356), _1717360), -(_1717358 = _1717360)], (52467 ^ _779203) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (52175 ^ _779203) ^ [_1831664, _1831666] : [class_Lattices_Olattice(_1831664), -(class_Lattices_Olattice(tc_fun(_1831666, _1831664)))], (47199 ^ _779203) ^ [_1728795, _1728797] : [-(c_List_Oinsert(_1728795, _1728797, c_List_Olist_ONil(_1728795)) = hAPP(hAPP(c_List_Olist_OCons(_1728795), _1728797), c_List_Olist_ONil(_1728795)))], (35385 ^ _779203) ^ [_1439651, _1439653, _1439655] : [-(c_Wellfounded_Omlex__prod(_1439651, _1439653, _1439655) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1439651), _1439651), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1439651, c_Wellfounded_Oless__than, _1439655)), hAPP(hAPP(c_COMBS(_1439651, _1439651, tc_prod(tc_Nat_Onat, _1439651)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1439651, tc_prod(tc_Nat_Onat, _1439651)), _1439651), c_Product__Type_OPair(tc_Nat_Onat, _1439651)), _1439653)), c_COMBI(_1439651))))], (49410 ^ _779203) ^ [_1777828, _1777830] : [c_Relation_Osym(_1777828, hAPP(c_Set_OCollect(tc_prod(_1777828, _1777828)), hAPP(c_Product__Type_Oprod_Oprod__case(_1777828, _1777828, tc_HOL_Obool), _1777830))), -(c_Predicate_Osymp(_1777828, _1777830))], (21925 ^ _779203) ^ [_1165476, _1165478, _1165480, _1165482] : [class_Divides_Osemiring__div(_1165476), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165476), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165476), _1165478), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1165476), _1165480), _1165478))), c_Divides_Odiv__class_Omod(_1165476, _1165480, _1165478))), _1165482) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165476), _1165480), _1165482))], (52285 ^ _779203) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (37015 ^ _779203) ^ [_1477256, _1477258, _1477260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1477256, _1477256), tc_HOL_Obool)), _1477258), _1477260)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1477256, tc_HOL_Obool)), c_Wellfounded_Oacc(_1477256, _1477260)), c_Wellfounded_Oacc(_1477256, _1477258))))], (41177 ^ _779203) ^ [_1589411, _1589413, _1589415, _1589417, _1589419] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589411, _1589411)), hAPP(hAPP(c_Product__Type_OPair(_1589411, _1589411), _1589413), _1589415)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589411, _1589411), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1589417)), _1589419))), 41181 ^ _779203 : [(41184 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589411, _1589411)), hAPP(hAPP(c_Product__Type_OPair(_1589411, _1589411), 41180 ^ [_1589411, _1589413, _1589415, _1589417, _1589419]), _1589415)), _1589419)))], (41182 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589411, _1589411)), hAPP(hAPP(c_Product__Type_OPair(_1589411, _1589411), _1589413), 41180 ^ [_1589411, _1589413, _1589415, _1589417, _1589419])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1589411, _1589411), tc_HOL_Obool), _1589417), _1589419))))]]], (26070 ^ _779203) ^ [_1237605, _1237607] : [class_Rings_Olinordered__idom(_1237605), 26073 ^ _779203 : [(26080 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237607)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237605), c_Groups_Ozero__class_Ozero(_1237605)), hAPP(c_Int_Oring__1__class_Oof__int(_1237605), _1237607))))], (26074 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237605), c_Groups_Ozero__class_Ozero(_1237605)), hAPP(c_Int_Oring__1__class_Oof__int(_1237605), _1237607))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237607)))]]], (48310 ^ _779203) ^ [_1753317, _1753319, _1753321, _1753323, _1753325] : [-(hAPP(hAPP(c_List_Omap(_1753317, _1753319), _1753321), c_List_Oreplicate(_1753317, _1753323, _1753325)) = c_List_Oreplicate(_1753319, _1753323, hAPP(_1753321, _1753325)))], (1870 ^ _779203) ^ [_805538, _805540] : [-(class_Rings_Osemiring(_805538)), _805540 = _805538, class_Rings_Osemiring(_805540)], (45957 ^ _779203) ^ [_1703898, _1703900, _1703902, _1703904] : [c_List_Oupt(_1703898, _1703900) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1703902), _1703904), 45960 ^ _779203 : [(45965 ^ _779203) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703898), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1703900) = _1703904)], (45963 ^ _779203) ^ [] : [-(_1703898 = _1703902)], (45961 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703898), _1703900)))]]], (52591 ^ _779203) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (21751 ^ _779203) ^ [_1162103, _1162105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1162103)), c_Int_OBit0(_1162105))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1162103), _1162105)))], (32339 ^ _779203) ^ [_1364432, _1364434, _1364436] : [class_Fields_Ofield(_1364432), -(_1364434 = c_Groups_Oone__class_Oone(_1364432)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1364432), hAPP(c_Power_Opower__class_Opower(_1364432), _1364434)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1364436)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364432), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1364432), hAPP(hAPP(c_Power_Opower__class_Opower(_1364432), _1364434), _1364436)), c_Groups_Oone__class_Oone(_1364432))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1364432), _1364434), c_Groups_Oone__class_Oone(_1364432))))], (47661 ^ _779203) ^ [_1739624, _1739626, _1739628] : [47662 ^ _779203 : [(47663 ^ _779203) ^ [_1739701, _1739703] : [_1739628 = hAPP(hAPP(c_List_Oappend(_1739624), _1739703), hAPP(hAPP(c_List_Olist_OCons(_1739624), _1739626), _1739701))]], -(hBOOL(hAPP(hAPP(c_member(_1739624), _1739626), hAPP(c_List_Oset(_1739624), _1739628))))], (44996 ^ _779203) ^ [_1681364, _1681366, _1681368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1681364, tc_HOL_Obool)), _1681366), _1681368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1681364), tc_HOL_Obool)), c_List_Olistsp(_1681364, _1681366)), c_List_Olistsp(_1681364, _1681368))))], (35641 ^ _779203) ^ [_1446932, _1446934, _1446936] : [_1446934 = c_Orderings_Obot__class_Obot(tc_fun(_1446932, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446932), _1446934), _1446936) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446932, tc_HOL_Obool), tc_HOL_Obool)))], (49486 ^ _779203) ^ [_1779110, _1779112] : [-(c_Equiv__Relations_Opart__equivp(_1779110, _1779112)), 49489 ^ _779203 : [(49490 ^ _779203) ^ [_1779230] : [hBOOL(hAPP(hAPP(_1779112, _1779230), _1779230))]], 49507 ^ _779203 : [(49510 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1779112, 49492 ^ [_1779110, _1779112]), 49492 ^ [_1779110, _1779112])))], (49512 ^ _779203) ^ [] : [-(hAPP(_1779112, 49491 ^ [_1779110, _1779112]) = hAPP(_1779112, 49492 ^ [_1779110, _1779112]))], (49514 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1779112, 49491 ^ [_1779110, _1779112]), 49492 ^ [_1779110, _1779112]))], (49508 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1779112, 49491 ^ [_1779110, _1779112]), 49491 ^ [_1779110, _1779112])))]], 49495 ^ _779203 : [(49498 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1779112, 49491 ^ [_1779110, _1779112]), 49491 ^ [_1779110, _1779112])), hBOOL(hAPP(hAPP(_1779112, 49492 ^ [_1779110, _1779112]), 49492 ^ [_1779110, _1779112])), hAPP(_1779112, 49491 ^ [_1779110, _1779112]) = hAPP(_1779112, 49492 ^ [_1779110, _1779112])], (49496 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1779112, 49491 ^ [_1779110, _1779112]), 49492 ^ [_1779110, _1779112])))]]], (29218 ^ _779203) ^ [_1296865, _1296867] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296865, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1296865, tc_HOL_Obool))), _1296867) = _1296867)], (49226 ^ _779203) ^ [_1774493, _1774495] : [c_Relation_Oantisym(_1774493, _1774495), -(c_Relation_Oantisym(_1774493, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1774493, _1774493), tc_HOL_Obool)), _1774495), c_Relation_OId(_1774493))))], (10201 ^ _779203) ^ [_954421, _954423, _954425, _954427, _954429, _954431] : [class_Rings_Oring(_954421), 10204 ^ _779203 : [(10211 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954421), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_954421), _954423), _954429)), _954425)), _954427) = _954431, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954421), _954423), _954425)), _954427) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954421), _954429), _954425)), _954431))], (10205 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954421), _954423), _954425)), _954427) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954421), _954429), _954425)), _954431), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954421), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_954421), _954423), _954429)), _954425)), _954427) = _954431)]]], (48094 ^ _779203) ^ [_1748747] : [-(c_Predicate_Oconversep(_1748747, _1748747, c_fequal) = c_fequal)], (37627 ^ _779203) ^ [_1492792, _1492794, _1492796, _1492798] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1492792), _1492794)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1492796), _1492798)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1492792, _1492796)), hAPP(hAPP(c_Product__Type_OSigma(_1492792, _1492796), _1492794), hAPP(c_COMBK(tc_fun(_1492796, tc_HOL_Obool), _1492792), _1492798)))))], (43582 ^ _779203) ^ [_1650695, _1650697, _1650699, _1650701] : [-(_1650695 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1650697), _1650695), hAPP(hAPP(c_List_Olist_OCons(_1650697), _1650699), _1650701)) = hAPP(hAPP(c_List_Odrop(_1650697), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1650695), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1650701))], (32481 ^ _779203) ^ [_1367995, _1367997] : [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), _1367995))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1367997), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1367995))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1367997), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1367995))), 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), _1367997))), c_COMBI(tc_Int_Oint))))], (28880 ^ _779203) ^ [_1290201, _1290203, _1290205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1290201, tc_HOL_Obool)), _1290203), _1290205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1290201, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1290201, _1290203)), c_Predicate_OPowp(_1290201, _1290205))))], (48830 ^ _779203) ^ [_1765261, _1765263] : [c_Relation_Otrans(_1765261, _1765263), -(c_Relation_Otrans(_1765261, hAPP(c_Relation_Oconverse(_1765261, _1765261), _1765263)))], (2344 ^ _779203) ^ [_813467, _813469, _813471, _813473] : [-(c_Nitpick_Onat__gcd(_813473, _813469) = c_Nitpick_Onat__gcd(_813471, _813467)), _813473 = _813471, _813469 = _813467], (13383 ^ _779203) ^ [_1010977, _1010979] : [class_Rings_Olinordered__idom(_1010977), 13386 ^ _779203 : [(13393 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010977), _1010979), c_Groups_Ozero__class_Ozero(_1010977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010977), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010977), _1010979), _1010979)), c_Groups_Ozero__class_Ozero(_1010977))))], (13387 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010977), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010977), _1010979), _1010979)), c_Groups_Ozero__class_Ozero(_1010977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010977), _1010979), c_Groups_Ozero__class_Ozero(_1010977))))]]], (52741 ^ _779203) ^ [_1837606, _1837608] : [hBOOL(_1837606), -(hBOOL(hAPP(hAPP(c_fdisj, _1837606), _1837608)))], (5715 ^ _779203) ^ [_869488, _869490] : [hBOOL(hAPP(hAPP(c_member(_869488), _869490), c_Orderings_Obot__class_Obot(tc_fun(_869488, tc_HOL_Obool))))], (52619 ^ _779203) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (5542 ^ _779203) ^ [_863906, _863908, _863910, _863912, _863914, _863916] : [-(c_COMBB(_863916, _863912, _863908) = c_COMBB(_863914, _863910, _863906)), _863916 = _863914, _863912 = _863910, _863908 = _863906], (24087 ^ _779203) ^ [_1203442, _1203444] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1203442))), _1203444) = 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)))), _1203442), _1203444))], (28067 ^ _779203) ^ [_1274802, _1274804] : [28075 ^ _779203 : [(28078 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1274804, 28074 ^ [_1274802, _1274804])))], (28076 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 28074 ^ [_1274802, _1274804]), _1274802)))]], 28068 ^ _779203 : [(28069 ^ _779203) ^ [_1274870] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1274870), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1274802))), hBOOL(hAPP(_1274804, _1274870))]]], (15580 ^ _779203) ^ [_1052336, _1052338, _1052340] : [class_Orderings_Olinorder(_1052336), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052336), _1052338), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1052336), _1052338), _1052340))))], (31823 ^ _779203) ^ [_1351628, _1351630, _1351632] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351628, tc_Nat_Onat), _1351630), _1351632)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351628, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1351628), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1351630)), _1351632))], (32998 ^ _779203) ^ [_1383769, _1383771] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1383769, _1383771) = 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), _1383769), _1383771)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1383769, _1383771)))], (39971 ^ _779203) ^ [_1558622, _1558624] : [39973 ^ _779203 : [(39976 ^ _779203) ^ [] : [39972 ^ [_1558622, _1558624] = c_Orderings_Obot__class_Obot(tc_fun(_1558622, tc_HOL_Obool))], (39974 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1558622, tc_HOL_Obool)), 39972 ^ [_1558622, _1558624]), hAPP(c_Relation_OImage(_1558622, _1558622, _1558624), 39972 ^ [_1558622, _1558624]))))]], -(c_Wellfounded_Owf(_1558622, _1558624))], (43774 ^ _779203) ^ [_1654928, _1654930, _1654932] : [hAPP(c_List_Orotate(_1654928, _1654930), _1654932) = c_List_Olist_ONil(_1654928), -(_1654932 = c_List_Olist_ONil(_1654928))], (47026 ^ _779203) ^ [_1725156, _1725158, _1725160, _1725162, _1725164] : [c_List_OdropWhile(_1725156, _1725158, _1725160) = hAPP(hAPP(c_List_Olist_OCons(_1725156), _1725162), _1725164), 47029 ^ _779203 : [(47032 ^ _779203) ^ [] : [hBOOL(hAPP(_1725158, _1725162))], (47030 ^ _779203) ^ [] : [-(_1725160 = hAPP(hAPP(c_List_Oappend(_1725156), c_List_OtakeWhile(_1725156, _1725158, _1725160)), hAPP(hAPP(c_List_Olist_OCons(_1725156), _1725162), _1725164)))]]], (23996 ^ _779203) ^ [_1201705, _1201707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201705)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1201707)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1201705), hAPP(c_Int_Onat, _1201707)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1201705, _1201707)))], (19212 ^ _779203) ^ [_1117694, _1117696] : [class_Groups_Oordered__ab__group__add__abs(_1117694), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1117694), c_Groups_Ozero__class_Ozero(_1117694)), _1117696)), -(hAPP(c_Groups_Oabs__class_Oabs(_1117694), _1117696) = _1117696)], (48534 ^ _779203) ^ [_1758171, _1758173, _1758175] : [-(c_List_Olist__ex1(_1758171, _1758173, _1758175)), 48535 ^ _779203 : [(48536 ^ _779203) ^ [_1758265] : [hBOOL(hAPP(hAPP(c_member(_1758171), _1758265), hAPP(c_List_Oset(_1758171), _1758175))), hBOOL(hAPP(_1758173, _1758265)), 48544 ^ _779203 : [(48549 ^ _779203) ^ [] : [48543 ^ [_1758171, _1758173, _1758175, _1758265] = _1758265], (48547 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1758173, 48543 ^ [_1758171, _1758173, _1758175, _1758265])))], (48545 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1758171), 48543 ^ [_1758171, _1758173, _1758175, _1758265]), hAPP(c_List_Oset(_1758171), _1758175))))]]]]], (52387 ^ _779203) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (17590 ^ _779203) ^ [_1089285, _1089287] : [class_Orderings_Olinorder(_1089285), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089285), _1089287)), -(c_Big__Operators_Olattice_OInf__fin(_1089285, c_Orderings_Oord__class_Omin(_1089285), _1089287) = hAPP(c_Finite__Set_Ofold1(_1089285, c_Orderings_Oord__class_Omin(_1089285)), _1089287))], (4170 ^ _779203) ^ [_842310, _842312, _842314, _842316] : [-(c_List_Ozip(_842316, _842312) = c_List_Ozip(_842314, _842310)), _842316 = _842314, _842312 = _842310], (8715 ^ _779203) ^ [_926105, _926107, _926109, _926111] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_926105), 8718 ^ _779203 : [(8725 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926105), _926109), _926111)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926105), _926107), _926109)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926105), _926107), _926111))))], (8719 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926105), _926107), _926109)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_926105), _926107), _926111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926105), _926109), _926111)))]]], (23429 ^ _779203) ^ [_1191514, _1191516, _1191518, _1191520] : [_1191514 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1191516), _1191518)), _1191520), -(_1191516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1191514, _1191516) = _1191520), 23436 ^ _779203 : [(23439 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191520)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191520), _1191516))], (23437 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191516)))]], 23444 ^ _779203 : [(23447 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191516), _1191520)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1191520), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23445 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191516))]]], (36304 ^ _779203) ^ [_1462277, _1462279, _1462281, _1462283, _1462285] : [c_Fun_Oinj__on(_1462277, _1462279, _1462281, _1462283), -(c_Fun_Oinj__on(_1462277, _1462279, _1462281, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1462277, tc_HOL_Obool)), _1462283), _1462285)))], (27000 ^ _779203) ^ [_1254786, _1254788] : [-(c_Random_Olog(_1254786, _1254788) = 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(_1254786, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1254788), _1254786)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1254786), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1254788), _1254786)))], (33081 ^ _779203) ^ [_1385284, _1385286] : [-(c_Divides_OposDivAlg(_1385284, _1385286) = hAPP(c_Divides_Oadjust(_1385286), c_Divides_OposDivAlg(_1385284, 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)))), _1385286)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1385284), _1385286))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1385286), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28720 ^ _779203) ^ [_1287112, _1287114] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1287112), _1287114) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1287112, _1287114))], (20961 ^ _779203) ^ [_1148894] : [class_Int_Onumber__ring(_1148894), -(c_Int_Oiszero(_1148894, hAPP(c_Int_Onumber__class_Onumber__of(_1148894), c_Int_OPls)))], (32589 ^ _779203) ^ [_1370765, _1370767, _1370769] : [32591 ^ _779203 : [(32594 ^ _779203) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1370769, 32590 ^ [_1370765, _1370767, _1370769]))], (32592 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1370765), 32590 ^ [_1370765, _1370767, _1370769]), _1370767)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1370765, tc_Int_Oint), _1370769), _1370767) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1370765, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1370765), c_Int_Onat), _1370769)), _1370767)))], (37789 ^ _779203) ^ [_1497266, _1497268, _1497270, _1497272, _1497274] : [class_Groups_Ocomm__monoid__add(_1497266), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497268), _1497270)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497268, _1497266), _1497272), hAPP(c_Set_OCollect(_1497268), hAPP(hAPP(c_COMBS(_1497268, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497268), c_fconj), hAPP(hAPP(c_COMBC(_1497268, tc_fun(_1497268, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497268)), _1497270))), hAPP(hAPP(c_COMBC(_1497268, tc_fun(_1497268, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497268)), _1497274)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497268, _1497266), hAPP(hAPP(c_COMBC(_1497268, _1497266, _1497266), hAPP(hAPP(c_COMBS(_1497268, _1497266, tc_fun(_1497266, _1497266)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1497266, tc_fun(_1497266, _1497266)), _1497268), c_If(_1497266)), hAPP(hAPP(c_COMBC(_1497268, tc_fun(_1497268, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497268)), _1497274))), _1497272)), c_Groups_Ozero__class_Ozero(_1497266))), _1497270))], (49812 ^ _779203) ^ [_1786723, _1786725] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1786723), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1786725, hAPP(c_Code__Numeral_Onat__of, 49817 ^ [_1786723, _1786725]))), -(hBOOL(hAPP(_1786725, _1786723)))], (38459 ^ _779203) ^ [_1521531, _1521533, _1521535, _1521537] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521531, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521533, _1521531), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1521533, _1521531), tc_HOL_Obool)), _1521535), _1521537))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1521531, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1521533, _1521531), _1521535)), hAPP(c_Relation_ORange(_1521533, _1521531), _1521537)))))], (4662 ^ _779203) ^ [_850106, _850108, _850110, _850112] : [-(c_Product__Type_Ofst(_850112, _850108) = c_Product__Type_Ofst(_850110, _850106)), _850112 = _850110, _850108 = _850106], (21143 ^ _779203) ^ [_1152067, _1152069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1152067)), c_Int_OBit1(_1152069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152067), _1152069)))], (12173 ^ _779203) ^ [_989449] : [_989449 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _989449), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (25646 ^ _779203) ^ [_1230749, _1230751] : [class_Int_Onumber__ring(_1230749), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230749), _1230751), hAPP(c_Int_Onumber__class_Onumber__of(_1230749), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1230749), _1230751))], (33223 ^ _779203) ^ [_1387582, _1387584] : [_1387582 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1387584, _1387582) = 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), _1387584)))], (8625 ^ _779203) ^ [_924481, _924483, _924485, _924487] : [class_Groups_Oab__semigroup__add(_924481), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924481), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924481), _924483), _924485)), _924487) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924481), _924483), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_924481), _924485), _924487)))], (23293 ^ _779203) ^ [_1188973, _1188975, _1188977, _1188979] : [_1188973 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1188975), _1188977)), _1188979), -(_1188975 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1188973), _1188975) = _1188977), 23300 ^ _779203 : [(23303 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1188979), _1188975))], (23301 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188975)))]], 23308 ^ _779203 : [(23311 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1188975), _1188979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1188979), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23309 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188975))]]], (32247 ^ _779203) ^ [_1362566, _1362568] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1362566), _1362568))), -(hAPP(c_Finite__Set_Ocard(_1362566), _1362568) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40580 ^ _779203) ^ [_1574070, _1574072, _1574074, _1574076] : [c_Wellfounded_Owf(_1574070, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1574070, _1574070)), hAPP(hAPP(c_Product__Type_OPair(_1574070, _1574070), _1574072), _1574074)), _1574076)), 40583 ^ _779203 : [(40586 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574070, _1574070)), hAPP(hAPP(c_Product__Type_OPair(_1574070, _1574070), _1574074), _1574072)), c_Transitive__Closure_Ortrancl(_1574070, _1574076)))], (40584 ^ _779203) ^ [] : [-(c_Wellfounded_Owf(_1574070, _1574076))]]], (19168 ^ _779203) ^ [_1116847, _1116849, _1116851] : [class_Rings_Olinordered__idom(_1116847), -(hAPP(c_Groups_Oabs__class_Oabs(_1116847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116847), _1116849), _1116851)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116847), hAPP(c_Groups_Oabs__class_Oabs(_1116847), _1116849)), hAPP(c_Groups_Oabs__class_Oabs(_1116847), _1116851)))], (37217 ^ _779203) ^ [_1482133, _1482135, _1482137, _1482139, _1482141] : [hBOOL(hAPP(hAPP(c_member(_1482133), _1482135), hAPP(c_Set_Ovimage(_1482133, _1482137, _1482139), _1482141))), -(hBOOL(hAPP(hAPP(c_member(_1482137), hAPP(_1482139, _1482135)), _1482141)))], (18124 ^ _779203) ^ [_1098958, _1098960] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1098958), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098958)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098960)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1098958), _1098960)))], (43255 ^ _779203) ^ [_1642249, _1642251, _1642253] : [-(_1642249 = c_List_Olist_ONil(_1642251)), -(c_List_Obutlast(_1642251, hAPP(hAPP(c_List_Oappend(_1642251), _1642253), _1642249)) = hAPP(hAPP(c_List_Oappend(_1642251), _1642253), c_List_Obutlast(_1642251, _1642249)))], (45799 ^ _779203) ^ [_1700316, _1700318] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1700316)), c_List_Otranspose__rel(_1700316)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700316)), c_List_Olist_ONil(_1700316)), _1700318))), -(c_List_Otranspose(_1700316, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1700316)), c_List_Olist_ONil(_1700316)), _1700318)) = c_List_Otranspose(_1700316, _1700318))], (48156 ^ _779203) ^ [_1750544, _1750546, _1750548] : [-(c_List_Oreplicate(_1750544, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750544)), hAPP(c_List_Ofilter(_1750544, hAPP(c_fequal, _1750546)), _1750548)), _1750546) = hAPP(c_List_Ofilter(_1750544, hAPP(c_fequal, _1750546)), _1750548))], (36686 ^ _779203) ^ [_1469997, _1469999, _1470001, _1470003, _1470005] : [c_Fun_Oinj__on(_1469997, _1469999, _1470001, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1469997, tc_HOL_Obool)), _1470003), _1470005)), 36689 ^ _779203 : [(36694 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1469999, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1469997, _1469999, _1470001), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469997, tc_HOL_Obool)), _1470003), _1470005))), hAPP(c_Set_Oimage(_1469997, _1469999, _1470001), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1469997, tc_HOL_Obool)), _1470005), _1470003))) = c_Orderings_Obot__class_Obot(tc_fun(_1469999, tc_HOL_Obool)))], (36692 ^ _779203) ^ [] : [-(c_Fun_Oinj__on(_1469997, _1469999, _1470001, _1470005))], (36690 ^ _779203) ^ [] : [-(c_Fun_Oinj__on(_1469997, _1469999, _1470001, _1470003))]]], (40490 ^ _779203) ^ [_1572117, _1572119, _1572121, _1572123] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1572117, _1572117)), hAPP(hAPP(c_Product__Type_OPair(_1572117, _1572117), _1572119), _1572121)), c_Transitive__Closure_Ortrancl(_1572117, _1572123))), -(_1572119 = _1572121), 40497 ^ _779203 : [(40500 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572117, _1572117)), hAPP(hAPP(c_Product__Type_OPair(_1572117, _1572117), _1572119), _1572121)), c_Transitive__Closure_Otrancl(_1572117, _1572123))))], (40498 ^ _779203) ^ [] : [_1572119 = _1572121]]], (29798 ^ _779203) ^ [_1308925, _1308927, _1308929, _1308931] : [class_Orderings_Oorder(_1308925), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308925, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1308925, _1308927, _1308929)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1308925, _1308929, _1308931)) = c_Orderings_Obot__class_Obot(tc_fun(_1308925, tc_HOL_Obool)))], (31354 ^ _779203) ^ [_1341297, _1341299] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1341297), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1341297, tc_HOL_Obool), _1341299)))), 31355 ^ _779203 : [(31356 ^ _779203) ^ [_1341361] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1341297, tc_HOL_Obool)), _1341361), _1341299)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1341297), _1341361))]]], (45701 ^ _779203) ^ [_1697587, _1697589, _1697591, _1697593] : [-(hBOOL(hAPP(_1697587, _1697589))), -(hAPP(c_List_Ofilter(_1697591, _1697587), hAPP(hAPP(c_List_Olist_OCons(_1697591), _1697589), _1697593)) = hAPP(c_List_Ofilter(_1697591, _1697587), _1697593))], (18963 ^ _779203) ^ [_1113267] : [class_Rings_Osemiring__1(_1113267), -(hBOOL(hAPP(hAPP(c_member(_1113267), c_Groups_Ozero__class_Ozero(_1113267)), c_Nat_Osemiring__1__class_ONats(_1113267))))], (11270 ^ _779203) ^ [_973206, _973208] : [class_Groups_Olinordered__ab__group__add(_973206), 11273 ^ _779203 : [(11280 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973206), _973208), c_Groups_Ozero__class_Ozero(_973206))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973206), _973208), _973208)), c_Groups_Ozero__class_Ozero(_973206))))], (11274 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973206), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973206), _973208), _973208)), c_Groups_Ozero__class_Ozero(_973206))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973206), _973208), c_Groups_Ozero__class_Ozero(_973206))))]]], (40055 ^ _779203) ^ [_1560834, _1560836, _1560838] : [c_Wellfounded_Owf(_1560834, _1560836), hBOOL(hAPP(hAPP(c_member(tc_prod(_1560834, _1560834)), hAPP(hAPP(c_Product__Type_OPair(_1560834, _1560834), hAPP(_1560838, hAPP(c_Nat_OSuc, 40058 ^ [_1560834, _1560836, _1560838]))), hAPP(_1560838, 40058 ^ [_1560834, _1560836, _1560838]))), _1560836))], (20024 ^ _779203) ^ [_1132200, _1132202, _1132204] : [class_Rings_Oring(_1132200), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132200), hAPP(c_Groups_Ouminus__class_Ouminus(_1132200), _1132202)), _1132204) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1132200), _1132202), hAPP(c_Groups_Ouminus__class_Ouminus(_1132200), _1132204)))], (45370 ^ _779203) ^ [_1689928, _1689930] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689928)), c_List_Oremdups(_1689928, _1689930)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689928)), _1689930), -(c_List_Oremdups(_1689928, _1689930) = _1689930)], (27484 ^ _779203) ^ [_1263429, _1263431, _1263433] : [class_Lattices_Osemilattice__sup(_1263429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263429), _1263431), _1263433)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263429), _1263433), _1263431) = _1263433)], (18877 ^ _779203) ^ [_1111822, _1111824] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1111822) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1111824), -(_1111822 = _1111824)], (45016 ^ _779203) ^ [_1681903, _1681905, _1681907, _1681909, _1681911] : [c_List_Olist__all2(_1681903, _1681905, _1681907, _1681909, _1681911), 45019 ^ _779203 : [(45022 ^ _779203) ^ [_1682069] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681903, _1681905)), _1682069), hAPP(c_List_Oset(tc_prod(_1681903, _1681905)), hAPP(hAPP(c_List_Ozip(_1681903, _1681905), _1681909), _1681911)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1681903, _1681905, tc_HOL_Obool), _1681907), _1682069)))], (45020 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681903)), _1681909) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681905)), _1681911))]]], (37912 ^ _779203) ^ [_1502048] : [-(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)))), _1502048)) = 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), _1502048), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (17464 ^ _779203) ^ [_1087220, _1087222] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1087220)), 17467 ^ _779203 : [(17476 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1087220), _1087222) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1087220 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1087222 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (17468 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1087220), _1087222) = c_Groups_Oone__class_Oone(tc_Int_Oint), 17471 ^ _779203 : [(17474 ^ _779203) ^ [] : [-(_1087222 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (17472 ^ _779203) ^ [] : [-(_1087220 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (9552 ^ _779203) ^ [_942364, _942366] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _942364), _942366), 9555 ^ _779203 : [(9558 ^ _779203) ^ [] : [-(_942366 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9556 ^ _779203) ^ [] : [-(_942364 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (28154 ^ _779203) ^ [_1276705] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276705, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1276705, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1276705, tc_HOL_Obool)))], (40775 ^ _779203) ^ [_1578748, _1578750, _1578752] : [c_Equiv__Relations_Oequiv(_1578748, _1578750, _1578752), -(hAPP(hAPP(c_Relation_Orel__comp(_1578748, _1578748, _1578748), hAPP(c_Relation_Oconverse(_1578748, _1578748), _1578752)), _1578752) = _1578752)], (28808 ^ _779203) ^ [_1288739, _1288741, _1288743] : [class_Orderings_Olinorder(_1288739), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288739), _1288741), _1288743)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288739, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1288739, _1288741, _1288743)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1288739), _1288743)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1288739), _1288741))], (5308 ^ _779203) ^ [_860395, _860397] : [_860397 = _860395, -(c_Groups_Ouminus__class_Ouminus(_860397) = c_Groups_Ouminus__class_Ouminus(_860395))], (23926 ^ _779203) ^ [_1200380, _1200382, _1200384] : [hBOOL(hAPP(_1200380, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1200382, _1200384))), 23929 ^ _779203 : [(23936 ^ _779203) ^ [] : [-(_1200384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 23939 ^ _779203 : [(23940 ^ _779203) ^ [_1200628, _1200630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1200628), _1200384)), _1200382 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1200384), _1200630)), _1200628), -(hBOOL(hAPP(_1200380, _1200628)))]]], (23930 ^ _779203) ^ [] : [_1200384 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1200380, _1200382)))]]], (38631 ^ _779203) ^ [_1527289, _1527291] : [c_Wellfounded_Owf(_1527289, _1527291), -(c_Wellfounded_Owf(tc_fun(_1527289, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1527289, _1527291)))], (19876 ^ _779203) ^ [_1129703, _1129705] : [class_Groups_Olinordered__ab__group__add(_1129703), 19879 ^ _779203 : [(19886 ^ _779203) ^ [] : [_1129705 = c_Groups_Ozero__class_Ozero(_1129703), -(_1129705 = hAPP(c_Groups_Ouminus__class_Ouminus(_1129703), _1129705))], (19880 ^ _779203) ^ [] : [_1129705 = hAPP(c_Groups_Ouminus__class_Ouminus(_1129703), _1129705), -(_1129705 = c_Groups_Ozero__class_Ozero(_1129703))]]], (41503 ^ _779203) ^ [_1599419, _1599421, _1599423, _1599425] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599419), tc_List_Olist(_1599419))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599419), tc_List_Olist(_1599419)), _1599421), _1599423)), c_List_Olistrel1(_1599419, _1599425))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599419)), _1599421) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1599419)), _1599423))], (40103 ^ _779203) ^ [_1562016, _1562018, _1562020, _1562022, _1562024, _1562026, _1562028] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1562016, _1562018, _1562020, _1562022), _1562024), _1562026), _1562028) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1562018, _1562020, _1562022), _1562026), hAPP(_1562024, _1562028)))], (49142 ^ _779203) ^ [_1772848, _1772850] : [c_Relation_Otrans(_1772848, _1772850), c_Relation_Oantisym(_1772848, _1772850), -(c_Relation_Otrans(_1772848, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1772848, _1772848), tc_HOL_Obool)), _1772850), c_Relation_OId(_1772848))))], (23633 ^ _779203) ^ [] : [-(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))))], (10161 ^ _779203) ^ [_953599] : [-(hAPP(c_Nat_OSuc, _953599) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _953599))], (22494 ^ _779203) ^ [_1175809, _1175811, _1175813, _1175815] : [class_Divides_Osemiring__div(_1175809), -(_1175811 = c_Groups_Ozero__class_Ozero(_1175809)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1175809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175809), _1175811), _1175813)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175809), _1175811), _1175815)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1175809), _1175813), _1175815))], (48933 ^ _779203) ^ [_1767489, _1767491, _1767493] : [c_List_Olist__ex(_1767489, _1767493, _1767491), 48937 ^ _779203 : [(48940 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1767493, 48936 ^ [_1767489, _1767491, _1767493])))], (48938 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767489), 48936 ^ [_1767489, _1767491, _1767493]), hAPP(c_List_Oset(_1767489), _1767491))))]]], (47177 ^ _779203) ^ [_1728429, _1728431, _1728433] : [-(hBOOL(hAPP(hAPP(c_member(_1728429), _1728431), hAPP(c_List_Oset(_1728429), _1728433)))), -(c_List_Oinsert(_1728429, _1728431, _1728433) = hAPP(hAPP(c_List_Olist_OCons(_1728429), _1728431), _1728433))], (20072 ^ _779203) ^ [_1133170, _1133172, _1133174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133170, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1133170, tc_HOL_Obool)), _1133172)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1133170, tc_HOL_Obool)), _1133174))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133170, tc_HOL_Obool)), _1133174), _1133172)))], (32035 ^ _779203) ^ [_1357182, _1357184, _1357186] : [-(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)), _1357182)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1357184, _1357186)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1357184), _1357182), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1357186), _1357182)))], (16238 ^ _779203) ^ [_1064240, _1064242, _1064244, _1064246] : [class_Orderings_Olinorder(_1064240), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064240), _1064242)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1064240, _1064240, c_Orderings_Oord__class_Omax(_1064240)), _1064244), hAPP(hAPP(c_Set_Oinsert(_1064240), _1064246), _1064242)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1064240), _1064246), hAPP(hAPP(c_Finite__Set_Ofold(_1064240, _1064240, c_Orderings_Oord__class_Omax(_1064240)), _1064244), _1064242)))], (44783 ^ _779203) ^ [_1676681, _1676683] : [hAPP(c_Code__Numeral_Onat__of, _1676681) = hAPP(c_Code__Numeral_Onat__of, _1676683), -(_1676681 = _1676683)], (41811 ^ _779203) ^ [_1608594, _1608596, _1608598] : [-(_1608594 = _1608596), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608598)), _1608594) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608598)), _1608596), 41817 ^ _779203 : [(41820 ^ _779203) ^ [] : [hAPP(hAPP(c_List_Onth(_1608598), _1608594), 41816 ^ [_1608594, _1608596, _1608598]) = hAPP(hAPP(c_List_Onth(_1608598), _1608596), 41816 ^ [_1608594, _1608596, _1608598])], (41818 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41816 ^ [_1608594, _1608596, _1608598]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608598)), _1608594))))]]], (23146 ^ _779203) ^ [_1186419, _1186421] : [23147 ^ _779203 : [(23150 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186421))], (23148 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186419))]], 23151 ^ _779203 : [(23158 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1186419), _1186421)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1186419)), hAPP(c_Int_Onat, _1186421))))], (23152 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1186419)), hAPP(c_Int_Onat, _1186421))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1186419), _1186421)))]]], (52335 ^ _779203) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (30834 ^ _779203) ^ [_1330787, _1330789] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1330787, tc_HOL_Obool)), _1330789)), 30840 ^ _779203 : [(30843 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1330787), 30839 ^ [_1330787, _1330789]))], (30841 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1330787, tc_HOL_Obool)), 30839 ^ [_1330787, _1330789]), _1330789)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1330787), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1330787, tc_HOL_Obool), _1330789))))], (39714 ^ _779203) ^ [_1552648, _1552650, _1552652, _1552654, _1552656, _1552658, _1552660, _1552662, _1552664, _1552666, _1552668] : [c_Finite__Set_Ofolding(_1552648, _1552650, _1552652, _1552654), -(hAPP(c_Fun_Ocomp(_1552656, _1552658, _1552660, _1552662), hAPP(c_Fun_Ocomp(_1552664, _1552656, _1552660, _1552666), _1552668)) = hAPP(c_Fun_Ocomp(_1552664, _1552658, _1552660, hAPP(c_Fun_Ocomp(_1552656, _1552658, _1552664, _1552662), _1552666)), _1552668))], (6991 ^ _779203) ^ [_894097, _894099, _894101, _894103] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_894097), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894097, tc_HOL_Obool)), _894099), _894103))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_894097), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894097, tc_HOL_Obool)), _894099), hAPP(hAPP(c_Set_Oinsert(_894097), _894101), _894103)))))], (40291 ^ _779203) ^ [_1566563, _1566565, _1566567, _1566569] : [-(c_Transitive__Closure_Otrancl(_1566563, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1566563, _1566563)), hAPP(hAPP(c_Product__Type_OPair(_1566563, _1566563), _1566565), _1566567)), _1566569)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1566563, _1566563), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1566563, _1566569)), hAPP(c_Set_OCollect(tc_prod(_1566563, _1566563)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566563, _1566563, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1566563, tc_fun(_1566563, tc_HOL_Obool), tc_fun(_1566563, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1566563, tc_HOL_Obool), tc_fun(_1566563, tc_HOL_Obool)), _1566563), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1566563)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1566563), c_fconj), hAPP(hAPP(c_COMBC(_1566563, tc_fun(tc_prod(_1566563, _1566563), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1566563, _1566563), tc_fun(tc_fun(tc_prod(_1566563, _1566563), tc_HOL_Obool), tc_HOL_Obool), _1566563), c_member(tc_prod(_1566563, _1566563))), hAPP(hAPP(c_COMBC(_1566563, _1566563, tc_prod(_1566563, _1566563)), c_Product__Type_OPair(_1566563, _1566563)), _1566565))), c_Transitive__Closure_Ortrancl(_1566563, _1566569))))), hAPP(hAPP(c_COMBC(_1566563, tc_fun(tc_prod(_1566563, _1566563), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1566563, _1566563), tc_fun(tc_fun(tc_prod(_1566563, _1566563), tc_HOL_Obool), tc_HOL_Obool), _1566563), c_member(tc_prod(_1566563, _1566563))), hAPP(c_Product__Type_OPair(_1566563, _1566563), _1566567))), c_Transitive__Closure_Ortrancl(_1566563, _1566569)))))))], (20933 ^ _779203) ^ [_1148412, _1148414] : [class_Rings_Olinordered__idom(_1148412), 20936 ^ _779203 : [(20943 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148412), _1148414), c_Groups_Ozero__class_Ozero(_1148412))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148412), c_Groups_Osgn__class_Osgn(_1148412, _1148414)), c_Groups_Ozero__class_Ozero(_1148412))))], (20937 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148412), c_Groups_Osgn__class_Osgn(_1148412, _1148414)), c_Groups_Ozero__class_Ozero(_1148412))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148412), _1148414), c_Groups_Ozero__class_Ozero(_1148412))))]]], (34979 ^ _779203) ^ [_1428968, _1428970, _1428972, _1428974, _1428976] : [_1428968 = c_Orderings_Obot__class_Obot(tc_fun(_1428970, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1428970, tc_fun(_1428972, tc_HOL_Obool)), _1428968), hAPP(hAPP(c_COMBB(tc_fun(_1428972, tc_HOL_Obool), tc_fun(_1428972, tc_HOL_Obool), _1428970), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1428972, tc_HOL_Obool)), _1428974)), _1428976)) = c_Orderings_Otop__class_Otop(tc_fun(_1428972, tc_HOL_Obool)))], (44291 ^ _779203) ^ [_1665050, _1665052] : [-(_1665050 = c_List_Olist_ONil(_1665052)), -(c_Random_Oselect__weight(_1665052, hAPP(hAPP(c_List_Omap(_1665052, tc_prod(tc_Code__Numeral_Ocode__numeral, _1665052)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1665052), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1665050)) = c_Random_Oselect(_1665052, _1665050))], (33889 ^ _779203) ^ [_1400140, _1400142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1400140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1400142)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1400140), _1400142) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1400140, _1400142)))], (2822 ^ _779203) ^ [_820954, _820956, _820958, _820960, _820962, _820964] : [-(c_Product__Type_Ointernal__split(_820964, _820960, _820956) = c_Product__Type_Ointernal__split(_820962, _820958, _820954)), _820964 = _820962, _820960 = _820958, _820956 = _820954], (45993 ^ _779203) ^ [_1704533, _1704535, _1704537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704533), _1704535)), _1704537)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1704533, _1704537)), _1704535) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1704533), _1704535))], (36808 ^ _779203) ^ [_1472878, _1472880, _1472882, _1472884, _1472886, _1472888] : [c_Fun_Oinj__on(_1472878, _1472880, _1472882, _1472884), hAPP(_1472882, _1472886) = _1472888, hBOOL(hAPP(hAPP(c_member(_1472878), _1472886), _1472884)), -(hAPP(c_Fun_Othe__inv__into(_1472878, _1472880, _1472884, _1472882), _1472888) = _1472886)], (47034 ^ _779203) ^ [_1725337, _1725339, _1725341, _1725343, _1725345] : [-(c_List_OdropWhile(_1725337, _1725339, _1725341) = hAPP(hAPP(c_List_Olist_OCons(_1725337), _1725343), _1725345)), _1725341 = hAPP(hAPP(c_List_Oappend(_1725337), c_List_OtakeWhile(_1725337, _1725339, _1725341)), hAPP(hAPP(c_List_Olist_OCons(_1725337), _1725343), _1725345)), -(hBOOL(hAPP(_1725339, _1725343)))], (32465 ^ _779203) ^ [_1367717, _1367719, _1367721] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1367717), _1367719))), 32468 ^ _779203 : [(32475 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1367721), _1367719))), -(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)), _1367717)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1367721), _1367719)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (32469 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1367721), _1367719)), -(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)), _1367717)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1367721), _1367719)) = 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))))]]], (7373 ^ _779203) ^ [_901157, _901159, _901161] : [class_Orderings_Oorder(_901157), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901157), _901159), _901161)), _901161 = _901159], (9833 ^ _779203) ^ [_947111, _947113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _947111), _947113)), -(_947111 = _947113), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947111), _947113)))], (49845 ^ _779203) ^ [_1787268, _1787270] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1787268), _1787270))), -(c_Quickcheck_Obeyond(_1787268, _1787270) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (26146 ^ _779203) ^ [_1239021, _1239023] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1239021, tc_HOL_Obool)), hAPP(c_Set_OPow(_1239021), _1239023))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1239021), _1239023)))], (52471 ^ _779203) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (36634 ^ _779203) ^ [_1468775] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1468775)), c_Int_OInteg)))], (46873 ^ _779203) ^ [_1721977, _1721979, _1721981] : [-(c_List_OtakeWhile(_1721977, _1721979, _1721981) = hAPP(hAPP(c_List_Otake(_1721977), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721977)), c_List_OtakeWhile(_1721977, _1721979, _1721981))), _1721981))], (24147 ^ _779203) ^ [_1204476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1204476)), -(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), _1204476), 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)))))))], (1260 ^ _779203) ^ [_797913, _797915] : [-(class_Rings_Oordered__ring(_797913)), _797915 = _797913, class_Rings_Oordered__ring(_797915)], (39566 ^ _779203) ^ [_1549416, _1549418, _1549420] : [-(hAPP(c_Fun_Ocomp(_1549416, _1549416, _1549418, c_Fun_Oid(_1549416)), _1549420) = _1549420)], (7005 ^ _779203) ^ [_894449, _894451, _894453, _894455, _894457, _894459, _894461, _894463] : [c_Finite__Set_Ofolding__image__simple(_894449, _894451, _894453, _894455, _894457, _894459), hBOOL(hAPP(c_Finite__Set_Ofinite(_894451), _894461)), hBOOL(hAPP(hAPP(c_member(_894451), _894463), _894461)), -(hAPP(_894459, _894461) = hAPP(hAPP(_894453, hAPP(_894457, _894463)), hAPP(_894459, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894451, tc_HOL_Obool)), _894461), hAPP(hAPP(c_Set_Oinsert(_894451), _894463), c_Orderings_Obot__class_Obot(tc_fun(_894451, tc_HOL_Obool)))))))], (42716 ^ _779203) ^ [_1630622, _1630624] : [c_Orderings_Obot__class_Obot(tc_fun(_1630622, tc_HOL_Obool)) = hAPP(c_List_Oset(_1630622), _1630624), -(_1630624 = c_List_Olist_ONil(_1630622))], (4628 ^ _779203) ^ [_849571, _849573, _849575, _849577, _849579, _849581, _849583, _849585] : [-(c_Random__Sequence_Obind(_849585, _849581, _849577, _849573) = c_Random__Sequence_Obind(_849583, _849579, _849575, _849571)), _849585 = _849583, _849581 = _849579, _849577 = _849575, _849573 = _849571], (41777 ^ _779203) ^ [_1607626, _1607628, _1607630, _1607632] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1607626), tc_List_Olist(_1607626))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1607626), tc_List_Olist(_1607626)), _1607628), _1607630)), c_List_Olistrel(_1607626, _1607632)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607626)), _1607628) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607626)), _1607630), 41783 ^ _779203 : [(41786 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607626, _1607626)), hAPP(hAPP(c_Product__Type_OPair(_1607626, _1607626), hAPP(hAPP(c_List_Onth(_1607626), _1607628), 41782 ^ [_1607626, _1607628, _1607630, _1607632])), hAPP(hAPP(c_List_Onth(_1607626), _1607630), 41782 ^ [_1607626, _1607628, _1607630, _1607632]))), _1607632))], (41784 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41782 ^ [_1607626, _1607628, _1607630, _1607632]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1607626)), _1607628))))]]], (7539 ^ _779203) ^ [_903774, _903776, _903778, _903780] : [-(c_Nitpick_Ofold__graph_H(_903774, _903776, _903778, _903780, c_Orderings_Obot__class_Obot(tc_fun(_903774, tc_HOL_Obool)), _903780))], (17078 ^ _779203) ^ [_1079913, _1079915, _1079917] : [class_Orderings_Olinorder(_1079913), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079913), _1079915)), 17085 ^ _779203 : [(17092 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079913, tc_HOL_Obool)), _1079915), hAPP(hAPP(c_Set_Oinsert(_1079913), _1079917), c_Orderings_Obot__class_Obot(tc_fun(_1079913, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1079913, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1079913, hAPP(hAPP(c_Set_Oinsert(_1079913), _1079917), _1079915)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1079913), _1079917), c_Big__Operators_Olinorder__class_OMin(_1079913, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079913, tc_HOL_Obool)), _1079915), hAPP(hAPP(c_Set_Oinsert(_1079913), _1079917), c_Orderings_Obot__class_Obot(tc_fun(_1079913, tc_HOL_Obool)))))))], (17086 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1079913, tc_HOL_Obool)), _1079915), hAPP(hAPP(c_Set_Oinsert(_1079913), _1079917), c_Orderings_Obot__class_Obot(tc_fun(_1079913, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1079913, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1079913, hAPP(hAPP(c_Set_Oinsert(_1079913), _1079917), _1079915)) = _1079917)]]], (48158 ^ _779203) ^ [_1750600, _1750602, _1750604] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750600)), c_List_Oreplicate(_1750600, _1750602, _1750604)) = _1750602)], (23681 ^ _779203) ^ [_1196031, _1196033] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1196031), _1196033)), _1196033) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1196031), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1196031, _1196033)))], (34514 ^ _779203) ^ [_1416338, _1416340, _1416342, _1416344, _1416346] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416338, tc_fun(_1416340, tc_HOL_Obool)), _1416342), hAPP(hAPP(c_COMBB(tc_fun(_1416340, tc_HOL_Obool), tc_fun(_1416340, tc_HOL_Obool), _1416338), hAPP(c_Set_Oinsert(_1416340), _1416344)), _1416346)) = hAPP(hAPP(c_Set_Oinsert(_1416340), _1416344), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416338, tc_fun(_1416340, tc_HOL_Obool)), _1416342), _1416346)))], (26128 ^ _779203) ^ [_1238596, _1238598, _1238600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1238596, tc_HOL_Obool)), _1238598), _1238600)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1238596, tc_HOL_Obool)), _1238598), hAPP(c_Set_OPow(_1238596), _1238600))))], (23323 ^ _779203) ^ [_1189460, _1189462, _1189464] : [hBOOL(hAPP(_1189460, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1189462), _1189464))), 23326 ^ _779203 : [(23351 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189464), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 23354 ^ _779203 : [(23355 ^ _779203) ^ [_1190124] : [-(hBOOL(hAPP(_1189460, _1190124))), 23356 ^ _779203 : [(23357 ^ _779203) ^ [_1190198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189464), _1190198)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1190198), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1189462 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1189464), _1190124)), _1190198)]]]]], (23333 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189464)), 23336 ^ _779203 : [(23337 ^ _779203) ^ [_1189794] : [-(hBOOL(hAPP(_1189460, _1189794))), 23338 ^ _779203 : [(23339 ^ _779203) ^ [_1189865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189865), _1189464)), _1189462 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1189464), _1189794)), _1189865)]]]]], (23327 ^ _779203) ^ [] : [_1189464 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1189460, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (51213 ^ _779203) ^ [_1815395, _1815397] : [51220 ^ _779203 : [(51223 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815397), _1815395))], (51221 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815395), _1815397)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1815395), _1815397)), -(_1815395 = _1815397)], (28178 ^ _779203) ^ [_1277157, _1277159, _1277161, _1277163, _1277165, _1277167, _1277169, _1277171] : [c_Finite__Set_Ofolding__image__simple__idem(_1277157, _1277159, _1277161, _1277163, _1277165, _1277167), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277159), _1277169)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277159), _1277171)), -(hAPP(_1277167, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1277159, tc_HOL_Obool)), _1277169), _1277171)) = hAPP(hAPP(_1277161, hAPP(_1277167, _1277169)), hAPP(_1277167, _1277171)))], (38887 ^ _779203) ^ [_1532607, _1532609] : [-(c_FunDef_Oreduction__pair(_1532607, _1532609)), c_Wellfounded_Owf(_1532607, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532607, _1532607), tc_HOL_Obool), tc_fun(tc_prod(_1532607, _1532607), tc_HOL_Obool)), _1532609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532607, _1532607), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1532607, _1532607, _1532607), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532607, _1532607), tc_HOL_Obool), tc_fun(tc_prod(_1532607, _1532607), tc_HOL_Obool)), _1532609)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1532607, _1532607), tc_HOL_Obool), tc_fun(tc_prod(_1532607, _1532607), tc_HOL_Obool)), _1532609))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1532607, _1532607), tc_HOL_Obool), tc_fun(tc_prod(_1532607, _1532607), tc_HOL_Obool)), _1532609)))], (33823 ^ _779203) ^ [_1398729, _1398731, _1398733, _1398735] : [hAPP(c_Product__Type_Ofst(_1398729, _1398731), _1398733) = hAPP(c_Product__Type_Ofst(_1398729, _1398731), _1398735), hAPP(c_Product__Type_Osnd(_1398729, _1398731), _1398733) = hAPP(c_Product__Type_Osnd(_1398729, _1398731), _1398735), -(_1398733 = _1398735)], (36806 ^ _779203) ^ [_1472820, _1472822, _1472824] : [-(c_Fun_Oinj__on(tc_prod(_1472820, _1472822), tc_prod(_1472822, _1472820), hAPP(c_Product__Type_Oprod_Oprod__case(_1472820, _1472822, tc_prod(_1472822, _1472820)), hAPP(c_COMBC(_1472822, _1472820, tc_prod(_1472822, _1472820)), c_Product__Type_OPair(_1472822, _1472820))), _1472824))], (22996 ^ _779203) ^ [_1184056, _1184058] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1184056), _1184058))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1184056))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1184058))))], (17740 ^ _779203) ^ [_1091816, _1091818, _1091820] : [class_Orderings_Olinorder(_1091816), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091816), _1091818)), -(hBOOL(hAPP(hAPP(c_member(_1091816), _1091820), _1091818))), -(_1091818 = c_Orderings_Obot__class_Obot(tc_fun(_1091816, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1091816, c_Orderings_Oord__class_Omax(_1091816), hAPP(hAPP(c_Set_Oinsert(_1091816), _1091820), _1091818)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1091816), _1091820), c_Big__Operators_Olattice_OSup__fin(_1091816, c_Orderings_Oord__class_Omax(_1091816), _1091818)))], (41365 ^ _779203) ^ [_1594872, _1594874, _1594876] : [hAPP(hAPP(c_List_Olist_OCons(_1594872), _1594874), _1594876) = _1594876], (37377 ^ _779203) ^ [_1486290] : [-(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)), _1486290)))))], (20578 ^ _779203) ^ [_1142131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1142131), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1142131) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1142131))], (11412 ^ _779203) ^ [_975728, _975730, _975732, _975734, _975736] : [class_Rings_Oordered__semiring(_975728), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975728), _975730), _975732)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975728), _975734), _975736)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975728), c_Groups_Ozero__class_Ozero(_975728)), _975732)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975728), c_Groups_Ozero__class_Ozero(_975728)), _975734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975728), _975730), _975734)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975728), _975732), _975736))))], (50033 ^ _779203) ^ [_1791245, _1791247, _1791249] : [c_Fun_Obij__betw(_1791245, _1791247, _1791249, c_Orderings_Otop__class_Otop(tc_fun(_1791245, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1791247, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1791245, _1791247, _1791249), c_Orderings_Otop__class_Otop(tc_fun(_1791245, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1791247, tc_HOL_Obool)))], (18481 ^ _779203) ^ [_1105137, _1105139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1105137), _1105139)), -(_1105139 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1105137), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 18484 ^ [_1105137, _1105139]))))], (14717 ^ _779203) ^ [_1035664, _1035666, _1035668, _1035670, _1035672] : [class_Fields_Ofield(_1035664), -(_1035666 = c_Groups_Ozero__class_Ozero(_1035664)), -(_1035668 = c_Groups_Ozero__class_Ozero(_1035664)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035664), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035664), _1035670), _1035666)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035664), _1035672), _1035668)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035664), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035664), _1035670), _1035668)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035664), _1035672), _1035666))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035664), _1035666), _1035668)))], (36202 ^ _779203) ^ [_1460310, _1460312, _1460314] : [-(c_Fun_Oinj__on(_1460310, _1460312, _1460314, c_Orderings_Obot__class_Obot(tc_fun(_1460310, tc_HOL_Obool))))], (9327 ^ _779203) ^ [_938210, _938212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938210), _938212)), _938210 = _938212], (16418 ^ _779203) ^ [_1067653, _1067655, _1067657, _1067659] : [class_Fields_Olinordered__field__inverse__zero(_1067653), class_Int_Onumber(_1067653), 16425 ^ _779203 : [(16426 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1067653), _1067655), _1067657)), hAPP(c_Int_Onumber__class_Onumber__of(_1067653), _1067659))), 16429 ^ _779203 : [(16436 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), c_Groups_Ozero__class_Ozero(_1067653)), _1067657))), 16439 ^ _779203 : [(16446 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), _1067657), c_Groups_Ozero__class_Ozero(_1067653)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), c_Groups_Ozero__class_Ozero(_1067653)), hAPP(c_Int_Onumber__class_Onumber__of(_1067653), _1067659))))], (16440 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), _1067657), c_Groups_Ozero__class_Ozero(_1067653))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067653), hAPP(c_Int_Onumber__class_Onumber__of(_1067653), _1067659)), _1067657)), _1067655)))]]], (16430 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), c_Groups_Ozero__class_Ozero(_1067653)), _1067657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), _1067655), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067653), hAPP(c_Int_Onumber__class_Onumber__of(_1067653), _1067659)), _1067657))))]]], (16452 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1067653), _1067655), _1067657)), hAPP(c_Int_Onumber__class_Onumber__of(_1067653), _1067659)))), 16455 ^ _779203 : [(16458 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), _1067655), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067653), hAPP(c_Int_Onumber__class_Onumber__of(_1067653), _1067659)), _1067657)))], (16456 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), c_Groups_Ozero__class_Ozero(_1067653)), _1067657)))]], 16459 ^ _779203 : [(16462 ^ _779203) ^ [] : [16463 ^ _779203 : [(16466 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067653), hAPP(c_Int_Onumber__class_Onumber__of(_1067653), _1067659)), _1067657)), _1067655))], (16464 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), _1067657), c_Groups_Ozero__class_Ozero(_1067653))))]], 16467 ^ _779203 : [(16470 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), c_Groups_Ozero__class_Ozero(_1067653)), hAPP(c_Int_Onumber__class_Onumber__of(_1067653), _1067659)))], (16468 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), _1067657), c_Groups_Ozero__class_Ozero(_1067653)))]]], (16460 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1067653), c_Groups_Ozero__class_Ozero(_1067653)), _1067657))]]]]], (11540 ^ _779203) ^ [_978174, _978176, _978178] : [class_Rings_Oordered__cancel__semiring(_978174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978174), _978176), c_Groups_Ozero__class_Ozero(_978174))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978174), c_Groups_Ozero__class_Ozero(_978174)), _978178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978174), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978174), _978176), _978178)), c_Groups_Ozero__class_Ozero(_978174))))], (39082 ^ _779203) ^ [_1537415, _1537417] : [c_Wellfounded_Owf(_1537415, hAPP(c_Set_OCollect(tc_prod(_1537415, _1537415)), hAPP(c_Product__Type_Oprod_Oprod__case(_1537415, _1537415, tc_HOL_Obool), _1537417))), -(c_Wellfounded_OwfP(_1537415, _1537417))], (7141 ^ _779203) ^ [_897318, _897320, _897322, _897324, _897326, _897328] : [c_Finite__Set_Ofun__left__comm__idem(_897318, _897320, _897322), hBOOL(hAPP(c_Finite__Set_Ofinite(_897318), _897324)), -(hAPP(hAPP(c_Finite__Set_Ofold(_897318, _897320, _897322), _897326), hAPP(hAPP(c_Set_Oinsert(_897318), _897328), _897324)) = hAPP(hAPP(c_Finite__Set_Ofold(_897318, _897320, _897322), hAPP(hAPP(_897322, _897328), _897326)), _897324))], (29370 ^ _779203) ^ [_1300023, _1300025] : [class_Lattices_Obounded__lattice__bot(_1300023), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1300023), c_Orderings_Obot__class_Obot(_1300023)), _1300025) = c_Orderings_Obot__class_Obot(_1300023))], (50481 ^ _779203) ^ [_1802152, _1802154, _1802156] : [c_List_Oall__interval__nat(_1802152, _1802154, _1802156), 50484 ^ _779203 : [(50485 ^ _779203) ^ [_1802232] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1802232), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1802154), _1802156))), -(hBOOL(hAPP(_1802152, _1802232)))]]], (24135 ^ _779203) ^ [_1204288] : [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, _1204288, 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, _1204288, 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))], (10011 ^ _779203) ^ [_950252, _950254, _950256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950252), _950254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950256), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _950254), _950256)), _950252))))], (9604 ^ _779203) ^ [_943307, _943309] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943307), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943309), _943307)))))], (4930 ^ _779203) ^ [_854330, _854332] : [_854332 = _854330, -(c_Lattices_Osemilattice__inf__class_Oinf(_854332) = c_Lattices_Osemilattice__inf__class_Oinf(_854330))], (10661 ^ _779203) ^ [_963733, _963735] : [_963733 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _963733), _963735) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34839 ^ _779203) ^ [_1425312, _1425314, _1425316, _1425318] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425312, tc_fun(_1425314, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1425312, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1425314, tc_HOL_Obool), tc_fun(_1425314, tc_HOL_Obool), _1425312), hAPP(c_COMBC(_1425314, tc_fun(_1425314, tc_HOL_Obool), tc_HOL_Obool), c_member(_1425314))), _1425316)), _1425318)), -(hBOOL(hAPP(hAPP(c_member(_1425314), _1425318), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425312, tc_fun(_1425314, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1425312, tc_HOL_Obool))), _1425316))))], (1430 ^ _779203) ^ [_800038, _800040] : [-(class_Lattices_Osemilattice__sup(_800038)), _800040 = _800038, class_Lattices_Osemilattice__sup(_800040)], (47817 ^ _779203) ^ [_1742844] : [class_Nat_Osize(_1742844), -(c_FunDef_Ois__measure(_1742844, c_Nat_Osize__class_Osize(_1742844)))], (50955 ^ _779203) ^ [_1810958, _1810960] : [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)))), _1810958, _1810960), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810958), _1810960)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810960), _1810958)))], (37625 ^ _779203) ^ [_1492691, _1492693, _1492695, _1492697] : [-(hAPP(c_Set_Oimage(tc_prod(_1492691, _1492693), tc_prod(_1492693, _1492691), hAPP(c_Product__Type_Oprod_Oprod__case(_1492691, _1492693, tc_prod(_1492693, _1492691)), hAPP(c_COMBC(_1492693, _1492691, tc_prod(_1492693, _1492691)), c_Product__Type_OPair(_1492693, _1492691)))), hAPP(hAPP(c_Product__Type_OSigma(_1492691, _1492693), _1492695), hAPP(c_COMBK(tc_fun(_1492693, tc_HOL_Obool), _1492691), _1492697))) = hAPP(hAPP(c_Product__Type_OSigma(_1492693, _1492691), _1492697), hAPP(c_COMBK(tc_fun(_1492691, tc_HOL_Obool), _1492693), _1492695)))], (37657 ^ _779203) ^ [_1493721, _1493723] : [-(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), _1493721)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1493723))))))], (47584 ^ _779203) ^ [_1737998, _1738000, _1738002] : [class_Enum_Oenum(_1737998), class_Enum_Oenum(_1738000), 47591 ^ _779203 : [(47598 ^ _779203) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1738000), hAPP(hAPP(c_COMBB(tc_fun(_1737998, tc_HOL_Obool), tc_HOL_Obool, _1738000), c_Enum_Oenum__class_Oenum__all(_1737998)), hAPP(hAPP(c_COMBB(tc_fun(_1737998, tc_prod(_1738000, _1737998)), tc_fun(_1737998, tc_HOL_Obool), _1738000), hAPP(c_COMBB(tc_prod(_1738000, _1737998), tc_HOL_Obool, _1737998), _1738002)), c_Product__Type_OPair(_1738000, _1737998))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1738000, _1737998)), _1738002)))], (47592 ^ _779203) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1738000, _1737998)), _1738002)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1738000), hAPP(hAPP(c_COMBB(tc_fun(_1737998, tc_HOL_Obool), tc_HOL_Obool, _1738000), c_Enum_Oenum__class_Oenum__all(_1737998)), hAPP(hAPP(c_COMBB(tc_fun(_1737998, tc_prod(_1738000, _1737998)), tc_fun(_1737998, tc_HOL_Obool), _1738000), hAPP(c_COMBB(tc_prod(_1738000, _1737998), tc_HOL_Obool, _1737998), _1738002)), c_Product__Type_OPair(_1738000, _1737998))))))]]], (8480 ^ _779203) ^ [_921413, _921415, _921417, _921419, _921421] : [class_Groups_Ocomm__monoid__add(_921413), hBOOL(hAPP(c_Finite__Set_Ofinite(_921415), _921417)), hBOOL(hAPP(hAPP(c_member(_921415), _921419), _921417)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_921415, _921413), _921421), _921417) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_921413), hAPP(_921421, _921419)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_921415, _921413), _921421), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921415, tc_HOL_Obool)), _921417), hAPP(hAPP(c_Set_Oinsert(_921415), _921419), c_Orderings_Obot__class_Obot(tc_fun(_921415, tc_HOL_Obool)))))))], (22201 ^ _779203) ^ [_1171244, _1171246] : [-(_1171244 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22204 ^ _779203 : [(22211 ^ _779203) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1171246, _1171244) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1171246), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1171244)) = 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), _1171246), _1171244))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (22205 ^ _779203) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1171246, _1171244) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1171246), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1171244)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1171246), _1171244)))]]], (8933 ^ _779203) ^ [_930204, _930206, _930208] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_930204), _930206)), -(hAPP(c_Finite__Set_Ocard(_930204), hAPP(hAPP(c_Set_Oinsert(_930204), _930208), _930206)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_930204), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_930204, tc_HOL_Obool)), _930206), hAPP(hAPP(c_Set_Oinsert(_930204), _930208), c_Orderings_Obot__class_Obot(tc_fun(_930204, tc_HOL_Obool)))))))], (48376 ^ _779203) ^ [_1754757, _1754759, _1754761, _1754763] : [-(c_Lazy__Sequence_Oappend(_1754757, c_Lazy__Sequence_Olazy__sequence_OInsert(_1754757, _1754759, _1754761), _1754763) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754757, _1754759, c_Lazy__Sequence_Oappend(_1754757, _1754761, _1754763)))], (50182 ^ _779203) ^ [_1793994, _1793996, _1793998, _1794000] : [c_Fun_Obij__betw(_1793994, _1793996, _1793998, c_Orderings_Otop__class_Otop(tc_fun(_1793994, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1793996, tc_HOL_Obool))), 50185 ^ _779203 : [(50192 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1793996), _1794000)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1793994), hAPP(c_Set_Ovimage(_1793994, _1793996, _1793998), _1794000))))], (50186 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1793994), hAPP(c_Set_Ovimage(_1793994, _1793996, _1793998), _1794000))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1793996), _1794000)))]]], (40721 ^ _779203) ^ [_1577681, _1577683] : [-(hAPP(c_Relation_Oconverse(_1577681, _1577681), c_Relation_OId__on(_1577681, _1577683)) = c_Relation_OId__on(_1577681, _1577683))], (23780 ^ _779203) ^ [_1197657, _1197659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1197657), _1197659)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197659, _1197657) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1197659), _1197657), _1197657))], (44622 ^ _779203) ^ [_1673309, _1673311] : [_1673309 = _1673311, -(hAPP(c_Code__Numeral_Oof__nat, _1673309) = hAPP(c_Code__Numeral_Oof__nat, _1673311))], (24279 ^ _779203) ^ [_1207080, _1207082, _1207084] : [class_Rings_Ocomm__semiring__1(_1207080), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207080), hAPP(hAPP(c_Power_Opower__class_Opower(_1207080), _1207082), _1207084)), _1207082) = hAPP(hAPP(c_Power_Opower__class_Opower(_1207080), _1207082), hAPP(c_Nat_OSuc, _1207084)))], (20684 ^ _779203) ^ [_1144189, _1144191, _1144193, _1144195, _1144197] : [-(hBOOL(hAPP(hAPP(c_member(_1144189), _1144191), c_SetInterval_Oord_OatLeastAtMost(_1144189, _1144193, _1144195, _1144197)))), hBOOL(hAPP(hAPP(_1144193, _1144195), _1144191)), hBOOL(hAPP(hAPP(_1144193, _1144191), _1144197))], (34256 ^ _779203) ^ [_1408224, _1408226, _1408228, _1408230, _1408232, _1408234] : [hBOOL(hAPP(hAPP(c_member(_1408224), _1408226), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408228, tc_fun(_1408224, tc_HOL_Obool)), _1408230), _1408232))), -(hBOOL(hAPP(hAPP(c_member(_1408224), _1408226), hAPP(_1408232, _1408234)))), hBOOL(hAPP(hAPP(c_member(_1408228), _1408234), _1408230))], (32169 ^ _779203) ^ [_1360567, _1360569, _1360571] : [class_Groups_Ocomm__monoid__add(_1360567), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1360567), _1360569), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1360571))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1360567), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1360567), _1360569), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1360571))), hAPP(_1360569, _1360571)))], (42187 ^ _779203) ^ [_1619497, _1619499] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1619497, _1619499) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1619497, _1619499)))], (9017 ^ _779203) ^ [_931802, _931804, _931806, _931808, _931810] : [class_Groups_Ocomm__monoid__add(_931802), hBOOL(hAPP(c_Finite__Set_Ofinite(_931804), _931806)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_931804, _931802), _931808), hAPP(hAPP(c_Set_Oinsert(_931804), _931810), _931806)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931802), hAPP(_931808, _931810)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_931804, _931802), _931808), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_931804, tc_HOL_Obool)), _931806), hAPP(hAPP(c_Set_Oinsert(_931804), _931810), c_Orderings_Obot__class_Obot(tc_fun(_931804, tc_HOL_Obool)))))))], (32569 ^ _779203) ^ [_1370287, _1370289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1370287)), _1370289)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1370287), _1370289)))], (40911 ^ _779203) ^ [_1582459, _1582461] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582459, _1582459), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1582461) = _1582461)], (9333 ^ _779203) ^ [_938298, _938300, _938302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938298), _938300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _938298), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _938300), _938302))))], (11554 ^ _779203) ^ [_978429, _978431, _978433] : [class_Rings_Oordered__cancel__semiring(_978429), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978429), c_Groups_Ozero__class_Ozero(_978429)), _978431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978429), _978433), c_Groups_Ozero__class_Ozero(_978429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978429), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_978429), _978433), _978431)), c_Groups_Ozero__class_Ozero(_978429))))], (33877 ^ _779203) ^ [_1399914, _1399916, _1399918, _1399920, _1399922] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1399914, _1399916, _1399918), _1399920), _1399922) = hAPP(hAPP(_1399920, hAPP(c_Product__Type_Ofst(_1399914, _1399916), _1399922)), hAPP(c_Product__Type_Osnd(_1399914, _1399916), _1399922)))], (2666 ^ _779203) ^ [_818524, _818526, _818528, _818530] : [-(c_Predicate_OPowp(_818530, _818526) = c_Predicate_OPowp(_818528, _818524)), _818530 = _818528, _818526 = _818524], (4720 ^ _779203) ^ [_851011, _851013] : [_851013 = _851011, -(c_Set_OBex(_851013) = c_Set_OBex(_851011))], (40095 ^ _779203) ^ [_1561730, _1561732, _1561734, _1561736, _1561738, _1561740, _1561742] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1561730, _1561732, _1561734, _1561736), _1561738), _1561740), _1561742) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1561732, _1561734, _1561736), _1561740), hAPP(_1561738, _1561742)))], (22676 ^ _779203) ^ [_1178895, _1178897] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178895)), 22679 ^ _779203 : [(22688 ^ _779203) ^ [] : [-(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), _1178895), _1178897)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178897), _1178895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178897))], (22680 ^ _779203) ^ [] : [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), _1178895), _1178897))), 22683 ^ _779203 : [(22686 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178897)))], (22684 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178897), _1178895)))]]]]], (38820 ^ _779203) ^ [_1531045, _1531047] : [c_Wellfounded_Owf(_1531045, _1531047), 38824 ^ _779203 : [(38825 ^ _779203) ^ [_1531181] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1531045, _1531045)), hAPP(hAPP(c_Product__Type_OPair(_1531045, _1531045), hAPP(_1531181, hAPP(c_Nat_OSuc, 38823 ^ [_1531045, _1531047, _1531181]))), hAPP(_1531181, 38823 ^ [_1531045, _1531047, _1531181]))), _1531047))]]], (47839 ^ _779203) ^ [_1743204, _1743206, _1743208] : [47841 ^ _779203 : [(47844 ^ _779203) ^ [] : [hBOOL(hAPP(_1743206, 47840 ^ [_1743204, _1743206, _1743208]))], (47842 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743204), 47840 ^ [_1743204, _1743206, _1743208]), hAPP(c_List_Oset(_1743204), _1743208))))]], -(c_List_Olist__all(_1743204, _1743206, _1743208))], (21939 ^ _779203) ^ [_1165871, _1165873, _1165875] : [-(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), _1165871), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1165873), _1165871))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1165873, _1165871))), _1165875) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1165873), _1165875))], (5412 ^ _779203) ^ [_862005, _862007, _862009, _862011, _862013, _862015] : [-(c_Divides_Odiv__class_Omod(_862015, _862011, _862007) = c_Divides_Odiv__class_Omod(_862013, _862009, _862005)), _862015 = _862013, _862011 = _862009, _862007 = _862005], (30303 ^ _779203) ^ [_1319840, _1319842, _1319844] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1319840), _1319842)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319840), _1319844)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319840, tc_HOL_Obool)), _1319842), _1319844) = c_Orderings_Obot__class_Obot(tc_fun(_1319840, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1319840), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319840, tc_HOL_Obool)), _1319842), _1319844)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1319840), _1319842)), hAPP(c_Finite__Set_Ocard(_1319840), _1319844)))], (24297 ^ _779203) ^ [_1207461, _1207463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1207461)), -(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), _1207461), _1207463))))], (30891 ^ _779203) ^ [_1331888, _1331890, _1331892] : [class_Lattices_Olattice(_1331888), hBOOL(hAPP(c_Finite__Set_Ofinite(_1331888), _1331890)), hBOOL(hAPP(hAPP(c_member(_1331888), _1331892), _1331890)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1331888), _1331892), c_Big__Operators_Olattice__class_OInf__fin(_1331888, _1331890)) = c_Big__Operators_Olattice__class_OInf__fin(_1331888, _1331890))], (16012 ^ _779203) ^ [_1060216, _1060218, _1060220] : [class_Int_Onumber(_1060216), class_Orderings_Olinorder(_1060216), 16019 ^ _779203 : [(16026 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060216), hAPP(c_Int_Onumber__class_Onumber__of(_1060216), _1060220)), hAPP(c_Int_Onumber__class_Onumber__of(_1060216), _1060218)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060216), hAPP(c_Int_Onumber__class_Onumber__of(_1060216), _1060218)), hAPP(c_Int_Onumber__class_Onumber__of(_1060216), _1060220))))], (16020 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1060216), hAPP(c_Int_Onumber__class_Onumber__of(_1060216), _1060218)), hAPP(c_Int_Onumber__class_Onumber__of(_1060216), _1060220))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1060216), hAPP(c_Int_Onumber__class_Onumber__of(_1060216), _1060220)), hAPP(c_Int_Onumber__class_Onumber__of(_1060216), _1060218)))]]], (5899 ^ _779203) ^ [_872694, _872696, _872698] : [_872694 = c_Orderings_Obot__class_Obot(tc_fun(_872696, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_872696), _872698), _872694))], (26210 ^ _779203) ^ [_1240236, _1240238, _1240240] : [class_Orderings_Oorder(_1240236), 26213 ^ _779203 : [(26220 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240236), _1240238), _1240240))), -(c_Orderings_Obot__class_Obot(tc_fun(_1240236, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1240236, _1240238, _1240240))], (26214 ^ _779203) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1240236, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1240236, _1240238, _1240240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1240236), _1240238), _1240240))]]], (2064 ^ _779203) ^ [_808973, _808975] : [_808975 = _808973, -(c_Int_Oring__1__class_OInts(_808975) = c_Int_Oring__1__class_OInts(_808973))], (42800 ^ _779203) ^ [_1632189, _1632191, _1632193] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632189), tc_List_Olist(_1632189))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632189), tc_List_Olist(_1632189)), _1632191), c_List_Olist_ONil(_1632189))), c_List_Olexord(_1632189, _1632193)))], (49518 ^ _779203) ^ [_1779778, _1779780, _1779782, _1779784] : [c_Equiv__Relations_Opart__equivp(_1779778, _1779780), hBOOL(hAPP(hAPP(_1779780, _1779782), _1779784)), -(hBOOL(hAPP(hAPP(_1779780, _1779784), _1779782)))], (1640 ^ _779203) ^ [_802663, _802665] : [-(class_Groups_Ocancel__semigroup__add(_802663)), _802665 = _802663, class_Groups_Ocancel__semigroup__add(_802665)], (18518 ^ _779203) ^ [_1105834] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1105834) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1105834), c_Int_OPls)))], (42754 ^ _779203) ^ [_1631250, _1631252, _1631254, _1631256] : [-(hBOOL(hAPP(hAPP(c_member(_1631250), _1631252), hAPP(c_List_Oset(_1631250), _1631254)))), hBOOL(hAPP(hAPP(c_member(_1631250), _1631252), hAPP(c_List_Oset(_1631250), c_List_Oremove1(_1631250, _1631256, _1631254))))], (42287 ^ _779203) ^ [_1621529, _1621531, _1621533, _1621535, _1621537, _1621539] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1621529, _1621531), hAPP(hAPP(c_List_Ozip(_1621529, _1621531), _1621533), _1621535)), _1621537), _1621539) = hAPP(hAPP(c_List_Ozip(_1621529, _1621531), hAPP(hAPP(c_List_Olist__update(_1621529, _1621533), _1621537), hAPP(c_Product__Type_Ofst(_1621529, _1621531), _1621539))), hAPP(hAPP(c_List_Olist__update(_1621531, _1621535), _1621537), hAPP(c_Product__Type_Osnd(_1621529, _1621531), _1621539))))], (28524 ^ _779203) ^ [_1283672, _1283674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1283672), _1283674)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1283672), hAPP(c_Nat_OSuc, _1283674)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1283674), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1283672), _1283674)))], (39314 ^ _779203) ^ [_1543403, _1543405] : [class_Complete__Lattice_Ocomplete__lattice(_1543403), -(c_Complete__Lattice_OSup__class_OSup(_1543403, _1543405) = c_Complete__Lattice_OInf__class_OInf(_1543403, hAPP(c_Set_OCollect(_1543403), hAPP(hAPP(c_COMBB(tc_fun(_1543403, tc_HOL_Obool), tc_HOL_Obool, _1543403), c_HOL_OAll(_1543403)), hAPP(hAPP(c_COMBB(tc_fun(_1543403, tc_HOL_Obool), tc_fun(_1543403, tc_HOL_Obool), _1543403), hAPP(c_COMBS(_1543403, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1543403), c_fimplies), hAPP(hAPP(c_COMBC(_1543403, tc_fun(_1543403, tc_HOL_Obool), tc_HOL_Obool), c_member(_1543403)), _1543405)))), hAPP(c_COMBC(_1543403, _1543403, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1543403)))))))], (37401 ^ _779203) ^ [_1487014, _1487016, _1487018] : [hBOOL(hAPP(hAPP(c_member(_1487014), _1487016), hAPP(c_Set_OCollect(_1487014), _1487018))), -(hBOOL(hAPP(_1487018, _1487016)))], (26868 ^ _779203) ^ [_1252489, _1252491, _1252493] : [class_Orderings_Olinorder(_1252489), 26871 ^ _779203 : [(26878 ^ _779203) ^ [] : [_1252491 = _1252493, -(hAPP(c_SetInterval_Oord__class_OatMost(_1252489), _1252491) = hAPP(c_SetInterval_Oord__class_OatMost(_1252489), _1252493))], (26872 ^ _779203) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1252489), _1252491) = hAPP(c_SetInterval_Oord__class_OatMost(_1252489), _1252493), -(_1252491 = _1252493)]]], (40354 ^ _779203) ^ [_1568750, _1568752] : [-(c_Transitive__Closure_Ortrancl(_1568750, _1568752) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1568750, _1568750), tc_HOL_Obool)), c_Relation_OId(_1568750)), hAPP(hAPP(c_Relation_Orel__comp(_1568750, _1568750, _1568750), c_Transitive__Closure_Ortrancl(_1568750, _1568752)), _1568752)))], (32553 ^ _779203) ^ [_1369978, _1369980, _1369982] : [class_Rings_Osemiring__1(_1369978), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1369978, _1369980, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1369982) = _1369982)], (3506 ^ _779203) ^ [_831576, _831578, _831580, _831582, _831584, _831586, _831588, _831590, _831592, _831594] : [-(c_List_Olinorder__class_Oinsort__insert__key(_831594, _831590, _831586, _831582, _831578) = c_List_Olinorder__class_Oinsort__insert__key(_831592, _831588, _831584, _831580, _831576)), _831594 = _831592, _831590 = _831588, _831586 = _831584, _831582 = _831580, _831578 = _831576], (35339 ^ _779203) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (21629 ^ _779203) ^ [_1159949, _1159951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159949), _1159951)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1159949)), c_Int_OBit1(_1159951))))], (12747 ^ _779203) ^ [_999361, _999363, _999365, _999367] : [class_Rings_Olinordered__semiring__strict(_999361), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999361), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999361), _999363), _999365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999361), _999367), _999365))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999361), c_Groups_Ozero__class_Ozero(_999361)), _999365)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999361), _999363), _999367)))], (48788 ^ _779203) ^ [_1764541, _1764543, _1764545, _1764547, _1764549] : [c_Relation_Otrans(_1764541, _1764543), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764541, _1764541)), hAPP(hAPP(c_Product__Type_OPair(_1764541, _1764541), _1764545), _1764547)), _1764543)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764541, _1764541)), hAPP(hAPP(c_Product__Type_OPair(_1764541, _1764541), _1764547), _1764549)), _1764543)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764541, _1764541)), hAPP(hAPP(c_Product__Type_OPair(_1764541, _1764541), _1764545), _1764549)), _1764543)))], (43903 ^ _779203) ^ [_1657562, _1657564, _1657566, _1657568, _1657570] : [c_Finite__Set_Ofun__left__comm__idem(_1657562, _1657564, _1657566), -(hAPP(hAPP(c_Finite__Set_Ofold(_1657562, _1657564, _1657566), _1657568), hAPP(c_List_Oset(_1657562), _1657570)) = hAPP(c_List_Ofoldl(_1657564, _1657562, hAPP(c_COMBC(_1657562, _1657564, _1657564), _1657566), _1657568), _1657570))], (43746 ^ _779203) ^ [_1654366, _1654368, _1654370] : [hBOOL(hAPP(c_List_Odistinct(_1654366), hAPP(c_List_Orotate(_1654366, _1654368), _1654370))), -(hBOOL(hAPP(c_List_Odistinct(_1654366), _1654370)))], (38252 ^ _779203) ^ [_1515296, _1515298, _1515300, _1515302, _1515304] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1515296, _1515298)), _1515300), hAPP(hAPP(c_Product__Type_OSigma(_1515296, _1515298), _1515302), _1515304))), 38256 ^ _779203 : [(38262 ^ _779203) ^ [] : [-(_1515300 = hAPP(hAPP(c_Product__Type_OPair(_1515296, _1515298), 38255 ^ [_1515296, _1515298, _1515300, _1515302, _1515304]), 38258 ^ [_1515296, _1515298, _1515300, _1515302, _1515304]))], (38260 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515298), 38258 ^ [_1515296, _1515298, _1515300, _1515302, _1515304]), hAPP(_1515304, 38255 ^ [_1515296, _1515298, _1515300, _1515302, _1515304]))))], (38257 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515296), 38255 ^ [_1515296, _1515298, _1515300, _1515302, _1515304]), _1515302)))]]], (19940 ^ _779203) ^ [_1130670, _1130672, _1130674] : [class_Groups_Oordered__ab__group__add(_1130670), 19943 ^ _779203 : [(19950 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130670), hAPP(c_Groups_Ouminus__class_Ouminus(_1130670), _1130674)), _1130672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130670), hAPP(c_Groups_Ouminus__class_Ouminus(_1130670), _1130672)), _1130674)))], (19944 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130670), hAPP(c_Groups_Ouminus__class_Ouminus(_1130670), _1130672)), _1130674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130670), hAPP(c_Groups_Ouminus__class_Ouminus(_1130670), _1130674)), _1130672)))]]], (43263 ^ _779203) ^ [_1642373, _1642375, _1642377, _1642379] : [-(hAPP(hAPP(c_List_Onth(_1642373), hAPP(hAPP(c_List_Oappend(_1642373), _1642375), _1642377)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642373)), _1642375)), _1642379)) = hAPP(hAPP(c_List_Onth(_1642373), _1642377), _1642379))], (27260 ^ _779203) ^ [_1259038] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1259038)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1259038)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1259038), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (37829 ^ _779203) ^ [_1499100, _1499102, _1499104] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1499100), _1499102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1499100, _1499100), tc_HOL_Obool)), _1499104), hAPP(hAPP(c_Product__Type_OSigma(_1499100, _1499100), _1499102), hAPP(c_COMBK(tc_fun(_1499100, tc_HOL_Obool), _1499100), _1499102)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1499100, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1499100), _1499102), _1499104))))], (26152 ^ _779203) ^ [_1239126, _1239128] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1239126), _1239128)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1239126, tc_HOL_Obool)), hAPP(c_Set_OPow(_1239126), _1239128))))], (45002 ^ _779203) ^ [_1681517, _1681519, _1681521] : [hBOOL(hAPP(c_List_Olistsp(_1681517, hAPP(hAPP(c_COMBC(_1681517, tc_fun(_1681517, tc_HOL_Obool), tc_HOL_Obool), c_member(_1681517)), _1681519)), _1681521)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1681517)), _1681521), c_List_Olists(_1681517, _1681519))))], (6050 ^ _779203) ^ [_875449] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_875449), c_Orderings_Obot__class_Obot(tc_fun(_875449, tc_HOL_Obool)))))], (30676 ^ _779203) ^ [_1327259, _1327261, _1327263] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1327259, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1327259, tc_HOL_Obool)), _1327261), _1327263)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327259, tc_HOL_Obool)), _1327261), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1327259, tc_HOL_Obool), _1327263)))], (37171 ^ _779203) ^ [_1480955, _1480957, _1480959] : [-(hAPP(c_Set_Ovimage(_1480955, _1480957, _1480959), c_Orderings_Otop__class_Otop(tc_fun(_1480957, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1480955, tc_HOL_Obool)))], (37075 ^ _779203) ^ [_1478750] : [-(c_Nitpick_Ozero__frac(_1478750) = c_Nitpick_OAbs__Frac(_1478750, 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))))], (48312 ^ _779203) ^ [_1753389, _1753391, _1753393, _1753395] : [hBOOL(hAPP(hAPP(c_member(_1753389), _1753391), hAPP(c_List_Oset(_1753389), c_List_Oreplicate(_1753389, _1753393, _1753395)))), 48315 ^ _779203 : [(48318 ^ _779203) ^ [] : [_1753393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48316 ^ _779203) ^ [] : [-(_1753391 = _1753395)]]], (11163 ^ _779203) ^ [_971313, _971315, _971317, _971319] : [class_Groups_Ocomm__monoid__mult(_971313), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_971315), _971317))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_971315, _971313), _971319), _971317) = c_Groups_Oone__class_Oone(_971313))], (23271 ^ _779203) ^ [_1188612, _1188614] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188614)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1188612)), hAPP(c_Int_Onat, _1188614)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1188612, _1188614)))], (15932 ^ _779203) ^ [_1058468, _1058470, _1058472, _1058474] : [class_Groups_Oordered__ab__group__add(_1058468), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058468), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1058468), _1058470), _1058472)), _1058474) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1058468), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058468), _1058470), _1058474)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1058468), _1058472), _1058474)))], (31971 ^ _779203) ^ [_1355399, _1355401, _1355403, _1355405, _1355407] : [-(hAPP(c_Set_Oimage(_1355399, _1355401, hAPP(hAPP(c_COMBB(_1355403, _1355401, _1355399), _1355405), _1355407)), c_Orderings_Otop__class_Otop(tc_fun(_1355399, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1355403, _1355401, _1355405), hAPP(c_Set_Oimage(_1355399, _1355403, _1355407), c_Orderings_Otop__class_Otop(tc_fun(_1355399, tc_HOL_Obool)))))], (45791 ^ _779203) ^ [_1699631, _1699633] : [-(c_List_Oconcat(tc_List_Olist(_1699631), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699631), tc_List_Olist(tc_List_Olist(_1699631))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1699631)), _1699631, c_List_Olist_ONil(tc_List_Olist(_1699631)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1699631), tc_List_Olist(tc_List_Olist(_1699631))), _1699631), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699631), tc_List_Olist(tc_List_Olist(_1699631)), tc_List_Olist(tc_List_Olist(_1699631))), c_List_Olist_OCons(tc_List_Olist(_1699631))), c_List_Olist_ONil(tc_List_Olist(_1699631)))))), _1699633)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1699631), tc_List_Olist(_1699631)), c_List_Otl(_1699631)), hAPP(c_List_Ofilter(tc_List_Olist(_1699631), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1699631)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699631), tc_List_Olist(_1699631), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1699631)))), _1699633)))], (9189 ^ _779203) ^ [_935948, _935950, _935952] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935948), _935950) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _935948), _935952), -(_935950 = _935952)], (5080 ^ _779203) ^ [_856683, _856685, _856687, _856689] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856689, _856685) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_856687, _856683)), _856689 = _856687, _856685 = _856683], (14539 ^ _779203) ^ [_1032331, _1032333, _1032335, _1032337] : [class_Fields_Olinordered__field(_1032331), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032331), c_Groups_Ozero__class_Ozero(_1032331)), _1032333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032331), _1032335), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032331), _1032337), _1032333))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032331), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1032331), _1032335), _1032333)), _1032337)))], (38264 ^ _779203) ^ [_1515598, _1515600, _1515602, _1515604, _1515606, _1515608] : [hAPP(c_Set_Oimage(_1515598, _1515600, _1515602), c_Orderings_Otop__class_Otop(tc_fun(_1515598, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1515600, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1515604, _1515606, _1515608), c_Orderings_Otop__class_Otop(tc_fun(_1515604, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1515606, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1515598, _1515604), tc_prod(_1515600, _1515606), c_Product__Type_Omap__pair(_1515598, _1515600, _1515604, _1515606, _1515602, _1515608)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1515598, _1515604), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1515600, _1515606), tc_HOL_Obool)))], (4524 ^ _779203) ^ [_847891, _847893, _847895, _847897, _847899, _847901, _847903, _847905] : [-(c_Product__Type_Oscomp(_847905, _847901, _847897, _847893) = c_Product__Type_Oscomp(_847903, _847899, _847895, _847891)), _847905 = _847903, _847901 = _847899, _847897 = _847895, _847893 = _847891], (24360 ^ _779203) ^ [_1208507] : [-(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)), _1208507)))], (31837 ^ _779203) ^ [_1351952, _1351954, _1351956, _1351958, _1351960] : [class_Groups_Ocomm__monoid__mult(_1351952), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351954, _1351952), hAPP(hAPP(c_COMBS(_1351954, _1351952, _1351952), hAPP(hAPP(c_COMBB(_1351952, tc_fun(_1351952, _1351952), _1351954), c_Groups_Otimes__class_Otimes(_1351952)), _1351956)), _1351958)), _1351960) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1351952), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351954, _1351952), _1351956), _1351960)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351954, _1351952), _1351958), _1351960)))], (1630 ^ _779203) ^ [_802538, _802540] : [-(class_Rings_Oordered__comm__semiring(_802538)), _802540 = _802538, class_Rings_Oordered__comm__semiring(_802540)], (29758 ^ _779203) ^ [_1307707, _1307709, _1307711] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307707, tc_HOL_Obool)), _1307709), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307707, tc_HOL_Obool)), _1307711), _1307709)) = c_Orderings_Obot__class_Obot(tc_fun(_1307707, tc_HOL_Obool)))], (33861 ^ _779203) ^ [_1399483, _1399485, _1399487, _1399489] : [-(hAPP(c_Product__Type_Ofst(_1399483, _1399485), hAPP(hAPP(c_Product__Type_OPair(_1399483, _1399485), _1399487), _1399489)) = _1399487)], (28600 ^ _779203) ^ [_1285169, _1285171, _1285173] : [class_Orderings_Olinorder(_1285169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285169), _1285171), _1285173)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285169, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1285169), _1285171), c_Orderings_Obot__class_Obot(tc_fun(_1285169, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1285169, _1285171, _1285173)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1285169, _1285171), _1285173))], (7725 ^ _779203) ^ [_906490, _906492, _906494] : [class_Orderings_Oorder(_906490), -(_906492 = _906494), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906490), _906494), _906492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_906490), _906494), _906492)))], (14249 ^ _779203) ^ [_1026925, _1026927, _1026929, _1026931, _1026933] : [class_Fields_Ofield(_1026925), -(_1026927 = c_Groups_Ozero__class_Ozero(_1026925)), -(_1026929 = c_Groups_Ozero__class_Ozero(_1026925)), 14260 ^ _779203 : [(14267 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026925), _1026931), _1026929) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026925), _1026933), _1026927), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026925), _1026931), _1026927) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026925), _1026933), _1026929))], (14261 ^ _779203) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026925), _1026931), _1026927) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1026925), _1026933), _1026929), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026925), _1026931), _1026929) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1026925), _1026933), _1026927))]]], (34991 ^ _779203) ^ [_1429263, _1429265, _1429267, _1429269, _1429271] : [_1429263 = c_Orderings_Obot__class_Obot(tc_fun(_1429265, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1429265, tc_fun(_1429267, tc_HOL_Obool)), _1429263), hAPP(hAPP(c_COMBC(_1429265, tc_fun(_1429267, tc_HOL_Obool), tc_fun(_1429267, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1429267, tc_HOL_Obool), tc_fun(tc_fun(_1429267, tc_HOL_Obool), tc_fun(_1429267, tc_HOL_Obool)), _1429265), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1429267, tc_HOL_Obool))), _1429269)), _1429271)) = c_Orderings_Otop__class_Otop(tc_fun(_1429267, tc_HOL_Obool)))], (52615 ^ _779203) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (9486 ^ _779203) ^ [_941022, _941024, _941026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941022), _941024)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941022), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941024), _941026))))], (5849 ^ _779203) ^ [_871781, _871783, _871785] : [_871781 = _871783, 5852 ^ _779203 : [(5855 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871785, tc_HOL_Obool)), _871783), _871781)))], (5853 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871785, tc_HOL_Obool)), _871781), _871783)))]]], (38506 ^ _779203) ^ [_1524637, _1524639, _1524641, _1524643, _1524645, _1524647, _1524649, _1524651] : [hBOOL(hAPP(hAPP(_1524637, _1524639), _1524641)), hBOOL(hAPP(hAPP(_1524643, _1524641), _1524645)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1524647, _1524649, _1524651, _1524637, _1524643), _1524639), _1524645)))], (49684 ^ _779203) ^ [_1783332, _1783334, _1783336, _1783338] : [hAPP(c_Set_Oimage(_1783332, _1783334, _1783336), c_Orderings_Otop__class_Otop(tc_fun(_1783332, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1783334, tc_HOL_Obool)), -(hAPP(_1783336, hAPP(c_Hilbert__Choice_Oinv__into(_1783332, _1783334, c_Orderings_Otop__class_Otop(tc_fun(_1783332, tc_HOL_Obool)), _1783336), _1783338)) = _1783338)], (45486 ^ _779203) ^ [_1692096, _1692098, _1692100, _1692102] : [class_Orderings_Olinorder(_1692096), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692098)), c_List_Olinorder__class_Osort__key(_1692098, _1692096, _1692100, _1692102)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692098)), _1692102))], (32916 ^ _779203) ^ [_1382111, _1382113, _1382115, _1382117, _1382119, _1382121, _1382123, _1382125] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1382111, _1382113, _1382115), _1382117), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1382119, _1382121, tc_prod(_1382111, _1382113)), _1382123), _1382125)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1382119, _1382121, _1382115), hAPP(hAPP(c_COMBB(tc_fun(_1382121, tc_prod(_1382111, _1382113)), tc_fun(_1382121, _1382115), _1382119), hAPP(c_COMBB(tc_prod(_1382111, _1382113), _1382115, _1382121), hAPP(c_Product__Type_Oprod_Oprod__case(_1382111, _1382113, _1382115), _1382117))), _1382123)), _1382125))], (45770 ^ _779203) ^ [_1699146, _1699148] : [c_List_Otranspose(_1699146, _1699148) = c_List_Olist_ONil(tc_List_Olist(_1699146)), 45773 ^ _779203 : [(45774 ^ _779203) ^ [_1699241] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699146)), _1699241), hAPP(c_List_Oset(tc_List_Olist(_1699146)), _1699148))), -(_1699241 = c_List_Olist_ONil(_1699146))]]], (51647 ^ _779203) ^ [_1822543, _1822545] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822543), _1822545)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822543), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1822545), _1822543))))], (49979 ^ _779203) ^ [_1790081, _1790083, _1790085, _1790087] : [c_Fun_Obij__betw(_1790081, _1790083, _1790085, c_Orderings_Otop__class_Otop(tc_fun(_1790081, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790083, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1790081, _1790083, _1790085), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1790081, tc_HOL_Obool)), _1790087)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1790083, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1790081, _1790083, _1790085), _1790087)))], (42604 ^ _779203) ^ [_1628744] : [-(hBOOL(hAPP(c_List_Odistinct(_1628744), c_List_Olist_ONil(_1628744))))], (27734 ^ _779203) ^ [_1267982, _1267984, _1267986, _1267988] : [class_Lattices_Osemilattice__sup(_1267982), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267982), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267982), _1267984), _1267986)), _1267988) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267982), _1267984), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1267982), _1267986), _1267988)))], (42289 ^ _779203) ^ [_1621618, _1621620, _1621622, _1621624, _1621626, _1621628] : [-(_1621618 = _1621620), -(hAPP(hAPP(c_List_Olist__update(_1621622, hAPP(hAPP(c_List_Olist__update(_1621622, _1621624), _1621618), _1621626)), _1621620), _1621628) = hAPP(hAPP(c_List_Olist__update(_1621622, hAPP(hAPP(c_List_Olist__update(_1621622, _1621624), _1621620), _1621628)), _1621618), _1621626))], (47960 ^ _779203) ^ [_1745548, _1745550] : [c_List_Olist__ex1(_1745548, _1745550, c_List_Olist_ONil(_1745548))], (23715 ^ _779203) ^ [_1196706, _1196708, _1196710] : [_1196706 = 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), _1196706), _1196708)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196706), _1196710)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46676 ^ _779203) ^ [_1717801, _1717803] : [class_Groups_Ocomm__monoid__add(_1717801), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1717801), hAPP(c_List_Orev(_1717801), _1717803)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1717801), _1717803))], (38475 ^ _779203) ^ [_1522458, _1522460, _1522462, _1522464] : [hBOOL(hAPP(c_Predicate_ORangeP(_1522458, _1522460, hAPP(hAPP(c_COMBC(_1522458, tc_fun(tc_prod(_1522458, _1522460), tc_HOL_Obool), tc_fun(_1522460, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522460, tc_fun(tc_fun(tc_prod(_1522458, _1522460), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1522458, _1522460), tc_HOL_Obool), tc_fun(_1522460, tc_HOL_Obool)), _1522458), c_COMBC(_1522460, tc_fun(tc_prod(_1522458, _1522460), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522460, tc_prod(_1522458, _1522460)), tc_fun(_1522460, tc_fun(tc_fun(tc_prod(_1522458, _1522460), tc_HOL_Obool), tc_HOL_Obool)), _1522458), hAPP(c_COMBB(tc_prod(_1522458, _1522460), tc_fun(tc_fun(tc_prod(_1522458, _1522460), tc_HOL_Obool), tc_HOL_Obool), _1522460), c_member(tc_prod(_1522458, _1522460)))), c_Product__Type_OPair(_1522458, _1522460)))), _1522462)), _1522464)), -(hBOOL(hAPP(hAPP(c_member(_1522460), _1522464), hAPP(c_Relation_ORange(_1522458, _1522460), _1522462))))], (28150 ^ _779203) ^ [_1276624, _1276626] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1276624), _1276626)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1276626), _1276624))], (50003 ^ _779203) ^ [_1790650, _1790652, _1790654] : [c_Fun_Oinj__on(_1790650, _1790652, _1790654, c_Orderings_Otop__class_Otop(tc_fun(_1790650, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1790650, _1790652, _1790654), c_Orderings_Otop__class_Otop(tc_fun(_1790650, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1790652, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1790650, _1790652, _1790654, c_Orderings_Otop__class_Otop(tc_fun(_1790650, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790652, tc_HOL_Obool))))], (35758 ^ _779203) ^ [_1449602, _1449604, _1449606, _1449608, _1449610] : [c_Equiv__Relations_Oequiv(_1449602, _1449604, _1449606), hBOOL(hAPP(hAPP(c_member(tc_prod(_1449602, _1449602)), hAPP(hAPP(c_Product__Type_OPair(_1449602, _1449602), _1449608), _1449610)), _1449606)), -(hAPP(c_Relation_OImage(_1449602, _1449602, _1449606), hAPP(hAPP(c_Set_Oinsert(_1449602), _1449608), c_Orderings_Obot__class_Obot(tc_fun(_1449602, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1449602, _1449602, _1449606), hAPP(hAPP(c_Set_Oinsert(_1449602), _1449610), c_Orderings_Obot__class_Obot(tc_fun(_1449602, tc_HOL_Obool)))))], (22059 ^ _779203) ^ [_1168429, _1168431, _1168433, _1168435, _1168437, _1168439] : [class_Divides_Osemiring__div(_1168429), c_Divides_Odiv__class_Omod(_1168429, _1168431, _1168433) = c_Divides_Odiv__class_Omod(_1168429, _1168435, _1168433), c_Divides_Odiv__class_Omod(_1168429, _1168437, _1168433) = c_Divides_Odiv__class_Omod(_1168429, _1168439, _1168433), -(c_Divides_Odiv__class_Omod(_1168429, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168429), _1168431), _1168437), _1168433) = c_Divides_Odiv__class_Omod(_1168429, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168429), _1168435), _1168439), _1168433))], (1220 ^ _779203) ^ [_797413, _797415] : [-(class_Rings_Oordered__ring__abs(_797413)), _797415 = _797413, class_Rings_Oordered__ring__abs(_797415)], (45991 ^ _779203) ^ [_1704501] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1704501) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1704501)))], (35689 ^ _779203) ^ [_1448068, _1448070, _1448072, _1448074, _1448076, _1448078] : [c_Equiv__Relations_Oequiv(_1448068, _1448070, _1448072), hBOOL(hAPP(hAPP(c_member(_1448068), _1448074), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1448068, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1448068, _1448068, _1448072), hAPP(hAPP(c_Set_Oinsert(_1448068), _1448076), c_Orderings_Obot__class_Obot(tc_fun(_1448068, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1448068, _1448068, _1448072), hAPP(hAPP(c_Set_Oinsert(_1448068), _1448078), c_Orderings_Obot__class_Obot(tc_fun(_1448068, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1448068, _1448068)), hAPP(hAPP(c_Product__Type_OPair(_1448068, _1448068), _1448076), _1448078)), _1448072)))], (48587 ^ _779203) ^ [_1759609, _1759611, _1759613] : [-(c_FunDef_OTHE__default(_1759611, _1759613, _1759609) = c_HOL_OThe(_1759611, _1759609)), 48588 ^ _779203 : [(48589 ^ _779203) ^ [_1759673] : [hBOOL(hAPP(_1759609, _1759673)), 48593 ^ _779203 : [(48596 ^ _779203) ^ [] : [48592 ^ [_1759609, _1759611, _1759613, _1759673] = _1759673], (48594 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1759609, 48592 ^ [_1759609, _1759611, _1759613, _1759673])))]]]]], (35387 ^ _779203) ^ [_1439754, _1439756, _1439758, _1439760] : [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), _1439754), _1439756)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1439758), _1439760))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1439754), _1439760) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1439758), _1439756))], (37858 ^ _779203) ^ [_1499896, _1499898, _1499900, _1499902] : [-(c_Fun_Oinj__on(_1499896, tc_prod(_1499898, _1499896), 37856 ^ [_1499896, _1499898, _1499900, _1499902], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1499898, tc_fun(_1499896, tc_HOL_Obool)), _1499900), _1499902)))], (17638 ^ _779203) ^ [_1090051, _1090053, _1090055] : [class_Orderings_Olinorder(_1090051), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090051), _1090053)), -(_1090055 = c_Orderings_Obot__class_Obot(tc_fun(_1090051, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1090051, tc_HOL_Obool)), _1090055), _1090053)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090051), c_Big__Operators_Olattice_OInf__fin(_1090051, c_Orderings_Oord__class_Omin(_1090051), _1090055)), c_Big__Operators_Olattice_OInf__fin(_1090051, c_Orderings_Oord__class_Omin(_1090051), _1090053)) = c_Big__Operators_Olattice_OInf__fin(_1090051, c_Orderings_Oord__class_Omin(_1090051), _1090053))], (49014 ^ _779203) ^ [_1770683, _1770685] : [c_Predicate_Otransp(_1770683, _1770685), -(c_Relation_Otrans(_1770683, hAPP(c_Set_OCollect(tc_prod(_1770683, _1770683)), hAPP(c_Product__Type_Oprod_Oprod__case(_1770683, _1770683, tc_HOL_Obool), _1770685))))], (52165 ^ _779203) ^ [_1831535, _1831537] : [-(class_Finite__Set_Ofinite(tc_fun(_1831535, _1831537))), class_Finite__Set_Ofinite(_1831535), class_Finite__Set_Ofinite(_1831537)], (49837 ^ _779203) ^ [_1787135, _1787137, _1787139, _1787141] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1787135, _1787137, _1787139, _1787141, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1787137)) = _1787139)], (3970 ^ _779203) ^ [_839172, _839174, _839176, _839178, _839180, _839182, _839184, _839186] : [-(c_New__Random__Sequence_Oneg__map(_839186, _839182, _839178, _839174) = c_New__Random__Sequence_Oneg__map(_839184, _839180, _839176, _839172)), _839186 = _839184, _839182 = _839180, _839178 = _839176, _839174 = _839172], (31374 ^ _779203) ^ [_1341702, _1341704, _1341706, _1341708] : [hBOOL(hAPP(hAPP(c_member(_1341702), _1341704), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1341702, tc_HOL_Obool), _1341706))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1341702, tc_HOL_Obool)), _1341708), _1341706)), -(hBOOL(hAPP(hAPP(c_member(_1341702), _1341704), _1341708)))], (34879 ^ _779203) ^ [_1426520, _1426522, _1426524, _1426526, _1426528] : [-(_1426520 = c_Orderings_Obot__class_Obot(tc_fun(_1426522, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_1426524), _1426526), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426522, tc_fun(_1426524, tc_HOL_Obool)), _1426520), _1426528)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426522, tc_fun(_1426524, tc_HOL_Obool)), _1426520), hAPP(hAPP(c_COMBB(tc_fun(_1426524, tc_HOL_Obool), tc_fun(_1426524, tc_HOL_Obool), _1426522), hAPP(c_Set_Oinsert(_1426524), _1426526)), _1426528)))], (36878 ^ _779203) ^ [_1474199, _1474201, _1474203, _1474205, _1474207, _1474209, _1474211] : [c_Typedef_Otype__definition(_1474199, _1474201, _1474203, _1474205, _1474207), 36881 ^ _779203 : [(36888 ^ _779203) ^ [] : [_1474209 = _1474211, -(hAPP(_1474203, _1474209) = hAPP(_1474203, _1474211))], (36882 ^ _779203) ^ [] : [hAPP(_1474203, _1474209) = hAPP(_1474203, _1474211), -(_1474209 = _1474211)]]], (9215 ^ _779203) ^ [_936493, _936495, _936497] : [class_Rings_Olinordered__idom(_936493), -(_936495 = _936497), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936493), _936495), _936497))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_936493), _936497), _936495)))], (1370 ^ _779203) ^ [_799288, _799290] : [-(class_Rings_Oidom(_799288)), _799290 = _799288, class_Rings_Oidom(_799290)], (33091 ^ _779203) ^ [_1385362, _1385364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385362)), 33094 ^ _779203 : [(33101 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385364))), 33104 ^ _779203 : [(33111 ^ _779203) ^ [] : [-(_1385362 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1385362, _1385364) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385362), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385364))))], (33105 ^ _779203) ^ [] : [_1385362 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1385362, _1385364) = 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)))]]], (33095 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1385364)), -(c_Divides_Odivmod__int(_1385362, _1385364) = c_Divides_OposDivAlg(_1385362, _1385364))]]], (52659 ^ _779203) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (18256 ^ _779203) ^ [_1101168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101168)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (41371 ^ _779203) ^ [_1595039, _1595041, _1595043, _1595045, _1595047, _1595049] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595039), tc_List_Olist(_1595039))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595039), tc_List_Olist(_1595039)), hAPP(hAPP(c_List_Olist_OCons(_1595039), _1595041), _1595043)), hAPP(hAPP(c_List_Olist_OCons(_1595039), _1595045), _1595047))), c_List_Olex(_1595039, _1595049))), 41376 ^ _779203 : [(41379 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595039)), _1595043) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1595039)), _1595047))], (41377 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595039, _1595039)), hAPP(hAPP(c_Product__Type_OPair(_1595039, _1595039), _1595041), _1595045)), _1595049)))]], 41380 ^ _779203 : [(41383 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595039), tc_List_Olist(_1595039))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595039), tc_List_Olist(_1595039)), _1595043), _1595047)), c_List_Olex(_1595039, _1595049))))], (41381 ^ _779203) ^ [] : [-(_1595041 = _1595045)]]], (590 ^ _779203) ^ [_788050, _788052, _788054, _788056, _788058, _788060] : [-(c_Finite__Set_Ofun__left__comm(_788058, _788054, _788050)), c_Finite__Set_Ofun__left__comm(_788060, _788056, _788052), _788060 = _788058, _788056 = _788054, _788052 = _788050], (39492 ^ _779203) ^ [_1547602, _1547604] : [39493 ^ _779203 : [(39494 ^ _779203) ^ [_1547648] : [hBOOL(hAPP(_1547602, _1547648))]], -(hBOOL(hAPP(_1547602, c_Hilbert__Choice_OEps(_1547604, _1547602))))], (826 ^ _779203) ^ [_791560, _791562, _791564, _791566] : [-(c_Relation_Osym(_791564, _791560)), c_Relation_Osym(_791566, _791562), _791566 = _791564, _791562 = _791560], (37483 ^ _779203) ^ [_1488770, _1488772, _1488774] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1488770), hAPP(c_Set_OCollect(_1488770), hAPP(hAPP(c_COMBS(_1488770, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1488770), c_fdisj), _1488772)), _1488774)))), 37486 ^ _779203 : [(37489 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1488770), hAPP(c_Set_OCollect(_1488770), _1488774))))], (37487 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1488770), hAPP(c_Set_OCollect(_1488770), _1488772))))]]], (36252 ^ _779203) ^ [_1461137, _1461139, _1461141, _1461143, _1461145, _1461147] : [c_Fun_Oinj__on(_1461137, _1461139, _1461141, _1461143), -(_1461145 = _1461147), hBOOL(hAPP(hAPP(c_member(_1461137), _1461145), _1461143)), hBOOL(hAPP(hAPP(c_member(_1461137), _1461147), _1461143)), hAPP(_1461141, _1461145) = hAPP(_1461141, _1461147)], (32934 ^ _779203) ^ [_1382549, _1382551, _1382553, _1382555] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1382549, _1382551, _1382553), hAPP(hAPP(c_COMBB(tc_fun(_1382551, tc_prod(_1382549, _1382551)), tc_fun(_1382551, _1382553), _1382549), hAPP(c_COMBB(tc_prod(_1382549, _1382551), _1382553, _1382551), _1382555)), c_Product__Type_OPair(_1382549, _1382551))) = _1382555)], (42606 ^ _779203) ^ [_1628773, _1628775, _1628777] : [hBOOL(hAPP(c_List_Odistinct(_1628773), _1628775)), -(hBOOL(hAPP(c_List_Odistinct(_1628773), c_List_Oremove1(_1628773, _1628777, _1628775))))], (25634 ^ _779203) ^ [_1230559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230559)), -(c_Nat__Transfer_Ois__nat(_1230559))], (10987 ^ _779203) ^ [_968761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _968761)), _968761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (17492 ^ _779203) ^ [_1087642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087642), 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)), _1087642)), _1087642)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7821 ^ _779203) ^ [_907801, _907803, _907805, _907807] : [class_Orderings_Opreorder(_907801), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907801), _907803), _907805)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907801), _907805), _907807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907801), _907803), _907807)))], (49528 ^ _779203) ^ [_1779935, _1779937, _1779939, _1779941, _1779943] : [c_Equiv__Relations_Opart__equivp(_1779935, _1779937), hBOOL(hAPP(hAPP(_1779937, _1779939), _1779941)), hBOOL(hAPP(hAPP(_1779937, _1779941), _1779943)), -(hBOOL(hAPP(hAPP(_1779937, _1779939), _1779943)))], (10029 ^ _779203) ^ [_950623, _950625, _950627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950623), _950625)), 10032 ^ _779203 : [(10039 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _950627), _950623)), _950625)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950627), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _950625), _950623))))], (10033 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950627), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _950625), _950623))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _950627), _950623)), _950625)))]]], (28746 ^ _779203) ^ [_1287565, _1287567, _1287569, _1287571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1287565, tc_HOL_Obool)), _1287567), _1287569)), hBOOL(hAPP(_1287567, _1287571)), -(hBOOL(hAPP(_1287569, _1287571)))], (25710 ^ _779203) ^ [_1231779] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1231779)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1231779)))], (1910 ^ _779203) ^ [_806038, _806040] : [-(class_Groups_Ozero(_806038)), _806040 = _806038, class_Groups_Ozero(_806040)], (41957 ^ _779203) ^ [_1612290, _1612292] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1612290), hAPP(c_List_Oset(_1612290), _1612292))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612290)), _1612292))))], (28148 ^ _779203) ^ [_1276559, _1276561, _1276563] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276559, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1276559, tc_HOL_Obool)), _1276561), _1276563)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1276559, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1276559, tc_HOL_Obool)), _1276561)), _1276563))], (35129 ^ _779203) ^ [_1432859, _1432861, _1432863, _1432865, _1432867, _1432869] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432859, tc_fun(_1432861, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1432863, tc_fun(_1432859, tc_HOL_Obool)), _1432865), _1432867)), _1432869) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432863, tc_fun(_1432861, tc_HOL_Obool)), _1432865), hAPP(hAPP(c_COMBC(_1432863, tc_fun(_1432859, tc_fun(_1432861, tc_HOL_Obool)), tc_fun(_1432861, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1432859, tc_HOL_Obool), tc_fun(tc_fun(_1432859, tc_fun(_1432861, tc_HOL_Obool)), tc_fun(_1432861, tc_HOL_Obool)), _1432863), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1432859, tc_fun(_1432861, tc_HOL_Obool))), _1432867)), _1432869)))], (20252 ^ _779203) ^ [_1136441, _1136443, _1136445] : [class_Groups_Ogroup__add(_1136441), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136441), _1136443), _1136445) = c_Groups_Ozero__class_Ozero(_1136441), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1136441), _1136443) = _1136445)], (38661 ^ _779203) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (9071 ^ _779203) ^ [_933107, _933109, _933111, _933113, _933115, _933117] : [class_Rings_Oordered__ring(_933107), 9074 ^ _779203 : [(9081 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933107), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933107), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933107), _933109), _933115)), _933111)), _933113)), _933117)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933107), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933107), _933109), _933111)), _933113)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933107), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933107), _933115), _933111)), _933117))))], (9075 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933107), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933107), _933109), _933111)), _933113)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933107), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933107), _933115), _933111)), _933117))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_933107), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_933107), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_933107), _933109), _933115)), _933111)), _933113)), _933117)))]]], (48386 ^ _779203) ^ [_1754947, _1754949, _1754951, _1754953, _1754955] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1754947, _1754949, _1754951) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1754947, _1754953, _1754955)), _1754949 = _1754953, _1754951 = _1754955], (20124 ^ _779203) ^ [_1134273, _1134275] : [class_Groups_Oordered__ab__group__add(_1134273), 20127 ^ _779203 : [(20134 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134273), _1134275), c_Groups_Ozero__class_Ozero(_1134273))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134273), c_Groups_Ozero__class_Ozero(_1134273)), hAPP(c_Groups_Ouminus__class_Ouminus(_1134273), _1134275))))], (20128 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134273), c_Groups_Ozero__class_Ozero(_1134273)), hAPP(c_Groups_Ouminus__class_Ouminus(_1134273), _1134275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134273), _1134275), c_Groups_Ozero__class_Ozero(_1134273))))]]], (32661 ^ _779203) ^ [_1374859, _1374861, _1374863, _1374865] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1374859, tc_fun(_1374861, tc_HOL_Obool))), _1374863), _1374865)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1374859, _1374861)), hAPP(hAPP(c_Product__Type_OPair(_1374859, _1374861), _1374863), _1374865)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1374859, _1374861), tc_HOL_Obool)))))], (31031 ^ _779203) ^ [_1334229, _1334231, _1334233] : [class_Lattices_Olattice(_1334229), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334229), _1334231)), -(_1334231 = c_Orderings_Obot__class_Obot(tc_fun(_1334229, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1334229), _1334233)), -(_1334233 = c_Orderings_Obot__class_Obot(tc_fun(_1334229, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1334229, tc_HOL_Obool)), _1334231), _1334233) = c_Orderings_Obot__class_Obot(tc_fun(_1334229, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1334229, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1334229, tc_HOL_Obool)), _1334231), _1334233)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1334229), c_Big__Operators_Olattice__class_OInf__fin(_1334229, _1334231)), c_Big__Operators_Olattice__class_OInf__fin(_1334229, _1334233)))], (18676 ^ _779203) ^ [_1108453, _1108455] : [class_Int_Onumber__ring(_1108453), class_Rings_Olinordered__idom(_1108453), 18683 ^ _779203 : [(18690 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1108455)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108453), c_Groups_Ozero__class_Ozero(_1108453)), hAPP(c_Int_Onumber__class_Onumber__of(_1108453), _1108455))))], (18684 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108453), c_Groups_Ozero__class_Ozero(_1108453)), hAPP(c_Int_Onumber__class_Onumber__of(_1108453), _1108455))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1108455)))]]], (35250 ^ _779203) ^ [_1436101] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1436101)), -(_1436101 = 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))), _1436101)), c_FunDef_Omax__strict)))], (24858 ^ _779203) ^ [_1217318, _1217320, _1217322, _1217324] : [class_Rings_Olinordered__semidom(_1217318), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1217320), _1217322)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217318), c_Groups_Ozero__class_Ozero(_1217318)), _1217324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217318), _1217324), c_Groups_Oone__class_Oone(_1217318))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1217318), hAPP(hAPP(c_Power_Opower__class_Opower(_1217318), _1217324), _1217322)), hAPP(hAPP(c_Power_Opower__class_Opower(_1217318), _1217324), _1217320))))], (20658 ^ _779203) ^ [_1143656, _1143658, _1143660, _1143662] : [hBOOL(hAPP(hAPP(_1143660, _1143658), _1143662)), -(hBOOL(hAPP(hAPP(c_member(_1143656), _1143658), c_SetInterval_Oord_OlessThan(_1143656, _1143660, _1143662))))], (19632 ^ _779203) ^ [_1125489, _1125491, _1125493, _1125495] : [19634 ^ _779203 : [(19639 ^ _779203) ^ [] : [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(_1125493, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 19633 ^ [_1125489, _1125491, _1125493, _1125495]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1125493, 19633 ^ [_1125489, _1125491, _1125493, _1125495])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (19637 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 19633 ^ [_1125489, _1125491, _1125493, _1125495]), _1125491)))], (19635 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1125489), 19633 ^ [_1125489, _1125491, _1125493, _1125495])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1125489), _1125491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1125493, _1125489)), _1125495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1125495), hAPP(_1125493, _1125491))), 19653 ^ _779203 : [(19658 ^ _779203) ^ [] : [-(hAPP(_1125493, 19652 ^ [_1125489, _1125491, _1125493, _1125495]) = _1125495)], (19656 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 19652 ^ [_1125489, _1125491, _1125493, _1125495]), _1125491)))], (19654 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1125489), 19652 ^ [_1125489, _1125491, _1125493, _1125495])))]]], (11218 ^ _779203) ^ [_972281, _972283, _972285, _972287] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_972281, _972283)), c_Sum__Type_OPlus(_972281, _972283, _972285, _972287))), 11221 ^ _779203 : [(11224 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_972283), _972287)))], (11222 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_972281), _972285)))]]], (33429 ^ _779203) ^ [_1390807, _1390809] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390807)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390809)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390807, _1390809), c_Divides_OposDivAlg(_1390807, _1390809))))], (34627 ^ _779203) ^ [_1419879, _1419881, _1419883, _1419885, _1419887, _1419889] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419879, tc_fun(_1419881, tc_fun(_1419883, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1419879, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1419881, _1419883), tc_HOL_Obool), tc_fun(_1419881, tc_fun(_1419883, tc_HOL_Obool)), _1419879), hAPP(c_COMBC(_1419881, tc_fun(tc_prod(_1419881, _1419883), tc_HOL_Obool), tc_fun(_1419883, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419883, tc_fun(tc_fun(tc_prod(_1419881, _1419883), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1419881, _1419883), tc_HOL_Obool), tc_fun(_1419883, tc_HOL_Obool)), _1419881), c_COMBC(_1419883, tc_fun(tc_prod(_1419881, _1419883), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1419883, tc_prod(_1419881, _1419883)), tc_fun(_1419883, tc_fun(tc_fun(tc_prod(_1419881, _1419883), tc_HOL_Obool), tc_HOL_Obool)), _1419881), hAPP(c_COMBB(tc_prod(_1419881, _1419883), tc_fun(tc_fun(tc_prod(_1419881, _1419883), tc_HOL_Obool), tc_HOL_Obool), _1419883), c_member(tc_prod(_1419881, _1419883)))), c_Product__Type_OPair(_1419881, _1419883))))), _1419885)), _1419887), _1419889)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1419881, _1419883)), hAPP(hAPP(c_Product__Type_OPair(_1419881, _1419883), _1419887), _1419889)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1419879, tc_fun(tc_prod(_1419881, _1419883), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1419879, tc_HOL_Obool))), _1419885))))], (20 ^ _779203) ^ [_779463, _779465, _779467, _779469] : [-(v_P(_779467, _779463)), v_P(_779469, _779465), _779469 = _779467, _779465 = _779463], (42413 ^ _779203) ^ [_1624571, _1624573, _1624575] : [hBOOL(hAPP(c_List_Odistinct(_1624571), _1624573)), -(hBOOL(hAPP(c_List_Odistinct(_1624571), hAPP(hAPP(c_List_Otake(_1624571), _1624575), _1624573))))], (36330 ^ _779203) ^ [_1462734, _1462736, _1462738, _1462740, _1462742] : [c_Fun_Oinj__on(_1462734, _1462736, _1462738, c_Orderings_Otop__class_Otop(tc_fun(_1462734, tc_HOL_Obool))), 36333 ^ _779203 : [(36340 ^ _779203) ^ [] : [_1462740 = _1462742, -(hAPP(_1462738, _1462740) = hAPP(_1462738, _1462742))], (36334 ^ _779203) ^ [] : [hAPP(_1462738, _1462740) = hAPP(_1462738, _1462742), -(_1462740 = _1462742)]]], (52481 ^ _779203) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (34340 ^ _779203) ^ [_1410863, _1410865, _1410867, _1410869, _1410871] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410863, tc_HOL_Obool)), _1410865), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410867, tc_fun(_1410863, tc_HOL_Obool)), _1410869), _1410871)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410867, tc_fun(_1410863, tc_HOL_Obool)), _1410869), hAPP(hAPP(c_COMBB(tc_fun(_1410863, tc_HOL_Obool), tc_fun(_1410863, tc_HOL_Obool), _1410867), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1410863, tc_HOL_Obool)), _1410865)), _1410871)))], (34545 ^ _779203) ^ [_1417152, _1417154, _1417156, _1417158] : [34547 ^ _779203 : [(34550 ^ _779203) ^ [] : [hAPP(_1417158, 34546 ^ [_1417152, _1417154, _1417156, _1417158]) = c_Orderings_Otop__class_Otop(tc_fun(_1417152, tc_HOL_Obool))], (34548 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1417154), 34546 ^ [_1417152, _1417154, _1417156, _1417158]), _1417156)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1417152, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1417154, tc_fun(_1417152, tc_HOL_Obool)), _1417156), _1417158))], (21789 ^ _779203) ^ [_1162804, _1162806] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1162804)), c_Int_OBit1(_1162806)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1162804)), _1162806)))], (31737 ^ _779203) ^ [_1349348, _1349350, _1349352, _1349354] : [hBOOL(hAPP(hAPP(c_member(_1349348), _1349354), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349348, tc_HOL_Obool)), _1349350), _1349352))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1349348, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1349348, tc_fun(_1349348, tc_HOL_Obool), tc_HOL_Obool), c_member(_1349348)), _1349350)), hAPP(hAPP(c_COMBC(_1349348, tc_fun(_1349348, tc_HOL_Obool), tc_HOL_Obool), c_member(_1349348)), _1349352)), _1349354)))], (35021 ^ _779203) ^ [_1430132, _1430134, _1430136, _1430138, _1430140] : [-(_1430132 = c_Orderings_Obot__class_Obot(tc_fun(_1430134, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1430136, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1430134, tc_fun(_1430136, tc_HOL_Obool)), _1430132), _1430138)), _1430140) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1430134, tc_fun(_1430136, tc_HOL_Obool)), _1430132), hAPP(hAPP(c_COMBC(_1430134, tc_fun(_1430136, tc_HOL_Obool), tc_fun(_1430136, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1430136, tc_HOL_Obool), tc_fun(tc_fun(_1430136, tc_HOL_Obool), tc_fun(_1430136, tc_HOL_Obool)), _1430134), c_Groups_Ominus__class_Ominus(tc_fun(_1430136, tc_HOL_Obool))), _1430138)), _1430140)))], (9673 ^ _779203) ^ [_944540, _944542] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944540), _944542))), 9676 ^ _779203 : [(9683 ^ _779203) ^ [] : [_944540 = _944542, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944540), hAPP(c_Nat_OSuc, _944542))))], (9677 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944540), hAPP(c_Nat_OSuc, _944542))), -(_944540 = _944542)]]], (2044 ^ _779203) ^ [_808667, _808669, _808671, _808673, _808675, _808677] : [-(c_Power_Opower_Opower(_808677, _808673, _808669) = c_Power_Opower_Opower(_808675, _808671, _808667)), _808677 = _808675, _808673 = _808671, _808669 = _808667], (11970 ^ _779203) ^ [_985950, _985952, _985954, _985956] : [class_Rings_Olinordered__semiring__strict(_985950), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985950), _985952), _985954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985950), c_Groups_Ozero__class_Ozero(_985950)), _985956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985950), _985956), _985952)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_985950), _985956), _985954))))], (27338 ^ _779203) ^ [_1260657, _1260659, _1260661] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260657, tc_HOL_Obool)), _1260659), _1260661) = _1260661, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260657, tc_HOL_Obool)), _1260659), _1260661)))], (25446 ^ _779203) ^ [_1227901] : [c_Int_OMin = _1227901, -(c_Int_OMin = c_Int_OBit1(_1227901))], (26086 ^ _779203) ^ [_1237858, _1237860] : [class_Rings_Olinordered__idom(_1237858), 26089 ^ _779203 : [(26096 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237860), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237858), hAPP(c_Int_Oring__1__class_Oof__int(_1237858), _1237860)), c_Groups_Ozero__class_Ozero(_1237858))))], (26090 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1237858), hAPP(c_Int_Oring__1__class_Oof__int(_1237858), _1237860)), c_Groups_Ozero__class_Ozero(_1237858))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237860), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (8258 ^ _779203) ^ [_916502, _916504, _916506] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_916502), _916504)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_916502), _916504)), hAPP(c_Finite__Set_Ocard(_916502), hAPP(hAPP(c_Set_Oinsert(_916502), _916506), _916504)))))], (37737 ^ _779203) ^ [_1496175, _1496177, _1496179, _1496181] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1496175, _1496177)), hAPP(hAPP(c_Product__Type_OSigma(_1496175, _1496177), _1496179), hAPP(c_COMBK(tc_fun(_1496177, tc_HOL_Obool), _1496175), _1496181)))), -(_1496179 = c_Orderings_Obot__class_Obot(tc_fun(_1496175, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1496177), _1496181)))], (23233 ^ _779203) ^ [_1187932, _1187934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187932)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1187932), _1187934)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1187932)), hAPP(c_Int_Onat, _1187934)))], (35840 ^ _779203) ^ [_1451377, _1451379, _1451381, _1451383, _1451385] : [c_Equiv__Relations_Oequiv(_1451377, _1451379, _1451381), hBOOL(hAPP(hAPP(c_member(_1451377), _1451383), _1451379)), hBOOL(hAPP(hAPP(c_member(_1451377), _1451385), _1451379)), 35851 ^ _779203 : [(35858 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1451377, _1451377)), hAPP(hAPP(c_Product__Type_OPair(_1451377, _1451377), _1451383), _1451385)), _1451381)), -(hAPP(c_Relation_OImage(_1451377, _1451377, _1451381), hAPP(hAPP(c_Set_Oinsert(_1451377), _1451383), c_Orderings_Obot__class_Obot(tc_fun(_1451377, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1451377, _1451377, _1451381), hAPP(hAPP(c_Set_Oinsert(_1451377), _1451385), c_Orderings_Obot__class_Obot(tc_fun(_1451377, tc_HOL_Obool)))))], (35852 ^ _779203) ^ [] : [hAPP(c_Relation_OImage(_1451377, _1451377, _1451381), hAPP(hAPP(c_Set_Oinsert(_1451377), _1451383), c_Orderings_Obot__class_Obot(tc_fun(_1451377, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1451377, _1451377, _1451381), hAPP(hAPP(c_Set_Oinsert(_1451377), _1451385), c_Orderings_Obot__class_Obot(tc_fun(_1451377, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1451377, _1451377)), hAPP(hAPP(c_Product__Type_OPair(_1451377, _1451377), _1451383), _1451385)), _1451381)))]]], (45881 ^ _779203) ^ [_1702629, _1702631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1702629), _1702631)), -(c_List_Oupt(_1702629, _1702631) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1702629), c_List_Oupt(hAPP(c_Nat_OSuc, _1702629), _1702631)))], (39125 ^ _779203) ^ [_1538135, _1538137] : [c_Wellfounded_OwfP(_1538135, hAPP(hAPP(c_COMBC(_1538135, tc_fun(tc_prod(_1538135, _1538135), tc_HOL_Obool), tc_fun(_1538135, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538135, tc_fun(tc_fun(tc_prod(_1538135, _1538135), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1538135, _1538135), tc_HOL_Obool), tc_fun(_1538135, tc_HOL_Obool)), _1538135), c_COMBC(_1538135, tc_fun(tc_prod(_1538135, _1538135), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1538135, tc_prod(_1538135, _1538135)), tc_fun(_1538135, tc_fun(tc_fun(tc_prod(_1538135, _1538135), tc_HOL_Obool), tc_HOL_Obool)), _1538135), hAPP(c_COMBB(tc_prod(_1538135, _1538135), tc_fun(tc_fun(tc_prod(_1538135, _1538135), tc_HOL_Obool), tc_HOL_Obool), _1538135), c_member(tc_prod(_1538135, _1538135)))), c_Product__Type_OPair(_1538135, _1538135)))), _1538137)), -(c_Wellfounded_Owf(_1538135, _1538137))], (40909 ^ _779203) ^ [_1582388, _1582390, _1582392] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1582388, _1582388, _1582388), _1582390), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582388, _1582388), tc_HOL_Obool), _1582392), _1582390)) = hAPP(hAPP(c_Relation_Orel__comp(_1582388, _1582388, _1582388), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1582388, _1582388), tc_HOL_Obool), _1582392), _1582390)), _1582390))], (52319 ^ _779203) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (30668 ^ _779203) ^ [_1327068] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1327068, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1327068, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1327068, tc_HOL_Obool)))], (38242 ^ _779203) ^ [_1515103, _1515105, _1515107, _1515109] : [class_Groups_Ocomm__monoid__mult(_1515103), c_Fun_Oinj__on(_1515105, _1515103, _1515107, _1515109), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1515105, _1515103), _1515107), _1515109) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1515103, _1515103), c_Fun_Oid(_1515103)), hAPP(c_Set_Oimage(_1515105, _1515103, _1515107), _1515109)))], (27330 ^ _779203) ^ [_1260474, _1260476, _1260478] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260474, tc_HOL_Obool)), _1260476), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260474, tc_HOL_Obool)), _1260478), _1260476))))], (19748 ^ _779203) ^ [_1127504, _1127506, _1127508] : [class_Lattices_Oboolean__algebra(_1127504), 19751 ^ _779203 : [(19758 ^ _779203) ^ [] : [_1127506 = _1127508, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1127504), _1127506) = hAPP(c_Groups_Ouminus__class_Ouminus(_1127504), _1127508))], (19752 ^ _779203) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1127504), _1127506) = hAPP(c_Groups_Ouminus__class_Ouminus(_1127504), _1127508), -(_1127506 = _1127508)]]], (49713 ^ _779203) ^ [_1784064, _1784066, _1784068, _1784070, _1784072] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1784064, _1784066, _1784068, _1784070), _1784072) = c_Hilbert__Choice_OEps(_1784064, hAPP(hAPP(c_COMBS(_1784064, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1784064), c_fconj), hAPP(hAPP(c_COMBC(_1784064, tc_fun(_1784064, tc_HOL_Obool), tc_HOL_Obool), c_member(_1784064)), _1784068))), hAPP(hAPP(c_COMBC(_1784064, _1784066, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1784066, tc_fun(_1784066, tc_HOL_Obool), _1784064), c_fequal), _1784070)), _1784072))))], (5873 ^ _779203) ^ [_872226, _872228, _872230] : [_872226 = _872228, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872230, tc_HOL_Obool)), _872226), _872228)))], (24323 ^ _779203) ^ [_1207942, _1207944] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1207942)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1207942)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1207944)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1207942)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1207944))))], (47122 ^ _779203) ^ [_1727383, _1727385] : [class_Orderings_Olinorder(_1727383), 47125 ^ _779203 : [(47146 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727383, _1727385)), 47147 ^ _779203 : [(47150 ^ _779203) ^ [_1727943, _1727945] : [_1727385 = hAPP(hAPP(c_List_Olist_OCons(_1727383), _1727943), _1727945), 47156 ^ _779203 : [(47159 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727383), _1727943), 47155 ^ [_1727383, _1727385, _1727943, _1727945]))], (47157 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1727383), 47155 ^ [_1727383, _1727385, _1727943, _1727945]), hAPP(c_List_Oset(_1727383), _1727945))))]], c_List_Olinorder__class_Osorted(_1727383, _1727945)], (47148 ^ _779203) ^ [] : [_1727385 = c_List_Olist_ONil(_1727383)]]], (47126 ^ _779203) ^ [] : [c_List_Olinorder__class_Osorted(_1727383, _1727385), -(_1727385 = c_List_Olist_ONil(_1727383)), 47135 ^ _779203 : [(47138 ^ _779203) ^ [_1727717] : [hBOOL(hAPP(hAPP(c_member(_1727383), _1727717), hAPP(c_List_Oset(_1727383), 47133 ^ [_1727383, _1727385]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1727383), 47134 ^ [_1727383, _1727385]), _1727717)))], (47144 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1727383, 47133 ^ [_1727383, _1727385]))], (47136 ^ _779203) ^ [] : [-(_1727385 = hAPP(hAPP(c_List_Olist_OCons(_1727383), 47134 ^ [_1727383, _1727385]), 47133 ^ [_1727383, _1727385]))]]]]], (26136 ^ _779203) ^ [_1238772, _1238774, _1238776] : [hAPP(c_Set_Oimage(_1238774, tc_fun(_1238774, tc_HOL_Obool), _1238772), _1238776) = hAPP(c_Set_OPow(_1238774), _1238776)], (10995 ^ _779203) ^ [_968880, _968882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968880), _968882)), _968882 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (52625 ^ _779203) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (19908 ^ _779203) ^ [_1130161, _1130163] : [class_Groups_Olinordered__ab__group__add(_1130161), 19911 ^ _779203 : [(19918 ^ _779203) ^ [] : [_1130163 = c_Groups_Ozero__class_Ozero(_1130161), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1130161), _1130163) = _1130163)], (19912 ^ _779203) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1130161), _1130163) = _1130163, -(_1130163 = c_Groups_Ozero__class_Ozero(_1130161))]]], (37109 ^ _779203) ^ [_1479396] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1479396), c_Int_OInteg)), -(_1479396 = hAPP(c_Int_ORep__Integ, 37112 ^ [_1479396]))], (48660 ^ _779203) ^ [_1761184, _1761186, _1761188] : [c_List_Oall__interval__int(_1761184, _1761186, _1761188), -(c_List_Olist__all(tc_Int_Oint, _1761184, c_List_Oupto(_1761186, _1761188)))], (15454 ^ _779203) ^ [_1050144, _1050146, _1050148, _1050150, _1050152] : [class_Orderings_Olinorder(_1050144), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050144), _1050146), _1050148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050144), _1050150), _1050152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050144), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1050144), _1050146), _1050150)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1050144), _1050148), _1050152))))], (22826 ^ _779203) ^ [_1181386, _1181388] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1181386)), hAPP(c_Int_Onat, _1181388)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181388)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181386), _1181388))], (45053 ^ _779203) ^ [_1682913, _1682915, _1682917, _1682919, _1682921, _1682923, _1682925] : [c_List_Olist__all2(_1682913, _1682915, _1682917, _1682919, hAPP(hAPP(c_List_Omap(_1682921, _1682915), _1682923), _1682925)), -(c_List_Olist__all2(_1682913, _1682921, hAPP(hAPP(c_COMBC(_1682913, tc_fun(_1682921, _1682915), tc_fun(_1682921, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1682915, tc_HOL_Obool), tc_fun(tc_fun(_1682921, _1682915), tc_fun(_1682921, tc_HOL_Obool)), _1682913), c_COMBB(_1682915, tc_HOL_Obool, _1682921)), _1682917)), _1682923), _1682919, _1682925))], (26462 ^ _779203) ^ [_1244617, _1244619, _1244621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244617)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244619), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1244621)), 26472 ^ _779203 : [(26478 ^ _779203) ^ [] : [-(_1244619 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26474 ^ [_1244617, _1244619, _1244621]), 26471 ^ [_1244617, _1244619, _1244621]))], (26476 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26474 ^ [_1244617, _1244619, _1244621]), _1244621)))], (26473 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26471 ^ [_1244617, _1244619, _1244621]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1244617))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244619), _1244617) = _1244619)], (13476 ^ _779203) ^ [_1012991, _1012993, _1012995] : [-(hAPP(c_Finite__Set_Ocard(_1012991), _1012993) = hAPP(c_Nat_OSuc, _1012995)), 13477 ^ _779203 : [(13478 ^ _779203) ^ [_1013091, _1013093] : [_1012993 = hAPP(hAPP(c_Set_Oinsert(_1012991), _1013093), _1013091), -(hBOOL(hAPP(hAPP(c_member(_1012991), _1013093), _1013091))), hAPP(c_Finite__Set_Ocard(_1012991), _1013091) = _1012995, 13489 ^ _779203 : [(13492 ^ _779203) ^ [] : [_1013091 = c_Orderings_Obot__class_Obot(tc_fun(_1012991, tc_HOL_Obool))], (13490 ^ _779203) ^ [] : [-(_1012995 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (50327 ^ _779203) ^ [_1796927, _1796929, _1796931, _1796933] : [c_Equiv__Relations_Oequivp(_1796927, _1796929), 50333 ^ _779203 : [(50336 ^ _779203) ^ [] : [hBOOL(hAPP(_1796933, 50332 ^ [_1796927, _1796929, _1796931, _1796933]))], (50334 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1796931, 50332 ^ [_1796927, _1796929, _1796931, _1796933])))]], 50339 ^ _779203 : [(50340 ^ _779203) ^ [_1797186] : [hBOOL(hAPP(_1796931, _1797186))]], 50342 ^ _779203 : [(50345 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1796933, 50341 ^ [_1796927, _1796929, _1796931, _1796933])))], (50343 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796927), 50341 ^ [_1796927, _1796929, _1796931, _1796933]), c_Quotient_ORespects(_1796927, _1796929))))]]], (5368 ^ _779203) ^ [_861313, _861315, _861317, _861319, _861321, _861323] : [-(c_SetInterval_Oord_OgreaterThan(_861323, _861319, _861315) = c_SetInterval_Oord_OgreaterThan(_861321, _861317, _861313)), _861323 = _861321, _861319 = _861317, _861315 = _861313], (44061 ^ _779203) ^ [_1661140, _1661142, _1661144, _1661146, _1661148] : [class_Orderings_Olinorder(_1661140), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661142, _1661140, _1661144), _1661146), _1661148) = c_List_Olist_ONil(_1661142)], (52631 ^ _779203) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (36320 ^ _779203) ^ [_1462565, _1462567, _1462569, _1462571, _1462573] : [c_Fun_Oinj__on(_1462565, _1462567, _1462569, _1462571), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1462565, tc_HOL_Obool)), _1462573), _1462571)), -(c_Fun_Oinj__on(_1462565, _1462567, _1462569, _1462573))], (35472 ^ _779203) ^ [_1442320, _1442322, _1442324, _1442326, _1442328] : [-(hAPP(c_Relation_OImage(_1442320, _1442322, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1442320, _1442322), tc_HOL_Obool)), _1442324), _1442326)), _1442328) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1442322, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1442320, _1442322, _1442324), _1442328)), hAPP(c_Relation_OImage(_1442320, _1442322, _1442326), _1442328)))], (38322 ^ _779203) ^ [_1517208, _1517210, _1517212, _1517214, _1517216, _1517218, _1517220, _1517222] : [c_Fun_Oinj__on(_1517208, _1517210, _1517212, _1517214), c_Fun_Oinj__on(_1517216, _1517218, _1517220, _1517222), -(c_Fun_Oinj__on(tc_prod(_1517208, _1517216), tc_prod(_1517210, _1517218), c_Product__Type_Omap__pair(_1517208, _1517210, _1517216, _1517218, _1517212, _1517220), hAPP(hAPP(c_Product__Type_OSigma(_1517208, _1517216), _1517214), hAPP(c_COMBK(tc_fun(_1517216, tc_HOL_Obool), _1517208), _1517222))))], (39498 ^ _779203) ^ [_1547706, _1547708, _1547710, _1547712, _1547714, _1547716, _1547718] : [-(hAPP(c_Product__Type_Oapsnd(_1547706, _1547708, _1547710, _1547712), hAPP(c_Product__Type_Oapsnd(_1547714, _1547706, _1547710, _1547716), _1547718)) = hAPP(c_Product__Type_Oapsnd(_1547714, _1547708, _1547710, hAPP(c_Fun_Ocomp(_1547706, _1547708, _1547714, _1547712), _1547716)), _1547718))], (20320 ^ _779203) ^ [_1137635, _1137637, _1137639] : [class_Groups_Ogroup__add(_1137635), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137635), _1137637), hAPP(c_Groups_Ouminus__class_Ouminus(_1137635), _1137639)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137635), _1137637), _1137639))], (43939 ^ _779203) ^ [_1658324, _1658326, _1658328] : [class_Orderings_Olinorder(_1658324), -(c_Big__Operators_Olinorder__class_OMax(_1658324, hAPP(c_List_Oset(_1658324), hAPP(hAPP(c_List_Olist_OCons(_1658324), _1658326), _1658328))) = hAPP(c_List_Ofoldl(_1658324, _1658324, c_Orderings_Oord__class_Omax(_1658324), _1658326), _1658328))], (9239 ^ _779203) ^ [_936830, _936832] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _936830)), _936832) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936830), hAPP(c_Nat_OSuc, _936832)))], (45492 ^ _779203) ^ [_1692213, _1692215, _1692217, _1692219] : [class_Orderings_Olinorder(_1692213), -(hAPP(c_List_Oset(_1692215), c_List_Olinorder__class_Osort__key(_1692215, _1692213, _1692217, _1692219)) = hAPP(c_List_Oset(_1692215), _1692219))], (12933 ^ _779203) ^ [_1002839, _1002841] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1002839), _1002841))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1002839), _1002841)))], (28258 ^ _779203) ^ [_1278723, _1278725, _1278727, _1278729, _1278731] : [class_Groups_Oab__group__add(_1278723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1278725), _1278727)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1278727), _1278729)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1278723), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1278723), _1278731), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1278725), _1278729))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1278723), _1278731), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1278725), _1278727))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1278723), _1278731), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1278727), _1278729)))], (29898 ^ _779203) ^ [_1311065, _1311067, _1311069, _1311071] : [class_Orderings_Oorder(_1311065), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311065, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1311065, _1311067, _1311069)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1311065, _1311069, _1311071)) = c_Orderings_Obot__class_Obot(tc_fun(_1311065, tc_HOL_Obool)))], (48719 ^ _779203) ^ [_1762591, _1762593, _1762595, _1762597, _1762599, _1762601, _1762603] : [hBOOL(hAPP(hAPP(_1762591, hAPP(c_Product__Type_Osnd(_1762593, _1762595), _1762597)), hAPP(c_Product__Type_Ofst(_1762593, _1762595), _1762597))), 48726 ^ _779203 : [(48729 ^ _779203) ^ [] : [hBOOL(hAPP(_1762599, hAPP(hAPP(_1762601, 48724 ^ [_1762591, _1762593, _1762595, _1762597, _1762599, _1762601, _1762603]), 48725 ^ [_1762591, _1762593, _1762595, _1762597, _1762599, _1762601, _1762603])))], (48727 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1762591, 48725 ^ [_1762591, _1762593, _1762595, _1762597, _1762599, _1762601, _1762603]), 48724 ^ [_1762591, _1762593, _1762595, _1762597, _1762599, _1762601, _1762603])))]], -(hBOOL(hAPP(_1762599, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1762593, _1762595, _1762603), _1762601), _1762597))))], (6851 ^ _779203) ^ [_890948, _890950, _890952, _890954] : [hBOOL(hAPP(hAPP(c_member(_890948), _890950), _890952)), -(hBOOL(hAPP(hAPP(c_member(_890948), _890950), _890954))), -(hBOOL(hAPP(hAPP(c_member(_890948), _890950), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890948, tc_HOL_Obool)), _890952), _890954))))], (34639 ^ _779203) ^ [_1420851, _1420853, _1420855, _1420857, _1420859] : [class_Complete__Lattice_Ocomplete__lattice(_1420851), 34642 ^ _779203 : [(34643 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420851), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1420853, _1420851), _1420855), _1420857)), _1420859)), 34646 ^ _779203 : [(34647 ^ _779203) ^ [_1421032] : [hBOOL(hAPP(hAPP(c_member(_1420853), _1421032), _1420855)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420851), hAPP(_1420857, _1421032)), _1420859)))]]], (34653 ^ _779203) ^ [] : [34655 ^ _779203 : [(34658 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420851), hAPP(_1420857, 34654 ^ [_1420851, _1420853, _1420855, _1420857, _1420859])), _1420859))], (34656 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1420853), 34654 ^ [_1420851, _1420853, _1420855, _1420857, _1420859]), _1420855)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420851), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1420853, _1420851), _1420855), _1420857)), _1420859)))]]], (37379 ^ _779203) ^ [_1486321] : [-(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)), _1486321)))))], (28244 ^ _779203) ^ [_1278400, _1278402, _1278404, _1278406, _1278408] : [class_Groups_Ocomm__monoid__add(_1278400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1278402), _1278404)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1278404), _1278406)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1278400), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1278400), _1278408), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1278402), _1278404))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1278400), _1278408), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1278404), _1278406))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1278400), _1278408), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1278402), _1278406)))], (22125 ^ _779203) ^ [_1169769] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1169769) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (40974 ^ _779203) ^ [_1583809, _1583811, _1583813, _1583815] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583809, _1583809), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1583811), _1583813)), _1583815) = hAPP(hAPP(c_Relation_Orel__comp(_1583809, _1583809, _1583809), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583809, _1583809), tc_HOL_Obool), _1583811), _1583815)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583809, _1583809), tc_HOL_Obool), _1583813), _1583815)))], (42411 ^ _779203) ^ [_1624541, _1624543] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1624541, _1624543))))], (49893 ^ _779203) ^ [_1788237, _1788239, _1788241] : [c_Fun_Obij__betw(_1788237, _1788239, _1788241, c_Orderings_Otop__class_Otop(tc_fun(_1788237, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788239, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1788239, _1788237, c_Hilbert__Choice_Oinv__into(_1788237, _1788239, c_Orderings_Otop__class_Otop(tc_fun(_1788237, tc_HOL_Obool)), _1788241), c_Orderings_Otop__class_Otop(tc_fun(_1788239, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788237, tc_HOL_Obool))))], (12711 ^ _779203) ^ [_998669, _998671, _998673, _998675, _998677] : [class_Rings_Olinordered__semiring__strict(_998669), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998669), _998671), _998673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998669), _998675), _998677)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998669), c_Groups_Ozero__class_Ozero(_998669)), _998671)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998669), c_Groups_Ozero__class_Ozero(_998669)), _998675)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998669), _998671), _998675)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998669), _998673), _998677))))], (45169 ^ _779203) ^ [_1685311, _1685313, _1685315] : [-(c_Enum_Oproduct(_1685311, _1685313, c_List_Olist_ONil(_1685311), _1685315) = c_List_Olist_ONil(tc_prod(_1685311, _1685313)))], (48164 ^ _779203) ^ [_1750762, _1750764, _1750766] : [-(c_List_Oreplicate(_1750762, hAPP(c_Nat_OSuc, _1750764), _1750766) = hAPP(hAPP(c_List_Olist_OCons(_1750762), _1750766), c_List_Oreplicate(_1750762, _1750764, _1750766)))], (31793 ^ _779203) ^ [_1350811, _1350813, _1350815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350811, tc_HOL_Obool)), _1350813), _1350815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1350811, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1350811, tc_fun(_1350811, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350811)), _1350813)), hAPP(hAPP(c_COMBC(_1350811, tc_fun(_1350811, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350811)), _1350815))))], (44215 ^ _779203) ^ [_1663637, _1663639] : [-(_1663637 = c_List_Olist_ONil(_1663639)), -(hBOOL(hAPP(hAPP(c_member(_1663639), c_List_Olast(_1663639, _1663637)), hAPP(c_List_Oset(_1663639), _1663637))))], (45244 ^ _779203) ^ [_1687082, _1687084, _1687086, _1687088] : [hBOOL(hAPP(c_List_Odistinct(_1687082), _1687084)), hBOOL(hAPP(c_List_Odistinct(_1687086), _1687088)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1687082, _1687086)), c_Enum_Oproduct(_1687082, _1687086, _1687084, _1687088))))], (50719 ^ _779203) ^ [_1806394, _1806396, _1806398, _1806400] : [class_Rings_Ocomm__semiring__1(_1806394), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806394), _1806396), _1806398)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806394), _1806396), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806394), _1806400), _1806398))))], (47604 ^ _779203) ^ [_1738437, _1738439, _1738441, _1738443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738437), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738439)), _1738441))), 47610 ^ _779203 : [(47613 ^ _779203) ^ [] : [hBOOL(hAPP(_1738443, 47609 ^ [_1738437, _1738439, _1738441, _1738443]))], (47611 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738439), 47609 ^ [_1738437, _1738439, _1738441, _1738443]), hAPP(c_List_Oset(_1738439), _1738441))))]], -(hBOOL(hAPP(_1738443, hAPP(hAPP(c_List_Onth(_1738439), _1738441), _1738437))))], (37956 ^ _779203) ^ [_1503304, _1503306, _1503308, _1503310] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503304), _1503306)), 37962 ^ _779203 : [(37965 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503308), hAPP(_1503310, 37961 ^ [_1503304, _1503306, _1503308, _1503310])))], (37963 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503304), 37961 ^ [_1503304, _1503306, _1503308, _1503310]), _1503306)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1503304, _1503308)), hAPP(hAPP(c_Product__Type_OSigma(_1503304, _1503308), _1503306), _1503310)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1503304, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1503308, tc_HOL_Obool), tc_Nat_Onat, _1503304), c_Finite__Set_Ocard(_1503308)), _1503310)), _1503306))], (43710 ^ _779203) ^ [_1653913, _1653915, _1653917] : [-(_1653913 = c_List_Olist_ONil(_1653915)), -(hAPP(c_List_Ohd(_1653915), hAPP(hAPP(c_List_Oappend(_1653915), _1653913), _1653917)) = hAPP(c_List_Ohd(_1653915), _1653913))], (19192 ^ _779203) ^ [_1117333, _1117335] : [class_Rings_Olinordered__idom(_1117333), -(hAPP(c_Groups_Oabs__class_Oabs(_1117333), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1117333), _1117335)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1117333), _1117335))], (32699 ^ _779203) ^ [] : [-(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)))))], (19118 ^ _779203) ^ [_1115992, _1115994] : [class_Groups_Oordered__ab__group__add__abs(_1115992), -(hAPP(c_Groups_Oabs__class_Oabs(_1115992), hAPP(c_Groups_Oabs__class_Oabs(_1115992), _1115994)) = hAPP(c_Groups_Oabs__class_Oabs(_1115992), _1115994))], (9747 ^ _779203) ^ [_945656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _945656)), _945656))], (43439 ^ _779203) ^ [_1647240, _1647242, _1647244, _1647246, _1647248] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647240), tc_List_Olist(_1647240))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647240), tc_List_Olist(_1647240)), hAPP(hAPP(c_List_Oappend(_1647240), _1647242), _1647244)), hAPP(hAPP(c_List_Oappend(_1647240), _1647242), _1647246))), c_List_Olexord(_1647240, _1647248))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1647240, _1647240)), hAPP(hAPP(c_Product__Type_OPair(_1647240, _1647240), 43444 ^ [_1647240, _1647242, _1647244, _1647246, _1647248]), 43444 ^ [_1647240, _1647242, _1647244, _1647246, _1647248])), _1647248))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1647240), tc_List_Olist(_1647240))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1647240), tc_List_Olist(_1647240)), _1647244), _1647246)), c_List_Olexord(_1647240, _1647248))))], (24227 ^ _779203) ^ [_1205964, _1205966] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1205964)), _1205966) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1205964), _1205966)))], (46064 ^ _779203) ^ [_1706242, _1706244] : [class_Orderings_Olinorder(_1706242), -(c_List_Olinorder__class_Osorted(_1706242, hAPP(hAPP(c_List_Olist_OCons(_1706242), _1706244), c_List_Olist_ONil(_1706242))))], (4446 ^ _779203) ^ [_846664, _846666, _846668, _846670] : [-(c_HOL_OThe(_846670, _846666) = c_HOL_OThe(_846668, _846664)), _846670 = _846668, _846666 = _846664], (13061 ^ _779203) ^ [_1005116, _1005118, _1005120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005116), _1005118)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005116), _1005120))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005118), _1005120)))], (8306 ^ _779203) ^ [_917484, _917486, _917488] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_917484, _917486, c_Orderings_Obot__class_Obot(tc_fun(_917484, tc_HOL_Obool))), _917488))], (20090 ^ _779203) ^ [] : [-(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))], (47191 ^ _779203) ^ [_1728635, _1728637, _1728639] : [hBOOL(hAPP(hAPP(c_member(_1728635), _1728637), hAPP(c_List_Oset(_1728635), _1728639))), -(c_List_Oinsert(_1728635, _1728637, _1728639) = _1728639)], (40825 ^ _779203) ^ [_1580187, _1580189, _1580191] : [c_Relation_Orefl__on(_1580187, _1580189, _1580191), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1580187, _1580187), tc_HOL_Obool)), _1580191), hAPP(hAPP(c_Relation_Orel__comp(_1580187, _1580187, _1580187), hAPP(c_Relation_Oconverse(_1580187, _1580187), _1580191)), _1580191))))], (42419 ^ _779203) ^ [_1624682, _1624684, _1624686] : [hBOOL(hAPP(c_List_Odistinct(_1624682), _1624684)), -(hBOOL(hAPP(c_List_Odistinct(_1624682), c_List_Osublist(_1624682, _1624684, _1624686))))], (50983 ^ _779203) ^ [_1811443, _1811445] : [50984 ^ _779203 : [(50987 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811445), _1811443))], (50985 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811443), _1811445)))]], -(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)))), _1811443, _1811445) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (3274 ^ _779203) ^ [_827964, _827966, _827968, _827970, _827972, _827974, _827976, _827978] : [-(c_Enum_Oproduct(_827978, _827974, _827970, _827966) = c_Enum_Oproduct(_827976, _827972, _827968, _827964)), _827978 = _827976, _827974 = _827972, _827970 = _827968, _827966 = _827964], (50563 ^ _779203) ^ [_1803694, _1803696] : [class_Rings_Ocomm__semiring__1(_1803694), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1803694), _1803696), c_Groups_Ozero__class_Ozero(_1803694))))], (42650 ^ _779203) ^ [_1629517, _1629519, _1629521] : [hAPP(hAPP(c_List_Otake(_1629517), _1629519), _1629521) = c_List_Olist_ONil(_1629517), -(_1629519 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1629521 = c_List_Olist_ONil(_1629517))], (37120 ^ _779203) ^ [_1479685, _1479687, _1479689, _1479691, _1479693] : [-(hAPP(c_Fun_Othe__inv__into(_1479685, _1479687, _1479689, _1479691), _1479693) = c_HOL_OThe(_1479685, hAPP(hAPP(c_COMBS(_1479685, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1479685), c_fconj), hAPP(hAPP(c_COMBC(_1479685, tc_fun(_1479685, tc_HOL_Obool), tc_HOL_Obool), c_member(_1479685)), _1479689))), hAPP(hAPP(c_COMBC(_1479685, _1479687, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1479687, tc_fun(_1479687, tc_HOL_Obool), _1479685), c_fequal), _1479691)), _1479693))))], (4610 ^ _779203) ^ [_849270, _849272, _849274, _849276, _849278, _849280, _849282, _849284] : [-(c_Random__Sequence_Omap(_849284, _849280, _849276, _849272) = c_Random__Sequence_Omap(_849282, _849278, _849274, _849270)), _849284 = _849282, _849280 = _849278, _849276 = _849274, _849272 = _849270], (2080 ^ _779203) ^ [_809207, _809209, _809211, _809213, _809215, _809217, _809219, _809221] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_809221, _809217, _809213, _809209) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_809219, _809215, _809211, _809207)), _809221 = _809219, _809217 = _809215, _809213 = _809211, _809209 = _809207], (28660 ^ _779203) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (34196 ^ _779203) ^ [_1406980, _1406982, _1406984, _1406986] : [class_Complete__Lattice_Ocomplete__lattice(_1406980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406982), _1406984)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1406982, _1406980), _1406984), _1406986) = hAPP(hAPP(c_Finite__Set_Ofold(_1406982, _1406980, hAPP(hAPP(c_COMBB(_1406980, tc_fun(_1406980, _1406980), _1406982), c_Lattices_Osemilattice__sup__class_Osup(_1406980)), _1406986)), c_Orderings_Obot__class_Obot(_1406980)), _1406984))], (42976 ^ _779203) ^ [_1636400, _1636402, _1636404, _1636406, _1636408] : [hAPP(hAPP(c_List_Olist_OCons(_1636400), _1636402), _1636404) = hAPP(hAPP(c_List_Oappend(_1636400), _1636406), _1636408), 42981 ^ _779203 : [(42984 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1636400), _1636402), _1636404) = _1636408)], (42982 ^ _779203) ^ [] : [-(_1636406 = c_List_Olist_ONil(_1636400))]], 42986 ^ _779203 : [(42989 ^ _779203) ^ [] : [-(_1636404 = hAPP(hAPP(c_List_Oappend(_1636400), 42985 ^ [_1636400, _1636402, _1636404, _1636406, _1636408]), _1636408))], (42987 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1636400), _1636402), 42985 ^ [_1636400, _1636402, _1636404, _1636406, _1636408]) = _1636406)]]], (42295 ^ _779203) ^ [_1621698, _1621700, _1621702, _1621704, _1621706] : [-(hAPP(hAPP(c_List_Olist__update(_1621698, hAPP(hAPP(c_List_Olist__update(_1621698, _1621700), _1621702), _1621704)), _1621702), _1621706) = hAPP(hAPP(c_List_Olist__update(_1621698, _1621700), _1621702), _1621706))], (25774 ^ _779203) ^ [_1232689, _1232691] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1232689), hAPP(c_Int_Onumber__class_Onumber__of(_1232689), c_Int_OMin)), _1232691) = hAPP(c_Groups_Ouminus__class_Ouminus(_1232689), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1232689), c_Groups_Oone__class_Oone(_1232689)), _1232691))), class_Fields_Ofield__inverse__zero(_1232689), class_Int_Onumber__ring(_1232689)], (33765 ^ _779203) ^ [_1397401, _1397403, _1397405, _1397407] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1397401, _1397401)), hAPP(hAPP(c_Product__Type_OPair(_1397401, _1397401), _1397403), _1397405)), hAPP(c_Wellfounded_Omeasure(_1397401), _1397407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1397407, _1397403)), hAPP(_1397407, _1397405))))], (37277 ^ _779203) ^ [_1483626, _1483628, _1483630, _1483632] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1483626), _1483628)), c_Fun_Oinj__on(_1483630, _1483626, _1483632, c_Orderings_Otop__class_Otop(tc_fun(_1483630, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1483630), hAPP(c_Set_Ovimage(_1483630, _1483626, _1483632), _1483628))))], (45171 ^ _779203) ^ [_1685374, _1685376, _1685378, _1685380, _1685382] : [c_List_Olist__all2(_1685374, _1685376, _1685378, _1685380, _1685382), 45174 ^ _779203 : [(45177 ^ _779203) ^ [_1685537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1685537), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685374)), _1685380))), -(hBOOL(hAPP(hAPP(_1685378, hAPP(hAPP(c_List_Onth(_1685374), _1685380), _1685537)), hAPP(hAPP(c_List_Onth(_1685376), _1685382), _1685537))))], (45175 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685374)), _1685380) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685376)), _1685382))]]], (298 ^ _779203) ^ [_783736, _783738, _783740, _783742] : [-(c_Nitpick_Orefl_H(_783740, _783736)), c_Nitpick_Orefl_H(_783742, _783738), _783742 = _783740, _783738 = _783736], (39640 ^ _779203) ^ [_1550999, _1551001, _1551003, _1551005, _1551007, _1551009, _1551011] : [c_Fun_Oinj__on(_1550999, _1551001, _1551003, hAPP(c_Set_Oimage(_1551005, _1550999, _1551007), _1551009)), c_Fun_Oinj__on(_1551005, _1550999, _1551007, _1551009), hBOOL(hAPP(hAPP(c_member(_1551001), _1551011), hAPP(c_Set_Oimage(_1550999, _1551001, _1551003), hAPP(c_Set_Oimage(_1551005, _1550999, _1551007), _1551009)))), -(hAPP(c_Fun_Othe__inv__into(_1551005, _1551001, _1551009, hAPP(c_Fun_Ocomp(_1550999, _1551001, _1551005, _1551003), _1551007)), _1551011) = hAPP(hAPP(c_Fun_Ocomp(_1550999, _1551005, _1551001, c_Fun_Othe__inv__into(_1551005, _1550999, _1551009, _1551007)), c_Fun_Othe__inv__into(_1550999, _1551001, hAPP(c_Set_Oimage(_1551005, _1550999, _1551007), _1551009), _1551003)), _1551011))], (25504 ^ _779203) ^ [_1228665, _1228667] : [c_Nat__Transfer_Ois__nat(_1228665), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1228665), _1228667)))], (43038 ^ _779203) ^ [_1637704, _1637706, _1637708, _1637710, _1637712, _1637714] : [hAPP(hAPP(c_List_Olist_OCons(_1637704), _1637706), _1637708) = _1637710, _1637712 = hAPP(hAPP(c_List_Oappend(_1637704), _1637708), _1637714), -(hAPP(hAPP(c_List_Olist_OCons(_1637704), _1637706), _1637712) = hAPP(hAPP(c_List_Oappend(_1637704), _1637710), _1637714))], (24055 ^ _779203) ^ [_1202767, _1202769, _1202771] : [-(hBOOL(hAPP(_1202767, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1202769), _1202771)))), 24056 ^ _779203 : [(24063 ^ _779203) ^ [_1202935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1202771), _1202935)), _1202769)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202769), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1202771), hAPP(c_Nat_OSuc, _1202935)))), hBOOL(hAPP(_1202767, _1202935))], (24057 ^ _779203) ^ [] : [_1202771 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1202767, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (10185 ^ _779203) ^ [_954024, _954026, _954028, _954030, _954032, _954034] : [class_Rings_Oring(_954024), 10188 ^ _779203 : [(10195 ^ _779203) ^ [] : [_954030 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954024), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_954024), _954032), _954026)), _954028)), _954034), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954024), _954026), _954028)), _954030) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954024), _954032), _954028)), _954034))], (10189 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954024), _954026), _954028)), _954030) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954024), _954032), _954028)), _954034), -(_954030 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_954024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_954024), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_954024), _954032), _954026)), _954028)), _954034))]]], (44203 ^ _779203) ^ [_1663480, _1663482, _1663484] : [_1663480 = c_List_Olist_ONil(_1663482), -(c_List_Olast(_1663482, hAPP(hAPP(c_List_Oappend(_1663482), _1663484), _1663480)) = c_List_Olast(_1663482, _1663484))], (25170 ^ _779203) ^ [_1222994, _1222996, _1222998, _1223000] : [class_Rings_Olinordered__semidom(_1222994), hAPP(hAPP(c_Power_Opower__class_Opower(_1222994), _1222996), hAPP(c_Nat_OSuc, _1222998)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1222994), _1223000), hAPP(c_Nat_OSuc, _1222998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222994), c_Groups_Ozero__class_Ozero(_1222994)), _1222996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1222994), c_Groups_Ozero__class_Ozero(_1222994)), _1223000)), -(_1222996 = _1223000)], (34174 ^ _779203) ^ [_1406484, _1406486, _1406488, _1406490, _1406492, _1406494, _1406496] : [-(hAPP(c_Product__Type_Oapsnd(_1406484, _1406486, _1406488, _1406490), hAPP(c_Product__Type_Oapfst(_1406492, _1406488, _1406484, _1406494), _1406496)) = hAPP(hAPP(c_Product__Type_OPair(_1406488, _1406486), hAPP(_1406494, hAPP(c_Product__Type_Ofst(_1406492, _1406484), _1406496))), hAPP(_1406490, hAPP(c_Product__Type_Osnd(_1406492, _1406484), _1406496))))], (6979 ^ _779203) ^ [_893690, _893692, _893694] : [-(hAPP(hAPP(c_Set_Oinsert(_893690), _893692), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893690, tc_HOL_Obool)), _893694), hAPP(hAPP(c_Set_Oinsert(_893690), _893692), c_Orderings_Obot__class_Obot(tc_fun(_893690, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_893690), _893692), _893694))], (26914 ^ _779203) ^ [_1253218, _1253220, _1253222] : [class_Orderings_Oord(_1253218), 26917 ^ _779203 : [(26924 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253218), _1253220), _1253222)), -(hBOOL(hAPP(hAPP(c_member(_1253218), _1253220), hAPP(c_SetInterval_Oord__class_OlessThan(_1253218), _1253222))))], (26918 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1253218), _1253220), hAPP(c_SetInterval_Oord__class_OlessThan(_1253218), _1253222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1253218), _1253220), _1253222)))]]], (46736 ^ _779203) ^ [_1719228, _1719230, _1719232, _1719234] : [class_Orderings_Olinorder(_1719228), c_List_Olinorder__class_Osorted(_1719228, hAPP(c_List_Orev(_1719228), _1719230)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1719232), _1719234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1719234), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719228)), _1719230))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1719228), hAPP(hAPP(c_List_Onth(_1719228), _1719230), _1719234)), hAPP(hAPP(c_List_Onth(_1719228), _1719230), _1719232))))], (49020 ^ _779203) ^ [_1770786, _1770788] : [c_Relation_Otrans(_1770786, hAPP(c_Set_OCollect(tc_prod(_1770786, _1770786)), hAPP(c_Product__Type_Oprod_Oprod__case(_1770786, _1770786, tc_HOL_Obool), _1770788))), -(c_Predicate_Otransp(_1770786, _1770788))], (23689 ^ _779203) ^ [_1196201, _1196203] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1196201), _1196203)), _1196201)))], (2938 ^ _779203) ^ [_822710, _822712] : [_822712 = _822710, -(c_Nitpick_ORep__Frac(_822712) = c_Nitpick_ORep__Frac(_822710))], (2390 ^ _779203) ^ [_814148, _814150, _814152, _814154, _814156, _814158, _814160, _814162, _814164, _814166] : [-(c_Product__Type_Oprod_Oprod__size(_814166, _814162, _814158, _814154, _814150) = c_Product__Type_Oprod_Oprod__size(_814164, _814160, _814156, _814152, _814148)), _814166 = _814164, _814162 = _814160, _814158 = _814156, _814154 = _814152, _814150 = _814148], (25440 ^ _779203) ^ [_1227826] : [c_Int_OMin = c_Int_OBit1(_1227826), -(c_Int_OMin = _1227826)], (37991 ^ _779203) ^ [_1504758, _1504760, _1504762] : [class_Orderings_Olinorder(_1504758), hBOOL(hAPP(c_Finite__Set_Ofinite(_1504758), _1504760)), -(_1504760 = c_Orderings_Obot__class_Obot(tc_fun(_1504758, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1504758), _1504762)), -(_1504762 = c_Orderings_Obot__class_Obot(tc_fun(_1504758, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1504758), c_Big__Operators_Olattice_OInf__fin(_1504758, c_Orderings_Oord__class_Omin(_1504758), _1504760)), c_Big__Operators_Olattice_OInf__fin(_1504758, c_Orderings_Oord__class_Omin(_1504758), _1504762)) = c_Big__Operators_Olattice_OInf__fin(_1504758, c_Orderings_Oord__class_Omin(_1504758), hAPP(c_Set_OCollect(_1504758), hAPP(hAPP(c_COMBB(tc_fun(_1504758, tc_HOL_Obool), tc_HOL_Obool, _1504758), c_HOL_OEx(_1504758)), hAPP(hAPP(c_COMBB(tc_fun(_1504758, tc_fun(_1504758, tc_HOL_Obool)), tc_fun(_1504758, tc_HOL_Obool), _1504758), hAPP(c_COMBB(tc_fun(_1504758, tc_HOL_Obool), tc_HOL_Obool, _1504758), c_HOL_OEx(_1504758))), hAPP(hAPP(c_COMBC(_1504758, tc_fun(_1504758, tc_fun(_1504758, tc_HOL_Obool)), tc_fun(_1504758, tc_fun(_1504758, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1504758, tc_fun(tc_fun(_1504758, tc_HOL_Obool), tc_fun(_1504758, tc_HOL_Obool))), tc_fun(tc_fun(_1504758, tc_fun(_1504758, tc_HOL_Obool)), tc_fun(_1504758, tc_fun(_1504758, tc_HOL_Obool))), _1504758), c_COMBS(_1504758, tc_fun(_1504758, tc_HOL_Obool), tc_fun(_1504758, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1504758, tc_fun(_1504758, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1504758, tc_fun(tc_fun(_1504758, tc_HOL_Obool), tc_fun(_1504758, tc_HOL_Obool))), _1504758), hAPP(c_COMBB(tc_fun(_1504758, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1504758, tc_HOL_Obool), tc_fun(_1504758, tc_HOL_Obool)), _1504758), c_COMBS(_1504758, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1504758, tc_fun(_1504758, tc_HOL_Obool)), tc_fun(_1504758, tc_fun(_1504758, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1504758), hAPP(c_COMBB(tc_fun(_1504758, tc_HOL_Obool), tc_fun(_1504758, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1504758), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1504758), c_fconj))), hAPP(hAPP(c_COMBC(_1504758, tc_fun(_1504758, tc_fun(_1504758, _1504758)), tc_fun(_1504758, tc_fun(_1504758, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1504758, _1504758), tc_fun(_1504758, tc_HOL_Obool)), tc_fun(tc_fun(_1504758, tc_fun(_1504758, _1504758)), tc_fun(_1504758, tc_fun(_1504758, tc_HOL_Obool))), _1504758), c_COMBB(tc_fun(_1504758, _1504758), tc_fun(_1504758, tc_HOL_Obool), _1504758)), hAPP(hAPP(c_COMBB(tc_fun(_1504758, tc_HOL_Obool), tc_fun(tc_fun(_1504758, _1504758), tc_fun(_1504758, tc_HOL_Obool)), _1504758), c_COMBB(_1504758, tc_HOL_Obool, _1504758)), c_fequal))), c_Orderings_Oord__class_Omax(_1504758)))))), hAPP(hAPP(c_COMBC(_1504758, tc_fun(_1504758, tc_HOL_Obool), tc_fun(_1504758, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1504758, tc_HOL_Obool), tc_fun(_1504758, tc_HOL_Obool)), _1504758), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1504758)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1504758), c_fconj), hAPP(hAPP(c_COMBC(_1504758, tc_fun(_1504758, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504758)), _1504760)))), hAPP(hAPP(c_COMBC(_1504758, tc_fun(_1504758, tc_HOL_Obool), tc_HOL_Obool), c_member(_1504758)), _1504762))))))))], (38434 ^ _779203) ^ [_1520891, _1520893, _1520895, _1520897] : [-(hAPP(c_Relation_ORange(_1520891, _1520893), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1520891, _1520893), tc_HOL_Obool)), _1520895), _1520897)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1520893, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1520891, _1520893), _1520895)), hAPP(c_Relation_ORange(_1520891, _1520893), _1520897)))], (26226 ^ _779203) ^ [_1240455, _1240457, _1240459] : [class_Orderings_Oorder(_1240455), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1240455), _1240457), _1240459)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1240455, _1240459, _1240457) = c_Orderings_Obot__class_Obot(tc_fun(_1240455, tc_HOL_Obool)))], (50027 ^ _779203) ^ [_1791114, _1791116, _1791118, _1791120] : [c_Fun_Obij__betw(_1791114, _1791116, _1791118, _1791120, c_Orderings_Otop__class_Otop(tc_fun(_1791116, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1791114, _1791116, _1791118), c_Orderings_Otop__class_Otop(tc_fun(_1791114, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1791116, tc_HOL_Obool)))], (51589 ^ _779203) ^ [_1821534, _1821536, _1821538, _1821540] : [class_Divides_Osemiring__div(_1821534), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821534), _1821536), _1821538)), -(c_Divides_Odiv__class_Omod(_1821534, c_Divides_Odiv__class_Omod(_1821534, _1821540, _1821538), _1821536) = c_Divides_Odiv__class_Omod(_1821534, _1821540, _1821536))], (32707 ^ _779203) ^ [_1377924, _1377926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1377924), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1377926, _1377924) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1377926), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1377924)))], (34312 ^ _779203) ^ [_1409748, _1409750, _1409752, _1409754, _1409756] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409748, tc_HOL_Obool)), _1409750), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409752, tc_fun(_1409748, tc_HOL_Obool)), _1409754), _1409756)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409752, tc_fun(_1409748, tc_HOL_Obool)), _1409754), hAPP(hAPP(c_COMBB(tc_fun(_1409748, tc_HOL_Obool), tc_fun(_1409748, tc_HOL_Obool), _1409752), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409748, tc_HOL_Obool)), _1409750)), _1409756)))], (19770 ^ _779203) ^ [_1127890, _1127892, _1127894] : [class_Groups_Oordered__ab__group__add(_1127890), 19773 ^ _779203 : [(19780 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127890), _1127894), hAPP(c_Groups_Ouminus__class_Ouminus(_1127890), _1127892))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127890), _1127892), hAPP(c_Groups_Ouminus__class_Ouminus(_1127890), _1127894))))], (19774 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127890), _1127892), hAPP(c_Groups_Ouminus__class_Ouminus(_1127890), _1127894))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1127890), _1127894), hAPP(c_Groups_Ouminus__class_Ouminus(_1127890), _1127892))))]]], (24239 ^ _779203) ^ [_1206252, _1206254, _1206256, _1206258] : [class_Rings_Ocomm__semiring__1(_1206252), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1206252), hAPP(hAPP(c_Power_Opower__class_Opower(_1206252), _1206254), _1206256)), _1206258) = hAPP(hAPP(c_Power_Opower__class_Opower(_1206252), _1206254), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206256), _1206258)))], (35041 ^ _779203) ^ [_1430636, _1430638, _1430640, _1430642, _1430644] : [class_Complete__Lattice_Ocomplete__lattice(_1430636), hBOOL(hAPP(hAPP(c_member(_1430638), _1430640), _1430642)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430636), hAPP(_1430644, _1430640)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1430638, _1430636), _1430642), _1430644))))], (51003 ^ _779203) ^ [_1811799] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811799), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1811799 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (608 ^ _779203) ^ [_788319, _788321] : [-(c_List_Onat__list(_788319)), _788321 = _788319, c_List_Onat__list(_788321)], (21309 ^ _779203) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (43494 ^ _779203) ^ [_1648622, _1648624, _1648626, _1648628] : [-(hAPP(hAPP(c_List_Otake(_1648622), _1648624), hAPP(hAPP(c_List_Odrop(_1648622), _1648626), _1648628)) = hAPP(hAPP(c_List_Odrop(_1648622), _1648626), hAPP(hAPP(c_List_Otake(_1648622), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1648624), _1648626)), _1648628)))], (23028 ^ _779203) ^ [_1184631, _1184633, _1184635] : [class_Divides_Osemiring__div(_1184631), -(_1184633 = c_Groups_Ozero__class_Ozero(_1184631)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1184631), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184631), _1184633), _1184635)), _1184633) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184631), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1184631), _1184635), _1184633)), c_Groups_Oone__class_Oone(_1184631)))], (37920 ^ _779203) ^ [_1502304] : [-(c_Int_Oint__ge__less__than(_1502304) = 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), _1502304)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (7343 ^ _779203) ^ [_900691, _900693, _900695] : [class_Orderings_Opreorder(_900691), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900691), _900693), _900695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900691), _900695), _900693))], (50901 ^ _779203) ^ [_1810056, _1810058] : [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), _1810056, _1810058), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1810056), _1810058))], (50729 ^ _779203) ^ [_1806573, _1806575, _1806577, _1806579] : [class_Rings_Ocomm__semiring__1(_1806573), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806573), _1806575), _1806577)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806573), _1806575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806573), _1806577), _1806579))))], (48030 ^ _779203) ^ [_1746999, _1747001, _1747003, _1747005, _1747007, _1747009, _1747011] : [-(c_New__Random__Sequence_Opos__decr__bind(_1746999, _1747001, _1747003, _1747005, _1747007, _1747009, _1747011) = c_New__DSequence_Opos__decr__bind(_1746999, _1747001, hAPP(hAPP(hAPP(_1747003, _1747007), _1747009), _1747011), hAPP(hAPP(c_COMBC(_1746999, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1747001))), hAPP(hAPP(c_COMBC(_1746999, 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(_1747001)))), hAPP(hAPP(c_COMBC(_1746999, 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(_1747001))))), _1747005), _1747007)), _1747009)), _1747011)))], (38398 ^ _779203) ^ [_1519902, _1519904, _1519906, _1519908] : [hAPP(hAPP(c_Relation_Orel__comp(_1519902, _1519902, _1519902), _1519904), _1519906) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519902, _1519902), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1519902, _1519902, _1519902), _1519904), _1519908) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519902, _1519902), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1519902, _1519902, _1519902), _1519904), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1519902, _1519902), tc_HOL_Obool)), _1519906), _1519908)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1519902, _1519902), tc_HOL_Obool)))], (38651 ^ _779203) ^ [_1527584, _1527586] : [-(hAPP(c_Relation_ODomain(_1527584, _1527584), c_Relation_OId__on(_1527584, _1527586)) = _1527586)], (52383 ^ _779203) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (29236 ^ _779203) ^ [_1297284, _1297286, _1297288, _1297290] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297284, tc_HOL_Obool)), _1297286), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297284, tc_HOL_Obool)), _1297288), _1297290)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297284, tc_HOL_Obool)), _1297288), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297284, tc_HOL_Obool)), _1297286), _1297290)))], (15318 ^ _779203) ^ [_1047565, _1047567, _1047569, _1047571] : [class_Orderings_Olinorder(_1047565), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1047565), _1047567), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1047565), _1047569), _1047571)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1047565), _1047569), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1047565), _1047567), _1047571)))], (37077 ^ _779203) ^ [_1478777, _1478779, _1478781, _1478783] : [-(_1478777 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1478779, tc_HOL_Obool), tc_HOL_Obool))), 37083 ^ _779203 : [(37086 ^ _779203) ^ [] : [c_Fun_Oinj__on(_1478779, _1478781, _1478783, 37082 ^ [_1478777, _1478779, _1478781, _1478783])], (37084 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1478779, tc_HOL_Obool)), 37082 ^ [_1478777, _1478779, _1478781, _1478783]), _1478777)))]], -(c_Fun_Oinj__on(_1478779, _1478781, _1478783, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1478779, tc_HOL_Obool), _1478777)))], (32057 ^ _779203) ^ [_1357777, _1357779, _1357781, _1357783, _1357785] : [class_Groups_Ocomm__monoid__add(_1357777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1357779), _1357781)), 32064 ^ _779203 : [(32071 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1357779), _1357783), _1357781))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357779, _1357777), hAPP(hAPP(c_COMBC(_1357779, _1357777, _1357777), hAPP(hAPP(c_COMBS(_1357779, _1357777, tc_fun(_1357777, _1357777)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1357777, tc_fun(_1357777, _1357777)), _1357779), c_If(_1357777)), hAPP(c_fequal, _1357783))), _1357785)), c_Groups_Ozero__class_Ozero(_1357777))), _1357781) = c_Groups_Ozero__class_Ozero(_1357777))], (32065 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1357779), _1357783), _1357781)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1357779, _1357777), hAPP(hAPP(c_COMBC(_1357779, _1357777, _1357777), hAPP(hAPP(c_COMBS(_1357779, _1357777, tc_fun(_1357777, _1357777)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1357777, tc_fun(_1357777, _1357777)), _1357779), c_If(_1357777)), hAPP(c_fequal, _1357783))), _1357785)), c_Groups_Ozero__class_Ozero(_1357777))), _1357781) = hAPP(_1357785, _1357783))]]], (29720 ^ _779203) ^ [_1306923, _1306925, _1306927, _1306929] : [-(hBOOL(hAPP(hAPP(c_member(_1306923), _1306925), _1306927))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306923, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1306923), _1306925), _1306929)), _1306927) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306923, tc_HOL_Obool)), _1306929), _1306927))], (13097 ^ _779203) ^ [_1005812, _1005814, _1005816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1005812)), 13100 ^ _779203 : [(13107 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005814), _1005816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005812), _1005814)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005812), _1005816))))], (13101 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005812), _1005814)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1005812), _1005816))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1005814), _1005816)))]]], (2412 ^ _779203) ^ [_814537, _814539, _814541, _814543, _814545, _814547, _814549, _814551, _814553, _814555] : [-(c_Product__Type_Oprod_Oprod__rec(_814555, _814551, _814547, _814543, _814539) = c_Product__Type_Oprod_Oprod__rec(_814553, _814549, _814545, _814541, _814537)), _814555 = _814553, _814551 = _814549, _814547 = _814545, _814543 = _814541, _814539 = _814537], (21919 ^ _779203) ^ [_1165343, _1165345, _1165347] : [class_Divides_Osemiring__div(_1165343), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165343), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165343), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1165343), _1165345), _1165347)), _1165347)), c_Divides_Odiv__class_Omod(_1165343, _1165345, _1165347)) = _1165345)], (45817 ^ _779203) ^ [_1700871, _1700873] : [-(c_List_Ofoldr(tc_List_Olist(_1700871), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1700871)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1700871))), c_List_Otranspose(_1700871, _1700873), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1700871))), hAPP(c_List_Ofilter(tc_List_Olist(_1700871), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1700871)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1700871), tc_List_Olist(_1700871), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1700871)))), _1700873)))], (45340 ^ _779203) ^ [_1689403, _1689405] : [-(hBOOL(hAPP(c_List_Odistinct(_1689403), c_List_Oremdups(_1689403, _1689405))))], (30712 ^ _779203) ^ [_1327967, _1327969, _1327971] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1327967), _1327969)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327967), _1327971)), 30722 ^ _779203 : [(30725 ^ _779203) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (30723 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327967), 30721 ^ [_1327967, _1327969, _1327971]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327967, tc_HOL_Obool)), _1327969), _1327971))))]], -(hAPP(c_Finite__Set_Ocard(_1327967), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327967, tc_HOL_Obool)), _1327969), _1327971)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1327967), _1327969)), hAPP(c_Finite__Set_Ocard(_1327967), _1327971)))], (9819 ^ _779203) ^ [_946839, _946841, _946843] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946841), _946843)), -(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, _946839)), _946841)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _946839)), _946843))))], (20122 ^ _779203) ^ [_1134230, _1134232] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1134230)), _1134232) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1134230), _1134232)))], (37445 ^ _779203) ^ [_1487999, _1488001, _1488003, _1488005] : [-(hAPP(c_Set_OCollect(tc_prod(_1487999, _1488001)), hAPP(c_Product__Type_Oprod_Oprod__case(_1487999, _1488001, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1487999, tc_fun(_1488001, tc_HOL_Obool), tc_fun(_1488001, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1488001, tc_HOL_Obool), tc_fun(_1488001, tc_HOL_Obool)), _1487999), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1488001)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1487999), c_fconj), _1488003))), _1488005))) = hAPP(hAPP(c_Product__Type_OSigma(_1487999, _1488001), hAPP(c_Set_OCollect(_1487999), _1488003)), hAPP(hAPP(c_COMBB(tc_fun(_1488001, tc_HOL_Obool), tc_fun(_1488001, tc_HOL_Obool), _1487999), c_Set_OCollect(_1488001)), _1488005)))], (21529 ^ _779203) ^ [_1158276, _1158278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1158276), _1158278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1158276)), c_Int_OBit0(_1158278))))], (18712 ^ _779203) ^ [_1109023] : [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), _1109023))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1109023)))], (25252 ^ _779203) ^ [_1224459, _1224461, _1224463, _1224465] : [class_Rings_Olinordered__semidom(_1224459), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224459), c_Groups_Oone__class_Oone(_1224459)), _1224461)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224459), hAPP(hAPP(c_Power_Opower__class_Opower(_1224459), _1224461), _1224463)), hAPP(hAPP(c_Power_Opower__class_Opower(_1224459), _1224461), _1224465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1224463), _1224465)))], (38182 ^ _779203) ^ [_1513579, _1513581, _1513583, _1513585] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513579), _1513581)), 38188 ^ _779203 : [(38191 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1513583), hAPP(_1513585, 38187 ^ [_1513579, _1513581, _1513583, _1513585])))], (38189 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513579), 38187 ^ [_1513579, _1513581, _1513583, _1513585]), _1513581)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1513579, _1513583)), hAPP(hAPP(c_Product__Type_OSigma(_1513579, _1513583), _1513581), _1513585))))], (43383 ^ _779203) ^ [_1645488, _1645490, _1645492, _1645494, _1645496, _1645498, _1645500] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1645488, _1645488)), hAPP(hAPP(c_Product__Type_OPair(_1645488, _1645488), _1645490), _1645492)), _1645494)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1645488), tc_List_Olist(_1645488))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1645488), tc_List_Olist(_1645488)), hAPP(hAPP(c_List_Oappend(_1645488), _1645496), hAPP(hAPP(c_List_Olist_OCons(_1645488), _1645490), _1645498))), hAPP(hAPP(c_List_Oappend(_1645488), _1645496), hAPP(hAPP(c_List_Olist_OCons(_1645488), _1645492), _1645500)))), c_List_Olexord(_1645488, _1645494))))], (28920 ^ _779203) ^ [_1290894, _1290896] : [class_Lattices_Olattice(_1290894), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290894), _1290896)), -(c_Big__Operators_Olattice__class_OSup__fin(_1290894, _1290896) = hAPP(c_Finite__Set_Ofold1(_1290894, c_Lattices_Osemilattice__sup__class_Osup(_1290894)), _1290896))], (25926 ^ _779203) ^ [_1235048, _1235050, _1235052] : [class_Rings_Olinordered__idom(_1235048), 25929 ^ _779203 : [(25936 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1235050), _1235052)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235048), hAPP(c_Int_Oring__1__class_Oof__int(_1235048), _1235050)), hAPP(c_Int_Oring__1__class_Oof__int(_1235048), _1235052))))], (25930 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1235048), hAPP(c_Int_Oring__1__class_Oof__int(_1235048), _1235050)), hAPP(c_Int_Oring__1__class_Oof__int(_1235048), _1235052))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1235050), _1235052)))]]], (48186 ^ _779203) ^ [_1751127, _1751129, _1751131, _1751133] : [48193 ^ _779203 : [(48196 ^ _779203) ^ [] : [_1751129 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48194 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1751133, _1751131)))]], 48187 ^ _779203 : [(48188 ^ _779203) ^ [_1751199] : [hBOOL(hAPP(hAPP(c_member(_1751127), _1751199), hAPP(c_List_Oset(_1751127), c_List_Oreplicate(_1751127, _1751129, _1751131)))), hBOOL(hAPP(_1751133, _1751199))]]], (37241 ^ _779203) ^ [_1482748, _1482750, _1482752, _1482754, _1482756] : [hBOOL(hAPP(hAPP(c_member(_1482748), _1482750), hAPP(c_Set_Ovimage(_1482748, _1482752, _1482754), hAPP(hAPP(c_Set_Oinsert(_1482752), _1482756), c_Orderings_Obot__class_Obot(tc_fun(_1482752, tc_HOL_Obool)))))), -(hAPP(_1482754, _1482750) = _1482756)], (27464 ^ _779203) ^ [_1263089, _1263091, _1263093, _1263095] : [class_Lattices_Osemilattice__sup(_1263089), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263089), _1263091), _1263093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1263089), _1263091), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1263089), _1263095), _1263093))))], (45624 ^ _779203) ^ [_1695939, _1695941, _1695943] : [-(hAPP(c_List_Ofilter(_1695939, _1695941), c_List_Oconcat(_1695939, _1695943)) = c_List_Oconcat(_1695939, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1695939), tc_List_Olist(_1695939)), c_List_Ofilter(_1695939, _1695941)), _1695943)))], (8182 ^ _779203) ^ [_915089, _915091, _915093, _915095, _915097, _915099] : [-(_915089 = _915091), -(hAPP(c_Fun_Ofun__upd(_915093, _915095, _915097, _915091, _915099), _915089) = hAPP(_915097, _915089))], (14287 ^ _779203) ^ [_1027629, _1027631, _1027633] : [class_Fields_Olinordered__field(_1027629), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027629), c_Groups_Ozero__class_Ozero(_1027629)), _1027631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1027629), _1027633), c_Groups_Ozero__class_Ozero(_1027629))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1027629), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1027629), _1027631), _1027633)), c_Groups_Ozero__class_Ozero(_1027629))))], (23788 ^ _779203) ^ [_1197818, _1197820] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197818)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1197820)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1197818), _1197820)))], (19996 ^ _779203) ^ [_1131752, _1131754, _1131756] : [class_Rings_Oidom(_1131752), 19999 ^ _779203 : [(20000 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131752), _1131754), _1131754) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131752), _1131756), _1131756), -(_1131754 = _1131756), -(_1131754 = hAPP(c_Groups_Ouminus__class_Ouminus(_1131752), _1131756))], (20010 ^ _779203) ^ [] : [20011 ^ _779203 : [(20014 ^ _779203) ^ [] : [_1131754 = hAPP(c_Groups_Ouminus__class_Ouminus(_1131752), _1131756)], (20012 ^ _779203) ^ [] : [_1131754 = _1131756]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131752), _1131754), _1131754) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1131752), _1131756), _1131756))]]], (10295 ^ _779203) ^ [_956187, _956189, _956191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956187), _956189)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956189), _956187))), _956191) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _956189)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _956187), _956191)))], (45280 ^ _779203) ^ [_1688042, _1688044] : [_1688042 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1688044, _1688042, c_List_Olist_ONil(_1688044)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1688044)), c_List_Olist_ONil(_1688044)), c_List_Olist_ONil(tc_List_Olist(_1688044))))], (3988 ^ _779203) ^ [_839473, _839475, _839477, _839479, _839481, _839483, _839485, _839487] : [-(c_New__Random__Sequence_Oneg__bind(_839487, _839483, _839479, _839475) = c_New__Random__Sequence_Oneg__bind(_839485, _839481, _839477, _839473)), _839487 = _839485, _839483 = _839481, _839479 = _839477, _839475 = _839473], (11051 ^ _779203) ^ [_969644] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _969644), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _969644)], (47250 ^ _779203) ^ [_1730236, _1730238, _1730240, _1730242, _1730244] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1730236, _1730236)), hAPP(hAPP(c_Product__Type_OPair(_1730236, _1730236), _1730238), _1730240)), c_List_Omeasures(_1730236, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1730236, tc_Nat_Onat)), _1730242), _1730244)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1730242, _1730238)), hAPP(_1730242, _1730240)))), 47257 ^ _779203 : [(47260 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730236, _1730236)), hAPP(hAPP(c_Product__Type_OPair(_1730236, _1730236), _1730238), _1730240)), c_List_Omeasures(_1730236, _1730244))))], (47258 ^ _779203) ^ [] : [-(hAPP(_1730242, _1730238) = hAPP(_1730242, _1730240))]]], (38593 ^ _779203) ^ [_1526622] : [-(c_Wellfounded_Owf(_1526622, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1526622, _1526622), tc_HOL_Obool))))], (10217 ^ _779203) ^ [_954818, _954820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _954818)), _954820)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _954818), _954820)))], (22159 ^ _779203) ^ [_1170440, _1170442] : [class_Divides_Osemiring__div(_1170440), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1170440), _1170442), c_Groups_Oone__class_Oone(_1170440)) = _1170442)], (10425 ^ _779203) ^ [_959036, _959038, _959040, _959042, _959044] : [class_Rings_Ocomm__semiring__1(_959036), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959036), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959036), _959038), _959040)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959036), _959042), _959044)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959036), _959038), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959036), _959040), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959036), _959042), _959044))))], (18204 ^ _779203) ^ [_1100311] : [_1100311 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1100311) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (42778 ^ _779203) ^ [_1631705, _1631707, _1631709] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1631705, tc_HOL_Obool)), hAPP(c_List_Oset(_1631705), c_List_Oremove1(_1631705, _1631707, _1631709))), hAPP(c_List_Oset(_1631705), _1631709))))], (37569 ^ _779203) ^ [_1491205, _1491207, _1491209] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491205, tc_HOL_Obool)), _1491207), _1491209) = hAPP(c_Set_OCollect(_1491205), hAPP(hAPP(c_COMBS(_1491205, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1491205), c_fconj), hAPP(hAPP(c_COMBC(_1491205, tc_fun(_1491205, tc_HOL_Obool), tc_HOL_Obool), c_member(_1491205)), _1491207))), hAPP(hAPP(c_COMBC(_1491205, tc_fun(_1491205, tc_HOL_Obool), tc_HOL_Obool), c_member(_1491205)), _1491209))))], (40679 ^ _779203) ^ [_1576572, _1576574, _1576576, _1576578, _1576580] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576572, _1576574)), hAPP(hAPP(c_Product__Type_OPair(_1576572, _1576574), _1576576), _1576578)), hAPP(c_Relation_Oconverse(_1576574, _1576572), _1576580))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576574, _1576572)), hAPP(hAPP(c_Product__Type_OPair(_1576574, _1576572), _1576578), _1576576)), _1576580)))], (44466 ^ _779203) ^ [_1669805, _1669807, _1669809, _1669811, _1669813] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1669805), tc_List_Olist(_1669807), tc_List_Olist(_1669809), hAPP(c_List_Omap(_1669805, _1669807), _1669811)), hAPP(c_List_Omap(_1669809, _1669805), _1669813)) = hAPP(c_List_Omap(_1669809, _1669807), hAPP(c_Fun_Ocomp(_1669805, _1669807, _1669809, _1669811), _1669813)))], (34472 ^ _779203) ^ [_1414839, _1414841] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1414839, tc_HOL_Obool), _1414841) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1414839, tc_HOL_Obool), tc_fun(_1414839, tc_HOL_Obool)), _1414841), c_COMBI(tc_fun(_1414839, tc_HOL_Obool))))], (31707 ^ _779203) ^ [_1348592, _1348594] : [-(hAPP(c_Finite__Set_Ocard(_1348592), _1348594) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348592, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1348592), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1348594))], (7973 ^ _779203) ^ [_910475, _910477, _910479, _910481, _910483, _910485] : [c_Finite__Set_Ofun__left__comm(_910475, _910477, _910479), hBOOL(hAPP(c_Finite__Set_Ofinite(_910475), _910481)), -(hAPP(hAPP(_910479, _910483), hAPP(hAPP(c_Finite__Set_Ofold(_910475, _910477, _910479), _910485), _910481)) = hAPP(hAPP(c_Finite__Set_Ofold(_910475, _910477, _910479), hAPP(hAPP(_910479, _910483), _910485)), _910481))], (41449 ^ _779203) ^ [_1597726, _1597728, _1597730, _1597732] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597726), tc_List_Olist(_1597726))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597726), tc_List_Olist(_1597726)), _1597728), _1597730)), c_List_Olex(_1597726, _1597732)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597726), tc_List_Olist(_1597726))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597726), tc_List_Olist(_1597726)), _1597728), _1597730)), c_List_Olexord(_1597726, _1597732))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597726)), _1597728) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1597726)), _1597730)], (44438 ^ _779203) ^ [_1669087, _1669089] : [-(hAPP(hAPP(c_List_Omap(_1669087, _1669087), c_COMBI(_1669087)), _1669089) = _1669089)], (42104 ^ _779203) ^ [_1617326, _1617328, _1617330] : [_1617326 = _1617328, 42107 ^ _779203 : [(42110 ^ _779203) ^ [_1617482] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1617330, _1617330)), _1617482), hAPP(c_List_Oset(tc_prod(_1617330, _1617330)), hAPP(hAPP(c_List_Ozip(_1617330, _1617330), _1617326), _1617328)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1617330, _1617330, tc_HOL_Obool), c_fequal), _1617482)))], (42108 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617330)), _1617326) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617330)), _1617328))]]], (14925 ^ _779203) ^ [_1039842, _1039844, _1039846, _1039848, _1039850] : [class_Groups_Ocomm__monoid__add(_1039842), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039844), _1039846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1039844, tc_HOL_Obool)), _1039848), _1039846)), 14939 ^ _779203 : [(14942 ^ _779203) ^ [] : [hAPP(_1039850, 14938 ^ [_1039842, _1039844, _1039846, _1039848, _1039850]) = c_Groups_Ozero__class_Ozero(_1039842)], (14940 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1039844), 14938 ^ [_1039842, _1039844, _1039846, _1039848, _1039850]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1039844, tc_HOL_Obool)), _1039846), _1039848))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1039844, _1039842), _1039850), _1039846) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1039844, _1039842), _1039850), _1039848))], (41485 ^ _779203) ^ [_1598778, _1598780, _1598782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598778, _1598778), tc_HOL_Obool)), _1598780), _1598782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1598778), tc_List_Olist(_1598778)), tc_HOL_Obool)), c_List_Olistrel1(_1598778, _1598780)), c_List_Olistrel1(_1598778, _1598782))))], (49326 ^ _779203) ^ [_1776559, _1776561] : [hAPP(c_Relation_Oconverse(_1776559, _1776559), _1776561) = _1776561, -(c_Relation_Osym(_1776559, _1776561))], (50561 ^ _779203) ^ [_1803666] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1803666), _1803666)))], (22143 ^ _779203) ^ [_1170157, _1170159] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1170157), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1170159)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1170157, _1170159)))], (9625 ^ _779203) ^ [_943634, _943636] : [9626 ^ _779203 : [(9627 ^ _779203) ^ [_943687] : [_943636 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _943634), _943687))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943634), _943636)))], (41321 ^ _779203) ^ [_1593177, _1593179, _1593181] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593177)), _1593179) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593177)), _1593181)), _1593179 = _1593181], (5432 ^ _779203) ^ [_862311, _862313, _862315, _862317] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862317, _862313) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_862315, _862311)), _862317 = _862315, _862313 = _862311], (20508 ^ _779203) ^ [_1140917, _1140919] : [class_Groups_Oordered__ab__group__add__abs(_1140917), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140917), _1140919), c_Groups_Ozero__class_Ozero(_1140917))), -(hAPP(c_Groups_Oabs__class_Oabs(_1140917), _1140919) = hAPP(c_Groups_Ouminus__class_Ouminus(_1140917), _1140919))], (4828 ^ _779203) ^ [_852717, _852719, _852721, _852723] : [-(c_Relation_Oinv__image(_852723, _852719) = c_Relation_Oinv__image(_852721, _852717)), _852723 = _852721, _852719 = _852717], (33411 ^ _779203) ^ [_1390549, _1390551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1390549), 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)), _1390551)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390549, _1390551), c_Divides_OnegDivAlg(_1390549, _1390551))))], (35523 ^ _779203) ^ [_1443740, _1443742, _1443744] : [class_Rings_Oring__1(_1443740), -(hAPP(c_Int_Oring__1__class_Oof__int(_1443740), 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), _1443742), _1443744)), 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(_1443740), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1443740), _1443742)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1443740), _1443744)))], (52449 ^ _779203) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (40691 ^ _779203) ^ [_1576912, _1576914, _1576916, _1576918, _1576920] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576912, _1576914)), hAPP(hAPP(c_Product__Type_OPair(_1576912, _1576914), _1576916), _1576918)), _1576920)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1576914, _1576912)), hAPP(hAPP(c_Product__Type_OPair(_1576914, _1576912), _1576918), _1576916)), hAPP(c_Relation_Oconverse(_1576912, _1576914), _1576920))))], (3124 ^ _779203) ^ [_825611, _825613, _825615, _825617] : [-(c_Big__Operators_Olinorder__class_OMax(_825617, _825613) = c_Big__Operators_Olinorder__class_OMax(_825615, _825611)), _825617 = _825615, _825613 = _825611], (9435 ^ _779203) ^ [_940015, _940017, _940019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940015), _940017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940015), _940019)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _940017), _940019))))], (7219 ^ _779203) ^ [_899090, _899092, _899094, _899096, _899098, _899100] : [c_Finite__Set_Ofun__left__comm(_899090, _899092, _899094), -(hAPP(hAPP(_899094, _899096), hAPP(hAPP(_899094, _899098), _899100)) = hAPP(hAPP(_899094, _899098), hAPP(hAPP(_899094, _899096), _899100)))], (37689 ^ _779203) ^ [_1494569, _1494571, _1494573, _1494575, _1494577, _1494579] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494569, _1494571)), hAPP(hAPP(c_Product__Type_OPair(_1494569, _1494571), _1494573), _1494575)), hAPP(hAPP(c_Product__Type_OSigma(_1494569, _1494571), _1494577), _1494579)))), hBOOL(hAPP(hAPP(c_member(_1494569), _1494573), _1494577)), hBOOL(hAPP(hAPP(c_member(_1494571), _1494575), hAPP(_1494579, _1494573)))], (15035 ^ _779203) ^ [_1041908, _1041910] : [class_Int_Oring__char__0(_1041908), hBOOL(hAPP(hAPP(c_member(_1041908), _1041910), c_Int_Oring__1__class_OInts(_1041908))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041908), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1041908), c_Groups_Oone__class_Oone(_1041908)), _1041910)), _1041910) = c_Groups_Ozero__class_Ozero(_1041908)], (24662 ^ _779203) ^ [_1213509, _1213511, _1213513] : [class_Rings_Olinordered__idom(_1213509), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213509), c_Groups_Ozero__class_Ozero(_1213509)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1213509), hAPP(hAPP(c_Power_Opower__class_Opower(_1213509), _1213511), 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(_1213509), _1213513), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (25814 ^ _779203) ^ [_1233323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1233323)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1233323) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1233323), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34945 ^ _779203) ^ [_1428250, _1428252, _1428254, _1428256] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1428250, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428252, tc_fun(_1428250, tc_HOL_Obool), _1428254), _1428256)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428252, tc_fun(_1428250, tc_HOL_Obool)), _1428256), _1428254))], (20472 ^ _779203) ^ [_1140300] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1140300)), _1140300) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25102 ^ _779203) ^ [_1221631, _1221633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1221631)), -(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), _1221631), _1221633))))], (2762 ^ _779203) ^ [_820036, _820038, _820040, _820042, _820044, _820046, _820048, _820050] : [-(c_Random_Oiterate(_820050, _820046, _820042, _820038) = c_Random_Oiterate(_820048, _820044, _820040, _820036)), _820050 = _820048, _820046 = _820044, _820042 = _820040, _820038 = _820036], (12961 ^ _779203) ^ [_1003303, _1003305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1003303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1003305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1003303), _1003305))))], (33133 ^ _779203) ^ [_1385960, _1385962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1385960)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1385960), _1385962)), -(c_Divides_Odivmod__nat(_1385962, _1385960) = 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), _1385962), _1385960)), _1385960))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1385962), _1385960), _1385960)))], (45663 ^ _779203) ^ [_1696817, _1696819, _1696821, _1696823] : [-(hAPP(c_List_Ofilter(_1696817, _1696819), hAPP(c_List_Ofilter(_1696817, _1696821), _1696823)) = hAPP(c_List_Ofilter(_1696817, hAPP(hAPP(c_COMBS(_1696817, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1696817), c_fconj), _1696821)), _1696819)), _1696823))], (6130 ^ _779203) ^ [_877123, _877125, _877127, _877129] : [c_Orderings_Obot__class_Obot(tc_fun(_877123, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_877125, _877123, _877127), _877129), -(_877129 = c_Orderings_Obot__class_Obot(tc_fun(_877125, tc_HOL_Obool)))], (24614 ^ _779203) ^ [_1212657, _1212659, _1212661] : [class_Rings_Ocomm__semiring__1(_1212657), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1212657), _1212659), 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)))), _1212661)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212657), hAPP(hAPP(c_Power_Opower__class_Opower(_1212657), _1212659), _1212661)), hAPP(hAPP(c_Power_Opower__class_Opower(_1212657), _1212659), _1212661)))], (8977 ^ _779203) ^ [_931100, _931102, _931104, _931106, _931108] : [class_Groups_Ocomm__monoid__add(_931100), hBOOL(hAPP(c_Finite__Set_Ofinite(_931102), _931104)), -(hBOOL(hAPP(hAPP(c_member(_931102), _931106), _931104))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_931102, _931100), _931108), hAPP(hAPP(c_Set_Oinsert(_931102), _931106), _931104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_931100), hAPP(_931108, _931106)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_931102, _931100), _931108), _931104)))], (9033 ^ _779203) ^ [_932248, _932250, _932252, _932254] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_932248), _932250)), hBOOL(hAPP(hAPP(c_member(_932248), _932252), _932250)), -(hBOOL(hAPP(hAPP(c_member(_932248), _932252), _932254))), -(hAPP(c_Finite__Set_Ocard(_932248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_932248, tc_HOL_Obool)), _932250), hAPP(hAPP(c_Set_Oinsert(_932248), _932252), _932254))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_932248), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_932248, tc_HOL_Obool)), _932250), _932254))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (18947 ^ _779203) ^ [_1113005, _1113007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1113005), _1113007)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1113005)), _1113007)))], (46007 ^ _779203) ^ [_1704827, _1704829, _1704831, _1704833] : [class_Groups_Ocomm__monoid__add(_1704827), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1704827), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1704827), _1704829), c_List_Oupt(_1704831, _1704833))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1704827), _1704829), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1704831, _1704833))))], (7445 ^ _779203) ^ [_902280, _902282, _902284, _902286] : [class_Orderings_Oorder(_902280), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902280), _902282), _902284)), _902282 = _902286, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_902280), _902286), _902284)))], (37908 ^ _779203) ^ [_1501647] : [-(c_Wellfounded_Ofinite__psubset(_1501647) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1501647, tc_HOL_Obool), tc_fun(_1501647, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1501647, tc_HOL_Obool), tc_fun(_1501647, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1501647, tc_HOL_Obool), tc_fun(tc_fun(_1501647, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1501647, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1501647, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1501647, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1501647, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1501647, tc_HOL_Obool)), c_COMBS(tc_fun(_1501647, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1501647, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1501647, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1501647, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1501647, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1501647, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1501647)))))], (1580 ^ _779203) ^ [_801913, _801915] : [-(class_Rings_Olinordered__semiring__strict(_801913)), _801915 = _801913, class_Rings_Olinordered__semiring__strict(_801915)], (34168 ^ _779203) ^ [_1406312, _1406314, _1406316, _1406318, _1406320] : [-(hAPP(c_Product__Type_Ofst(_1406312, _1406314), hAPP(c_Product__Type_Oapfst(_1406316, _1406312, _1406314, _1406318), _1406320)) = hAPP(_1406318, hAPP(c_Product__Type_Ofst(_1406316, _1406314), _1406320)))], (47014 ^ _779203) ^ [_1724893, _1724895, _1724897, _1724899, _1724901] : [-(c_List_OdropWhile(_1724893, _1724895, hAPP(hAPP(c_List_Omap(_1724897, _1724893), _1724899), _1724901)) = hAPP(hAPP(c_List_Omap(_1724897, _1724893), _1724899), c_List_OdropWhile(_1724897, hAPP(c_Fun_Ocomp(_1724893, tc_HOL_Obool, _1724897, _1724895), _1724899), _1724901)))], (21411 ^ _779203) ^ [_1156299, _1156301] : [class_Int_Onumber__ring(_1156299), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156299), hAPP(c_Int_Onumber__class_Onumber__of(_1156299), _1156301)), c_Groups_Oone__class_Oone(_1156299)) = hAPP(c_Int_Onumber__class_Onumber__of(_1156299), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1156301), c_Int_OBit1(c_Int_OPls))))], (25658 ^ _779203) ^ [_1230957] : [class_Int_Onumber__ring(_1230957), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1230957), c_Groups_Oone__class_Oone(_1230957)) = hAPP(c_Int_Onumber__class_Onumber__of(_1230957), c_Int_OMin))], (45923 ^ _779203) ^ [_1703246] : [-(c_List_Oupt(_1703246, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (43528 ^ _779203) ^ [_1649399, _1649401] : [-(hAPP(hAPP(c_List_Odrop(_1649399), _1649401), c_List_Olist_ONil(_1649399)) = c_List_Olist_ONil(_1649399))], (34120 ^ _779203) ^ [_1405088, _1405090, _1405092, _1405094, _1405096, _1405098] : [class_Groups_Oordered__ab__group__add(_1405088), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405090), _1405092)), 34130 ^ _779203 : [(34133 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405088), c_Groups_Ozero__class_Ozero(_1405088)), hAPP(_1405094, 34129 ^ [_1405088, _1405090, _1405092, _1405094, _1405096, _1405098])))], (34131 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405090), 34129 ^ [_1405088, _1405090, _1405092, _1405094, _1405096, _1405098]), _1405092)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1405090, _1405088), _1405094), _1405092) = _1405096, hBOOL(hAPP(hAPP(c_member(_1405090), _1405098), _1405092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1405088), hAPP(_1405094, _1405098)), _1405096)))], (21899 ^ _779203) ^ [_1164893, _1164895, _1164897] : [class_Divides_Osemiring__div(_1164893), -(c_Divides_Odiv__class_Omod(_1164893, c_Divides_Odiv__class_Omod(_1164893, _1164895, _1164897), _1164897) = c_Divides_Odiv__class_Omod(_1164893, _1164895, _1164897))], (42944 ^ _779203) ^ [_1635456, _1635458, _1635460, _1635462, _1635464] : [_1635456 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1635458, _1635460, _1635462), _1635456), _1635464) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635460), _1635458), c_List_Olist_ONil(_1635460)), _1635464))], (16000 ^ _779203) ^ [_1060058] : [class_Orderings_Olinorder(_1060058), -(c_Finite__Set_Ofun__left__comm__idem(_1060058, _1060058, c_Orderings_Oord__class_Omax(_1060058)))], (25562 ^ _779203) ^ [_1229535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229535), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1229535)), c_Int_OMin)))], (48454 ^ _779203) ^ [_1756415, _1756417, _1756419, _1756421, _1756423] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1756415, _1756417, _1756419, _1756421, _1756423) = c_Option_Ooption_Ooption__case(_1756415, tc_prod(_1756417, tc_Lazy__Sequence_Olazy__sequence(_1756417)), _1756419, hAPP(c_Product__Type_Oprod_Oprod__case(_1756417, tc_Lazy__Sequence_Olazy__sequence(_1756417), _1756415), _1756421), hAPP(c_Lazy__Sequence_Oyield(_1756417), _1756423)))], (25868 ^ _779203) ^ [_1234198, _1234200] : [_1234198 = _1234200, -(c_Code__Numeral_OSuc__code__numeral(_1234198) = c_Code__Numeral_OSuc__code__numeral(_1234200))], (25886 ^ _779203) ^ [_1234484] : [c_Code__Numeral_OSuc__code__numeral(_1234484) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (29606 ^ _779203) ^ [_1304496, _1304498, _1304500, _1304502] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304496, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304496, tc_HOL_Obool)), _1304498), _1304500)), _1304502) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1304496, tc_HOL_Obool)), _1304498), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1304496, tc_HOL_Obool)), _1304500), _1304502)))], (12689 ^ _779203) ^ [_998246, _998248, _998250, _998252, _998254] : [class_Rings_Olinordered__semiring__strict(_998246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998246), _998248), _998250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998246), _998252), _998254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_998246), c_Groups_Ozero__class_Ozero(_998246)), _998248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998246), c_Groups_Ozero__class_Ozero(_998246)), _998252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998246), _998248), _998252)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_998246), _998250), _998254))))], (19535 ^ _779203) ^ [_1123632] : [19537 ^ _779203 : [(19540 ^ _779203) ^ [_1123742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 19536 ^ [_1123632, _1123742]), _1123742))], (19538 ^ _779203) ^ [_1123708] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 19536 ^ [_1123632, _1123708]), _1123632)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1123632)))], (45041 ^ _779203) ^ [_1682599, _1682601, _1682603, _1682605, _1682607, _1682609, _1682611] : [c_List_Olist__all2(_1682599, _1682601, _1682603, hAPP(hAPP(c_List_Omap(_1682605, _1682599), _1682607), _1682609), _1682611), -(c_List_Olist__all2(_1682605, _1682601, hAPP(hAPP(c_COMBB(_1682599, tc_fun(_1682601, tc_HOL_Obool), _1682605), _1682603), _1682607), _1682609, _1682611))], (8595 ^ _779203) ^ [_923984, _923986] : [class_Groups_Omonoid__mult(_923984), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_923984), _923986), c_Groups_Oone__class_Oone(_923984)) = _923986)], (25198 ^ _779203) ^ [_1223532, _1223534, _1223536] : [class_Rings_Olinordered__semidom(_1223532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1223532), c_Groups_Oone__class_Oone(_1223532)), _1223534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1223532), c_Groups_Oone__class_Oone(_1223532)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223532), _1223534), hAPP(hAPP(c_Power_Opower__class_Opower(_1223532), _1223534), _1223536)))))], (4202 ^ _779203) ^ [_842778, _842780, _842782, _842784] : [-(c_List_Oconcat(_842784, _842780) = c_List_Oconcat(_842782, _842778)), _842784 = _842782, _842780 = _842778], (51561 ^ _779203) ^ [_1821052, _1821054, _1821056, _1821058] : [class_Divides_Osemiring__div(_1821052), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821052), _1821054), c_Divides_Odiv__class_Omod(_1821052, _1821056, _1821058))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821052), _1821054), _1821058)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821052), _1821054), _1821056)))], (10275 ^ _779203) ^ [_955821, _955823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955821), _955823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _955821)), _955823)))], (51879 ^ _779203) ^ [_1826781, _1826783, _1826785, _1826787] : [class_Rings_Ocomm__semiring__1(_1826781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1826783), _1826785)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1826781), hAPP(hAPP(c_Power_Opower__class_Opower(_1826781), _1826787), _1826783)), hAPP(hAPP(c_Power_Opower__class_Opower(_1826781), _1826787), _1826785))))], (37902 ^ _779203) ^ [_1501440, _1501442] : [-(hAPP(c_Set_OPow(_1501440), _1501442) = hAPP(c_Set_OCollect(tc_fun(_1501440, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1501440, tc_HOL_Obool), tc_fun(_1501440, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1501440, tc_HOL_Obool))), _1501442)))], (27218 ^ _779203) ^ [_1258373, _1258375] : [class_Orderings_Olinorder(_1258373), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1258373, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1258373), _1258375)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1258373), _1258375))], (43814 ^ _779203) ^ [_1655713, _1655715, _1655717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655713)), _1655715)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1655713, _1655717), _1655715) = _1655715)], (2488 ^ _779203) ^ [_815713, _815715, _815717, _815719] : [-(c_Set_Othe__elem(_815719, _815715) = c_Set_Othe__elem(_815717, _815713)), _815719 = _815717, _815715 = _815713], (43508 ^ _779203) ^ [_1648996, _1648998, _1649000, _1649002] : [hBOOL(hAPP(hAPP(c_member(_1648996), _1648998), hAPP(c_List_Oset(_1648996), hAPP(hAPP(c_List_Odrop(_1648996), _1649000), _1649002)))), -(hBOOL(hAPP(hAPP(c_member(_1648996), _1648998), hAPP(c_List_Oset(_1648996), _1649002))))], (37771 ^ _779203) ^ [_1496916, _1496918, _1496920, _1496922] : [_1496916 = c_Orderings_Obot__class_Obot(tc_fun(_1496918, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1496918, _1496920), _1496920, c_Product__Type_Osnd(_1496918, _1496920)), hAPP(hAPP(c_Product__Type_OSigma(_1496918, _1496920), _1496916), hAPP(c_COMBK(tc_fun(_1496920, tc_HOL_Obool), _1496918), _1496922))) = c_Orderings_Obot__class_Obot(tc_fun(_1496920, tc_HOL_Obool)))], (18586 ^ _779203) ^ [_1106978, _1106980] : [18587 ^ _779203 : [(18590 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106978), c_Int_OPls))], (18588 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1106978), _1106980))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106978)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106980))))], (40761 ^ _779203) ^ [_1578501, _1578503, _1578505] : [c_Relation_Orefl__on(_1578501, _1578503, _1578505), -(c_Relation_Orefl__on(_1578501, _1578503, hAPP(c_Relation_Oconverse(_1578501, _1578501), _1578505)))], (10871 ^ _779203) ^ [_967050, _967052, _967054] : [class_Rings_Ono__zero__divisors(_967050), -(_967052 = c_Groups_Ozero__class_Ozero(_967050)), -(_967054 = c_Groups_Ozero__class_Ozero(_967050)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_967050), _967052), _967054) = c_Groups_Ozero__class_Ozero(_967050)], (42852 ^ _779203) ^ [_1633276, _1633278] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633276)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633278)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633276), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1633278)) = c_List_Olist_ONil(tc_Int_Oint))], (43329 ^ _779203) ^ [_1644206, _1644208, _1644210] : [-(hBOOL(hAPP(c_List_Odistinct(_1644206), hAPP(hAPP(c_List_Oappend(_1644206), _1644208), _1644210)))), hBOOL(hAPP(c_List_Odistinct(_1644206), _1644208)), hBOOL(hAPP(c_List_Odistinct(_1644206), _1644210)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1644206, tc_HOL_Obool)), hAPP(c_List_Oset(_1644206), _1644208)), hAPP(c_List_Oset(_1644206), _1644210)) = c_Orderings_Obot__class_Obot(tc_fun(_1644206, tc_HOL_Obool))], (6209 ^ _779203) ^ [_878849, _878851, _878853] : [hBOOL(hAPP(hAPP(c_member(_878849), _878851), hAPP(hAPP(c_Set_Oinsert(_878849), _878853), c_Orderings_Obot__class_Obot(tc_fun(_878849, tc_HOL_Obool))))), -(_878851 = _878853)], (21259 ^ _779203) ^ [_1154035] : [class_Int_Onumber__ring(_1154035), -(c_Groups_Oone__class_Oone(_1154035) = hAPP(c_Int_Onumber__class_Onumber__of(_1154035), c_Int_OBit1(c_Int_OPls)))], (20612 ^ _779203) ^ [_1142652, _1142654, _1142656, _1142658] : [class_Int_Onumber__ring(_1142652), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142652), hAPP(c_Int_Onumber__class_Onumber__of(_1142652), _1142654)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1142652), _1142656), hAPP(c_Int_Onumber__class_Onumber__of(_1142652), _1142658))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1142652), hAPP(c_Int_Onumber__class_Onumber__of(_1142652), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1142654), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1142658)))), _1142656))], (28002 ^ _779203) ^ [_1273506, _1273508] : [class_Orderings_Olinorder(_1273506), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1273506, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1273506), _1273508), c_Orderings_Obot__class_Obot(tc_fun(_1273506, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1273506), _1273508)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1273506), _1273508))], (45008 ^ _779203) ^ [_1681656, _1681658, _1681660] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1681656)), _1681660), c_List_Olists(_1681656, _1681658))), -(hBOOL(hAPP(c_List_Olistsp(_1681656, hAPP(hAPP(c_COMBC(_1681656, tc_fun(_1681656, tc_HOL_Obool), tc_HOL_Obool), c_member(_1681656)), _1681658)), _1681660)))], (48735 ^ _779203) ^ [_1763114, _1763116, _1763118, _1763120, _1763122] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1763114), tc_List_Olist(_1763114))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1763114), tc_List_Olist(_1763114)), _1763116), _1763118)), c_List_Olexord(_1763114, _1763120))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1763114), tc_List_Olist(_1763114))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1763114), tc_List_Olist(_1763114)), _1763118), _1763122)), c_List_Olexord(_1763114, _1763120))), c_Relation_Otrans(_1763114, _1763120), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1763114), tc_List_Olist(_1763114))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1763114), tc_List_Olist(_1763114)), _1763116), _1763122)), c_List_Olexord(_1763114, _1763120))))], (20819 ^ _779203) ^ [_1146683, _1146685] : [class_Rings_Olinordered__idom(_1146683), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146683), _1146685), c_Groups_Ozero__class_Ozero(_1146683))), -(c_Groups_Osgn__class_Osgn(_1146683, _1146685) = hAPP(c_Groups_Ouminus__class_Ouminus(_1146683), c_Groups_Oone__class_Oone(_1146683)))], (35533 ^ _779203) ^ [_1444042] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1444042)) = _1444042)], (50230 ^ _779203) ^ [_1795087, _1795089] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795087), _1795089)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1795087, 50233 ^ [_1795087, _1795089], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1795087), _1795089)), _1795089))], (26036 ^ _779203) ^ [_1237059] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1237059)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1237059)], (4456 ^ _779203) ^ [_846813, _846815, _846817, _846819, _846821, _846823] : [-(c_FunDef_OTHE__default(_846823, _846819, _846815) = c_FunDef_OTHE__default(_846821, _846817, _846813)), _846823 = _846821, _846819 = _846817, _846815 = _846813], (44173 ^ _779203) ^ [_1663086, _1663088, _1663090] : [-(_1663086 = c_List_Olist_ONil(_1663088)), -(c_List_Olast(_1663088, hAPP(hAPP(c_List_Olist_OCons(_1663088), _1663090), _1663086)) = c_List_Olast(_1663088, _1663086))], (45498 ^ _779203) ^ [_1692322, _1692324, _1692326, _1692328] : [class_Orderings_Olinorder(_1692322), 45501 ^ _779203 : [(45508 ^ _779203) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1692324), _1692328)), -(hBOOL(hAPP(c_List_Odistinct(_1692324), c_List_Olinorder__class_Osort__key(_1692324, _1692322, _1692326, _1692328))))], (45502 ^ _779203) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1692324), c_List_Olinorder__class_Osort__key(_1692324, _1692322, _1692326, _1692328))), -(hBOOL(hAPP(c_List_Odistinct(_1692324), _1692328)))]]], (42670 ^ _779203) ^ [_1629807, _1629809] : [-(c_List_Osublist(_1629807, c_List_Olist_ONil(_1629807), _1629809) = c_List_Olist_ONil(_1629807))], (27072 ^ _779203) ^ [_1255914, _1255916, _1255918, _1255920, _1255922] : [class_Orderings_Olinorder(_1255914), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255914, _1255916), _1255918) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1255914, _1255920), _1255922), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255914), _1255916), _1255918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255914), _1255920), _1255922)), -(_1255916 = _1255920)], (43802 ^ _779203) ^ [_1655416, _1655418, _1655420] : [-(hAPP(hAPP(c_List_Odrop(_1655416), hAPP(c_Nat_OSuc, _1655418)), _1655420) = hAPP(hAPP(c_List_Odrop(_1655416), _1655418), hAPP(c_List_Otl(_1655416), _1655420)))], (46830 ^ _779203) ^ [_1721112, _1721114, _1721116] : [46832 ^ _779203 : [(46835 ^ _779203) ^ [] : [hBOOL(hAPP(_1721114, 46831 ^ [_1721112, _1721114, _1721116]))], (46833 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1721112), 46831 ^ [_1721112, _1721114, _1721116]), hAPP(c_List_Oset(_1721112), _1721116))))]], -(c_List_OtakeWhile(_1721112, _1721114, _1721116) = _1721116)], (40787 ^ _779203) ^ [_1578996, _1578998] : [-(c_Relation_Ototal__on(_1578996, c_Orderings_Obot__class_Obot(tc_fun(_1578996, tc_HOL_Obool)), _1578998))], (44960 ^ _779203) ^ [_1680687, _1680689, _1680691, _1680693] : [hBOOL(hAPP(c_List_Olistsp(_1680687, _1680689), hAPP(hAPP(c_List_Olist_OCons(_1680687), _1680691), _1680693))), 44963 ^ _779203 : [(44966 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1680687, _1680689), _1680693)))], (44964 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1680689, _1680691)))]]], (23473 ^ _779203) ^ [_1192238, _1192240, _1192242, _1192244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192238)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192240), _1192242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1192242), 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), _1192240), _1192238)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192240), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1192244, _1192238))), _1192242))))], (44353 ^ _779203) ^ [_1666830, _1666832, _1666834, _1666836, _1666838, _1666840] : [-(hAPP(hAPP(c_List_Omap(_1666830, _1666832), _1666834), hAPP(hAPP(c_List_Olist__update(_1666830, _1666836), _1666838), _1666840)) = hAPP(hAPP(c_List_Olist__update(_1666832, hAPP(hAPP(c_List_Omap(_1666830, _1666832), _1666834), _1666836)), _1666838), hAPP(_1666834, _1666840)))], (1710 ^ _779203) ^ [_803538, _803540] : [-(class_Rings_Ono__zero__divisors(_803538)), _803540 = _803538, class_Rings_Ono__zero__divisors(_803540)], (36596 ^ _779203) ^ [_1467923, _1467925, _1467927, _1467929, _1467931, _1467933] : [c_Fun_Oinj__on(_1467923, _1467925, _1467927, _1467929), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467923, tc_HOL_Obool)), _1467931), _1467929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1467923, tc_HOL_Obool)), _1467933), _1467929)), -(hAPP(c_Set_Oimage(_1467923, _1467925, _1467927), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467923, tc_HOL_Obool)), _1467931), _1467933)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1467925, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1467923, _1467925, _1467927), _1467931)), hAPP(c_Set_Oimage(_1467923, _1467925, _1467927), _1467933)))], (52337 ^ _779203) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (33853 ^ _779203) ^ [_1399319, _1399321, _1399323, _1399325, _1399327] : [-(hAPP(c_Product__Type_Ofst(_1399319, _1399321), hAPP(c_Product__Type_Oapsnd(_1399323, _1399321, _1399319, _1399325), _1399327)) = hAPP(c_Product__Type_Ofst(_1399319, _1399323), _1399327))], (43878 ^ _779203) ^ [_1657125, _1657127] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657125), _1657127) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43881 ^ _779203 : [(43884 ^ _779203) ^ [_1657239] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1657239), hAPP(c_List_Oset(tc_Nat_Onat), _1657127))), -(_1657239 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43882 ^ _779203) ^ [] : [-(_1657125 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (37449 ^ _779203) ^ [_1488178, _1488180] : [hAPP(c_Set_OCollect(_1488178), _1488180) = c_Orderings_Obot__class_Obot(tc_fun(_1488178, tc_HOL_Obool)), 37452 ^ _779203 : [(37453 ^ _779203) ^ [_1488263] : [hBOOL(hAPP(_1488180, _1488263))]]], (25208 ^ _779203) ^ [_1223731, _1223733] : [class_Power_Opower(_1223731), class_Rings_Osemiring__0(_1223731), 25215 ^ _779203 : [(25222 ^ _779203) ^ [] : [-(_1223733 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1223731), c_Groups_Ozero__class_Ozero(_1223731)), _1223733) = c_Groups_Ozero__class_Ozero(_1223731))], (25216 ^ _779203) ^ [] : [_1223733 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1223731), c_Groups_Ozero__class_Ozero(_1223731)), _1223733) = c_Groups_Oone__class_Oone(_1223731))]]], (514 ^ _779203) ^ [_786858, _786860, _786862, _786864, _786866, _786868, _786870, _786872] : [-(c_List_Olistrelp(_786870, _786866, _786862, _786858)), c_List_Olistrelp(_786872, _786868, _786864, _786860), _786872 = _786870, _786868 = _786866, _786864 = _786862, _786860 = _786858], (1028 ^ _779203) ^ [_794683, _794685, _794687, _794689, _794691, _794693] : [-(c_List_Olist__all(_794691, _794687, _794683)), c_List_Olist__all(_794693, _794689, _794685), _794693 = _794691, _794689 = _794687, _794685 = _794683], (49542 ^ _779203) ^ [_1780164, _1780166] : [c_Equiv__Relations_Oequivp(_1780164, _1780166), -(c_Equiv__Relations_Opart__equivp(_1780164, _1780166))], (31889 ^ _779203) ^ [_1353022, _1353024, _1353026] : [class_Groups_Ocomm__monoid__add(_1353022), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1353024, _1353022), hAPP(c_COMBK(_1353022, _1353024), c_Groups_Ozero__class_Ozero(_1353022))), _1353026) = c_Groups_Ozero__class_Ozero(_1353022))], (24077 ^ _779203) ^ [_1203214, _1203216] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1203214)))), _1203216) = 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)))), _1203214)), _1203216))], (39407 ^ _779203) ^ [_1545853, _1545855, _1545857, _1545859, _1545861, _1545863] : [c_Fun_Oinj__on(_1545853, _1545855, hAPP(c_Fun_Ocomp(_1545857, _1545855, _1545853, _1545859), _1545861), _1545863), -(c_Fun_Oinj__on(_1545853, _1545857, _1545861, _1545863))], (18696 ^ _779203) ^ [_1108758, _1108760] : [class_Rings_Olinordered__semidom(_1108758), 18699 ^ _779203 : [(18706 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108758), c_Groups_Ozero__class_Ozero(_1108758)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1108758), _1108760))))], (18700 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108758), c_Groups_Ozero__class_Ozero(_1108758)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1108758), _1108760))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1108760)))]]], (26140 ^ _779203) ^ [_1238866, _1238868] : [hAPP(c_Set_OPow(_1238866), _1238868) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1238866, tc_HOL_Obool), tc_HOL_Obool))], (7209 ^ _779203) ^ [_898851, _898853, _898855, _898857, _898859, _898861, _898863] : [hBOOL(hAPP(hAPP(c_member(_898851), _898853), _898855)), c_Nitpick_Ofold__graph_H(_898851, _898857, _898859, _898861, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_898851, tc_HOL_Obool)), _898855), hAPP(hAPP(c_Set_Oinsert(_898851), _898853), c_Orderings_Obot__class_Obot(tc_fun(_898851, tc_HOL_Obool)))), _898863), -(c_Nitpick_Ofold__graph_H(_898851, _898857, _898859, _898861, _898855, hAPP(hAPP(_898859, _898853), _898863)))], (31462 ^ _779203) ^ [_1343383, _1343385, _1343387] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1343383, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1343383, tc_HOL_Obool), tc_HOL_Obool)), _1343385), _1343387)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343383, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1343383, tc_HOL_Obool), _1343385)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1343383, tc_HOL_Obool), _1343387)))], (35294 ^ _779203) ^ [_1436910] : [-(hAPP(c_Int_Onat, _1436910) = 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, _1436910)), 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)))))))], (52233 ^ _779203) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (26884 ^ _779203) ^ [_1252730] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1252730)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1252730))], (15526 ^ _779203) ^ [_1051414, _1051416, _1051418, _1051420] : [class_Orderings_Olinorder(_1051414), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051414), _1051416), _1051418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051414), _1051416), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1051414), _1051418), _1051420))))], (42143 ^ _779203) ^ [_1618367, _1618369, _1618371, _1618373, _1618375, _1618377] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618367, _1618369)), hAPP(hAPP(c_Product__Type_OPair(_1618367, _1618369), _1618371), _1618373)), hAPP(c_List_Oset(tc_prod(_1618367, _1618369)), hAPP(hAPP(c_List_Ozip(_1618367, _1618369), _1618375), _1618377)))), -(hBOOL(hAPP(hAPP(c_member(_1618367), _1618371), hAPP(c_List_Oset(_1618367), _1618375))))], (7517 ^ _779203) ^ [_903381, _903383, _903385, _903387, _903389] : [class_Groups_Oordered__ab__group__add(_903381), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_903381), _903383), _903385) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_903381), _903387), _903389), 7524 ^ _779203 : [(7531 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903381), _903387), _903389)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903381), _903383), _903385)))], (7525 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903381), _903383), _903385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903381), _903387), _903389)))]]], (35724 ^ _779203) ^ [_1448968, _1448970, _1448972] : [c_Equiv__Relations_Oequiv(_1448968, _1448970, _1448972), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1448968, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1448968), _1448970), _1448972)) = _1448970)], (48270 ^ _779203) ^ [_1752689, _1752691, _1752693, _1752695] : [hBOOL(hAPP(_1752689, _1752691)), -(hAPP(c_List_Ofilter(_1752693, _1752689), c_List_Oreplicate(_1752693, _1752695, _1752691)) = c_List_Oreplicate(_1752693, _1752695, _1752691))], (37573 ^ _779203) ^ [_1491381, _1491383, _1491385, _1491387, _1491389] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1491381, _1491383), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491381, tc_HOL_Obool)), _1491385), _1491387)), hAPP(c_COMBK(tc_fun(_1491383, tc_HOL_Obool), _1491381), _1491389)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1491381, _1491383), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1491381, _1491383), _1491385), hAPP(c_COMBK(tc_fun(_1491383, tc_HOL_Obool), _1491381), _1491389))), hAPP(hAPP(c_Product__Type_OSigma(_1491381, _1491383), _1491387), hAPP(c_COMBK(tc_fun(_1491383, tc_HOL_Obool), _1491381), _1491389))))], (19302 ^ _779203) ^ [_1119306, _1119308, _1119310] : [class_Groups_Oordered__ab__group__add__abs(_1119306), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119306), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1119306), hAPP(c_Groups_Oabs__class_Oabs(_1119306), _1119308)), hAPP(c_Groups_Oabs__class_Oabs(_1119306), _1119310))), hAPP(c_Groups_Oabs__class_Oabs(_1119306), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1119306), _1119308), _1119310)))))], (2682 ^ _779203) ^ [_818758, _818760] : [_818760 = _818758, -(c_HOL_OAll(_818760) = c_HOL_OAll(_818758))], (11372 ^ _779203) ^ [_974976, _974978, _974980] : [class_Rings_Oordered__cancel__semiring(_974976), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_974976), _974978), _974980)), c_Groups_Ozero__class_Ozero(_974976)))), 11377 ^ _779203 : [(11384 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974976), _974978), c_Groups_Ozero__class_Ozero(_974976))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974976), c_Groups_Ozero__class_Ozero(_974976)), _974980))], (11378 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974976), c_Groups_Ozero__class_Ozero(_974976)), _974978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974976), _974980), c_Groups_Ozero__class_Ozero(_974976)))]]], (6951 ^ _779203) ^ [_893021, _893023, _893025, _893027, _893029, _893031, _893033, _893035] : [c_Finite__Set_Ofolding__image__simple(_893021, _893023, _893025, _893027, _893029, _893031), hBOOL(hAPP(c_Finite__Set_Ofinite(_893023), _893033)), -(hAPP(_893031, hAPP(hAPP(c_Set_Oinsert(_893023), _893035), _893033)) = hAPP(hAPP(_893025, hAPP(_893029, _893035)), hAPP(_893031, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893023, tc_HOL_Obool)), _893033), hAPP(hAPP(c_Set_Oinsert(_893023), _893035), c_Orderings_Obot__class_Obot(tc_fun(_893023, tc_HOL_Obool)))))))], (40737 ^ _779203) ^ [_1577983, _1577985, _1577987] : [-(hAPP(c_Relation_Oconverse(_1577983, _1577985), hAPP(c_Relation_Oconverse(_1577985, _1577983), _1577987)) = _1577987)], (22141 ^ _779203) ^ [_1170115, _1170117] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1170115, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1170117)) = 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), _1170115), _1170117)))], (38500 ^ _779203) ^ [_1523996, _1523998, _1524000, _1524002, _1524004, _1524006, _1524008] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1523996, _1524000)), hAPP(hAPP(c_Product__Type_OPair(_1523996, _1524000), _1524006), _1524008)), hAPP(hAPP(c_Relation_Orel__comp(_1523996, _1523998, _1524000), _1524002), _1524004))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1523996, _1523998, _1524000, hAPP(hAPP(c_COMBC(_1523996, tc_fun(tc_prod(_1523996, _1523998), tc_HOL_Obool), tc_fun(_1523998, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523998, tc_fun(tc_fun(tc_prod(_1523996, _1523998), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1523996, _1523998), tc_HOL_Obool), tc_fun(_1523998, tc_HOL_Obool)), _1523996), c_COMBC(_1523998, tc_fun(tc_prod(_1523996, _1523998), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1523998, tc_prod(_1523996, _1523998)), tc_fun(_1523998, tc_fun(tc_fun(tc_prod(_1523996, _1523998), tc_HOL_Obool), tc_HOL_Obool)), _1523996), hAPP(c_COMBB(tc_prod(_1523996, _1523998), tc_fun(tc_fun(tc_prod(_1523996, _1523998), tc_HOL_Obool), tc_HOL_Obool), _1523998), c_member(tc_prod(_1523996, _1523998)))), c_Product__Type_OPair(_1523996, _1523998)))), _1524002), hAPP(hAPP(c_COMBC(_1523998, tc_fun(tc_prod(_1523998, _1524000), tc_HOL_Obool), tc_fun(_1524000, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524000, tc_fun(tc_fun(tc_prod(_1523998, _1524000), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1523998, _1524000), tc_HOL_Obool), tc_fun(_1524000, tc_HOL_Obool)), _1523998), c_COMBC(_1524000, tc_fun(tc_prod(_1523998, _1524000), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524000, tc_prod(_1523998, _1524000)), tc_fun(_1524000, tc_fun(tc_fun(tc_prod(_1523998, _1524000), tc_HOL_Obool), tc_HOL_Obool)), _1523998), hAPP(c_COMBB(tc_prod(_1523998, _1524000), tc_fun(tc_fun(tc_prod(_1523998, _1524000), tc_HOL_Obool), tc_HOL_Obool), _1524000), c_member(tc_prod(_1523998, _1524000)))), c_Product__Type_OPair(_1523998, _1524000)))), _1524004)), _1524006), _1524008)))], (43506 ^ _779203) ^ [_1648956, _1648958] : [-(hAPP(c_List_Oset(_1648956), hAPP(c_List_Orotate1(_1648956), _1648958)) = hAPP(c_List_Oset(_1648956), _1648958))], (30563 ^ _779203) ^ [_1324855, _1324857, _1324859, _1324861] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1324855, tc_HOL_Obool)), _1324857), _1324859)), hBOOL(hAPP(hAPP(c_member(_1324855), _1324861), _1324857)), -(hBOOL(hAPP(hAPP(c_member(_1324855), _1324861), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1324855, tc_HOL_Obool), _1324859))))], (13927 ^ _779203) ^ [_1021426, _1021428, _1021430, _1021432] : [class_Fields_Olinordered__field__inverse__zero(_1021426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021426), _1021428), _1021430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021426), c_Groups_Ozero__class_Ozero(_1021426)), _1021432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1021426), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1021426), _1021428), _1021432)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1021426), _1021430), _1021432))))], (32395 ^ _779203) ^ [_1365874, _1365876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1365874)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365876))), -(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(_1365876))), 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), _1365874)), c_Int_Onat))))))], (42257 ^ _779203) ^ [_1620930, _1620932, _1620934, _1620936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1620930)), _1620932)), _1620934)), -(hAPP(hAPP(c_List_Olist__update(_1620930, _1620932), _1620934), _1620936) = _1620932)], (24175 ^ _779203) ^ [_1204925, _1204927] : [c_Nat__Transfer_Onat__set(_1204925), c_Nat__Transfer_Onat__set(_1204927), 24182 ^ _779203 : [(24189 ^ _779203) ^ [] : [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), _1204925)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1204927))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1204925), _1204927)))], (24183 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1204925), _1204927)), -(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), _1204925)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1204927))))]]], (42365 ^ _779203) ^ [_1623277, _1623279] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623277)), c_List_Obutlast(_1623277, _1623279)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1623277)), _1623279)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7055 ^ _779203) ^ [_895526, _895528, _895530, _895532, _895534, _895536] : [c_Finite__Set_Ofun__left__comm(_895526, _895528, _895530), hBOOL(hAPP(c_Finite__Set_Ofinite(_895526), _895532)), -(hAPP(hAPP(c_Finite__Set_Ofold(_895526, _895528, _895530), _895534), hAPP(hAPP(c_Set_Oinsert(_895526), _895536), _895532)) = hAPP(hAPP(_895530, _895536), hAPP(hAPP(c_Finite__Set_Ofold(_895526, _895528, _895530), _895534), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895526, tc_HOL_Obool)), _895532), hAPP(hAPP(c_Set_Oinsert(_895526), _895536), c_Orderings_Obot__class_Obot(tc_fun(_895526, tc_HOL_Obool)))))))], (27694 ^ _779203) ^ [_1267336] : [class_Finite__Set_Ofinite(_1267336), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1267336), c_Orderings_Otop__class_Otop(tc_fun(_1267336, tc_HOL_Obool)))))], (22009 ^ _779203) ^ [_1167312, _1167314, _1167316, _1167318, _1167320, _1167322] : [class_Divides_Osemiring__div(_1167312), c_Divides_Odiv__class_Omod(_1167312, _1167314, _1167316) = c_Divides_Odiv__class_Omod(_1167312, _1167318, _1167316), c_Divides_Odiv__class_Omod(_1167312, _1167320, _1167316) = c_Divides_Odiv__class_Omod(_1167312, _1167322, _1167316), -(c_Divides_Odiv__class_Omod(_1167312, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167312), _1167314), _1167320), _1167316) = c_Divides_Odiv__class_Omod(_1167312, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167312), _1167318), _1167322), _1167316))], (27652 ^ _779203) ^ [_1266526, _1266528, _1266530] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1266526), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266526, tc_HOL_Obool)), _1266528), _1266530))), 27655 ^ _779203 : [(27658 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1266526), _1266530)))], (27656 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1266526), _1266528)))]]], (15378 ^ _779203) ^ [_1048753, _1048755, _1048757] : [class_Orderings_Olinorder(_1048753), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1048753), _1048755), _1048757) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1048753), _1048757), _1048755))], (47928 ^ _779203) ^ [_1744934, _1744936, _1744938, _1744940] : [c_List_Olist__ex1(_1744934, _1744936, hAPP(hAPP(c_List_Olist_OCons(_1744934), _1744938), _1744940)), 47931 ^ _779203 : [(47938 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1744936, _1744938))), -(c_List_Olist__ex1(_1744934, _1744936, _1744940))], (47932 ^ _779203) ^ [] : [hBOOL(hAPP(_1744936, _1744938)), -(c_List_Olist__all(_1744934, hAPP(hAPP(c_COMBS(_1744934, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1744934), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1744934), c_fNot), _1744936))), hAPP(c_fequal, _1744938)), _1744940))]]], (45528 ^ _779203) ^ [_1692882, _1692884] : [45530 ^ _779203 : [(45533 ^ _779203) ^ [] : [45529 ^ [_1692882, _1692884] = c_List_Olist_ONil(_1692882)], (45531 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1692882)), 45529 ^ [_1692882, _1692884]), hAPP(c_List_Oset(tc_List_Olist(_1692882)), _1692884))))]], -(c_List_Olist_ONil(_1692882) = c_List_Oconcat(_1692882, _1692884))], (52413 ^ _779203) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (15838 ^ _779203) ^ [_1056750, _1056752, _1056754, _1056756] : [class_Orderings_Olinorder(_1056750), 15841 ^ _779203 : [(15850 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056750), _1056752), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1056750), _1056754), _1056756)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056750), _1056752), _1056754)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056750), _1056752), _1056756))], (15842 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056750), _1056752), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1056750), _1056754), _1056756))), 15845 ^ _779203 : [(15848 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056750), _1056752), _1056756)))], (15846 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1056750), _1056752), _1056754)))]]]]], (4988 ^ _779203) ^ [_855243, _855245, _855247, _855249, _855251, _855253, _855255, _855257] : [-(c_Hilbert__Choice_Oinv__into(_855257, _855253, _855249, _855245) = c_Hilbert__Choice_Oinv__into(_855255, _855251, _855247, _855243)), _855257 = _855255, _855253 = _855251, _855249 = _855247, _855245 = _855243], (12444 ^ _779203) ^ [_993837, _993839, _993841] : [-(hAPP(c_Finite__Set_Ofold1(_993837, _993839), hAPP(hAPP(c_Set_Oinsert(_993837), _993841), c_Orderings_Obot__class_Obot(tc_fun(_993837, tc_HOL_Obool)))) = _993841)], (50063 ^ _779203) ^ [_1791809, _1791811, _1791813, _1791815, _1791817] : [c_Fun_Obij__betw(_1791809, _1791811, _1791813, _1791815, _1791817), -(c_Fun_Oinj__on(_1791809, _1791811, _1791813, _1791815))], (51363 ^ _779203) ^ [_1817756, _1817758, _1817760] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817756), _1817758)), 51374 ^ _779203 : [(51377 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817760), _1817756))], (51375 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817756), _1817760)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817758), _1817760)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1817760), _1817758)))], (19500 ^ _779203) ^ [_1123036] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1123036)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1123036)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1123036))], (34859 ^ _779203) ^ [_1426024, _1426026, _1426028, _1426030, _1426032] : [_1426024 = c_Orderings_Obot__class_Obot(tc_fun(_1426026, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426026, tc_fun(_1426028, tc_HOL_Obool)), _1426024), hAPP(hAPP(c_COMBB(tc_fun(_1426028, tc_HOL_Obool), tc_fun(_1426028, tc_HOL_Obool), _1426026), hAPP(c_Set_Oinsert(_1426028), _1426030)), _1426032)) = c_Orderings_Obot__class_Obot(tc_fun(_1426028, tc_HOL_Obool)))], (3562 ^ _779203) ^ [_832484, _832486, _832488, _832490] : [-(c_List_Olist__update(_832490, _832486) = c_List_Olist__update(_832488, _832484)), _832490 = _832488, _832486 = _832484], (43768 ^ _779203) ^ [_1654764, _1654766, _1654768] : [-(c_List_Orotate(_1654764, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1654766), _1654768)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1654764), tc_List_Olist(_1654764), tc_List_Olist(_1654764), c_List_Orotate(_1654764, _1654766)), c_List_Orotate(_1654764, _1654768)))], (37435 ^ _779203) ^ [_1487686, _1487688, _1487690] : [hBOOL(hAPP(hAPP(c_member(_1487686), _1487688), hAPP(c_Set_OCollect(_1487686), _1487690))), -(hBOOL(hAPP(_1487690, _1487688)))], (6911 ^ _779203) ^ [_892183, _892185] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892183, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_892183, tc_HOL_Obool))), _892185) = c_Orderings_Obot__class_Obot(tc_fun(_892183, tc_HOL_Obool)))], (46110 ^ _779203) ^ [_1706923, _1706925, _1706927] : [class_Orderings_Olinorder(_1706923), c_List_Olinorder__class_Osorted(_1706923, _1706925), -(c_List_Olinorder__class_Osorted(_1706923, c_List_Oremove1(_1706923, _1706927, _1706925)))], (46674 ^ _779203) ^ [_1717766, _1717768] : [-(hAPP(c_List_Orev(_1717766), hAPP(c_List_Orev(_1717766), _1717768)) = _1717768)], (20955 ^ _779203) ^ [_1148787, _1148789] : [class_Rings_Olinordered__idom(_1148787), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148787), c_Groups_Osgn__class_Osgn(_1148787, _1148789)), hAPP(c_Groups_Oabs__class_Oabs(_1148787), _1148789)) = _1148789)], (11033 ^ _779203) ^ [_969387] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _969387) = _969387)], (18184 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (9498 ^ _779203) ^ [_941244, _941246, _941248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941244), _941246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941244), _941248)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941246), _941248))))], (36778 ^ _779203) ^ [] : [-(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))], (44843 ^ _779203) ^ [_1677684, _1677686] : [-(c_Code__Numeral_Onat__of__aux(_1677684, _1677686) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1677684)), _1677686))], (18961 ^ _779203) ^ [_1113236] : [-(c_Int_Osucc(_1113236) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1113236), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (47736 ^ _779203) ^ [_1740968, _1740970, _1740972] : [hBOOL(hAPP(hAPP(c_member(_1740968), _1740970), hAPP(c_List_Oset(_1740968), _1740972))), 47741 ^ _779203 : [(47744 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1740968), _1740970), hAPP(c_List_Oset(_1740968), 47739 ^ [_1740968, _1740970, _1740972])))], (47742 ^ _779203) ^ [] : [-(_1740972 = hAPP(hAPP(c_List_Oappend(_1740968), 47739 ^ [_1740968, _1740970, _1740972]), hAPP(hAPP(c_List_Olist_OCons(_1740968), _1740970), 47740 ^ [_1740968, _1740970, _1740972])))]]], (52775 ^ _779203) ^ [_1838001, _1838003] : [hBOOL(hAPP(hAPP(c_fimplies, _1838001), _1838003)), hBOOL(_1838001), -(hBOOL(_1838003))], (21523 ^ _779203) ^ [_1158175, _1158177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1158175)), c_Int_OBit0(_1158177))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1158175), _1158177)))], (10371 ^ _779203) ^ [_957729, _957731] : [class_Rings_Ocomm__semiring__1(_957729), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_957729), _957731), c_Groups_Oone__class_Oone(_957729)) = _957731)], (35974 ^ _779203) ^ [_1454907] : [-(c_Equiv__Relations_Oequivp(_1454907, c_fequal))], (47046 ^ _779203) ^ [_1725601, _1725603, _1725605, _1725607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1725601), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725603)), c_List_OdropWhile(_1725603, _1725605, _1725607)))), -(hAPP(hAPP(c_List_Onth(_1725603), c_List_OdropWhile(_1725603, _1725605, _1725607)), _1725601) = hAPP(hAPP(c_List_Onth(_1725603), _1725607), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1725601), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725603)), c_List_OtakeWhile(_1725603, _1725605, _1725607)))))], (34035 ^ _779203) ^ [_1402974] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1402974)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1402974)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (19174 ^ _779203) ^ [_1116986, _1116988] : [class_Rings_Olinordered__idom(_1116986), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116986), hAPP(c_Groups_Oabs__class_Oabs(_1116986), _1116988)), hAPP(c_Groups_Oabs__class_Oabs(_1116986), _1116988)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1116986), _1116988), _1116988))], (9175 ^ _779203) ^ [_935637, _935639, _935641, _935643] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _935637), _935639)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _935641), _935639)), _935643)) = 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), _935637), _935641)), _935639)), _935643))], (36622 ^ _779203) ^ [_1468571, _1468573, _1468575, _1468577, _1468579, _1468581] : [c_Fun_Oinj__on(_1468571, _1468573, _1468575, _1468577), -(hBOOL(hAPP(hAPP(c_member(_1468573), _1468579), hAPP(c_Set_Oimage(_1468571, _1468573, _1468575), _1468577)))), -(c_Fun_Oinj__on(_1468571, _1468573, c_Fun_Ofun__upd(_1468571, _1468573, _1468575, _1468581, _1468579), _1468577))], (35531 ^ _779203) ^ [_1443917, _1443919, _1443921, _1443923] : [-(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), _1443917), _1443919)), 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), _1443921), _1443923)), 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), _1443917), _1443921)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1443919), _1443923))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1443917), _1443923)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1443919), _1443921)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37203 ^ _779203) ^ [_1481763, _1481765, _1481767, _1481769, _1481771, _1481773] : [-(hAPP(c_Set_Ovimage(_1481763, _1481765, _1481767), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481769, tc_fun(_1481765, tc_HOL_Obool)), _1481771), _1481773)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1481769, tc_fun(_1481763, tc_HOL_Obool)), _1481771), hAPP(hAPP(c_COMBB(tc_fun(_1481765, tc_HOL_Obool), tc_fun(_1481763, tc_HOL_Obool), _1481769), c_Set_Ovimage(_1481763, _1481765, _1481767)), _1481773)))], (39213 ^ _779203) ^ [_1539846, _1539848, _1539850, _1539852] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1539846), _1539848))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539850), hAPP(c_Set_Oimage(_1539846, _1539850, _1539852), _1539848))), 39221 ^ _779203 : [(39224 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1539846), hAPP(c_Set_OCollect(_1539846), hAPP(hAPP(c_COMBS(_1539846, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1539846), c_fconj), hAPP(hAPP(c_COMBC(_1539846, tc_fun(_1539846, tc_HOL_Obool), tc_HOL_Obool), c_member(_1539846)), _1539848))), hAPP(hAPP(c_COMBC(_1539846, _1539850, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1539850, tc_fun(_1539850, tc_HOL_Obool), _1539846), c_fequal), _1539852)), hAPP(_1539852, 39220 ^ [_1539846, _1539848, _1539850, _1539852]))))))], (39222 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1539846), 39220 ^ [_1539846, _1539848, _1539850, _1539852]), _1539848)))]]], (23627 ^ _779203) ^ [_1195185, _1195187] : [-(_1195185 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1195185, _1195187) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1195185), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1195187)))], (18542 ^ _779203) ^ [_1106221, _1106223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106221)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1106223))), 18545 ^ _779203 : [(18546 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106221), _1106223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1106223)))], (18552 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1106221), _1106223)))]]], (49348 ^ _779203) ^ [_1776898, _1776900] : [-(c_Relation_Osym(_1776898, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1776898, _1776898), tc_HOL_Obool)), _1776900), hAPP(c_Relation_Oconverse(_1776898, _1776898), _1776900))))], (29958 ^ _779203) ^ [_1312471, _1312473, _1312475] : [class_Orderings_Oorder(_1312471), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312471, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1312471), _1312473)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1312471, _1312473, _1312475)) = c_Orderings_Obot__class_Obot(tc_fun(_1312471, tc_HOL_Obool)))], (48016 ^ _779203) ^ [_1746705, _1746707, _1746709, _1746711, _1746713] : [_1746705 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1746707, _1746709, _1746711, _1746713), _1746705) = c_Lazy__Sequence_Oempty(_1746709))], (39090 ^ _779203) ^ [_1537577, _1537579] : [c_Wellfounded_OwfP(_1537577, _1537579), 39093 ^ _779203 : [(39094 ^ _779203) ^ [_1537641] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1537577, _1537579), _1537641)))]]], (8613 ^ _779203) ^ [_924265, _924267] : [class_Lattices_Oab__semigroup__idem__mult(_924265), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924265), _924267), _924267) = _924267)], (50528 ^ _779203) ^ [_1802947, _1802949, _1802951, _1802953, _1802955, _1802957, _1802959, _1802961] : [c_Finite__Set_Ofolding__image(_1802947, _1802949, _1802951, _1802953, _1802955), hBOOL(hAPP(c_Finite__Set_Ofinite(_1802949), _1802957)), 50538 ^ _779203 : [(50541 ^ _779203) ^ [] : [hAPP(_1802959, 50537 ^ [_1802947, _1802949, _1802951, _1802953, _1802955, _1802957, _1802959, _1802961]) = hAPP(_1802961, 50537 ^ [_1802947, _1802949, _1802951, _1802953, _1802955, _1802957, _1802959, _1802961])], (50539 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1802949), 50537 ^ [_1802947, _1802949, _1802951, _1802953, _1802955, _1802957, _1802959, _1802961]), _1802957)))]], -(hAPP(hAPP(_1802955, _1802959), _1802957) = hAPP(hAPP(_1802955, _1802961), _1802957))], (19854 ^ _779203) ^ [_1129380] : [class_Groups_Ogroup__add(_1129380), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1129380), c_Groups_Ozero__class_Ozero(_1129380)) = c_Groups_Ozero__class_Ozero(_1129380))], (41092 ^ _779203) ^ [_1586890, _1586892, _1586894, _1586896, _1586898] : [c_Relation_Osingle__valued(_1586890, _1586892, hAPP(c_Relation_Oconverse(_1586892, _1586890), _1586894)), -(hAPP(c_Relation_OImage(_1586892, _1586890, _1586894), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1586892, tc_HOL_Obool)), _1586896), _1586898)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1586890, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1586892, _1586890, _1586894), _1586896)), hAPP(c_Relation_OImage(_1586892, _1586890, _1586894), _1586898)))], (48848 ^ _779203) ^ [_1765545, _1765547, _1765549, _1765551] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765545), _1765547)), 48851 ^ _779203 : [(48852 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765549), hAPP(c_Set_OCollect(_1765549), hAPP(hAPP(c_COMBB(tc_fun(_1765545, tc_HOL_Obool), tc_HOL_Obool, _1765549), c_HOL_OEx(_1765545)), hAPP(hAPP(c_COMBB(tc_fun(_1765545, tc_HOL_Obool), tc_fun(_1765545, tc_HOL_Obool), _1765549), hAPP(c_COMBS(_1765545, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765545), c_fconj), hAPP(hAPP(c_COMBC(_1765545, tc_fun(_1765545, tc_HOL_Obool), tc_HOL_Obool), c_member(_1765545)), _1765547)))), _1765551))))), 48855 ^ _779203 : [(48856 ^ _779203) ^ [_1765853] : [hBOOL(hAPP(hAPP(c_member(_1765545), _1765853), _1765547)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1765549), hAPP(c_Set_OCollect(_1765549), hAPP(hAPP(c_COMBC(_1765549, _1765545, tc_HOL_Obool), _1765551), _1765853)))))]]], (48862 ^ _779203) ^ [] : [48864 ^ _779203 : [(48867 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1765549), hAPP(c_Set_OCollect(_1765549), hAPP(hAPP(c_COMBC(_1765549, _1765545, tc_HOL_Obool), _1765551), 48863 ^ [_1765545, _1765547, _1765549, _1765551]))))], (48865 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765545), 48863 ^ [_1765545, _1765547, _1765549, _1765551]), _1765547)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1765549), hAPP(c_Set_OCollect(_1765549), hAPP(hAPP(c_COMBB(tc_fun(_1765545, tc_HOL_Obool), tc_HOL_Obool, _1765549), c_HOL_OEx(_1765545)), hAPP(hAPP(c_COMBB(tc_fun(_1765545, tc_HOL_Obool), tc_fun(_1765545, tc_HOL_Obool), _1765549), hAPP(c_COMBS(_1765545, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1765545), c_fconj), hAPP(hAPP(c_COMBC(_1765545, tc_fun(_1765545, tc_HOL_Obool), tc_HOL_Obool), c_member(_1765545)), _1765547)))), _1765551))))))]]], (4726 ^ _779203) ^ [_851096, _851098] : [_851098 = _851096, -(c_List_Oset(_851098) = c_List_Oset(_851096))], (25238 ^ _779203) ^ [_1224194, _1224196, _1224198, _1224200] : [class_Rings_Olinordered__semidom(_1224194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1224196), _1224198)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224194), c_Groups_Oone__class_Oone(_1224194)), _1224200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1224194), hAPP(hAPP(c_Power_Opower__class_Opower(_1224194), _1224200), _1224196)), hAPP(hAPP(c_Power_Opower__class_Opower(_1224194), _1224200), _1224198))))], (24952 ^ _779203) ^ [_1218922, _1218924, _1218926] : [class_Rings_Osemiring__1(_1218922), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1218922), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1218924), _1218926)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1218922), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1218922), _1218924)), _1218926))], (43143 ^ _779203) ^ [_1640117, _1640119, _1640121, _1640123, _1640125, _1640127] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640117)), _1640119) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640121)), _1640123), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640117)), _1640125) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640121)), _1640127), -(hAPP(hAPP(c_List_Ozip(_1640117, _1640121), hAPP(hAPP(c_List_Oappend(_1640117), _1640119), _1640125)), hAPP(hAPP(c_List_Oappend(_1640121), _1640123), _1640127)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1640117, _1640121)), hAPP(hAPP(c_List_Ozip(_1640117, _1640121), _1640119), _1640123)), hAPP(hAPP(c_List_Ozip(_1640117, _1640121), _1640125), _1640127)))], (42890 ^ _779203) ^ [_1633963, _1633965, _1633967] : [-(_1633963 = c_List_Olist_ONil(_1633965)), -(hBOOL(hAPP(hAPP(c_member(_1633965), hAPP(c_Product__Type_Ofst(_1633965, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1633965, _1633963), _1633967))), hAPP(c_List_Oset(_1633965), _1633963))))], (18090 ^ _779203) ^ [_1098395, _1098397] : [class_Int_Onumber__ring(_1098395), 18093 ^ _779203 : [(18100 ^ _779203) ^ [] : [-(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), _1098397)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1098395), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098397)) = c_Groups_Ozero__class_Ozero(_1098395))], (18094 ^ _779203) ^ [] : [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), _1098397))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1098395), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1098397)) = hAPP(c_Int_Onumber__class_Onumber__of(_1098395), _1098397))]]], (36514 ^ _779203) ^ [_1466207, _1466209] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466207), c_Orderings_Otop__class_Otop(tc_fun(_1466207, tc_HOL_Obool)))), c_Fun_Oinj__on(_1466207, _1466207, _1466209, c_Orderings_Otop__class_Otop(tc_fun(_1466207, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1466207, _1466207, _1466209), c_Orderings_Otop__class_Otop(tc_fun(_1466207, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1466207, tc_HOL_Obool)))], (9209 ^ _779203) ^ [_936368, _936370, _936372] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936368), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936370), _936372)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936370), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936368), _936372)))], (37381 ^ _779203) ^ [_1486352, _1486354, _1486356, _1486358, _1486360, _1486362] : [hBOOL(hAPP(hAPP(c_member(_1486352), _1486354), _1486356)), hBOOL(hAPP(hAPP(c_member(_1486358), _1486360), hAPP(_1486362, _1486354))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486352, _1486358)), hAPP(hAPP(c_Product__Type_OPair(_1486352, _1486358), _1486354), _1486360)), hAPP(hAPP(c_Product__Type_OSigma(_1486352, _1486358), _1486356), _1486362))))], (52789 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pn), v_U)))], (6869 ^ _779203) ^ [_891285, _891287, _891289, _891291, _891293, _891295, _891297] : [c_Finite__Set_Ofolding__image__simple__idem(_891285, _891287, _891289, _891291, _891293, _891295), -(hAPP(hAPP(_891289, _891297), _891297) = _891297)], (41497 ^ _779203) ^ [_1599164, _1599166, _1599168, _1599170, _1599172] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599164), tc_List_Olist(_1599164))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599164), tc_List_Olist(_1599164)), _1599166), _1599168)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1599164), c_List_Olistrel1(_1599164, _1599170)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599164), tc_List_Olist(_1599164))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599164), tc_List_Olist(_1599164)), hAPP(hAPP(c_List_Olist_OCons(_1599164), _1599172), _1599166)), hAPP(hAPP(c_List_Olist_OCons(_1599164), _1599172), _1599168))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1599164), c_List_Olistrel1(_1599164, _1599170)))))], (33705 ^ _779203) ^ [_1396259, _1396261, _1396263, _1396265, _1396267, _1396269] : [hAPP(_1396265, hAPP(c_Product__Type_Osnd(_1396263, _1396259), _1396267)) = hAPP(_1396269, hAPP(c_Product__Type_Osnd(_1396263, _1396259), _1396267)), -(hAPP(c_Product__Type_Oapsnd(_1396259, _1396261, _1396263, _1396265), _1396267) = hAPP(c_Product__Type_Oapsnd(_1396259, _1396261, _1396263, _1396269), _1396267))], (9749 ^ _779203) ^ [_945696, _945698] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _945696), _945698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _945698)), _945696)))], (21555 ^ _779203) ^ [_1158656] : [_1158656 = c_Int_OPls, -(c_Int_OBit0(_1158656) = c_Int_OPls)], (45127 ^ _779203) ^ [_1684608, _1684610, _1684612] : [_1684608 = _1684610, -(c_List_Olist__all2(_1684612, _1684612, c_fequal, _1684608, _1684610))], (44167 ^ _779203) ^ [_1662985, _1662987, _1662989] : [_1662985 = c_List_Olist_ONil(_1662987), -(c_List_Olast(_1662987, hAPP(hAPP(c_List_Olist_OCons(_1662987), _1662989), _1662985)) = _1662989)], (31959 ^ _779203) ^ [_1355205, _1355207, _1355209, _1355211] : [_1355205 = c_Orderings_Obot__class_Obot(tc_fun(_1355207, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1355207, _1355209, hAPP(c_COMBK(_1355209, _1355207), _1355211)), _1355205) = c_Orderings_Obot__class_Obot(tc_fun(_1355209, tc_HOL_Obool)))], (38481 ^ _779203) ^ [_1522809, _1522811, _1522813, _1522815] : [hBOOL(hAPP(hAPP(c_member(_1522811), _1522815), hAPP(c_Relation_ORange(_1522809, _1522811), _1522813))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1522809, _1522811, hAPP(hAPP(c_COMBC(_1522809, tc_fun(tc_prod(_1522809, _1522811), tc_HOL_Obool), tc_fun(_1522811, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522811, tc_fun(tc_fun(tc_prod(_1522809, _1522811), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1522809, _1522811), tc_HOL_Obool), tc_fun(_1522811, tc_HOL_Obool)), _1522809), c_COMBC(_1522811, tc_fun(tc_prod(_1522809, _1522811), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1522811, tc_prod(_1522809, _1522811)), tc_fun(_1522811, tc_fun(tc_fun(tc_prod(_1522809, _1522811), tc_HOL_Obool), tc_HOL_Obool)), _1522809), hAPP(c_COMBB(tc_prod(_1522809, _1522811), tc_fun(tc_fun(tc_prod(_1522809, _1522811), tc_HOL_Obool), tc_HOL_Obool), _1522811), c_member(tc_prod(_1522809, _1522811)))), c_Product__Type_OPair(_1522809, _1522811)))), _1522813)), _1522815)))], (1680 ^ _779203) ^ [_803163, _803165] : [-(class_Groups_Ocomm__monoid__mult(_803163)), _803165 = _803163, class_Groups_Ocomm__monoid__mult(_803165)], (26498 ^ _779203) ^ [_1245285, _1245287, _1245289, _1245291] : [class_Groups_Ocomm__monoid__add(_1245285), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1245287), _1245289)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245285), _1245291), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1245287, _1245289)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245285), hAPP(_1245291, _1245287)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245285), _1245291), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1245287), _1245289))))], (50263 ^ _779203) ^ [_1795694, _1795696] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1795694), _1795696)), -(c_Fun_Obij__betw(_1795694, tc_Nat_Onat, 50266 ^ [_1795694, _1795696], _1795696, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1795694), _1795696))))], (45687 ^ _779203) ^ [_1697235, _1697237, _1697239] : [-(c_List_Opartition(_1697235, _1697237, _1697239) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1697235), tc_List_Olist(_1697235)), hAPP(c_List_Ofilter(_1697235, _1697237), _1697239)), hAPP(c_List_Ofilter(_1697235, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1697235, c_fNot), _1697237)), _1697239)))], (37503 ^ _779203) ^ [_1489284] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1489284, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1489284), hAPP(c_COMBK(tc_HOL_Obool, _1489284), c_fTrue)))], (42594 ^ _779203) ^ [_1628593, _1628595] : [-(_1628593 = c_List_Olist_ONil(_1628595)), hBOOL(hAPP(c_List_Odistinct(_1628595), _1628593)), -(hBOOL(hAPP(c_List_Odistinct(_1628595), c_List_Obutlast(_1628595, _1628593))))], (1820 ^ _779203) ^ [_804913, _804915] : [-(class_Groups_Omonoid__add(_804913)), _804915 = _804913, class_Groups_Omonoid__add(_804915)], (40588 ^ _779203) ^ [_1574265, _1574267, _1574269, _1574271] : [-(c_Wellfounded_Owf(_1574265, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1574265, _1574265)), hAPP(hAPP(c_Product__Type_OPair(_1574265, _1574265), _1574267), _1574269)), _1574271))), c_Wellfounded_Owf(_1574265, _1574271), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1574265, _1574265)), hAPP(hAPP(c_Product__Type_OPair(_1574265, _1574265), _1574269), _1574267)), c_Transitive__Closure_Ortrancl(_1574265, _1574271))))], (19087 ^ _779203) ^ [_1115475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1115475)), 19091 ^ _779203 : [(19094 ^ _779203) ^ [] : [-(_1115475 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 19090 ^ [_1115475]))], (19092 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 19090 ^ [_1115475])))]]], (18194 ^ _779203) ^ [_1100175] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1100175), c_Int_OPls) = _1100175)], (10673 ^ _779203) ^ [_963887] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _963887), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22165 ^ _779203) ^ [_1170535, _1170537, _1170539] : [class_Divides_Osemiring__div(_1170535), -(c_Divides_Odiv__class_Omod(_1170535, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170535), _1170537), _1170539), _1170539) = c_Groups_Ozero__class_Ozero(_1170535))], (4900 ^ _779203) ^ [_853859, _853861] : [_853861 = _853859, -(c_Set_OCollect(_853861) = c_Set_OCollect(_853859))], (34899 ^ _779203) ^ [_1427024, _1427026, _1427028, _1427030, _1427032] : [_1427024 = c_Orderings_Obot__class_Obot(tc_fun(_1427026, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427026, tc_fun(_1427028, tc_HOL_Obool)), _1427024), hAPP(hAPP(c_COMBC(_1427026, tc_fun(_1427028, tc_HOL_Obool), tc_fun(_1427028, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1427028, tc_HOL_Obool), tc_fun(tc_fun(_1427028, tc_HOL_Obool), tc_fun(_1427028, tc_HOL_Obool)), _1427026), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427028, tc_HOL_Obool))), _1427030)), _1427032)) = c_Orderings_Obot__class_Obot(tc_fun(_1427028, tc_HOL_Obool)))], (51653 ^ _779203) ^ [_1822654, _1822656, _1822658, _1822660] : [class_Rings_Ocomm__semiring__1(_1822654), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1822654), _1822656), _1822658)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1822654), _1822656), _1822660)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1822654), _1822656), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1822654), _1822658), _1822660))))], (41565 ^ _779203) ^ [_1601413, _1601415, _1601417, _1601419] : [41568 ^ _779203 : [(41573 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601413, _1601413)), hAPP(hAPP(c_Product__Type_OPair(_1601413, _1601413), 41567 ^ [_1601413, _1601415, _1601417, _1601419]), 41566 ^ [_1601413, _1601415, _1601417, _1601419])), _1601415))], (41571 ^ _779203) ^ [] : [41566 ^ [_1601413, _1601415, _1601417, _1601419] = 41567 ^ [_1601413, _1601415, _1601417, _1601419]], (41569 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601413, _1601413)), hAPP(hAPP(c_Product__Type_OPair(_1601413, _1601413), 41566 ^ [_1601413, _1601415, _1601417, _1601419]), 41567 ^ [_1601413, _1601415, _1601417, _1601419])), _1601415))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601413), tc_List_Olist(_1601413))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601413), tc_List_Olist(_1601413)), _1601417), _1601419)), c_List_Olexord(_1601413, _1601415)))), -(_1601417 = _1601419), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1601413), tc_List_Olist(_1601413))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1601413), tc_List_Olist(_1601413)), _1601419), _1601417)), c_List_Olexord(_1601413, _1601415))))], (31556 ^ _779203) ^ [_1345265, _1345267, _1345269, _1345271] : [class_Lattices_Osemilattice__inf(_1345265), hBOOL(hAPP(c_Finite__Set_Ofinite(_1345265), _1345267)), 31566 ^ _779203 : [(31569 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345265), _1345269), 31565 ^ [_1345265, _1345267, _1345269, _1345271]))], (31567 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1345265), 31565 ^ [_1345265, _1345267, _1345269, _1345271]), _1345267)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345265), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1345265), _1345269), _1345271)), hAPP(hAPP(c_Finite__Set_Ofold(_1345265, _1345265, c_Lattices_Osemilattice__inf__class_Oinf(_1345265)), _1345271), _1345267))))], (45805 ^ _779203) ^ [_1700475, _1700477, _1700479, _1700481] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1700475, tc_Nat_Onat), _1700475), c_Product__Type_Ofst(_1700475, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1700475, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1700475, tc_Nat_Onat)), _1700477), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1700475, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1700475, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1700475, tc_Nat_Onat), _1700479), _1700481))) = hAPP(hAPP(c_List_Omap(tc_prod(_1700475, tc_Nat_Onat), _1700475), c_Product__Type_Ofst(_1700475, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1700475, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1700475, tc_Nat_Onat)), _1700477), c_Product__Type_Osnd(_1700475, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1700475, tc_Nat_Onat), _1700479), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1700481)))))], (3104 ^ _779203) ^ [_825313, _825315, _825317, _825319] : [-(c_Big__Operators_Olattice__class_OInf__fin(_825319, _825315) = c_Big__Operators_Olattice__class_OInf__fin(_825317, _825313)), _825319 = _825317, _825315 = _825313], (31949 ^ _779203) ^ [_1354923, _1354925, _1354927, _1354929, _1354931] : [class_Groups_Ocomm__monoid__add(_1354923), hBOOL(hAPP(c_Finite__Set_Ofinite(_1354925), _1354927)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354925, _1354923), hAPP(hAPP(c_COMBS(_1354925, _1354923, _1354923), hAPP(hAPP(c_COMBB(_1354923, tc_fun(_1354923, _1354923), _1354925), c_Groups_Oplus__class_Oplus(_1354923)), _1354929)), _1354931)), _1354927) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1354923), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354925, _1354923), _1354929), _1354927)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1354925, _1354923), _1354931), _1354927)))], (19356 ^ _779203) ^ [_1120209, _1120211, _1120213] : [class_Rings_Oordered__ring__abs(_1120209), -(hAPP(c_Groups_Oabs__class_Oabs(_1120209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120209), _1120211), _1120213)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1120209), hAPP(c_Groups_Oabs__class_Oabs(_1120209), _1120211)), hAPP(c_Groups_Oabs__class_Oabs(_1120209), _1120213))), 19363 ^ _779203 : [(19366 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120209), _1120211), c_Groups_Ozero__class_Ozero(_1120209)))], (19364 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120209), c_Groups_Ozero__class_Ozero(_1120209)), _1120211))]], 19367 ^ _779203 : [(19370 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120209), _1120213), c_Groups_Ozero__class_Ozero(_1120209)))], (19368 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120209), c_Groups_Ozero__class_Ozero(_1120209)), _1120213))]]], (24582 ^ _779203) ^ [_1212163, _1212165] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1212163), hAPP(c_Int_Onumber__class_Onumber__of(_1212163), _1212165)), 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(_1212163), hAPP(c_Int_Onumber__class_Onumber__of(_1212163), _1212165)), hAPP(c_Int_Onumber__class_Onumber__of(_1212163), _1212165))), class_Groups_Omonoid__mult(_1212163), class_Int_Onumber(_1212163)], (48162 ^ _779203) ^ [_1750693, _1750695, _1750697, _1750699] : [-(hAPP(hAPP(c_List_Oappend(_1750693), c_List_Oreplicate(_1750693, _1750695, _1750697)), hAPP(hAPP(c_List_Olist_OCons(_1750693), _1750697), _1750699)) = hAPP(hAPP(c_List_Olist_OCons(_1750693), _1750697), hAPP(hAPP(c_List_Oappend(_1750693), c_List_Oreplicate(_1750693, _1750695, _1750697)), _1750699)))], (9550 ^ _779203) ^ [_942323] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _942323) = _942323)], (5500 ^ _779203) ^ [_863289, _863291, _863293, _863295] : [-(tc_Nitpick_Opair__box(_863295, _863291) = tc_Nitpick_Opair__box(_863293, _863289)), _863295 = _863293, _863291 = _863289], (20855 ^ _779203) ^ [_1147245, _1147247] : [class_Rings_Olinordered__idom(_1147245), -(c_Groups_Osgn__class_Osgn(_1147245, c_Groups_Osgn__class_Osgn(_1147245, _1147247)) = c_Groups_Osgn__class_Osgn(_1147245, _1147247))], (12298 ^ _779203) ^ [_991269, _991271] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _991269), _991271) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _991269 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _991271 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24133 ^ _779203) ^ [_1204238] : [-(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), _1204238)) = 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), _1204238))))], (22868 ^ _779203) ^ [_1182045, _1182047, _1182049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182045)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182049), _1182045)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1182047), _1182049)), _1182045))], (32799 ^ _779203) ^ [_1379635, _1379637, _1379639, _1379641, _1379643] : [hBOOL(hAPP(hAPP(_1379635, _1379637), _1379639)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1379641, _1379643, tc_HOL_Obool), _1379635), hAPP(hAPP(c_Product__Type_OPair(_1379641, _1379643), _1379637), _1379639))))], (1108 ^ _779203) ^ [_795935, _795937, _795939, _795941, _795943, _795945, _795947, _795949] : [-(c_Orderings_Oorder_Ostrict__mono(_795947, _795943, _795939, _795935)), c_Orderings_Oorder_Ostrict__mono(_795949, _795945, _795941, _795937), _795949 = _795947, _795945 = _795943, _795941 = _795939, _795937 = _795935], (39726 ^ _779203) ^ [_1552956, _1552958, _1552960, _1552962, _1552964, _1552966, _1552968, _1552970] : [c_Finite__Set_Ofolding(_1552956, _1552958, _1552960, _1552962), -(hAPP(c_Fun_Ocomp(_1552958, _1552958, _1552964, hAPP(_1552960, _1552966)), hAPP(c_Fun_Ocomp(_1552958, _1552958, _1552964, hAPP(_1552960, _1552968)), _1552970)) = hAPP(c_Fun_Ocomp(_1552958, _1552958, _1552964, hAPP(_1552960, _1552968)), hAPP(c_Fun_Ocomp(_1552958, _1552958, _1552964, hAPP(_1552960, _1552966)), _1552970)))], (46915 ^ _779203) ^ [_1722833, _1722835, _1722837, _1722839, _1722841] : [class_Orderings_Olinorder(_1722833), c_List_Olinorder__class_Osorted(_1722833, hAPP(c_List_Orev(_1722833), hAPP(hAPP(c_List_Omap(_1722835, _1722833), _1722837), _1722839))), -(hAPP(c_List_Ofilter(_1722835, hAPP(hAPP(c_COMBB(_1722833, tc_HOL_Obool, _1722835), hAPP(c_Orderings_Oord__class_Oless(_1722833), _1722841)), _1722837)), _1722839) = c_List_OtakeWhile(_1722835, hAPP(hAPP(c_COMBB(_1722833, tc_HOL_Obool, _1722835), hAPP(c_Orderings_Oord__class_Oless(_1722833), _1722841)), _1722837), _1722839))], (44259 ^ _779203) ^ [_1664405, _1664407, _1664409] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664405)), _1664407), c_List_Olists(_1664405, _1664409))), -(_1664407 = c_List_Olist_ONil(_1664405)), 44268 ^ _779203 : [(44273 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664405)), 44267 ^ [_1664405, _1664407, _1664409]), c_List_Olists(_1664405, _1664409))))], (44271 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1664405), 44266 ^ [_1664405, _1664407, _1664409]), _1664409)))], (44269 ^ _779203) ^ [] : [-(_1664407 = hAPP(hAPP(c_List_Olist_OCons(_1664405), 44266 ^ [_1664405, _1664407, _1664409]), 44267 ^ [_1664405, _1664407, _1664409]))]]], (47530 ^ _779203) ^ [_1737102, _1737104, _1737106, _1737108] : [class_Orderings_Oorder(_1737102), class_Enum_Oenum(_1737104), 47537 ^ _779203 : [(47544 ^ _779203) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737104), hAPP(hAPP(c_COMBS(_1737104, _1737102, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1737102, tc_fun(_1737102, tc_HOL_Obool), _1737104), c_Orderings_Oord__class_Oless__eq(_1737102)), _1737106)), _1737108))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1737104, _1737102)), _1737106), _1737108)))], (47538 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1737104, _1737102)), _1737106), _1737108)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1737104), hAPP(hAPP(c_COMBS(_1737104, _1737102, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1737102, tc_fun(_1737102, tc_HOL_Obool), _1737104), c_Orderings_Oord__class_Oless__eq(_1737102)), _1737106)), _1737108))))]]], (15093 ^ _779203) ^ [_1043106, _1043108, _1043110] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1043106), _1043108)), 15099 ^ _779203 : [(15102 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1043110, 15098 ^ [_1043106, _1043108, _1043110])))], (15100 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1043106), 15098 ^ [_1043106, _1043108, _1043110]), _1043108)))]], -(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(_1043106, tc_Nat_Onat), _1043110), _1043108))))], (44347 ^ _779203) ^ [_1666721, _1666723, _1666725, _1666727] : [_1666727 = c_List_Olist_ONil(_1666721), -(hAPP(hAPP(c_List_Omap(_1666721, _1666723), _1666725), _1666727) = c_List_Olist_ONil(_1666723))], (21691 ^ _779203) ^ [_1161056, _1161058] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1161056)), c_Int_OBit1(_1161058)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1161056), _1161058)))], (23659 ^ _779203) ^ [_1195567] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1195567))), -(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), _1195567)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (43389 ^ _779203) ^ [_1645737, _1645739, _1645741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645737), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645739)), _1645741))), -(hAPP(hAPP(c_List_Otake(_1645739), hAPP(c_Nat_OSuc, _1645737)), _1645741) = hAPP(hAPP(c_List_Oappend(_1645739), hAPP(hAPP(c_List_Otake(_1645739), _1645737), _1645741)), hAPP(hAPP(c_List_Olist_OCons(_1645739), hAPP(hAPP(c_List_Onth(_1645739), _1645741), _1645737)), c_List_Olist_ONil(_1645739))))], (21647 ^ _779203) ^ [_1160252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1160252)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160252), c_Int_OPls)))], (202 ^ _779203) ^ [_782246, _782248, _782250, _782252, _782254, _782256, _782258, _782260, _782262, _782264] : [-(c_Big__Operators_Ocomm__monoid__big(_782262, _782258, _782254, _782250, _782246)), c_Big__Operators_Ocomm__monoid__big(_782264, _782260, _782256, _782252, _782248), _782264 = _782262, _782260 = _782258, _782256 = _782254, _782252 = _782250, _782248 = _782246], (3552 ^ _779203) ^ [_832335, _832337, _832339, _832341] : [-(c_List_Orotate(_832341, _832337) = c_List_Orotate(_832339, _832335)), _832341 = _832339, _832337 = _832335], (9007 ^ _779203) ^ [_931644, _931646, _931648] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_931644), _931646)), -(hBOOL(hAPP(hAPP(c_member(_931644), _931648), _931646))), -(hAPP(c_Finite__Set_Ocard(_931644), hAPP(hAPP(c_Set_Oinsert(_931644), _931648), _931646)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_931644), _931646)))], (32259 ^ _779203) ^ [_1362746] : [-(c_Finite__Set_Ofun__left__comm__idem(_1362746, tc_fun(_1362746, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1362746, tc_HOL_Obool), tc_fun(tc_fun(_1362746, tc_HOL_Obool), tc_fun(_1362746, tc_HOL_Obool)), _1362746), hAPP(c_COMBC(tc_fun(_1362746, tc_HOL_Obool), tc_fun(_1362746, tc_HOL_Obool), tc_fun(_1362746, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1362746, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1362746, tc_fun(_1362746, tc_HOL_Obool), tc_fun(_1362746, tc_HOL_Obool)), c_Set_Oinsert(_1362746)), c_Orderings_Obot__class_Obot(tc_fun(_1362746, tc_HOL_Obool))))))], (28530 ^ _779203) ^ [_1283795, _1283797] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1283795), _1283797))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1283795), hAPP(c_Nat_OSuc, _1283797)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (92 ^ _779203) ^ [_780595, _780597] : [-(class_Rings_Odivision__ring__inverse__zero(_780595)), _780597 = _780595, class_Rings_Odivision__ring__inverse__zero(_780597)], (46632 ^ _779203) ^ [_1716969, _1716971, _1716973, _1716975, _1716977] : [c_List_Olist__all2(_1716969, _1716971, _1716973, _1716975, hAPP(c_List_Orev(_1716971), _1716977)), -(c_List_Olist__all2(_1716969, _1716971, _1716973, hAPP(c_List_Orev(_1716969), _1716975), _1716977))], (42958 ^ _779203) ^ [_1635984, _1635986, _1635988, _1635990, _1635992] : [hAPP(hAPP(c_List_Oappend(_1635984), _1635986), hAPP(hAPP(c_List_Olist_OCons(_1635984), _1635988), c_List_Olist_ONil(_1635984))) = hAPP(hAPP(c_List_Oappend(_1635984), _1635990), hAPP(hAPP(c_List_Olist_OCons(_1635984), _1635992), c_List_Olist_ONil(_1635984))), 42961 ^ _779203 : [(42964 ^ _779203) ^ [] : [-(_1635988 = _1635992)], (42962 ^ _779203) ^ [] : [-(_1635986 = _1635990)]]], (40153 ^ _779203) ^ [_1563392, _1563394] : [-(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)))), _1563392)) = 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)))), _1563394))), 40155 ^ _779203 : [(40158 ^ _779203) ^ [] : [40159 ^ _779203 : [(40162 ^ _779203) ^ [] : [hBOOL(hAPP(_1563394, 40154 ^ [_1563392, _1563394]))], (40160 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1563392, 40154 ^ [_1563392, _1563394])))]], 40163 ^ _779203 : [(40166 ^ _779203) ^ [] : [hBOOL(hAPP(_1563392, 40154 ^ [_1563392, _1563394]))], (40164 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1563394, 40154 ^ [_1563392, _1563394])))]]], (40156 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 40154 ^ [_1563392, _1563394])))]]], (41677 ^ _779203) ^ [_1605095, _1605097, _1605099, _1605101, _1605103, _1605105] : [-(c_List_Olistrelp(_1605095, _1605097, hAPP(hAPP(c_List_Olist_OCons(_1605095), _1605099), _1605101), hAPP(hAPP(c_List_Olist_OCons(_1605095), _1605103), _1605105))), hBOOL(hAPP(hAPP(_1605097, _1605099), _1605103)), c_List_Olistrelp(_1605095, _1605097, _1605101, _1605105)], (10849 ^ _779203) ^ [_966752, _966754, _966756] : [class_Rings_Oring__no__zero__divisors(_966752), 10852 ^ _779203 : [(10853 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966752), _966754), _966756) = c_Groups_Ozero__class_Ozero(_966752), -(_966754 = c_Groups_Ozero__class_Ozero(_966752)), -(_966756 = c_Groups_Ozero__class_Ozero(_966752))], (10863 ^ _779203) ^ [] : [10864 ^ _779203 : [(10867 ^ _779203) ^ [] : [_966756 = c_Groups_Ozero__class_Ozero(_966752)], (10865 ^ _779203) ^ [] : [_966754 = c_Groups_Ozero__class_Ozero(_966752)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966752), _966754), _966756) = c_Groups_Ozero__class_Ozero(_966752))]]], (36934 ^ _779203) ^ [_1475153, _1475155, _1475157, _1475159, _1475161] : [class_Groups_Ocomm__monoid__add(_1475153), class_Groups_Ocomm__monoid__mult(_1475153), _1475155 = _1475157, c_Nat__Transfer_Onat__set(_1475157), 36952 ^ _779203 : [(36955 ^ _779203) ^ [] : [hAPP(_1475159, 36951 ^ [_1475153, _1475155, _1475157, _1475159, _1475161]) = hAPP(_1475161, 36951 ^ [_1475153, _1475155, _1475157, _1475159, _1475161])], (36953 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36951 ^ [_1475153, _1475155, _1475157, _1475159, _1475161])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1475153), _1475159), _1475155) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1475153), _1475161), _1475157))], (49404 ^ _779203) ^ [_1777725, _1777727] : [c_Predicate_Osymp(_1777725, _1777727), -(c_Relation_Osym(_1777725, hAPP(c_Set_OCollect(tc_prod(_1777725, _1777725)), hAPP(c_Product__Type_Oprod_Oprod__case(_1777725, _1777725, tc_HOL_Obool), _1777727))))], (5667 ^ _779203) ^ [_868610, _868612] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_868610, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_868610, tc_HOL_Obool))), _868612)))], (976 ^ _779203) ^ [_793785, _793787, _793789, _793791, _793793, _793795, _793797, _793799, _793801, _793803, _793805, _793807] : [-(c_Equiv__Relations_Ocongruent2(_793805, _793801, _793797, _793793, _793789, _793785)), c_Equiv__Relations_Ocongruent2(_793807, _793803, _793799, _793795, _793791, _793787), _793807 = _793805, _793803 = _793801, _793799 = _793797, _793795 = _793793, _793791 = _793789, _793787 = _793785], (30317 ^ _779203) ^ [_1320139, _1320141, _1320143] : [class_Groups_Oab__semigroup__mult(_1320139), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320139), _1320141)), -(_1320141 = c_Orderings_Obot__class_Obot(tc_fun(_1320139, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320139), _1320143)), -(_1320143 = c_Orderings_Obot__class_Obot(tc_fun(_1320139, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1320139, tc_HOL_Obool)), _1320141), _1320143) = c_Orderings_Obot__class_Obot(tc_fun(_1320139, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1320139, c_Groups_Otimes__class_Otimes(_1320139)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1320139, tc_HOL_Obool)), _1320141), _1320143)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1320139), hAPP(c_Finite__Set_Ofold1(_1320139, c_Groups_Otimes__class_Otimes(_1320139)), _1320141)), hAPP(c_Finite__Set_Ofold1(_1320139, c_Groups_Otimes__class_Otimes(_1320139)), _1320143)))], (52217 ^ _779203) ^ [_1832217, _1832219] : [-(class_Enum_Oenum(tc_fun(_1832217, _1832219))), class_Enum_Oenum(_1832217), class_Enum_Oenum(_1832219)], (45315 ^ _779203) ^ [_1688777, _1688779, _1688781, _1688783] : [45317 ^ _779203 : [(45320 ^ _779203) ^ [] : [hBOOL(hAPP(_1688781, hAPP(hAPP(c_List_Onth(_1688777), _1688779), 45316 ^ [_1688777, _1688779, _1688781, _1688783])))], (45318 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45316 ^ [_1688777, _1688779, _1688781, _1688783]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688777)), _1688779))))]], hBOOL(hAPP(hAPP(c_member(_1688777), _1688783), hAPP(c_List_Oset(_1688777), _1688779))), -(hBOOL(hAPP(_1688781, _1688783)))], (21223 ^ _779203) ^ [_1153443, _1153445] : [c_Int_Oiszero(_1153443, hAPP(c_Int_Onumber__class_Onumber__of(_1153443), c_Int_OBit1(_1153445))), class_Int_Onumber__ring(_1153443), class_Int_Oring__char__0(_1153443)], (25640 ^ _779203) ^ [_1230638, _1230640] : [class_Int_Onumber__ring(_1230638), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230638), hAPP(c_Int_Onumber__class_Onumber__of(_1230638), c_Int_OMin)), _1230640) = hAPP(c_Groups_Ouminus__class_Ouminus(_1230638), _1230640))], (47452 ^ _779203) ^ [_1734990, _1734992, _1734994, _1734996, _1734998] : [hAPP(c_List_Ofilter(_1734990, _1734992), _1734994) = hAPP(hAPP(c_List_Olist_OCons(_1734990), _1734996), _1734998), 47457 ^ _779203 : [(47466 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1734992, _1734996)))], (47468 ^ _779203) ^ [] : [-(_1734998 = hAPP(c_List_Ofilter(_1734990, _1734992), 47456 ^ [_1734990, _1734992, _1734994, _1734996, _1734998]))], (47460 ^ _779203) ^ [_1735304] : [hBOOL(hAPP(hAPP(c_member(_1734990), _1735304), hAPP(c_List_Oset(_1734990), 47455 ^ [_1734990, _1734992, _1734994, _1734996, _1734998]))), hBOOL(hAPP(_1734992, _1735304))], (47458 ^ _779203) ^ [] : [-(_1734994 = hAPP(hAPP(c_List_Oappend(_1734990), 47455 ^ [_1734990, _1734992, _1734994, _1734996, _1734998]), hAPP(hAPP(c_List_Olist_OCons(_1734990), _1734996), 47456 ^ [_1734990, _1734992, _1734994, _1734996, _1734998])))]]], (27210 ^ _779203) ^ [_1258221, _1258223] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1258221), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1258223), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1258221, _1258223))], (28818 ^ _779203) ^ [_1288934, _1288936] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1288934, _1288936)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1288936), _1288934)))], (24982 ^ _779203) ^ [_1219565, _1219567, _1219569] : [class_Rings_Olinordered__semidom(_1219565), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219565), c_Groups_Ozero__class_Ozero(_1219565)), _1219567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219565), c_Groups_Ozero__class_Ozero(_1219565)), hAPP(hAPP(c_Power_Opower__class_Opower(_1219565), _1219567), _1219569))))], (36014 ^ _779203) ^ [_1455661, _1455663, _1455665, _1455667] : [c_Equiv__Relations_Oequivp(_1455661, _1455663), hBOOL(hAPP(hAPP(_1455663, _1455665), _1455667)), -(hBOOL(hAPP(hAPP(_1455663, _1455667), _1455665)))], (15468 ^ _779203) ^ [_1050415, _1050417, _1050419, _1050421] : [class_Orderings_Olinorder(_1050415), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050415), _1050417), _1050419)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050415), _1050421), _1050419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1050415), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1050415), _1050417), _1050421)), _1050419)))], (20861 ^ _779203) ^ [_1147338, _1147340] : [class_Rings_Olinordered__idom(_1147338), 20864 ^ _779203 : [(20871 ^ _779203) ^ [] : [_1147340 = c_Groups_Ozero__class_Ozero(_1147338), -(c_Groups_Osgn__class_Osgn(_1147338, _1147340) = c_Groups_Ozero__class_Ozero(_1147338))], (20865 ^ _779203) ^ [] : [c_Groups_Osgn__class_Osgn(_1147338, _1147340) = c_Groups_Ozero__class_Ozero(_1147338), -(_1147340 = c_Groups_Ozero__class_Ozero(_1147338))]]], (40785 ^ _779203) ^ [_1578951, _1578953, _1578955] : [-(hAPP(c_Relation_ORange(_1578951, _1578953), _1578955) = hAPP(c_Relation_ODomain(_1578953, _1578951), hAPP(c_Relation_Oconverse(_1578951, _1578953), _1578955)))], (13420 ^ _779203) ^ [_1011767, _1011769, _1011771, _1011773] : [c_Sum__Type_OPlus(_1011767, _1011769, _1011771, _1011773) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1011767, _1011769), tc_HOL_Obool)), 13423 ^ _779203 : [(13426 ^ _779203) ^ [] : [-(_1011773 = c_Orderings_Obot__class_Obot(tc_fun(_1011769, tc_HOL_Obool)))], (13424 ^ _779203) ^ [] : [-(_1011771 = c_Orderings_Obot__class_Obot(tc_fun(_1011767, tc_HOL_Obool)))]]], (34827 ^ _779203) ^ [_1425036, _1425038, _1425040, _1425042, _1425044] : [-(_1425036 = c_Orderings_Obot__class_Obot(tc_fun(_1425038, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425040, tc_HOL_Obool)), _1425042), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1425038, tc_fun(_1425040, tc_HOL_Obool)), _1425036), _1425044)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1425038, tc_fun(_1425040, tc_HOL_Obool)), _1425036), hAPP(hAPP(c_COMBB(tc_fun(_1425040, tc_HOL_Obool), tc_fun(_1425040, tc_HOL_Obool), _1425038), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1425040, tc_HOL_Obool)), _1425042)), _1425044)))], (34476 ^ _779203) ^ [_1414980, _1414982, _1414984, _1414986, _1414988] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414980, tc_fun(_1414982, tc_HOL_Obool)), _1414984), hAPP(hAPP(c_COMBC(_1414980, tc_fun(_1414982, tc_HOL_Obool), tc_fun(_1414982, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1414982, tc_HOL_Obool), tc_fun(tc_fun(_1414982, tc_HOL_Obool), tc_fun(_1414982, tc_HOL_Obool)), _1414980), c_Groups_Ominus__class_Ominus(tc_fun(_1414982, tc_HOL_Obool))), _1414986)), _1414988)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1414982, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414980, tc_fun(_1414982, tc_HOL_Obool)), _1414984), _1414986)), _1414988))], (36524 ^ _779203) ^ [_1466402, _1466404] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1466402), c_Orderings_Otop__class_Otop(tc_fun(_1466402, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1466402, _1466402, _1466404), c_Orderings_Otop__class_Otop(tc_fun(_1466402, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1466402, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1466402, _1466402, _1466404, c_Orderings_Otop__class_Otop(tc_fun(_1466402, tc_HOL_Obool))))], (10455 ^ _779203) ^ [_959785, _959787, _959789] : [class_Rings_Ocomm__semiring__1(_959785), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959785), _959787), _959789) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959785), _959789), _959787))], (30211 ^ _779203) ^ [_1317937, _1317939, _1317941] : [class_Complete__Lattice_Ocomplete__lattice(_1317937), hBOOL(hAPP(c_Finite__Set_Ofinite(_1317937), _1317939)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1317937), _1317941), c_Complete__Lattice_OSup__class_OSup(_1317937, _1317939)) = hAPP(hAPP(c_Finite__Set_Ofold(_1317937, _1317937, c_Lattices_Osemilattice__sup__class_Osup(_1317937)), _1317941), _1317939))], (3620 ^ _779203) ^ [_833405, _833407] : [_833407 = _833405, -(c_List_Oreturn__list(_833407) = c_List_Oreturn__list(_833405))], (51115 ^ _779203) ^ [_1813785, _1813787, _1813789] : [class_Rings_Olinordered__idom(_1813785), 51118 ^ _779203 : [(51125 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813785), _1813787), _1813789)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813785), hAPP(c_Groups_Oabs__class_Oabs(_1813785), _1813787)), _1813789)))], (51119 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813785), hAPP(c_Groups_Oabs__class_Oabs(_1813785), _1813787)), _1813789)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813785), _1813787), _1813789)))]]], (9849 ^ _779203) ^ [_947335, _947337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _947335), _947337)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947335), _947337))), -(_947335 = _947337)], (47756 ^ _779203) ^ [_1741524, _1741526, _1741528] : [hBOOL(hAPP(hAPP(c_member(_1741524), _1741526), hAPP(c_List_Oset(_1741524), _1741528))), 47761 ^ _779203 : [(47764 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1741524), _1741526), hAPP(c_List_Oset(_1741524), 47760 ^ [_1741524, _1741526, _1741528])))], (47762 ^ _779203) ^ [] : [-(_1741528 = hAPP(hAPP(c_List_Oappend(_1741524), 47759 ^ [_1741524, _1741526, _1741528]), hAPP(hAPP(c_List_Olist_OCons(_1741524), _1741526), 47760 ^ [_1741524, _1741526, _1741528])))]]], (43696 ^ _779203) ^ [_1653692, _1653694, _1653696] : [-(hAPP(c_List_Ohd(_1653692), hAPP(hAPP(c_List_Olist_OCons(_1653692), _1653694), _1653696)) = _1653694)], (18319 ^ _779203) ^ [_1102403, _1102405] : [18320 ^ _779203 : [(18321 ^ _779203) ^ [_1102456] : [_1102405 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1102403), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1102456))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1102403), _1102405)))], (47379 ^ _779203) ^ [_1733280, _1733282, _1733284, _1733286] : [47381 ^ _779203 : [(47384 ^ _779203) ^ [] : [hBOOL(hAPP(_1733284, 47380 ^ [_1733280, _1733282, _1733284, _1733286]))], (47382 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733280), 47380 ^ [_1733280, _1733282, _1733284, _1733286]), hAPP(c_List_Oset(_1733280), _1733282))))]], -(c_List_OdropWhile(_1733280, _1733284, hAPP(hAPP(c_List_Oappend(_1733280), _1733282), _1733286)) = c_List_OdropWhile(_1733280, _1733284, _1733286))], (21795 ^ _779203) ^ [_1162912, _1162914] : [class_Int_Onumber__ring(_1162912), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162912), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162912), c_Groups_Oone__class_Oone(_1162912)), c_Groups_Oone__class_Oone(_1162912))), hAPP(c_Int_Onumber__class_Onumber__of(_1162912), _1162914)) = hAPP(c_Int_Onumber__class_Onumber__of(_1162912), c_Int_OBit0(_1162914)))], (37118 ^ _779203) ^ [_1479607, _1479609, _1479611] : [-(c_HOL_OThe(tc_prod(_1479607, _1479609), _1479611) = c_HOL_OThe(tc_prod(_1479607, _1479609), hAPP(c_Product__Type_Oprod_Oprod__case(_1479607, _1479609, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1479609, tc_prod(_1479607, _1479609)), tc_fun(_1479609, tc_HOL_Obool), _1479607), hAPP(c_COMBB(tc_prod(_1479607, _1479609), tc_HOL_Obool, _1479609), _1479611)), c_Product__Type_OPair(_1479607, _1479609)))))], (39980 ^ _779203) ^ [_1558819, _1558821, _1558823, _1558825, _1558827, _1558829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1558819, tc_HOL_Obool)), _1558821), _1558823)), 39986 ^ _779203 : [(39989 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1558825, tc_HOL_Obool)), hAPP(_1558827, 39985 ^ [_1558819, _1558821, _1558823, _1558825, _1558827, _1558829])), hAPP(_1558829, 39985 ^ [_1558819, _1558821, _1558823, _1558825, _1558827, _1558829])))], (39987 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1558819), 39985 ^ [_1558819, _1558821, _1558823, _1558825, _1558827, _1558829]), _1558821)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1558819, _1558825), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1558819, _1558825), _1558821), _1558827)), hAPP(hAPP(c_Product__Type_OSigma(_1558819, _1558825), _1558823), _1558829))))], (37369 ^ _779203) ^ [_1486079, _1486081, _1486083] : [37370 ^ _779203 : [(37373 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1486079), hAPP(c_Set_OCollect(_1486079), _1486083)))], (37371 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1486079), hAPP(c_Set_OCollect(_1486079), _1486081)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1486079), hAPP(c_Set_OCollect(_1486079), hAPP(hAPP(c_COMBS(_1486079, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1486079), c_fconj), _1486081)), _1486083)))))], (45568 ^ _779203) ^ [_1693794, _1693796, _1693798] : [-(c_List_Oconcat(_1693794, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1693794)), _1693796), _1693798)) = hAPP(hAPP(c_List_Oappend(_1693794), c_List_Oconcat(_1693794, _1693796)), c_List_Oconcat(_1693794, _1693798)))], (43007 ^ _779203) ^ [_1637064, _1637066, _1637068, _1637070, _1637072] : [hAPP(hAPP(c_List_Oappend(_1637064), _1637066), _1637068) = hAPP(hAPP(c_List_Olist_OCons(_1637064), _1637070), _1637072), 43012 ^ _779203 : [(43015 ^ _779203) ^ [] : [-(_1637068 = hAPP(hAPP(c_List_Olist_OCons(_1637064), _1637070), _1637072))], (43013 ^ _779203) ^ [] : [-(_1637066 = c_List_Olist_ONil(_1637064))]], 43017 ^ _779203 : [(43020 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1637064), 43016 ^ [_1637064, _1637066, _1637068, _1637070, _1637072]), _1637068) = _1637072)], (43018 ^ _779203) ^ [] : [-(_1637066 = hAPP(hAPP(c_List_Olist_OCons(_1637064), _1637070), 43016 ^ [_1637064, _1637066, _1637068, _1637070, _1637072]))]]], (35065 ^ _779203) ^ [_1431322, _1431324, _1431326, _1431328, _1431330] : [class_Complete__Lattice_Ocomplete__lattice(_1431322), hBOOL(hAPP(c_Finite__Set_Ofinite(_1431324), _1431326)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1431322), _1431328), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1431324, _1431322), _1431326), _1431330)) = hAPP(hAPP(c_Finite__Set_Ofold(_1431324, _1431322, hAPP(hAPP(c_COMBB(_1431322, tc_fun(_1431322, _1431322), _1431324), c_Lattices_Osemilattice__sup__class_Osup(_1431322)), _1431330)), _1431328), _1431326))], (6015 ^ _779203) ^ [_874699, _874701, _874703, _874705, _874707, _874709] : [hBOOL(hAPP(hAPP(c_member(_874699), _874701), _874703)), _874705 = hAPP(_874707, _874701), -(hBOOL(hAPP(hAPP(c_member(_874709), _874705), hAPP(c_Set_Oimage(_874699, _874709, _874707), _874703))))], (28460 ^ _779203) ^ [_1282543, _1282545, _1282547] : [class_Orderings_Olinorder(_1282543), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282543), _1282545)), -(_1282545 = c_Orderings_Obot__class_Obot(tc_fun(_1282543, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282543), _1282547)), -(_1282547 = c_Orderings_Obot__class_Obot(tc_fun(_1282543, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1282543, c_Orderings_Oord__class_Omin(_1282543), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282543, tc_HOL_Obool)), _1282545), _1282547)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1282543), c_Big__Operators_Olattice_OInf__fin(_1282543, c_Orderings_Oord__class_Omin(_1282543), _1282545)), c_Big__Operators_Olattice_OInf__fin(_1282543, c_Orderings_Oord__class_Omin(_1282543), _1282547)))], (2028 ^ _779203) ^ [_808433, _808435, _808437, _808439] : [-(c_Nat__Transfer_Otsub(_808439, _808435) = c_Nat__Transfer_Otsub(_808437, _808433)), _808439 = _808437, _808435 = _808433], (35399 ^ _779203) ^ [_1440054, _1440056, _1440058, _1440060] : [c_FunDef_Oreduction__pair(_1440054, _1440056), -(c_FunDef_Oreduction__pair(_1440058, hAPP(hAPP(c_FunDef_Orp__inv__image(_1440054, _1440058), _1440056), _1440060)))], (26814 ^ _779203) ^ [_1251559] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1251559) = 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), _1251559))))], (41347 ^ _779203) ^ [_1594545, _1594547, _1594549, _1594551, _1594553] : [hAPP(hAPP(c_List_Olist_OCons(_1594545), _1594547), _1594549) = hAPP(hAPP(c_List_Olist_OCons(_1594545), _1594551), _1594553), 41350 ^ _779203 : [(41353 ^ _779203) ^ [] : [-(_1594549 = _1594553)], (41351 ^ _779203) ^ [] : [-(_1594547 = _1594551)]]], (31089 ^ _779203) ^ [_1335268, _1335270] : [class_Lattices_Olattice(_1335268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1335268), _1335270)), -(_1335270 = c_Orderings_Obot__class_Obot(tc_fun(_1335268, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1335268), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1335268), 31102 ^ [_1335268, _1335270]), 31103 ^ [_1335268, _1335270])), hAPP(hAPP(c_Set_Oinsert(_1335268), 31102 ^ [_1335268, _1335270]), hAPP(hAPP(c_Set_Oinsert(_1335268), 31103 ^ [_1335268, _1335270]), c_Orderings_Obot__class_Obot(tc_fun(_1335268, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1335268), c_Big__Operators_Olattice__class_OInf__fin(_1335268, _1335270)), _1335270)))], (1150 ^ _779203) ^ [_796538, _796540] : [-(class_Groups_Oordered__ab__group__add__abs(_796538)), _796540 = _796538, class_Groups_Oordered__ab__group__add__abs(_796540)], (30610 ^ _779203) ^ [_1325963, _1325965, _1325967] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1325963, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1325963, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1325963, tc_HOL_Obool), tc_HOL_Obool)), _1325965), _1325967))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325963, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1325963, tc_HOL_Obool), _1325965)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1325963, tc_HOL_Obool), _1325967)))))], (52441 ^ _779203) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (4142 ^ _779203) ^ [_841906, _841908] : [_841908 = _841906, -(c_List_Odrop(_841908) = c_List_Odrop(_841906))], (22073 ^ _779203) ^ [_1168712, _1168714, _1168716, _1168718] : [class_Divides_Oring__div(_1168712), -(c_Divides_Odiv__class_Omod(_1168712, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168712), _1168714), _1168716), _1168718) = c_Divides_Odiv__class_Omod(_1168712, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168712), _1168714), c_Divides_Odiv__class_Omod(_1168712, _1168716, _1168718)), _1168718))], (52679 ^ _779203) ^ [_1836711] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1836711)))], (37407 ^ _779203) ^ [_1487117, _1487119, _1487121] : [hBOOL(hAPP(_1487121, _1487119)), -(hBOOL(hAPP(hAPP(c_member(_1487117), _1487119), hAPP(c_Set_OCollect(_1487117), _1487121))))], (20592 ^ _779203) ^ [_1142300, _1142302] : [class_Int_Onumber__ring(_1142300), class_Rings_Olinordered__idom(_1142300), 20599 ^ _779203 : [(20606 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142300), hAPP(c_Int_Onumber__class_Onumber__of(_1142300), _1142302)), c_Groups_Ozero__class_Ozero(_1142300)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1142300), hAPP(c_Int_Onumber__class_Onumber__of(_1142300), _1142302)) = hAPP(c_Int_Onumber__class_Onumber__of(_1142300), _1142302))], (20600 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142300), hAPP(c_Int_Onumber__class_Onumber__of(_1142300), _1142302)), c_Groups_Ozero__class_Ozero(_1142300))), -(hAPP(c_Groups_Oabs__class_Oabs(_1142300), hAPP(c_Int_Onumber__class_Onumber__of(_1142300), _1142302)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1142300), hAPP(c_Int_Onumber__class_Onumber__of(_1142300), _1142302)))]]], (19210 ^ _779203) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (51147 ^ _779203) ^ [_1814321, _1814323] : [class_Rings_Ocomm__semiring__1(_1814321), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1814321), c_Groups_Oone__class_Oone(_1814321)), _1814323)))], (49985 ^ _779203) ^ [_1790266, _1790268, _1790270] : [c_Fun_Obij__betw(_1790266, _1790268, _1790270, c_Orderings_Otop__class_Otop(tc_fun(_1790266, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1790268, tc_HOL_Obool))), 49988 ^ _779203 : [(49991 ^ _779203) ^ [] : [-(hAPP(c_Set_Oimage(_1790266, _1790268, _1790270), c_Orderings_Otop__class_Otop(tc_fun(_1790266, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1790268, tc_HOL_Obool)))], (49989 ^ _779203) ^ [] : [-(c_Fun_Oinj__on(_1790266, _1790268, _1790270, c_Orderings_Otop__class_Otop(tc_fun(_1790266, tc_HOL_Obool))))]]], (15396 ^ _779203) ^ [_1049044, _1049046, _1049048, _1049050] : [class_Orderings_Olinorder(_1049044), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1049044), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1049044), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049044), _1049046), _1049048)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049044), _1049046), _1049050))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1049044), _1049046), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1049044), _1049048), _1049050)))))], (15128 ^ _779203) ^ [_1043749, _1043751, _1043753] : [class_Orderings_Olinorder(_1043749), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043749), _1043751)), 15138 ^ _779203 : [(15141 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043749), _1043753), 15137 ^ [_1043749, _1043751, _1043753]))], (15139 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1043749), 15137 ^ [_1043749, _1043751, _1043753]), _1043751)))]], hBOOL(hAPP(hAPP(c_member(_1043749), _1043753), _1043751)), -(c_Big__Operators_Olinorder__class_OMin(_1043749, _1043751) = _1043753)], (22978 ^ _779203) ^ [_1183836, _1183838] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183836, _1183838) = 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), _1183836), _1183838) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1183838), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183836, _1183838)))], (47795 ^ _779203) ^ [] : [-(c_FunDef_Ois__measure(tc_Int_Oint, hAPP(c_Fun_Ocomp(tc_Int_Oint, tc_Nat_Onat, tc_Int_Oint, c_Int_Onat), c_Groups_Oabs__class_Oabs(tc_Int_Oint))))], (25840 ^ _779203) ^ [_1233766, _1233768] : [-(c_Nitpick_Oint__lcm(_1233766, _1233768) = 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), _1233766)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1233768)))))], (19308 ^ _779203) ^ [_1119459, _1119461, _1119463] : [class_Groups_Oordered__ab__group__add__abs(_1119459), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1119459), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1119459), hAPP(c_Groups_Oabs__class_Oabs(_1119459), _1119461)), hAPP(c_Groups_Oabs__class_Oabs(_1119459), _1119463))), hAPP(c_Groups_Oabs__class_Oabs(_1119459), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1119459), _1119463), _1119461)))))], (2244 ^ _779203) ^ [_811945, _811947, _811949, _811951] : [-(c_Orderings_Oord_Omin(_811951, _811947) = c_Orderings_Oord_Omin(_811949, _811945)), _811951 = _811949, _811947 = _811945], (21481 ^ _779203) ^ [_1157404, _1157406] : [_1157404 = _1157406, -(c_Int_OBit0(_1157404) = c_Int_OBit0(_1157406))], (23866 ^ _779203) ^ [_1199201, _1199203, _1199205] : [hBOOL(hAPP(_1199201, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1199203), _1199205))), 23869 ^ _779203 : [(23876 ^ _779203) ^ [] : [-(_1199205 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 23879 ^ _779203 : [(23880 ^ _779203) ^ [_1199453, _1199455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1199453), _1199205)), _1199203 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1199205), _1199455)), _1199453), -(hBOOL(hAPP(_1199201, _1199455)))]]], (23870 ^ _779203) ^ [] : [_1199205 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1199201, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (22183 ^ _779203) ^ [_1170900, _1170902, _1170904, _1170906] : [class_Divides_Osemiring__div(_1170900), -(c_Divides_Odiv__class_Omod(_1170900, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170900), _1170902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170900), _1170904), _1170906)), _1170904) = c_Divides_Odiv__class_Omod(_1170900, _1170902, _1170904))], (33869 ^ _779203) ^ [_1399682, _1399684] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1399682), _1399684) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1399682, _1399684)))], (15774 ^ _779203) ^ [_1055694, _1055696, _1055698, _1055700] : [class_Orderings_Olinorder(_1055694), 15777 ^ _779203 : [(15778 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055694), _1055696), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1055694), _1055698), _1055700))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055694), _1055696), _1055698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055694), _1055696), _1055700)))], (15788 ^ _779203) ^ [] : [15789 ^ _779203 : [(15792 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055694), _1055696), _1055700))], (15790 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055694), _1055696), _1055698))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055694), _1055696), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1055694), _1055698), _1055700))))]]], (25586 ^ _779203) ^ [_1229939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1229939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1229939))))], (18656 ^ _779203) ^ [_1108139, _1108141] : [class_Int_Onumber__ring(_1108139), class_Rings_Olinordered__idom(_1108139), 18663 ^ _779203 : [(18670 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108141), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108139), hAPP(c_Int_Onumber__class_Onumber__of(_1108139), _1108141)), c_Groups_Ozero__class_Ozero(_1108139))))], (18664 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1108139), hAPP(c_Int_Onumber__class_Onumber__of(_1108139), _1108141)), c_Groups_Ozero__class_Ozero(_1108139))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1108141), c_Int_OPls)))]]], (1550 ^ _779203) ^ [_801538, _801540] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_801538)), _801540 = _801538, class_Groups_Oordered__ab__semigroup__add__imp__le(_801540)], (19282 ^ _779203) ^ [_1118832, _1118834, _1118836, _1118838, _1118840] : [class_Rings_Olinordered__idom(_1118832), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118832), hAPP(c_Groups_Oabs__class_Oabs(_1118832), _1118834)), _1118836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118832), hAPP(c_Groups_Oabs__class_Oabs(_1118832), _1118838)), _1118840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118832), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118832), hAPP(c_Groups_Oabs__class_Oabs(_1118832), _1118834)), hAPP(c_Groups_Oabs__class_Oabs(_1118832), _1118838))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1118832), _1118836), _1118840))))], (22235 ^ _779203) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (49162 ^ _779203) ^ [_1773168, _1773170] : [c_Relation_Oantisym(_1773168, _1773170), -(c_Relation_Oantisym(_1773168, hAPP(c_Relation_Oconverse(_1773168, _1773168), _1773170)))], (2108 ^ _779203) ^ [_809657, _809659, _809661, _809663, _809665, _809667] : [-(c_Random_Ominus__shift(_809667, _809663, _809659) = c_Random_Ominus__shift(_809665, _809661, _809657)), _809667 = _809665, _809663 = _809661, _809659 = _809657], (23856 ^ _779203) ^ [_1199035, _1199037] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1199035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1199037), _1199035))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1199037), _1199035) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1199037), _1199035)), _1199035)))], (6587 ^ _779203) ^ [_885446, _885448, _885450] : [class_Orderings_Olinorder(_885446), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885446), _885448), _885450))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885446), _885450), _885448)))], (33401 ^ _779203) ^ [_1390419, _1390421, _1390423, _1390425] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1390419, _1390421), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1390423), _1390425))), -(_1390421 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1390419), _1390421) = _1390423)], (20078 ^ _779203) ^ [_1133317, _1133319, _1133321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133317, tc_HOL_Obool)), _1133321), _1133319)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133317, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1133317, tc_HOL_Obool)), _1133319)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1133317, tc_HOL_Obool)), _1133321))))], (5945 ^ _779203) ^ [_873437, _873439, _873441, _873443] : [-(hBOOL(hAPP(hAPP(c_member(_873437), _873439), _873441))), -(hBOOL(hAPP(hAPP(c_member(_873437), _873439), _873443))), 5952 ^ _779203 : [(5959 ^ _779203) ^ [] : [_873441 = _873443, -(hAPP(hAPP(c_Set_Oinsert(_873437), _873439), _873441) = hAPP(hAPP(c_Set_Oinsert(_873437), _873439), _873443))], (5953 ^ _779203) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_873437), _873439), _873441) = hAPP(hAPP(c_Set_Oinsert(_873437), _873439), _873443), -(_873441 = _873443)]]], (48260 ^ _779203) ^ [_1752443, _1752445, _1752447, _1752449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752443), _1752445)), -(hAPP(hAPP(c_List_Onth(_1752447), c_List_Oreplicate(_1752447, _1752445, _1752449)), _1752443) = _1752449)], (19342 ^ _779203) ^ [_1120009] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1120009)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1120009), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (40667 ^ _779203) ^ [_1576263, _1576265, _1576267] : [c_Relation_Ototal__on(_1576263, _1576265, _1576267), -(c_Relation_Ototal__on(_1576263, _1576265, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1576263, _1576263), tc_HOL_Obool)), _1576267), c_Relation_OId(_1576263))))], (11226 ^ _779203) ^ [_972424, _972426, _972428, _972430] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_972424, _972426)), c_Sum__Type_OPlus(_972424, _972426, _972428, _972430)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_972424), _972428)), hBOOL(hAPP(c_Finite__Set_Ofinite(_972426), _972430))], (41715 ^ _779203) ^ [_1606121] : [-(c_List_Olists(_1606121, c_Orderings_Otop__class_Otop(tc_fun(_1606121, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1606121), tc_HOL_Obool)))], (38663 ^ _779203) ^ [_1527753, _1527755, _1527757] : [c_Wellfounded_Owf(_1527753, _1527755), -(c_Wellfounded_Owf(_1527753, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1527753, _1527753), tc_HOL_Obool)), _1527757), _1527755)))], (38300 ^ _779203) ^ [_1516537, _1516539, _1516541, _1516543, _1516545, _1516547, _1516549] : [-(hAPP(c_Product__Type_Osnd(_1516537, _1516539), hAPP(c_Product__Type_Omap__pair(_1516541, _1516537, _1516543, _1516539, _1516545, _1516547), _1516549)) = hAPP(_1516547, hAPP(c_Product__Type_Osnd(_1516541, _1516543), _1516549)))], (9699 ^ _779203) ^ [_944921, _944923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944921), _944923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944921), hAPP(c_Nat_OSuc, _944923))))], (42401 ^ _779203) ^ [_1624323, _1624325, _1624327, _1624329] : [hBOOL(hAPP(c_List_Odistinct(_1624323), _1624325)), -(hBOOL(hAPP(hAPP(c_member(_1624323), _1624327), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1624323, tc_HOL_Obool)), hAPP(c_List_Oset(_1624323), _1624325)), hAPP(hAPP(c_Set_Oinsert(_1624323), hAPP(hAPP(c_List_Onth(_1624323), _1624325), _1624329)), c_Orderings_Obot__class_Obot(tc_fun(_1624323, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1624323), hAPP(hAPP(c_List_Olist__update(_1624323, _1624325), _1624329), _1624327))))], (18186 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (20448 ^ _779203) ^ [_1139778, _1139780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1139778, tc_HOL_Obool)), _1139780), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1139778, tc_HOL_Obool)), _1139780))), -(_1139780 = c_Orderings_Obot__class_Obot(tc_fun(_1139778, tc_HOL_Obool)))], (9741 ^ _779203) ^ [_945538, _945540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _945538)), hAPP(c_Nat_OSuc, _945540))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945538), _945540)))], (12080 ^ _779203) ^ [_987967, _987969, _987971, _987973, _987975, _987977] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_987967), -(_987969 = c_Groups_Ozero__class_Ozero(_987967)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987967), _987971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987967), _987969), _987975)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_987967), _987973), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_987967), _987969), _987977)), _987971 = _987973, -(_987975 = _987977)], (29258 ^ _779203) ^ [_1297721, _1297723, _1297725] : [class_Lattices_Olattice(_1297721), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297721), _1297723), _1297725) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297721), _1297725), _1297723))], (44744 ^ _779203) ^ [_1675643, _1675645, _1675647, _1675649] : [class_Groups_Ocomm__monoid__add(_1675643), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1675643), _1675645), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1675647, _1675649))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1675643), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1675643), _1675645), c_List_Oupto(_1675647, _1675649))))], (40709 ^ _779203) ^ [_1577354, _1577356] : [c_Wellfounded_Oacyclic(_1577354, _1577356), -(c_Wellfounded_Oacyclic(_1577354, hAPP(c_Relation_Oconverse(_1577354, _1577354), _1577356)))], (45661 ^ _779203) ^ [_1696765, _1696767, _1696769] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696765)), hAPP(c_List_Ofilter(_1696765, _1696767), _1696769))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696765)), _1696769))))], (49899 ^ _779203) ^ [_1788388, _1788390, _1788392, _1788394, _1788396] : [c_Fun_Obij__betw(_1788388, _1788390, _1788392, c_Orderings_Otop__class_Otop(tc_fun(_1788388, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788390, tc_HOL_Obool))), c_Fun_Obij__betw(_1788394, _1788388, _1788396, c_Orderings_Otop__class_Otop(tc_fun(_1788394, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788388, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1788394, _1788390, c_Orderings_Otop__class_Otop(tc_fun(_1788394, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1788388, _1788390, _1788394, _1788392), _1788396)) = hAPP(c_Fun_Ocomp(_1788388, _1788394, _1788390, c_Hilbert__Choice_Oinv__into(_1788394, _1788388, c_Orderings_Otop__class_Otop(tc_fun(_1788394, tc_HOL_Obool)), _1788396)), c_Hilbert__Choice_Oinv__into(_1788388, _1788390, c_Orderings_Otop__class_Otop(tc_fun(_1788388, tc_HOL_Obool)), _1788392)))], (40454 ^ _779203) ^ [_1571181, _1571183, _1571185] : [_1571183 = _1571185, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571181, _1571181)), hAPP(hAPP(c_Product__Type_OPair(_1571181, _1571181), _1571183), _1571185)), c_Relation_OId(_1571181))))], (42898 ^ _779203) ^ [_1634077, _1634079, _1634081, _1634083, _1634085] : [-(hAPP(hAPP(c_List_Ozip(_1634077, _1634079), _1634081), hAPP(hAPP(c_List_Olist_OCons(_1634079), _1634083), _1634085)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1634077, _1634079)), _1634077, c_List_Olist_ONil(tc_prod(_1634077, _1634079)), hAPP(hAPP(c_COMBC(_1634077, tc_fun(tc_List_Olist(_1634077), tc_List_Olist(tc_prod(_1634077, _1634079))), tc_fun(tc_List_Olist(_1634077), tc_List_Olist(tc_prod(_1634077, _1634079)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1634077, _1634079)), tc_List_Olist(tc_prod(_1634077, _1634079))), tc_fun(tc_fun(tc_List_Olist(_1634077), tc_List_Olist(tc_prod(_1634077, _1634079))), tc_fun(tc_List_Olist(_1634077), tc_List_Olist(tc_prod(_1634077, _1634079)))), _1634077), c_COMBB(tc_List_Olist(tc_prod(_1634077, _1634079)), tc_List_Olist(tc_prod(_1634077, _1634079)), tc_List_Olist(_1634077))), hAPP(hAPP(c_COMBB(tc_prod(_1634077, _1634079), tc_fun(tc_List_Olist(tc_prod(_1634077, _1634079)), tc_List_Olist(tc_prod(_1634077, _1634079))), _1634077), c_List_Olist_OCons(tc_prod(_1634077, _1634079))), hAPP(hAPP(c_COMBC(_1634077, _1634079, tc_prod(_1634077, _1634079)), c_Product__Type_OPair(_1634077, _1634079)), _1634083)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1634077), tc_List_Olist(_1634079), tc_List_Olist(tc_prod(_1634077, _1634079))), c_List_Ozip(_1634077, _1634079)), _1634085))), _1634081))], (6116 ^ _779203) ^ [_876830, _876832, _876834, _876836] : [hAPP(c_Set_Oimage(_876830, _876832, _876834), _876836) = c_Orderings_Obot__class_Obot(tc_fun(_876832, tc_HOL_Obool)), -(_876836 = c_Orderings_Obot__class_Obot(tc_fun(_876830, tc_HOL_Obool)))], (39734 ^ _779203) ^ [_1553212, _1553214, _1553216, _1553218, _1553220, _1553222] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1553212, _1553214), _1553212, tc_prod(_1553216, _1553218), c_Product__Type_Ofst(_1553212, _1553214)), c_Product__Type_Omap__pair(_1553216, _1553212, _1553218, _1553214, _1553220, _1553222)) = hAPP(c_Fun_Ocomp(_1553216, _1553212, tc_prod(_1553216, _1553218), _1553220), c_Product__Type_Ofst(_1553216, _1553218)))], (18502 ^ _779203) ^ [_1105546, _1105548] : [class_Rings_Osemiring__1(_1105546), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1105546), hAPP(c_Nat_OSuc, _1105548)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1105546), c_Groups_Oone__class_Oone(_1105546)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1105546), _1105548)))], (9725 ^ _779203) ^ [_945317, _945319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945317), hAPP(c_Nat_OSuc, _945319))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945317), _945319))), -(_945317 = _945319)], (21787 ^ _779203) ^ [_1162757, _1162759] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1162757)), _1162759) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1162757), _1162759))), _1162759))], (46820 ^ _779203) ^ [_1720916, _1720918, _1720920] : [c_List_OtakeWhile(_1720916, _1720918, _1720920) = _1720920, 46823 ^ _779203 : [(46824 ^ _779203) ^ [_1721003] : [hBOOL(hAPP(hAPP(c_member(_1720916), _1721003), hAPP(c_List_Oset(_1720916), _1720920))), -(hBOOL(hAPP(_1720918, _1721003)))]]], (51629 ^ _779203) ^ [_1822255] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822255), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_1822255 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (19860 ^ _779203) ^ [_1129471, _1129473] : [class_Groups_Ogroup__add(_1129471), 19863 ^ _779203 : [(19870 ^ _779203) ^ [] : [c_Groups_Ozero__class_Ozero(_1129471) = _1129473, -(c_Groups_Ozero__class_Ozero(_1129471) = hAPP(c_Groups_Ouminus__class_Ouminus(_1129471), _1129473))], (19864 ^ _779203) ^ [] : [c_Groups_Ozero__class_Ozero(_1129471) = hAPP(c_Groups_Ouminus__class_Ouminus(_1129471), _1129473), -(c_Groups_Ozero__class_Ozero(_1129471) = _1129473)]]], (14567 ^ _779203) ^ [_1032869, _1032871, _1032873, _1032875] : [class_Fields_Olinordered__field(_1032869), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032869), _1032871), c_Groups_Ozero__class_Ozero(_1032869))), 14574 ^ _779203 : [(14581 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032869), _1032875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032869), _1032873), _1032871))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032869), _1032873), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1032869), _1032875), _1032871))))], (14575 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032869), _1032873), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1032869), _1032875), _1032871))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1032869), _1032875), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1032869), _1032873), _1032871))))]]], (42467 ^ _779203) ^ [_1625659, _1625661] : [hBOOL(hAPP(c_List_Odistinct(_1625659), _1625661)), 42470 ^ _779203 : [(42471 ^ _779203) ^ [_1625791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625791), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625659)), _1625661))), 42474 ^ _779203 : [(42475 ^ _779203) ^ [_1625918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1625918), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1625659)), _1625661))), -(_1625791 = _1625918), hAPP(hAPP(c_List_Onth(_1625659), _1625661), _1625791) = hAPP(hAPP(c_List_Onth(_1625659), _1625661), _1625918)]]]]], (29072 ^ _779203) ^ [_1293661, _1293663] : [class_Complete__Lattice_Ocomplete__lattice(_1293661), hBOOL(hAPP(c_Finite__Set_Ofinite(_1293661), _1293663)), -(c_Complete__Lattice_OSup__class_OSup(_1293661, _1293663) = hAPP(hAPP(c_Finite__Set_Ofold(_1293661, _1293661, c_Lattices_Osemilattice__sup__class_Osup(_1293661)), c_Orderings_Obot__class_Obot(_1293661)), _1293663))], (43758 ^ _779203) ^ [_1654578, _1654580] : [hBOOL(hAPP(c_List_Odistinct(_1654578), _1654580)), -(hBOOL(hAPP(c_List_Odistinct(_1654578), hAPP(c_List_Otl(_1654578), _1654580))))], (22772 ^ _779203) ^ [_1180448, _1180450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180448), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180450), _1180448)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180448), _1180450) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13496 ^ _779203) ^ [_1013413, _1013415, _1013417, _1013419, _1013421] : [class_Groups_Ocomm__monoid__add(_1013413), class_Groups_Oordered__ab__semigroup__add(_1013413), hBOOL(hAPP(c_Finite__Set_Ofinite(_1013415), _1013417)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1013415, tc_HOL_Obool)), _1013419), _1013417)), 13514 ^ _779203 : [(13517 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013413), c_Groups_Ozero__class_Ozero(_1013413)), hAPP(_1013421, 13513 ^ [_1013413, _1013415, _1013417, _1013419, _1013421])))], (13515 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1013415), 13513 ^ [_1013413, _1013415, _1013417, _1013419, _1013421]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013415, tc_HOL_Obool)), _1013417), _1013419))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013413), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013415, _1013413), _1013421), _1013419)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1013415, _1013413), _1013421), _1013417))))], (1160 ^ _779203) ^ [_796663, _796665] : [-(class_Groups_Olinordered__ab__group__add(_796663)), _796665 = _796663, class_Groups_Olinordered__ab__group__add(_796665)], (3226 ^ _779203) ^ [_827262, _827264] : [_827264 = _827262, -(c_Random_Orange(_827264) = c_Random_Orange(_827262))], (10971 ^ _779203) ^ [_968555] : [hAPP(c_Nat_OSuc, _968555) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13747 ^ _779203) ^ [_1017965, _1017967, _1017969, _1017971] : [class_Fields_Olinordered__field(_1017965), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1017965), _1017967), c_Groups_Ozero__class_Ozero(_1017965))), 13754 ^ _779203 : [(13761 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017965), _1017971), _1017967)), _1017969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017965), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017965), _1017969), _1017967)), _1017971)))], (13755 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017965), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1017965), _1017969), _1017967)), _1017971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1017965), _1017971), _1017967)), _1017969)))]]], (7019 ^ _779203) ^ [_894774, _894776, _894778] : [hBOOL(hAPP(hAPP(c_member(_894774), _894776), _894778)), -(hAPP(hAPP(c_Set_Oinsert(_894774), _894776), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894774, tc_HOL_Obool)), _894778), hAPP(hAPP(c_Set_Oinsert(_894774), _894776), c_Orderings_Obot__class_Obot(tc_fun(_894774, tc_HOL_Obool))))) = _894778)], (32123 ^ _779203) ^ [_1359484, _1359486, _1359488, _1359490] : [class_Rings_Osemiring__1(_1359484), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1359486, _1359484), hAPP(c_COMBK(_1359484, _1359486), _1359488)), _1359490) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359484), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1359484), hAPP(c_Finite__Set_Ocard(_1359486), _1359490))), _1359488))], (36570 ^ _779203) ^ [_1467456, _1467458, _1467460, _1467462] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1467456), _1467458)), 36573 ^ _779203 : [(36580 ^ _779203) ^ [] : [hAPP(c_Finite__Set_Ocard(_1467460), hAPP(c_Set_Oimage(_1467456, _1467460, _1467462), _1467458)) = hAPP(c_Finite__Set_Ocard(_1467456), _1467458), -(c_Fun_Oinj__on(_1467456, _1467460, _1467462, _1467458))], (36574 ^ _779203) ^ [] : [c_Fun_Oinj__on(_1467456, _1467460, _1467462, _1467458), -(hAPP(c_Finite__Set_Ocard(_1467460), hAPP(c_Set_Oimage(_1467456, _1467460, _1467462), _1467458)) = hAPP(c_Finite__Set_Ocard(_1467456), _1467458))]]], (52353 ^ _779203) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (27194 ^ _779203) ^ [_1257929, _1257931, _1257933] : [class_Orderings_Olinorder(_1257929), 27197 ^ _779203 : [(27204 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257929), _1257933), _1257931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257929, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257929), _1257931)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257929), _1257933))))], (27198 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1257929, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257929), _1257931)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1257929), _1257933))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1257929), _1257933), _1257931)))]]], (48481 ^ _779203) ^ [_1757089, _1757091] : [hBOOL(hAPP(hAPP(c_List_Omember(_1757089), c_List_Olist_ONil(_1757089)), _1757091))], (39814 ^ _779203) ^ [_1555058, _1555060, _1555062, _1555064, _1555066, _1555068, _1555070] : [c_Finite__Set_Ofolding__image(_1555058, _1555060, _1555062, _1555064, _1555066), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555060), _1555068)), -(hAPP(hAPP(_1555066, _1555070), _1555068) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1555058, _1555060, _1555062), _1555070), _1555064), _1555068))], (11246 ^ _779203) ^ [_972823, _972825, _972827, _972829] : [11247 ^ _779203 : [(11250 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_972827), _972829)))], (11248 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_972823), _972825)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_972823, _972827)), c_Sum__Type_OPlus(_972823, _972827, _972825, _972829)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (24668 ^ _779203) ^ [_1213652, _1213654, _1213656] : [class_Rings_Olinordered__idom(_1213652), 24671 ^ _779203 : [(24680 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213652), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1213652), hAPP(hAPP(c_Power_Opower__class_Opower(_1213652), _1213654), 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(_1213652), _1213656), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1213652)))), _1213654 = c_Groups_Ozero__class_Ozero(_1213652), _1213656 = c_Groups_Ozero__class_Ozero(_1213652)], (24672 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213652), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1213652), hAPP(hAPP(c_Power_Opower__class_Opower(_1213652), _1213654), 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(_1213652), _1213656), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1213652))), 24675 ^ _779203 : [(24678 ^ _779203) ^ [] : [-(_1213656 = c_Groups_Ozero__class_Ozero(_1213652))], (24676 ^ _779203) ^ [] : [-(_1213654 = c_Groups_Ozero__class_Ozero(_1213652))]]]]], (15516 ^ _779203) ^ [_1051235, _1051237, _1051239, _1051241] : [class_Orderings_Olinorder(_1051235), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051235), _1051237), _1051239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051235), _1051237), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1051235), _1051241), _1051239))))], (45458 ^ _779203) ^ [_1691453, _1691455] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691453)), c_List_Oremdups(_1691453, _1691455)) = hAPP(c_Finite__Set_Ocard(_1691453), hAPP(c_List_Oset(_1691453), _1691455)))], (46871 ^ _779203) ^ [_1721944, _1721946] : [-(c_List_OtakeWhile(_1721944, _1721946, c_List_Olist_ONil(_1721944)) = c_List_Olist_ONil(_1721944))], (7497 ^ _779203) ^ [_903125, _903127, _903129] : [class_Orderings_Olinorder(_903125), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903125), _903127), _903129))), -(_903127 = _903129), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_903125), _903129), _903127)))], (32151 ^ _779203) ^ [_1360216] : [class_Orderings_Olinorder(_1360216), -(c_Orderings_Oord_Omin(_1360216, hAPP(c_COMBC(_1360216, _1360216, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1360216))) = c_Orderings_Oord__class_Omax(_1360216))], (30581 ^ _779203) ^ [_1325267] : [class_Complete__Lattice_Ocomplete__lattice(_1325267), -(c_Complete__Lattice_OSup__class_OSup(_1325267, c_Orderings_Otop__class_Otop(tc_fun(_1325267, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1325267))], (32129 ^ _779203) ^ [_1359629, _1359631, _1359633] : [class_Int_Onumber__ring(_1359629), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1359629), _1359631), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1359633))) = hAPP(hAPP(c_HOL_OLet(_1359629, _1359629), hAPP(hAPP(c_Power_Opower__class_Opower(_1359629), _1359631), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1359633))), hAPP(hAPP(c_COMBS(_1359629, _1359629, _1359629), c_Groups_Otimes__class_Otimes(_1359629)), c_COMBI(_1359629))))], (52391 ^ _779203) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (25846 ^ _779203) ^ [_1233861, _1233863, _1233865] : [class_Int_Oring__char__0(_1233861), 25849 ^ _779203 : [(25856 ^ _779203) ^ [] : [_1233863 = _1233865, -(hAPP(c_Int_Oring__1__class_Oof__int(_1233861), _1233863) = hAPP(c_Int_Oring__1__class_Oof__int(_1233861), _1233865))], (25850 ^ _779203) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1233861), _1233863) = hAPP(c_Int_Oring__1__class_Oof__int(_1233861), _1233865), -(_1233863 = _1233865)]]], (35057 ^ _779203) ^ [] : [-(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)))], (40781 ^ _779203) ^ [_1578861, _1578863, _1578865] : [-(hAPP(c_Relation_ORange(_1578861, _1578863), hAPP(c_Relation_Oconverse(_1578863, _1578861), _1578865)) = hAPP(c_Relation_ODomain(_1578863, _1578861), _1578865))], (48642 ^ _779203) ^ [_1760852] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1760852)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760852)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48354 ^ _779203) ^ [_1754099, _1754101] : [class_Lazy__Sequence_Osmall__lazy(_1754099), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1754099), _1754101) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1754099), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1754099)), c_List_Olist_ONil(_1754099)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1754099))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1754101)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1754099, tc_List_Olist(_1754099)), tc_List_Olist(_1754099), c_Lazy__Sequence_Oproduct(_1754099, tc_List_Olist(_1754099), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1754099, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1754101), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1754099), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1754101), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1754099, tc_List_Olist(_1754099), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1754099))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1754099), tc_List_Olist(_1754099)), tc_fun(tc_List_Olist(_1754099), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1754099))), _1754099), hAPP(c_COMBB(tc_List_Olist(_1754099), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1754099)), tc_List_Olist(_1754099)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1754099)))), c_List_Olist_OCons(_1754099))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1754099)))))], (2652 ^ _779203) ^ [_818303, _818305, _818307, _818309, _818311, _818313] : [-(c_FunDef_Oin__rel(_818313, _818309, _818305) = c_FunDef_Oin__rel(_818311, _818307, _818303)), _818313 = _818311, _818309 = _818307, _818305 = _818303], (17520 ^ _779203) ^ [_1088069] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1088069) = _1088069)], (10395 ^ _779203) ^ [_958287, _958289, _958291, _958293] : [class_Rings_Ocomm__semiring__1(_958287), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958287), _958289), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958287), _958291), _958293)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958287), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958287), _958289), _958291)), _958293))], (46774 ^ _779203) ^ [_1719879, _1719881] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1719879), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1719879))), _1719881))), 46777 ^ _779203 : [(46784 ^ _779203) ^ [] : [-(_1719881 = c_List_Olist_ONil(tc_List_Olist(_1719879))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719879))), c_List_Otranspose(_1719879, _1719881)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719879)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1719879)), _1719881), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (46778 ^ _779203) ^ [] : [_1719881 = c_List_Olist_ONil(tc_List_Olist(_1719879)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1719879))), c_List_Otranspose(_1719879, _1719881)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7025 ^ _779203) ^ [_894927, _894929, _894931] : [-(hBOOL(hAPP(hAPP(c_member(_894927), _894929), _894931))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_894927, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_894927), _894929), _894931)), hAPP(hAPP(c_Set_Oinsert(_894927), _894929), c_Orderings_Obot__class_Obot(tc_fun(_894927, tc_HOL_Obool)))) = _894931)], (37148 ^ _779203) ^ [_1480470, _1480472, _1480474, _1480476, _1480478, _1480480] : [-(_1480470 = c_Orderings_Obot__class_Obot(tc_fun(_1480472, tc_HOL_Obool))), 37154 ^ _779203 : [(37157 ^ _779203) ^ [] : [c_Fun_Oinj__on(_1480474, _1480476, _1480478, hAPP(_1480480, 37153 ^ [_1480470, _1480472, _1480474, _1480476, _1480478, _1480480]))], (37155 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1480472), 37153 ^ [_1480470, _1480472, _1480474, _1480476, _1480478, _1480480]), _1480470)))]], -(c_Fun_Oinj__on(_1480474, _1480476, _1480478, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1480472, tc_fun(_1480474, tc_HOL_Obool)), _1480470), _1480480)))], (34953 ^ _779203) ^ [] : [-(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)))], (47280 ^ _779203) ^ [_1731009, _1731011, _1731013, _1731015, _1731017, _1731019, _1731021, _1731023] : [47282 ^ _779203 : [(47285 ^ _779203) ^ [] : [hAPP(c_Fun_Ocomp(_1731013, _1731013, _1731015, hAPP(_1731017, 47281 ^ [_1731009, _1731011, _1731013, _1731015, _1731017, _1731019, _1731021, _1731023])), _1731019) = hAPP(c_Fun_Ocomp(_1731015, _1731013, _1731015, _1731019), hAPP(_1731021, 47281 ^ [_1731009, _1731011, _1731013, _1731015, _1731017, _1731019, _1731021, _1731023]))], (47283 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1731009), 47281 ^ [_1731009, _1731011, _1731013, _1731015, _1731017, _1731019, _1731021, _1731023]), hAPP(c_List_Oset(_1731009), _1731011))))]], -(hAPP(c_List_Ofoldl(_1731013, _1731009, hAPP(c_COMBC(_1731009, _1731013, _1731013), _1731017), hAPP(_1731019, _1731023)), _1731011) = hAPP(_1731019, hAPP(c_List_Ofoldl(_1731015, _1731009, hAPP(c_COMBC(_1731009, _1731015, _1731015), _1731021), _1731023), _1731011)))], (32902 ^ _779203) ^ [_1381808, _1381810, _1381812] : [hBOOL(hAPP(_1381808, hAPP(hAPP(c_Product__Type_OPair(_1381810, _1381812), 32903 ^ [_1381808, _1381810, _1381812]), 32904 ^ [_1381808, _1381810, _1381812]))), 32907 ^ _779203 : [(32908 ^ _779203) ^ [_1381955] : [-(hBOOL(hAPP(_1381808, _1381955)))]]], (34821 ^ _779203) ^ [_1424903, _1424905, _1424907, _1424909, _1424911] : [_1424903 = c_Orderings_Obot__class_Obot(tc_fun(_1424905, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1424907, tc_HOL_Obool)), _1424909), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424905, tc_fun(_1424907, tc_HOL_Obool)), _1424903), _1424911)) = _1424909)], (34316 ^ _779203) ^ [_1409959, _1409961, _1409963, _1409965, _1409967] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409959, tc_fun(_1409961, tc_HOL_Obool)), _1409963), hAPP(hAPP(c_COMBC(_1409959, tc_fun(_1409961, tc_HOL_Obool), tc_fun(_1409961, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409961, tc_HOL_Obool), tc_fun(tc_fun(_1409961, tc_HOL_Obool), tc_fun(_1409961, tc_HOL_Obool)), _1409959), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409961, tc_HOL_Obool))), _1409965)), _1409967)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409961, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1409959, tc_fun(_1409961, tc_HOL_Obool)), _1409963), _1409965)), _1409967))], (37393 ^ _779203) ^ [_1486643, _1486645, _1486647, _1486649, _1486651] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1486643, _1486645), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1486643, tc_HOL_Obool)), _1486647), _1486649)), _1486651) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1486643, _1486645), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1486643, _1486645), _1486647), _1486651)), hAPP(hAPP(c_Product__Type_OSigma(_1486643, _1486645), _1486649), _1486651)))], (39736 ^ _779203) ^ [_1553283, _1553285, _1553287, _1553289, _1553291, _1553293] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1553283, _1553285), _1553285, tc_prod(_1553287, _1553289), c_Product__Type_Osnd(_1553283, _1553285)), c_Product__Type_Omap__pair(_1553287, _1553283, _1553289, _1553285, _1553291, _1553293)) = hAPP(c_Fun_Ocomp(_1553289, _1553285, tc_prod(_1553287, _1553289), _1553293), c_Product__Type_Osnd(_1553287, _1553289)))], (32419 ^ _779203) ^ [_1366445, _1366447] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366445)), hAPP(c_Nat_OSuc, _1366447)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1366445))), 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, _1366447))), 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)), _1366447)))))], (35097 ^ _779203) ^ [_1432059, _1432061, _1432063, _1432065] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1432059), _1432061)), 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)), _1432059), _1432063)), 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)), _1432061), _1432065)), 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)), _1432061), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1432063), _1432065))), c_FunDef_Omin__strict)))], (35651 ^ _779203) ^ [_1447188, _1447190, _1447192] : [-(hAPP(c_Relation_OImage(_1447188, _1447188, c_Relation_OId__on(_1447188, _1447190)), _1447192) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1447188, tc_HOL_Obool)), _1447190), _1447192))], (22836 ^ _779203) ^ [_1181553, _1181555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181555)), 22843 ^ _779203 : [(22850 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181553), _1181555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1181553)), hAPP(c_Int_Onat, _1181555))))], (22844 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1181553)), hAPP(c_Int_Onat, _1181555))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181553), _1181555)))]]], (9905 ^ _779203) ^ [_948268, _948270] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _948268), _948270))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _948270), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948268), _948270)) = _948268)], (52239 ^ _779203) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (31749 ^ _779203) ^ [_1349724, _1349726, _1349728] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349724, tc_Nat_Onat), _1349726), _1349728) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1349724, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1349724), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1349726)), _1349728)))], (25594 ^ _779203) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (38364 ^ _779203) ^ [_1518759, _1518761, _1518763, _1518765] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1518759, _1518761, _1518763), _1518765), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518761, _1518763), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1518759, _1518763), tc_HOL_Obool)))], (15980 ^ _779203) ^ [_1059664] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1059664), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1059664)], (7579 ^ _779203) ^ [_904413, _904415, _904417] : [class_Orderings_Olinorder(_904413), 7582 ^ _779203 : [(7589 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904413), _904417), _904415)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904413), _904415), _904417))], (7583 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904413), _904415), _904417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904413), _904417), _904415)))]]], (8601 ^ _779203) ^ [_924079, _924081] : [class_Groups_Ocomm__monoid__mult(_924079), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_924079), _924081), c_Groups_Oone__class_Oone(_924079)) = _924081)], (28138 ^ _779203) ^ [_1276372, _1276374] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1276372), c_Orderings_Otop__class_Otop(tc_fun(_1276372, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1276372), _1276374) = hAPP(c_Finite__Set_Ocard(_1276372), c_Orderings_Otop__class_Otop(tc_fun(_1276372, tc_HOL_Obool))), -(_1276374 = c_Orderings_Otop__class_Otop(tc_fun(_1276372, tc_HOL_Obool)))], (42236 ^ _779203) ^ [_1620366, _1620368, _1620370, _1620372] : [42238 ^ _779203 : [(42241 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1620370, 42237 ^ [_1620366, _1620368, _1620370, _1620372])), hAPP(_1620372, 42237 ^ [_1620366, _1620368, _1620370, _1620372])))], (42239 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620366), 42237 ^ [_1620366, _1620368, _1620370, _1620372]), hAPP(c_List_Oset(_1620366), _1620368))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1620366, _1620370, _1620368)), c_List_Olist_Olist__size(_1620366, _1620372, _1620368))))], (19524 ^ _779203) ^ [_1123445] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1123445)), 19528 ^ _779203 : [(19529 ^ _779203) ^ [_1123525] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1123525), _1123445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1123525), 19527 ^ [_1123445])))]]], (1064 ^ _779203) ^ [_795221, _795223, _795225, _795227, _795229, _795231] : [-(c_List_Oall__interval__nat(_795229, _795225, _795221)), c_List_Oall__interval__nat(_795231, _795227, _795223), _795231 = _795229, _795227 = _795225, _795223 = _795221], (31273 ^ _779203) ^ [_1339302, _1339304, _1339306, _1339308, _1339310] : [class_Groups_Ocomm__monoid__mult(_1339302), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339304), _1339306)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1339304), _1339308)), 31287 ^ _779203 : [(31290 ^ _779203) ^ [] : [hAPP(_1339310, 31286 ^ [_1339302, _1339304, _1339306, _1339308, _1339310]) = c_Groups_Oone__class_Oone(_1339302)], (31288 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1339304), 31286 ^ [_1339302, _1339304, _1339306, _1339308, _1339310]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339304, tc_HOL_Obool)), _1339306), _1339308))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1339302, _1339304, c_Groups_Otimes__class_Otimes(_1339302)), _1339310), c_Groups_Oone__class_Oone(_1339302)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1339304, tc_HOL_Obool)), _1339306), _1339308)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339302), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1339302, _1339304, c_Groups_Otimes__class_Otimes(_1339302)), _1339310), c_Groups_Oone__class_Oone(_1339302)), _1339306)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1339302, _1339304, c_Groups_Otimes__class_Otimes(_1339302)), _1339310), c_Groups_Oone__class_Oone(_1339302)), _1339308)))], (37916 ^ _779203) ^ [_1502130, _1502132, _1502134, _1502136] : [-(c_Nitpick_Oprod(_1502130, _1502132, _1502134, _1502136) = hAPP(c_Set_OCollect(tc_prod(_1502130, _1502132)), hAPP(c_Product__Type_Oprod_Oprod__case(_1502130, _1502132, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1502130, tc_fun(_1502132, tc_HOL_Obool), tc_fun(_1502132, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1502132, tc_HOL_Obool), tc_fun(_1502132, tc_HOL_Obool)), _1502130), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1502132)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1502130), c_fconj), hAPP(hAPP(c_COMBC(_1502130, tc_fun(_1502130, tc_HOL_Obool), tc_HOL_Obool), c_member(_1502130)), _1502134)))), hAPP(hAPP(c_COMBC(_1502132, tc_fun(_1502132, tc_HOL_Obool), tc_HOL_Obool), c_member(_1502132)), _1502136)))))], (25392 ^ _779203) ^ [_1227124, _1227126] : [class_Int_Onumber__ring(_1227124), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1227124), hAPP(c_Int_Onumber__class_Onumber__of(_1227124), 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)))), _1227126)) = c_Groups_Oone__class_Oone(_1227124))], (46562 ^ _779203) ^ [_1715452, _1715454] : [c_List_Olist_ONil(_1715452) = hAPP(c_List_Orev(_1715452), _1715454), -(_1715454 = c_List_Olist_ONil(_1715452))], (51259 ^ _779203) ^ [_1816102, _1816104] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816102), _1816104)), 51264 ^ _779203 : [(51267 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816104), _1816102))], (51265 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1816102), _1816104)))]], -(_1816102 = _1816104)], (4710 ^ _779203) ^ [_850862, _850864, _850866, _850868] : [-(c_List_Olexord(_850868, _850864) = c_List_Olexord(_850866, _850862)), _850868 = _850866, _850864 = _850862], (23890 ^ _779203) ^ [_1199638, _1199640, _1199642] : [-(hBOOL(hAPP(_1199638, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1199640), _1199642)))), 23893 ^ _779203 : [(23896 ^ _779203) ^ [] : [hBOOL(hAPP(_1199638, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23894 ^ _779203) ^ [] : [-(_1199642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 23897 ^ _779203 : [(23902 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 23900 ^ [_1199638, _1199640, _1199642]), _1199642)))], (23904 ^ _779203) ^ [] : [-(_1199640 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1199642), 23899 ^ [_1199638, _1199640, _1199642])), 23900 ^ [_1199638, _1199640, _1199642]))], (23906 ^ _779203) ^ [] : [hBOOL(hAPP(_1199638, 23899 ^ [_1199638, _1199640, _1199642]))], (23898 ^ _779203) ^ [] : [_1199642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (37910 ^ _779203) ^ [_1501807, _1501809, _1501811, _1501813] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1501807, _1501809), _1501811), _1501813) = hAPP(c_Set_OCollect(tc_prod(_1501809, _1501809)), hAPP(c_Product__Type_Oprod_Oprod__case(_1501809, _1501809, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1501809, tc_fun(tc_prod(_1501807, _1501807), tc_HOL_Obool), tc_fun(_1501809, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501809, tc_fun(tc_fun(tc_prod(_1501807, _1501807), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1501807, _1501807), tc_HOL_Obool), tc_fun(_1501809, tc_HOL_Obool)), _1501809), c_COMBC(_1501809, tc_fun(tc_prod(_1501807, _1501807), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1501809, tc_prod(_1501807, _1501807)), tc_fun(_1501809, tc_fun(tc_fun(tc_prod(_1501807, _1501807), tc_HOL_Obool), tc_HOL_Obool)), _1501809), hAPP(c_COMBB(tc_prod(_1501807, _1501807), tc_fun(tc_fun(tc_prod(_1501807, _1501807), tc_HOL_Obool), tc_HOL_Obool), _1501809), c_member(tc_prod(_1501807, _1501807)))), hAPP(hAPP(c_COMBC(_1501809, tc_fun(_1501809, _1501807), tc_fun(_1501809, tc_prod(_1501807, _1501807))), hAPP(hAPP(c_COMBB(tc_fun(_1501807, tc_prod(_1501807, _1501807)), tc_fun(tc_fun(_1501809, _1501807), tc_fun(_1501809, tc_prod(_1501807, _1501807))), _1501809), c_COMBB(_1501807, tc_prod(_1501807, _1501807), _1501809)), hAPP(hAPP(c_COMBB(_1501807, tc_fun(_1501807, tc_prod(_1501807, _1501807)), _1501809), c_Product__Type_OPair(_1501807, _1501807)), _1501813))), _1501813)))), _1501811))))], (17040 ^ _779203) ^ [_1079117, _1079119, _1079121] : [class_Orderings_Olinorder(_1079117), -(_1079119 = c_Orderings_Obot__class_Obot(tc_fun(_1079117, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1079117, tc_HOL_Obool)), _1079119), _1079121)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079117), _1079121)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079117), hAPP(c_Finite__Set_Ofold1(_1079117, c_Orderings_Oord__class_Omin(_1079117)), _1079121)), hAPP(c_Finite__Set_Ofold1(_1079117, c_Orderings_Oord__class_Omin(_1079117)), _1079119))))], (29922 ^ _779203) ^ [_1311641, _1311643, _1311645, _1311647] : [class_Orderings_Olinorder(_1311641), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311641, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1311641), _1311643)), c_SetInterval_Oord__class_OatLeastAtMost(_1311641, _1311645, _1311647)) = c_SetInterval_Oord__class_OatLeastAtMost(_1311641, _1311645, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311641), _1311643), _1311647)))], (10744 ^ _779203) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (52261 ^ _779203) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11526 ^ _779203) ^ [_977919, _977921, _977923] : [class_Rings_Oordered__ring(_977919), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977919), _977921), c_Groups_Ozero__class_Ozero(_977919))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977919), _977923), c_Groups_Ozero__class_Ozero(_977919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977919), c_Groups_Ozero__class_Ozero(_977919)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_977919), _977921), _977923))))], (21171 ^ _779203) ^ [_1152578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1152578)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152578), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33803 ^ _779203) ^ [_1398307, _1398309, _1398311] : [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), _1398307), _1398309))), -(hBOOL(hAPP(hAPP(_1398311, _1398307), _1398309))), 33810 ^ _779203 : [(33813 ^ _779203) ^ [] : [-(33809 ^ [_1398307, _1398309, _1398311] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1398311, 33809 ^ [_1398307, _1398309, _1398311]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 33808 ^ [_1398307, _1398309, _1398311], 33809 ^ [_1398307, _1398309, _1398311]))))], (33819 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1398311, 33808 ^ [_1398307, _1398309, _1398311]), 33809 ^ [_1398307, _1398309, _1398311]))], (33811 ^ _779203) ^ [] : [-(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), 33808 ^ [_1398307, _1398309, _1398311]), 33809 ^ [_1398307, _1398309, _1398311]))))]]], (44033 ^ _779203) ^ [_1660575] : [class_Orderings_Olinorder(_1660575), -(c_Finite__Set_Ofun__left__comm(_1660575, tc_List_Olist(_1660575), c_List_Olinorder__class_Oinsort__key(_1660575, _1660575, c_COMBI(_1660575))))], (42230 ^ _779203) ^ [_1620287] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1620287)), -(c_List_Onat__list(_1620287))], (13361 ^ _779203) ^ [_1010670, _1010672] : [_1010670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1010670), _1010672) = _1010672)], (32535 ^ _779203) ^ [_1369439, _1369441, _1369443, _1369445] : [-(c_Nat_Onat_Onat__case(_1369439, _1369441, _1369443, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369445)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1369439), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1369445))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1369439, _1369439), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1369439, tc_fun(_1369439, _1369439)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1369439, tc_fun(_1369439, _1369439)), tc_Int_Oint), c_If(_1369439)), c_Nat__Numeral_Oneg)), _1369441)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1369439, tc_Int_Oint), _1369443), c_Int_Onat))))], (8121 ^ _779203) ^ [_913935, _913937, _913939, _913941, _913943] : [8123 ^ _779203 : [(8126 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_913939), hAPP(_913941, 8122 ^ [_913935, _913937, _913939, _913941, _913943])), _913943))], (8124 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_913935), 8122 ^ [_913935, _913937, _913939, _913941, _913943]), _913937)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913939, tc_HOL_Obool)), hAPP(c_Set_Oimage(_913935, _913939, _913941), _913937)), _913943)))], (34454 ^ _779203) ^ [_1414113, _1414115, _1414117, _1414119, _1414121, _1414123] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414113, tc_fun(_1414115, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1414117, _1414113, _1414119), _1414121)), _1414123) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1414117, tc_fun(_1414115, tc_HOL_Obool)), _1414121), hAPP(hAPP(c_COMBB(_1414113, tc_fun(_1414115, tc_HOL_Obool), _1414117), _1414123), _1414119)))], (21069 ^ _779203) ^ [_1150581, _1150583] : [class_Int_Onumber__ring(_1150581), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1150581), hAPP(c_Int_Onumber__class_Onumber__of(_1150581), _1150583)), c_Groups_Oone__class_Oone(_1150581)) = hAPP(c_Int_Onumber__class_Onumber__of(_1150581), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1150583), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (44616 ^ _779203) ^ [_1673224, _1673226] : [hAPP(c_Code__Numeral_Oof__nat, _1673224) = hAPP(c_Code__Numeral_Oof__nat, _1673226), -(_1673224 = _1673226)], (28630 ^ _779203) ^ [_1285672, _1285674, _1285676, _1285678] : [28631 ^ _779203 : [(28634 ^ _779203) ^ [] : [hBOOL(hAPP(_1285676, _1285674))], (28632 ^ _779203) ^ [] : [hBOOL(hAPP(_1285672, _1285674))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1285678, tc_HOL_Obool)), _1285676), _1285672), _1285674)))], (52407 ^ _779203) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (12464 ^ _779203) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (49973 ^ _779203) ^ [_1789956, _1789958, _1789960, _1789962, _1789964] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1789956, _1789958, tc_HOL_Obool, _1789960), _1789962), _1789964)), -(hBOOL(hAPP(_1789960, hAPP(hAPP(c_Product__Type_OPair(_1789956, _1789958), _1789962), _1789964))))], (9797 ^ _779203) ^ [_946463, _946465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946463), hAPP(c_Nat_OSuc, _946465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946463), _946465))), -(_946463 = hAPP(c_Nat_OSuc, _946465))], (8194 ^ _779203) ^ [_915246, _915248, _915250] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_915246), _915248)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_915246, tc_HOL_Obool)), _915250), _915248)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_915246), _915250)), hAPP(c_Finite__Set_Ocard(_915246), _915248))))], (15384 ^ _779203) ^ [_1048862, _1048864] : [class_Orderings_Olinorder(_1048862), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1048862), _1048864), _1048864) = _1048864)], (38780 ^ _779203) ^ [_1530173, _1530175] : [-(hAPP(c_Relation_ODomain(_1530173, _1530175), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530173, _1530175), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1530173, tc_HOL_Obool)))], (25540 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (44580 ^ _779203) ^ [_1672335, _1672337, _1672339, _1672341, _1672343] : [class_Groups_Ocomm__monoid__add(_1672335), hBOOL(hAPP(hAPP(c_member(_1672337), _1672339), hAPP(c_List_Oset(_1672337), _1672341))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672335), hAPP(hAPP(c_List_Omap(_1672337, _1672335), _1672343), _1672341)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1672335), hAPP(_1672343, _1672339)), hAPP(c_List_Omonoid__add__class_Olistsum(_1672335), hAPP(hAPP(c_List_Omap(_1672337, _1672335), _1672343), c_List_Oremove1(_1672337, _1672339, _1672341)))))], (26112 ^ _779203) ^ [_1238277, _1238279] : [-(c_Nitpick_Onat__lcm(_1238277, _1238279) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1238277), _1238279)), c_Nitpick_Onat__gcd(_1238277, _1238279)))], (40675 ^ _779203) ^ [_1576423] : [-(hAPP(c_Relation_Oconverse(_1576423, _1576423), c_Relation_OId(_1576423)) = c_Relation_OId(_1576423))], (49320 ^ _779203) ^ [_1776474, _1776476] : [c_Relation_Osym(_1776474, _1776476), -(hAPP(c_Relation_Oconverse(_1776474, _1776474), _1776476) = _1776476)], (50502 ^ _779203) ^ [_1802569, _1802571, _1802573] : [c_List_Olist__all(tc_Nat_Onat, _1802569, c_List_Oupt(_1802571, _1802573)), -(c_List_Oall__interval__nat(_1802569, _1802571, _1802573))], (52343 ^ _779203) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (44875 ^ _779203) ^ [_1678286, _1678288, _1678290, _1678292, _1678294] : [c_List_Opartition(_1678286, _1678288, _1678290) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1678286), tc_List_Olist(_1678286)), _1678292), _1678294), 44878 ^ _779203 : [(44885 ^ _779203) ^ [_1678548] : [hBOOL(hAPP(hAPP(c_member(_1678286), _1678548), hAPP(c_List_Oset(_1678286), _1678294))), hBOOL(hAPP(_1678288, _1678548))], (44879 ^ _779203) ^ [_1678439] : [hBOOL(hAPP(hAPP(c_member(_1678286), _1678439), hAPP(c_List_Oset(_1678286), _1678292))), -(hBOOL(hAPP(_1678288, _1678439)))]]], (27726 ^ _779203) ^ [_1267797, _1267799] : [-(c_Sum__Type_OPlus(_1267797, _1267799, c_Orderings_Otop__class_Otop(tc_fun(_1267797, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1267799, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1267797, _1267799), tc_HOL_Obool)))], (42730 ^ _779203) ^ [_1630878, _1630880, _1630882, _1630884] : [hAPP(hAPP(c_List_Olist__update(_1630878, _1630880), _1630882), _1630884) = c_List_Olist_ONil(_1630878), -(_1630880 = c_List_Olist_ONil(_1630878))], (42055 ^ _779203) ^ [_1614554, _1614556] : [-(c_List_Olists(_1614554, _1614556) = hAPP(c_Set_OCollect(tc_List_Olist(_1614554)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1614554), tc_fun(_1614554, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1614554, tc_HOL_Obool), tc_fun(tc_fun(_1614554, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1614554)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1614554, tc_HOL_Obool))), c_List_Oset(_1614554))), _1614556)))], (48054 ^ _779203) ^ [_1747800, _1747802, _1747804] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747800)), c_List_Osplice(_1747800, _1747802, _1747804)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747800)), _1747802)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1747800)), _1747804)))], (39323 ^ _779203) ^ [_1543670] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 39319 ^ [_1543670]), c_Int_OInteg)))], (3482 ^ _779203) ^ [_831190, _831192] : [_831192 = _831190, -(c_SetInterval_Oord__class_OatMost(_831192) = c_SetInterval_Oord__class_OatMost(_831190))], (10837 ^ _779203) ^ [_966554, _966556] : [class_Rings_Omult__zero(_966554), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_966554), c_Groups_Ozero__class_Ozero(_966554)), _966556) = c_Groups_Ozero__class_Ozero(_966554))], (29940 ^ _779203) ^ [_1312058, _1312060, _1312062] : [class_Orderings_Oorder(_1312058), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312058, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1312058, _1312060, _1312062)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1312058), _1312062)) = c_Orderings_Obot__class_Obot(tc_fun(_1312058, tc_HOL_Obool)))], (41842 ^ _779203) ^ [_1609272, _1609274, _1609276, _1609278] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609272) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1609274), hAPP(hAPP(c_List_Olist_OCons(_1609274), _1609276), _1609278)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609272)) = _1609276)], (39147 ^ _779203) ^ [_1538935, _1538937, _1538939] : [c_Wellfounded_Oacyclic(_1538935, _1538937), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1538935, _1538935), tc_HOL_Obool)), _1538939), _1538937)), -(c_Wellfounded_Oacyclic(_1538935, _1538939))], (19384 ^ _779203) ^ [_1120805, _1120807, _1120809] : [class_Groups_Oordered__ab__group__add__abs(_1120805), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1120805), hAPP(c_Groups_Oabs__class_Oabs(_1120805), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1120805), _1120807), _1120809))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1120805), hAPP(c_Groups_Oabs__class_Oabs(_1120805), _1120807)), hAPP(c_Groups_Oabs__class_Oabs(_1120805), _1120809)))))], (22484 ^ _779203) ^ [_1175647, _1175649, _1175651, _1175653] : [class_Divides_Osemiring__div(_1175647), -(_1175649 = c_Groups_Ozero__class_Ozero(_1175647)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1175647), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175647), _1175651), _1175649)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175647), _1175653), _1175649)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1175647), _1175651), _1175653))], (34917 ^ _779203) ^ [_1427509, _1427511, _1427513, _1427515, _1427517] : [-(_1427509 = c_Orderings_Obot__class_Obot(tc_fun(_1427511, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427513, tc_HOL_Obool)), _1427515), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427511, tc_fun(_1427513, tc_HOL_Obool)), _1427509), _1427517)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427511, tc_fun(_1427513, tc_HOL_Obool)), _1427509), hAPP(hAPP(c_COMBB(tc_fun(_1427513, tc_HOL_Obool), tc_fun(_1427513, tc_HOL_Obool), _1427511), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427513, tc_HOL_Obool)), _1427515)), _1427517)))], (44221 ^ _779203) ^ [_1663690, _1663692, _1663694] : [-(c_List_Olast(_1663690, hAPP(hAPP(c_List_Oappend(_1663690), _1663692), hAPP(hAPP(c_List_Olist_OCons(_1663690), _1663694), c_List_Olist_ONil(_1663690)))) = _1663694)], (11852 ^ _779203) ^ [_983770, _983772, _983774] : [class_Rings_Olinordered__semiring__strict(_983770), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983770), c_Groups_Ozero__class_Ozero(_983770)), _983772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983770), _983774), c_Groups_Ozero__class_Ozero(_983770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983770), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983770), _983772), _983774)), c_Groups_Ozero__class_Ozero(_983770))))], (43173 ^ _779203) ^ [_1640818, _1640820, _1640822] : [hAPP(hAPP(c_List_Oappend(_1640818), _1640820), _1640822) = _1640820, -(_1640822 = c_List_Olist_ONil(_1640818))], (51071 ^ _779203) ^ [_1812927, _1812929, _1812931, _1812933] : [class_Divides_Osemiring__div(_1812927), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812927), _1812929), _1812931)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1812927), _1812929), _1812933)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812927), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1812927), _1812931), _1812933)), _1812929) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1812927), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812927), _1812931), _1812929)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1812927), _1812933), _1812929)))], (44099 ^ _779203) ^ [_1661820, _1661822, _1661824] : [class_Orderings_Olinorder(_1661820), -(hBOOL(hAPP(hAPP(c_member(_1661820), _1661822), hAPP(c_List_Oset(_1661820), _1661824)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1661820, _1661820, c_COMBI(_1661820), _1661822, _1661824) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1661820, _1661820, c_COMBI(_1661820)), _1661822), _1661824))], (45216 ^ _779203) ^ [_1686484, _1686486, _1686488, _1686490, _1686492, _1686494, _1686496, _1686498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686484), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686486)), _1686488))), c_List_Olist__all2(_1686486, _1686490, _1686492, _1686488, _1686494), hBOOL(hAPP(hAPP(_1686492, _1686496), _1686498)), -(c_List_Olist__all2(_1686486, _1686490, _1686492, hAPP(hAPP(c_List_Olist__update(_1686486, _1686488), _1686484), _1686496), hAPP(hAPP(c_List_Olist__update(_1686490, _1686494), _1686484), _1686498)))], (35677 ^ _779203) ^ [_1447786, _1447788, _1447790, _1447792] : [_1447786 = _1447788, hBOOL(hAPP(hAPP(c_member(_1447790), _1447786), _1447792)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1447790, _1447790)), hAPP(hAPP(c_Product__Type_OPair(_1447790, _1447790), _1447786), _1447788)), c_Relation_OId__on(_1447790, _1447792))))], (34037 ^ _779203) ^ [_1403012, _1403014, _1403016, _1403018, _1403020, _1403022] : [-(c_Product__Type_Oprod_Oprod__rec(_1403012, _1403014, _1403016, _1403018, hAPP(hAPP(c_Product__Type_OPair(_1403012, _1403014), _1403020), _1403022)) = hAPP(hAPP(_1403018, _1403020), _1403022))], (5510 ^ _779203) ^ [_863438, _863440, _863442, _863444] : [-(tc_prod(_863444, _863440) = tc_prod(_863442, _863438)), _863444 = _863442, _863440 = _863438], (21793 ^ _779203) ^ [] : [-(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))], (37333 ^ _779203) ^ [_1484963, _1484965, _1484967, _1484969, _1484971, _1484973] : [-(hBOOL(hAPP(hAPP(c_member(_1484963), _1484965), _1484967))), 37336 ^ _779203 : [(37343 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1484963), _1484969), _1484967))), -(hAPP(c_Set_Ovimage(_1484971, _1484963, hAPP(hAPP(c_COMBC(_1484971, _1484963, _1484963), hAPP(hAPP(c_COMBC(_1484971, _1484963, tc_fun(_1484963, _1484963)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1484963, tc_fun(_1484963, _1484963)), _1484971), c_If(_1484963)), hAPP(hAPP(c_COMBC(_1484971, tc_fun(_1484971, tc_HOL_Obool), tc_HOL_Obool), c_member(_1484971)), _1484973))), _1484965)), _1484969)), _1484967) = c_Orderings_Obot__class_Obot(tc_fun(_1484971, tc_HOL_Obool)))], (37337 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1484963), _1484969), _1484967)), -(hAPP(c_Set_Ovimage(_1484971, _1484963, hAPP(hAPP(c_COMBC(_1484971, _1484963, _1484963), hAPP(hAPP(c_COMBC(_1484971, _1484963, tc_fun(_1484963, _1484963)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1484963, tc_fun(_1484963, _1484963)), _1484971), c_If(_1484963)), hAPP(hAPP(c_COMBC(_1484971, tc_fun(_1484971, tc_HOL_Obool), tc_HOL_Obool), c_member(_1484971)), _1484973))), _1484965)), _1484969)), _1484967) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1484971, tc_HOL_Obool)), _1484973))]]], (37231 ^ _779203) ^ [_1482467, _1482469, _1482471, _1482473] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1482467, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1482469, _1482467, _1482471), hAPP(c_Set_Ovimage(_1482469, _1482467, _1482471), _1482473))), _1482473)))], (13597 ^ _779203) ^ [_1015493, _1015495, _1015497, _1015499] : [class_Rings_Odivision__ring(_1015493), -(_1015495 = c_Groups_Ozero__class_Ozero(_1015493)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1015493), _1015497), _1015495) = _1015499, -(_1015497 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1015493), _1015499), _1015495))], (40957 ^ _779203) ^ [_1583393, _1583395, _1583397] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583393, _1583393)), _1583395), c_Transitive__Closure_Ortrancl(_1583393, _1583397))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583393, _1583393)), _1583395), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583393, _1583393), tc_HOL_Obool), 40960 ^ [_1583393, _1583395, _1583397]), _1583397))))], (35509 ^ _779203) ^ [_1443361, _1443363, _1443365, _1443367, _1443369] : [hBOOL(hAPP(hAPP(c_member(_1443361), _1443363), hAPP(c_Relation_OImage(_1443365, _1443361, _1443367), hAPP(hAPP(c_Set_Oinsert(_1443365), _1443369), c_Orderings_Obot__class_Obot(tc_fun(_1443365, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1443365, _1443361)), hAPP(hAPP(c_Product__Type_OPair(_1443365, _1443361), _1443369), _1443363)), _1443367)))], (43155 ^ _779203) ^ [_1640487, _1640489, _1640491] : [_1640487 = _1640489, -(_1640487 = hAPP(hAPP(c_List_Oappend(_1640491), c_List_Olist_ONil(_1640491)), _1640489))], (48266 ^ _779203) ^ [_1752558, _1752560, _1752562, _1752564] : [-(hAPP(hAPP(c_List_Oappend(_1752558), c_List_Oreplicate(_1752558, _1752560, _1752562)), c_List_Oreplicate(_1752558, _1752564, _1752562)) = hAPP(hAPP(c_List_Oappend(_1752558), c_List_Oreplicate(_1752558, _1752564, _1752562)), c_List_Oreplicate(_1752558, _1752560, _1752562)))], (42820 ^ _779203) ^ [_1632669, _1632671, _1632673] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1632669)), -(c_List_Osublist(_1632671, hAPP(hAPP(c_List_Olist_OCons(_1632671), _1632673), c_List_Olist_ONil(_1632671)), _1632669) = hAPP(hAPP(c_List_Olist_OCons(_1632671), _1632673), c_List_Olist_ONil(_1632671)))], (37777 ^ _779203) ^ [_1497073, _1497075, _1497077, _1497079] : [-(_1497073 = c_Orderings_Obot__class_Obot(tc_fun(_1497075, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1497075, _1497077), _1497077, c_Product__Type_Osnd(_1497075, _1497077)), hAPP(hAPP(c_Product__Type_OSigma(_1497075, _1497077), _1497073), hAPP(c_COMBK(tc_fun(_1497077, tc_HOL_Obool), _1497075), _1497079))) = _1497079)], (42736 ^ _779203) ^ [_1630981, _1630983, _1630985, _1630987] : [_1630983 = c_List_Olist_ONil(_1630981), -(hAPP(hAPP(c_List_Olist__update(_1630981, _1630983), _1630985), _1630987) = c_List_Olist_ONil(_1630981))], (46853 ^ _779203) ^ [_1721676, _1721678, _1721680, _1721682, _1721684] : [-(hBOOL(hAPP(_1721676, _1721678))), -(c_List_OtakeWhile(_1721680, _1721676, hAPP(hAPP(c_List_Oappend(_1721680), _1721682), hAPP(hAPP(c_List_Olist_OCons(_1721680), _1721678), _1721684))) = c_List_OtakeWhile(_1721680, _1721676, _1721682))], (46592 ^ _779203) ^ [_1715986, _1715988, _1715990] : [_1715988 = hAPP(hAPP(c_List_Olist_OCons(_1715986), _1715990), c_List_Olist_ONil(_1715986)), -(hAPP(c_List_Orev(_1715986), _1715988) = hAPP(hAPP(c_List_Olist_OCons(_1715986), _1715990), c_List_Olist_ONil(_1715986)))], (46893 ^ _779203) ^ [_1722316, _1722318, _1722320, _1722322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722316), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722318)), c_List_OtakeWhile(_1722318, _1722320, _1722322)))), -(hAPP(hAPP(c_List_Onth(_1722318), c_List_OtakeWhile(_1722318, _1722320, _1722322)), _1722316) = hAPP(hAPP(c_List_Onth(_1722318), _1722322), _1722316))], (29234 ^ _779203) ^ [_1297224, _1297226, _1297228] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297224, tc_HOL_Obool)), _1297226), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297224, tc_HOL_Obool)), _1297226), _1297228)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1297224, tc_HOL_Obool)), _1297226), _1297228))], (3114 ^ _779203) ^ [_825462, _825464, _825466, _825468] : [-(c_Big__Operators_Olinorder__class_OMin(_825468, _825464) = c_Big__Operators_Olinorder__class_OMin(_825466, _825462)), _825468 = _825466, _825464 = _825462], (5995 ^ _779203) ^ [_874329, _874331, _874333, _874335] : [hBOOL(hAPP(hAPP(c_member(_874329), _874331), _874333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874329, tc_HOL_Obool)), _874333), _874335)), -(hBOOL(hAPP(hAPP(c_member(_874329), _874331), _874335)))], (20574 ^ _779203) ^ [_1142042] : [-(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), _1142042))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32537 ^ _779203) ^ [_1369541, _1369543, _1369545, _1369547, _1369549] : [-(hAPP(c_Nat_Onat_Onat__rec(_1369541, _1369543, _1369545), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1369547)), _1369549)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1369541), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1369547))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1369541, _1369541), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1369541, tc_fun(_1369541, _1369541)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1369541, tc_fun(_1369541, _1369541)), tc_Int_Oint), c_If(_1369541)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1369541, _1369543, _1369545), _1369549))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1369541, _1369541), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1369541, _1369541), tc_Int_Oint), _1369545), 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)), _1369549))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1369541, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1369541, _1369543, _1369545)), 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)), _1369549))))))], (39590 ^ _779203) ^ [_1549916, _1549918, _1549920, _1549922, _1549924, _1549926, _1549928, _1549930] : [class_Groups_Ocomm__monoid__mult(_1549916), c_Fun_Oinj__on(_1549918, _1549920, _1549922, _1549924), _1549926 = hAPP(c_Set_Oimage(_1549918, _1549920, _1549922), _1549924), _1549928 = hAPP(c_Fun_Ocomp(_1549920, _1549916, _1549918, _1549930), _1549922), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549920, _1549916), _1549930), _1549926) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1549918, _1549916), _1549928), _1549924))], (33201 ^ _779203) ^ [_1387268, _1387270] : [-(c_Divides_Odivmod__nat(_1387268, _1387270) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1387268), _1387270)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1387268, _1387270)))], (2272 ^ _779203) ^ [_812395, _812397] : [_812397 = _812395, -(c_Int_Opred(_812397) = c_Int_Opred(_812395))], (37701 ^ _779203) ^ [_1494879, _1494881, _1494883, _1494885, _1494887, _1494889] : [hBOOL(hAPP(hAPP(c_member(_1494879), _1494881), _1494883)), 37704 ^ _779203 : [(37711 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494885, tc_HOL_Obool)), _1494887), _1494889)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1494885, _1494879), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1494885, _1494879), _1494887), hAPP(c_COMBK(tc_fun(_1494879, tc_HOL_Obool), _1494885), _1494883))), hAPP(hAPP(c_Product__Type_OSigma(_1494885, _1494879), _1494889), hAPP(c_COMBK(tc_fun(_1494879, tc_HOL_Obool), _1494885), _1494883)))))], (37705 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1494885, _1494879), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1494885, _1494879), _1494887), hAPP(c_COMBK(tc_fun(_1494879, tc_HOL_Obool), _1494885), _1494883))), hAPP(hAPP(c_Product__Type_OSigma(_1494885, _1494879), _1494889), hAPP(c_COMBK(tc_fun(_1494879, tc_HOL_Obool), _1494885), _1494883)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1494885, tc_HOL_Obool)), _1494887), _1494889)))]]], (1760 ^ _779203) ^ [_804163, _804165] : [-(class_Rings_Ocomm__semiring(_804163)), _804165 = _804163, class_Rings_Ocomm__semiring(_804165)], (18038 ^ _779203) ^ [_1097411, _1097413, _1097415] : [class_Orderings_Olinorder(_1097411), hAPP(_1097413, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1097411), 18043 ^ [_1097411, _1097413, _1097415]), 18044 ^ [_1097411, _1097413, _1097415])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1097411), hAPP(_1097413, 18043 ^ [_1097411, _1097413, _1097415])), hAPP(_1097413, 18044 ^ [_1097411, _1097413, _1097415])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1097411), _1097415)), -(_1097415 = c_Orderings_Obot__class_Obot(tc_fun(_1097411, tc_HOL_Obool))), -(hAPP(_1097413, c_Big__Operators_Olattice_OSup__fin(_1097411, c_Orderings_Oord__class_Omax(_1097411), _1097415)) = c_Big__Operators_Olattice_OSup__fin(_1097411, c_Orderings_Oord__class_Omax(_1097411), hAPP(c_Set_Oimage(_1097411, _1097411, _1097413), _1097415)))], (45440 ^ _779203) ^ [_1691135, _1691137, _1691139] : [hBOOL(hAPP(c_List_Odistinct(_1691135), _1691137)), -(c_List_Oremove1(_1691135, _1691139, _1691137) = hAPP(c_List_OremoveAll(_1691135, _1691139), _1691137))], (41527 ^ _779203) ^ [_1600279, _1600281, _1600283, _1600285, _1600287, _1600289] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600279), tc_List_Olist(_1600279))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600279), tc_List_Olist(_1600279)), hAPP(hAPP(c_List_Olist_OCons(_1600279), _1600281), _1600283)), hAPP(hAPP(c_List_Olist_OCons(_1600279), _1600285), _1600287))), c_List_Olistrel1(_1600279, _1600289))), 41532 ^ _779203 : [(41535 ^ _779203) ^ [] : [-(_1600283 = _1600287)], (41533 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600279, _1600279)), hAPP(hAPP(c_Product__Type_OPair(_1600279, _1600279), _1600281), _1600285)), _1600289)))]], 41536 ^ _779203 : [(41539 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1600279), tc_List_Olist(_1600279))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1600279), tc_List_Olist(_1600279)), _1600283), _1600287)), c_List_Olistrel1(_1600279, _1600289))))], (41537 ^ _779203) ^ [] : [-(_1600281 = _1600285)]]], (45376 ^ _779203) ^ [_1690041, _1690043] : [c_List_Oremdups(_1690041, _1690043) = _1690043, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690041)), c_List_Oremdups(_1690041, _1690043)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690041)), _1690043))], (29446 ^ _779203) ^ [_1301628, _1301630, _1301632] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1301628, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301628, tc_HOL_Obool)), _1301630), _1301632)), _1301630)))], (43470 ^ _779203) ^ [_1648142, _1648144] : [hBOOL(hAPP(c_List_Odistinct(_1648142), hAPP(c_List_Orotate1(_1648142), _1648144))), -(hBOOL(hAPP(c_List_Odistinct(_1648142), _1648144)))], (40340 ^ _779203) ^ [_1568380, _1568382, _1568384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568380, _1568380), tc_HOL_Obool)), c_Relation_OId(_1568380)), _1568382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568380, _1568380), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1568380, _1568380, _1568380), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1568380, _1568380), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1568380, _1568384)), _1568382)), _1568384)), _1568382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1568380, _1568380), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1568380, _1568384)), _1568382)))], (52401 ^ _779203) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (2812 ^ _779203) ^ [_820805, _820807, _820809, _820811] : [-(c_Nitpick_Oint__lcm(_820811, _820807) = c_Nitpick_Oint__lcm(_820809, _820805)), _820811 = _820809, _820807 = _820805], (9504 ^ _779203) ^ [_941367, _941369, _941371, _941373] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941367), _941369)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _941371), _941373)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941367), _941371)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _941369), _941373))))], (2098 ^ _779203) ^ [_809508, _809510, _809512, _809514] : [-(c_Random_Olog(_809514, _809510) = c_Random_Olog(_809512, _809508)), _809514 = _809512, _809510 = _809508], (20364 ^ _779203) ^ [_1138324, _1138326, _1138328] : [class_Rings_Odivision__ring(_1138324), -(_1138326 = c_Groups_Ozero__class_Ozero(_1138324)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1138324), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138324), _1138328), _1138326)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138324), _1138328), hAPP(c_Groups_Ouminus__class_Ouminus(_1138324), _1138326)))], (52487 ^ _779203) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (33295 ^ _779203) ^ [_1388950, _1388952, _1388954, _1388956] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1388950, _1388952), _1388954)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1388950, _1388952), _1388956)), -(_1388954 = _1388956)], (22289 ^ _779203) ^ [_1172660, _1172662] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1172662)), 22296 ^ _779203 : [(22303 ^ _779203) ^ [] : [_1172660 = _1172662, -(hAPP(c_Int_Onat, _1172660) = hAPP(c_Int_Onat, _1172662))], (22297 ^ _779203) ^ [] : [hAPP(c_Int_Onat, _1172660) = hAPP(c_Int_Onat, _1172662), -(_1172660 = _1172662)]]], (10555 ^ _779203) ^ [_961724, _961726, _961728, _961730, _961732] : [class_Groups_Ocomm__monoid__mult(_961724), hBOOL(hAPP(c_Finite__Set_Ofinite(_961726), _961728)), hBOOL(hAPP(hAPP(c_member(_961726), _961730), _961728)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_961726, _961724), _961732), _961728) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961724), hAPP(_961732, _961730)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_961726, _961724), _961732), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_961726, tc_HOL_Obool)), _961728), hAPP(hAPP(c_Set_Oinsert(_961726), _961730), c_Orderings_Obot__class_Obot(tc_fun(_961726, tc_HOL_Obool)))))))], (34587 ^ _779203) ^ [_1418124, _1418126, _1418128, _1418130, _1418132] : [34589 ^ _779203 : [(34592 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1418124), _1418126), hAPP(_1418132, 34588 ^ [_1418124, _1418126, _1418128, _1418130, _1418132])))], (34590 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1418128), 34588 ^ [_1418124, _1418126, _1418128, _1418130, _1418132]), _1418130)))]], -(hBOOL(hAPP(hAPP(c_member(_1418124), _1418126), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1418128, tc_fun(_1418124, tc_HOL_Obool)), _1418130), _1418132))))], (46614 ^ _779203) ^ [_1716507, _1716509, _1716511, _1716513] : [-(hAPP(c_List_Orev(_1716507), hAPP(hAPP(c_List_Omap(_1716509, _1716507), _1716511), _1716513)) = hAPP(hAPP(c_List_Omap(_1716509, _1716507), _1716511), hAPP(c_List_Orev(_1716509), _1716513)))], (31873 ^ _779203) ^ [_1352670, _1352672, _1352674, _1352676] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1352670), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1352672, tc_Int_Oint), _1352674), _1352676)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1352672, _1352670), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1352670, _1352672), c_Int_Oring__1__class_Oof__int(_1352670)), _1352674)), _1352676)), class_Groups_Ocomm__monoid__mult(_1352670), class_Rings_Oring__1(_1352670)], (24006 ^ _779203) ^ [_1201876, _1201878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1201876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1201876), _1201878)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1201878), _1201876) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1201878), _1201876)), _1201876)))], (20883 ^ _779203) ^ [_1147651, _1147653, _1147655] : [class_Rings_Olinordered__idom(_1147651), -(c_Groups_Osgn__class_Osgn(_1147651, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147651), _1147653), _1147655)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147651), c_Groups_Osgn__class_Osgn(_1147651, _1147653)), c_Groups_Osgn__class_Osgn(_1147651, _1147655)))], (43848 ^ _779203) ^ [_1656445, _1656447, _1656449, _1656451] : [-(hAPP(c_List_Ofoldl(_1656445, _1656447, _1656449, _1656451), c_List_Olist_ONil(_1656447)) = _1656451)], (44758 ^ _779203) ^ [_1676067, _1676069] : [-(c_Random_Oselect(_1676067, _1676069) = 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(_1676067, 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(_1676067)), _1676069)))), hAPP(hAPP(c_COMBB(_1676067, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1676067, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1676067, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1676067, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1676067), _1676069)), c_Code__Numeral_Onat__of))))], (31323 ^ _779203) ^ [_1340627, _1340629] : [class_Complete__Lattice_Ocomplete__lattice(_1340627), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340627), _1340629)), -(c_Complete__Lattice_OInf__class_OInf(_1340627, _1340629) = hAPP(hAPP(c_Finite__Set_Ofold(_1340627, _1340627, c_Lattices_Osemilattice__inf__class_Oinf(_1340627)), c_Orderings_Otop__class_Otop(_1340627)), _1340629))], (48040 ^ _779203) ^ [_1747362, _1747364, _1747366, _1747368, _1747370] : [-(hAPP(c_New__DSequence_Opos__bind(_1747362, _1747364, _1747366, _1747368), _1747370) = hAPP(c_Lazy__Sequence_Obind(_1747362, _1747364, hAPP(_1747366, _1747370)), hAPP(hAPP(c_COMBC(_1747362, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1747364)), _1747368), _1747370)))], (45139 ^ _779203) ^ [_1684776, _1684778, _1684780, _1684782, _1684784] : [c_List_Olist__all2(_1684776, _1684778, _1684780, _1684782, _1684784), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684776)), _1684782) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684778)), _1684784))], (11083 ^ _779203) ^ [_970146, _970148, _970150] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970146), _970148) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970146), _970150), -(_970148 = _970150), -(_970146 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41312 ^ _779203) ^ [_1592910, _1592912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 41313 ^ [_1592910, _1592912]), hAPP(_1592910, 41313 ^ [_1592910, _1592912]))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_OCollect(tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_Nat_Onat), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), _1592910)), _1592912)))))], (7759 ^ _779203) ^ [_907025, _907027, _907029] : [class_Orderings_Olinorder(_907025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_907025), _907027), _907029)), 7766 ^ _779203 : [(7773 ^ _779203) ^ [] : [_907027 = _907029, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907025), _907027), _907029))], (7767 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_907025), _907027), _907029))), -(_907027 = _907029)]]], (41959 ^ _779203) ^ [_1612355, _1612357, _1612359] : [41961 ^ _779203 : [(41964 ^ _779203) ^ [] : [hBOOL(hAPP(_1612359, 41960 ^ [_1612355, _1612357, _1612359]))], (41962 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1612355), 41960 ^ [_1612355, _1612357, _1612359]), hAPP(c_List_Oset(_1612355), _1612357))))]], 41965 ^ _779203 : [(41966 ^ _779203) ^ [_1612539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1612539), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1612355)), _1612357))), -(hBOOL(hAPP(_1612359, hAPP(hAPP(c_List_Onth(_1612355), _1612357), _1612539))))]]], (40299 ^ _779203) ^ [_1567252, _1567254, _1567256, _1567258] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1567252, _1567252)), hAPP(hAPP(c_Product__Type_OPair(_1567252, _1567252), _1567256), _1567258)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567252, _1567252), tc_HOL_Obool)), _1567254), c_Relation_OId(_1567252)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1567252, tc_fun(_1567252, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1567252, tc_fun(tc_prod(_1567252, _1567252), tc_HOL_Obool), tc_fun(_1567252, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1567252, tc_fun(tc_fun(tc_prod(_1567252, _1567252), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1567252, _1567252), tc_HOL_Obool), tc_fun(_1567252, tc_HOL_Obool)), _1567252), c_COMBC(_1567252, tc_fun(tc_prod(_1567252, _1567252), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1567252, tc_prod(_1567252, _1567252)), tc_fun(_1567252, tc_fun(tc_fun(tc_prod(_1567252, _1567252), tc_HOL_Obool), tc_HOL_Obool)), _1567252), hAPP(c_COMBB(tc_prod(_1567252, _1567252), tc_fun(tc_fun(tc_prod(_1567252, _1567252), tc_HOL_Obool), tc_HOL_Obool), _1567252), c_member(tc_prod(_1567252, _1567252)))), c_Product__Type_OPair(_1567252, _1567252)))), _1567254)), c_fequal), _1567256), _1567258)))], (41913 ^ _779203) ^ [_1611315, _1611317, _1611319, _1611321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1611315), _1611317)), -(hAPP(hAPP(c_List_Onth(_1611319), hAPP(hAPP(c_List_Otake(_1611319), _1611317), _1611321)), _1611315) = hAPP(hAPP(c_List_Onth(_1611319), _1611321), _1611315))], (10775 ^ _779203) ^ [_965597, _965599] : [class_Groups_Omonoid__add(_965597), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_965597), _965599), c_Groups_Ozero__class_Ozero(_965597)) = _965599)], (20156 ^ _779203) ^ [_1134815, _1134817] : [class_Groups_Oordered__ab__group__add(_1134815), 20159 ^ _779203 : [(20166 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134815), c_Groups_Ozero__class_Ozero(_1134815)), _1134817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134815), hAPP(c_Groups_Ouminus__class_Ouminus(_1134815), _1134817)), c_Groups_Ozero__class_Ozero(_1134815))))], (20160 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134815), hAPP(c_Groups_Ouminus__class_Ouminus(_1134815), _1134817)), c_Groups_Ozero__class_Ozero(_1134815))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134815), c_Groups_Ozero__class_Ozero(_1134815)), _1134817)))]]], (50321 ^ _779203) ^ [_1796826, _1796828, _1796830] : [hBOOL(hAPP(hAPP(_1796828, _1796830), _1796830)), -(hBOOL(hAPP(c_Quotient_ORespects(_1796826, _1796828), _1796830)))], (19075 ^ _779203) ^ [_1115332] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1115332))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1115332)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (46078 ^ _779203) ^ [_1706454, _1706456, _1706458] : [class_Orderings_Olinorder(_1706454), c_List_Olinorder__class_Osorted(_1706454, _1706456), -(c_List_Olinorder__class_Osorted(_1706454, c_List_Olinorder__class_Oinsort__insert__key(_1706454, _1706454, c_COMBI(_1706454), _1706458, _1706456)))], (52439 ^ _779203) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (2886 ^ _779203) ^ [_821936, _821938] : [_821938 = _821936, -(c_Nitpick_Ofrac(_821938) = c_Nitpick_Ofrac(_821936))], (22972 ^ _779203) ^ [_1183743, _1183745] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183743, _1183745) = 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), _1183743), _1183745) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51463 ^ _779203) ^ [_1819377, _1819379, _1819381] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819377), _1819379)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819379), _1819377))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819379), _1819381)), 51474 ^ _779203 : [(51477 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819381), _1819377))], (51475 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819377), _1819381)))]]], (46969 ^ _779203) ^ [_1724070, _1724072, _1724074] : [c_List_OdropWhile(_1724070, _1724072, _1724074) = c_List_Olist_ONil(_1724070), 46972 ^ _779203 : [(46973 ^ _779203) ^ [_1724161] : [hBOOL(hAPP(hAPP(c_member(_1724070), _1724161), hAPP(c_List_Oset(_1724070), _1724074))), -(hBOOL(hAPP(_1724072, _1724161)))]]], (37299 ^ _779203) ^ [_1484070, _1484072, _1484074, _1484076] : [-(hBOOL(hAPP(hAPP(c_member(_1484070), _1484072), _1484074))), -(hAPP(c_Set_Ovimage(_1484076, _1484070, hAPP(c_COMBK(_1484070, _1484076), _1484072)), _1484074) = c_Orderings_Obot__class_Obot(tc_fun(_1484076, tc_HOL_Obool)))], (44895 ^ _779203) ^ [_1679135, _1679137, _1679139] : [-(c_List_Olistsp(_1679135, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1679135, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1679135, tc_fun(_1679135, tc_HOL_Obool), tc_HOL_Obool), c_member(_1679135)), _1679137)), hAPP(hAPP(c_COMBC(_1679135, tc_fun(_1679135, tc_HOL_Obool), tc_HOL_Obool), c_member(_1679135)), _1679139))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1679135), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1679135), tc_fun(tc_List_Olist(_1679135), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1679135))), c_List_Olists(_1679135, _1679137))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1679135), tc_fun(tc_List_Olist(_1679135), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1679135))), c_List_Olists(_1679135, _1679139))))], (47899 ^ _779203) ^ [_1744327, _1744329, _1744331] : [c_List_Olist__all(_1744327, _1744331, _1744329), 47902 ^ _779203 : [(47903 ^ _779203) ^ [_1744408] : [hBOOL(hAPP(hAPP(c_member(_1744327), _1744408), hAPP(c_List_Oset(_1744327), _1744329))), -(hBOOL(hAPP(_1744331, _1744408)))]]], (45823 ^ _779203) ^ [_1701174, _1701176, _1701178, _1701180, _1701182, _1701184] : [-(c_List_Ofoldr(_1701174, _1701176, _1701178, hAPP(hAPP(c_List_Olist_OCons(_1701174), _1701180), _1701182), _1701184) = hAPP(hAPP(_1701178, _1701180), c_List_Ofoldr(_1701174, _1701176, _1701178, _1701182, _1701184)))], (30641 ^ _779203) ^ [_1326608, _1326610, _1326612] : [class_Complete__Lattice_Ocomplete__lattice(_1326608), class_Orderings_Olinorder(_1326608), 30648 ^ _779203 : [(30658 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1326608), _1326610), c_Complete__Lattice_OSup__class_OSup(_1326608, _1326612)))), 30659 ^ _779203 : [(30660 ^ _779203) ^ [_1326914] : [hBOOL(hAPP(hAPP(c_member(_1326608), _1326914), _1326612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1326608), _1326610), _1326914))]]], (30649 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1326608), _1326610), c_Complete__Lattice_OSup__class_OSup(_1326608, _1326612))), 30653 ^ _779203 : [(30656 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1326608), _1326610), 30652 ^ [_1326608, _1326610, _1326612])))], (30654 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1326608), 30652 ^ [_1326608, _1326610, _1326612]), _1326612)))]]]]], (32167 ^ _779203) ^ [_1360516, _1360518] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1360516), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1360518))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1360516), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1360518))), 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))))], (26164 ^ _779203) ^ [_1239380, _1239382, _1239384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1239380, tc_HOL_Obool)), _1239382), _1239384)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1239380, tc_HOL_Obool)), _1239382), hAPP(c_Set_OPow(_1239380), _1239384))))], (41848 ^ _779203) ^ [_1609391, _1609393, _1609395, _1609397] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609391) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1609393), hAPP(hAPP(c_List_Olist_OCons(_1609393), _1609395), _1609397)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609391)) = hAPP(hAPP(c_List_Onth(_1609393), _1609397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1609391)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (14961 ^ _779203) ^ [_1040642] : [class_Rings_Oring__1(_1040642), -(hBOOL(hAPP(hAPP(c_member(_1040642), c_Groups_Ozero__class_Ozero(_1040642)), c_Int_Oring__1__class_OInts(_1040642))))], (52505 ^ _779203) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (22922 ^ _779203) ^ [_1182910, _1182912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182910)), -(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, _1182912, _1182910))))], (36066 ^ _779203) ^ [_1456635, _1456637, _1456639, _1456641, _1456643, _1456645] : [c_Equiv__Relations_Ocongruent(_1456635, _1456637, _1456639, _1456641), hBOOL(hAPP(hAPP(c_member(tc_prod(_1456635, _1456635)), hAPP(hAPP(c_Product__Type_OPair(_1456635, _1456635), _1456643), _1456645)), _1456639)), -(hAPP(_1456641, _1456643) = hAPP(_1456641, _1456645))], (50142 ^ _779203) ^ [_1793161, _1793163, _1793165] : [_1793163 = _1793165, -(c_Fun_Obij__betw(_1793161, _1793161, c_Fun_Oid(_1793161), _1793163, _1793165))], (34458 ^ _779203) ^ [_1414274, _1414276, _1414278, _1414280, _1414282, _1414284] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414274, tc_fun(_1414276, tc_HOL_Obool)), _1414278), hAPP(hAPP(c_COMBB(_1414280, tc_fun(_1414276, tc_HOL_Obool), _1414274), _1414282), _1414284)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414280, tc_fun(_1414276, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1414274, _1414280, _1414284), _1414278)), _1414282))], (5584 ^ _779203) ^ [_864569, _864571] : [_864571 = _864569, -(c_Finite__Set_Ofinite(_864571) = c_Finite__Set_Ofinite(_864569))], (39608 ^ _779203) ^ [_1550265, _1550267, _1550269] : [-(c_Hilbert__Choice_OEps(tc_prod(_1550265, _1550267), _1550269) = c_Hilbert__Choice_OEps(tc_prod(_1550265, _1550267), hAPP(c_Product__Type_Oprod_Oprod__case(_1550265, _1550267, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1550267, tc_prod(_1550265, _1550267)), tc_fun(_1550267, tc_HOL_Obool), _1550265), hAPP(c_COMBB(tc_prod(_1550265, _1550267), tc_HOL_Obool, _1550267), _1550269)), c_Product__Type_OPair(_1550265, _1550267)))))], (43167 ^ _779203) ^ [_1640699, _1640701, _1640703] : [_1640701 = c_List_Olist_ONil(_1640699), -(hAPP(hAPP(c_List_Oappend(_1640699), _1640701), _1640703) = _1640703)], (52059 ^ _779203) ^ [_1830018, _1830020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1830018)), 52062 ^ _779203 : [(52069 ^ _779203) ^ [] : [_1830020 = 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), _1830020), _1830018)), _1830018)))], (52063 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1830020), _1830018)), _1830018)), -(_1830020 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (52091 ^ _779203) ^ [_1830506, _1830508, _1830510, _1830512] : [class_Orderings_Oorder(_1830506), c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat, _1830506, 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)))), _1830508), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1830506), hAPP(_1830508, _1830510)), hAPP(_1830508, _1830512)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830510), _1830512)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1830512), _1830510)))], (38595 ^ _779203) ^ [_1526653, _1526655, _1526657, _1526659] : [c_Wellfounded_Owf(_1526653, _1526655), -(c_Wellfounded_Owf(_1526657, hAPP(hAPP(c_Relation_Oinv__image(_1526653, _1526657), _1526655), _1526659)))], (26978 ^ _779203) ^ [] : [-(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))))], (27776 ^ _779203) ^ [_1268965, _1268967, _1268969] : [class_Lattices_Olattice(_1268965), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268965), _1268967), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268965), _1268967), _1268969)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268965), _1268967), _1268969))], (35327 ^ _779203) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (43556 ^ _779203) ^ [_1650087, _1650089, _1650091, _1650093] : [hAPP(hAPP(c_List_Oappend(_1650087), _1650089), _1650091) = _1650093, 43559 ^ _779203 : [(43562 ^ _779203) ^ [] : [-(_1650091 = hAPP(hAPP(c_List_Odrop(_1650087), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650087)), _1650089)), _1650093))], (43560 ^ _779203) ^ [] : [-(_1650089 = hAPP(hAPP(c_List_Otake(_1650087), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650087)), _1650089)), _1650093))]]], (10383 ^ _779203) ^ [_958001, _958003, _958005, _958007] : [class_Rings_Ocomm__semiring__1(_958001), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958001), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958001), _958003), _958005)), _958007) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958001), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958001), _958003), _958007)), _958005))], (27978 ^ _779203) ^ [_1273175, _1273177] : [c_Nat__Transfer_Onat__set(_1273175), c_Nat__Transfer_Onat__set(_1273177), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1273175), _1273177)))], (8136 ^ _779203) ^ [_914342, _914344, _914346, _914348] : [-(c_Fun_Ofun__upd(_914342, _914344, _914346, _914348, hAPP(_914346, _914348)) = _914346)], (16306 ^ _779203) ^ [_1065470, _1065472, _1065474, _1065476] : [class_Fields_Olinordered__field__inverse__zero(_1065470), class_Int_Onumber(_1065470), 16313 ^ _779203 : [(16314 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), _1065472), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1065470), _1065474), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476)))), 16317 ^ _779203 : [(16324 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), c_Groups_Ozero__class_Ozero(_1065470)), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476)))), 16327 ^ _779203 : [(16334 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476)), c_Groups_Ozero__class_Ozero(_1065470)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), _1065472), c_Groups_Ozero__class_Ozero(_1065470))))], (16328 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476)), c_Groups_Ozero__class_Ozero(_1065470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), _1065474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065470), _1065472), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476)))))]]], (16318 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), c_Groups_Ozero__class_Ozero(_1065470)), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065470), _1065472), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476))), _1065474)))]]], (16340 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), _1065472), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1065470), _1065474), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476))))), 16343 ^ _779203 : [(16346 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065470), _1065472), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476))), _1065474))], (16344 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), c_Groups_Ozero__class_Ozero(_1065470)), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476))))]], 16347 ^ _779203 : [(16350 ^ _779203) ^ [] : [16351 ^ _779203 : [(16354 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), _1065474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065470), _1065472), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476))))], (16352 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476)), c_Groups_Ozero__class_Ozero(_1065470))))]], 16355 ^ _779203 : [(16358 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), _1065472), c_Groups_Ozero__class_Ozero(_1065470)))], (16356 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476)), c_Groups_Ozero__class_Ozero(_1065470)))]]], (16348 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1065470), c_Groups_Ozero__class_Ozero(_1065470)), hAPP(c_Int_Onumber__class_Onumber__of(_1065470), _1065476)))]]]]], (20374 ^ _779203) ^ [_1138472, _1138474, _1138476] : [class_Groups_Oordered__ab__group__add__abs(_1138472), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138472), hAPP(c_Groups_Oabs__class_Oabs(_1138472), _1138474)), _1138476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138472), hAPP(c_Groups_Ouminus__class_Ouminus(_1138472), _1138474)), _1138476)))], (21815 ^ _779203) ^ [_1163307, _1163309] : [class_Int_Onumber__ring(_1163307), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163307), hAPP(c_Int_Onumber__class_Onumber__of(_1163307), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1163309) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163307), _1163309), _1163309))], (39467 ^ _779203) ^ [_1547084, _1547086, _1547088, _1547090, _1547092, _1547094] : [-(hAPP(c_Set_Ovimage(_1547084, _1547086, hAPP(c_Fun_Ocomp(_1547088, _1547086, _1547084, _1547090), _1547092)), _1547094) = hAPP(c_Set_Ovimage(_1547084, _1547088, _1547092), hAPP(c_Set_Ovimage(_1547088, _1547086, _1547090), _1547094)))], (1750 ^ _779203) ^ [_804038, _804040] : [-(class_Divides_Osemiring__div(_804038)), _804040 = _804038, class_Divides_Osemiring__div(_804040)], (48104 ^ _779203) ^ [_1748940, _1748942, _1748944, _1748946, _1748948] : [hBOOL(hAPP(hAPP(_1748944, _1748948), _1748946)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748940, _1748942, _1748944), _1748946), _1748948)))], (23729 ^ _779203) ^ [_1196915, _1196917] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1196915, _1196917)) = _1196917, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1196915), _1196917) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48961 ^ _779203) ^ [_1768017, _1768019, _1768021, _1768023] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1768017, tc_fun(_1768019, tc_HOL_Obool)), _1768021), _1768023) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1768019, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1768019, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1768017, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1768019, tc_HOL_Obool)), c_HOL_OEx(_1768017)), hAPP(hAPP(c_COMBB(tc_fun(_1768017, tc_HOL_Obool), tc_fun(_1768017, tc_HOL_Obool), tc_fun(_1768019, tc_HOL_Obool)), hAPP(c_COMBS(_1768017, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1768017), c_fconj), hAPP(hAPP(c_COMBC(_1768017, tc_fun(_1768017, tc_HOL_Obool), tc_HOL_Obool), c_member(_1768017)), _1768021)))), hAPP(hAPP(c_COMBC(tc_fun(_1768019, tc_HOL_Obool), tc_fun(_1768017, tc_fun(_1768019, tc_HOL_Obool)), tc_fun(_1768017, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1768019, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1768017, tc_fun(_1768019, tc_HOL_Obool)), tc_fun(_1768017, tc_HOL_Obool)), tc_fun(_1768019, tc_HOL_Obool)), c_COMBB(tc_fun(_1768019, tc_HOL_Obool), tc_HOL_Obool, _1768017)), c_fequal)), _1768023))))))], (18223 ^ _779203) ^ [_1100609] : [hBOOL(hAPP(_1100609, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 18224 ^ [_1100609]))), 18227 ^ _779203 : [(18228 ^ _779203) ^ [_1100709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1100709)), -(hBOOL(hAPP(_1100609, _1100709)))]]], (13665 ^ _779203) ^ [_1016609, _1016611, _1016613] : [class_Rings_Odivision__ring(_1016609), -(_1016611 = c_Groups_Ozero__class_Ozero(_1016609)), 13672 ^ _779203 : [(13679 ^ _779203) ^ [] : [_1016613 = _1016611, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1016609), _1016613), _1016611) = c_Groups_Oone__class_Oone(_1016609))], (13673 ^ _779203) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1016609), _1016613), _1016611) = c_Groups_Oone__class_Oone(_1016609), -(_1016613 = _1016611)]]], (1790 ^ _779203) ^ [_804538, _804540] : [-(class_Orderings_Opreorder(_804538)), _804540 = _804538, class_Orderings_Opreorder(_804540)], (21537 ^ _779203) ^ [_1158413] : [c_Int_OPls = c_Int_OBit0(_1158413), -(c_Int_OPls = _1158413)], (29820 ^ _779203) ^ [_1309330, _1309332, _1309334, _1309336] : [class_Lattices_Osemilattice__inf(_1309330), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309330), _1309332)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1309330, _1309330, c_Lattices_Osemilattice__inf__class_Oinf(_1309330)), _1309334), hAPP(hAPP(c_Set_Oinsert(_1309330), _1309336), _1309332)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1309330), _1309336), hAPP(hAPP(c_Finite__Set_Ofold(_1309330, _1309330, c_Lattices_Osemilattice__inf__class_Oinf(_1309330)), _1309334), _1309332)))], (45736 ^ _779203) ^ [_1698184, _1698186, _1698188] : [-(c_List_Oremdups(_1698184, hAPP(c_List_Ofilter(_1698184, _1698186), _1698188)) = hAPP(c_List_Ofilter(_1698184, _1698186), c_List_Oremdups(_1698184, _1698188)))], (49715 ^ _779203) ^ [_1784164, _1784166, _1784168, _1784170, _1784172] : [c_Fun_Oinj__on(_1784164, _1784166, _1784168, _1784170), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1784164, tc_HOL_Obool)), _1784172), _1784170)), -(hAPP(c_Set_Oimage(_1784166, _1784164, c_Hilbert__Choice_Oinv__into(_1784164, _1784166, _1784170, _1784168)), hAPP(c_Set_Oimage(_1784164, _1784166, _1784168), _1784172)) = _1784172)], (49416 ^ _779203) ^ [_1777952, _1777954] : [c_Equiv__Relations_Opart__equivp(_1777952, _1777954), 49420 ^ _779203 : [(49425 ^ _779203) ^ [] : [-(c_Predicate_Otransp(_1777952, _1777954))], (49423 ^ _779203) ^ [] : [-(c_Predicate_Osymp(_1777952, _1777954))], (49421 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1777954, 49419 ^ [_1777952, _1777954]), 49419 ^ [_1777952, _1777954])))]]], (10431 ^ _779203) ^ [_959213, _959215, _959217, _959219] : [class_Rings_Ocomm__semiring__1(_959213), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959213), _959215), _959217)), _959219) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959213), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959213), _959215), _959219)), _959217))], (39469 ^ _779203) ^ [_1547146, _1547148, _1547150, _1547152, _1547154, _1547156, _1547158] : [-(hAPP(c_Product__Type_Oapfst(_1547146, _1547148, _1547150, _1547152), hAPP(c_Product__Type_Oapfst(_1547154, _1547146, _1547150, _1547156), _1547158)) = hAPP(c_Product__Type_Oapfst(_1547154, _1547148, _1547150, hAPP(c_Fun_Ocomp(_1547146, _1547148, _1547154, _1547152), _1547156)), _1547158))], (8549 ^ _779203) ^ [_923233, _923235, _923237, _923239, _923241] : [class_Groups_Oab__semigroup__mult(_923233), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_923233, _923233, c_Groups_Otimes__class_Otimes(_923233), _923235, _923237), _923239)), hBOOL(hAPP(hAPP(c_member(_923233), _923241), _923237)), -(hBOOL(hAPP(hAPP(c_member(_923233), _923235), _923237))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_923233, _923233, c_Groups_Otimes__class_Otimes(_923233), _923241, hAPP(hAPP(c_Set_Oinsert(_923233), _923235), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923233, tc_HOL_Obool)), _923237), hAPP(hAPP(c_Set_Oinsert(_923233), _923241), c_Orderings_Obot__class_Obot(tc_fun(_923233, tc_HOL_Obool)))))), _923239)))], (22115 ^ _779203) ^ [_1169595, _1169597, _1169599] : [class_Divides_Oring__div(_1169595), -(c_Divides_Odiv__class_Omod(_1169595, hAPP(c_Groups_Ouminus__class_Ouminus(_1169595), _1169597), _1169599) = c_Divides_Odiv__class_Omod(_1169595, hAPP(c_Groups_Ouminus__class_Ouminus(_1169595), c_Divides_Odiv__class_Omod(_1169595, _1169597, _1169599)), _1169599))], (42684 ^ _779203) ^ [_1630066] : [class_Groups_Omonoid__add(_1630066), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1630066), c_List_Olist_ONil(_1630066)) = c_Groups_Ozero__class_Ozero(_1630066))], (21693 ^ _779203) ^ [_1161111] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1161111)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1161111))))], (33229 ^ _779203) ^ [_1387671, _1387673] : [-(_1387671 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1387673, _1387671) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1387673), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1387671)))], (21435 ^ _779203) ^ [_1156663, _1156665] : [class_Fields_Olinordered__field__inverse__zero(_1156663), class_Int_Onumber__ring(_1156663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156663), c_Groups_Ozero__class_Ozero(_1156663)), _1156665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156663), c_Groups_Ozero__class_Ozero(_1156663)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1156663), _1156665), hAPP(c_Int_Onumber__class_Onumber__of(_1156663), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (43890 ^ _779203) ^ [_1657336, _1657338] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1657336), _1657338) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1657336 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43896 ^ _779203 : [(43899 ^ _779203) ^ [] : [43895 ^ [_1657336, _1657338] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43897 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43895 ^ [_1657336, _1657338]), hAPP(c_List_Oset(tc_Nat_Onat), _1657338))))]]], (38344 ^ _779203) ^ [_1518216, _1518218, _1518220] : [-(hAPP(c_Relation_ORange(_1518216, _1518218), hAPP(c_Set_OCollect(tc_prod(_1518216, _1518218)), hAPP(c_Product__Type_Oprod_Oprod__case(_1518216, _1518218, tc_HOL_Obool), _1518220))) = hAPP(c_Set_OCollect(_1518218), hAPP(hAPP(c_COMBB(tc_fun(_1518216, tc_HOL_Obool), tc_HOL_Obool, _1518218), c_HOL_OEx(_1518216)), hAPP(c_COMBC(_1518216, _1518218, tc_HOL_Obool), _1518220))))], (18730 ^ _779203) ^ [_1109320, _1109322] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109320), c_Int_OPls))), 18733 ^ _779203 : [(18740 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109322), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109320)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109322)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1109320), _1109322)))], (18734 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1109322), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109320)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109322)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1109320))]]], (19238 ^ _779203) ^ [_1118102, _1118104] : [class_Groups_Oordered__ab__group__add__abs(_1118102), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118102), c_Groups_Ozero__class_Ozero(_1118102)), hAPP(c_Groups_Oabs__class_Oabs(_1118102), _1118104))))], (52333 ^ _779203) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (47958 ^ _779203) ^ [] : [-(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)))], (15968 ^ _779203) ^ [_1059394, _1059396, _1059398] : [class_Int_Onumber__ring(_1059394), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1059394), hAPP(c_Int_Onumber__class_Onumber__of(_1059394), _1059396)), hAPP(c_Int_Onumber__class_Onumber__of(_1059394), _1059398)) = hAPP(c_Int_Onumber__class_Onumber__of(_1059394), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1059396), _1059398)))], (11208 ^ _779203) ^ [_972083, _972085, _972087, _972089] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_972083), _972085)), hBOOL(hAPP(c_Finite__Set_Ofinite(_972087), _972089)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_972083, _972087)), c_Sum__Type_OPlus(_972083, _972087, _972085, _972089))))], (9963 ^ _779203) ^ [_949299, _949301, _949303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949299), _949301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _949299), _949303)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949301), _949299)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949303), _949299)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _949301), _949303))], (1660 ^ _779203) ^ [_802913, _802915] : [-(class_Rings_Olinordered__semidom(_802913)), _802915 = _802913, class_Rings_Olinordered__semidom(_802915)], (23487 ^ _779203) ^ [_1192509, _1192511, _1192513, _1192515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192509)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192511)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192511), _1192513)), -(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), _1192513), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1192515, _1192509))), _1192511)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1192513), _1192509))))], (51527 ^ _779203) ^ [_1820456, _1820458] : [class_Rings_Ocomm__semiring__1(_1820456), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1820456), c_Groups_Ozero__class_Ozero(_1820456)), _1820458)), -(_1820458 = c_Groups_Ozero__class_Ozero(_1820456))], (43297 ^ _779203) ^ [_1643288, _1643290, _1643292, _1643294, _1643296, _1643298] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643288), tc_List_Olist(_1643288))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643288), tc_List_Olist(_1643288)), hAPP(hAPP(c_List_Oappend(_1643288), _1643290), _1643296)), hAPP(hAPP(c_List_Oappend(_1643288), _1643292), _1643298))), c_List_Olistrel1(_1643288, _1643294)))), 43298 ^ _779203 : [(43305 ^ _779203) ^ [] : [_1643290 = _1643292, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643288), tc_List_Olist(_1643288))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643288), tc_List_Olist(_1643288)), _1643296), _1643298)), c_List_Olistrel1(_1643288, _1643294)))], (43299 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643288), tc_List_Olist(_1643288))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643288), tc_List_Olist(_1643288)), _1643290), _1643292)), c_List_Olistrel1(_1643288, _1643294))), _1643296 = _1643298]]], (37571 ^ _779203) ^ [_1491298, _1491300, _1491302, _1491304, _1491306] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1491298, _1491300), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491298, tc_HOL_Obool)), _1491302), _1491304)), _1491306) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1491298, _1491300), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1491298, _1491300), _1491302), _1491306)), hAPP(hAPP(c_Product__Type_OSigma(_1491298, _1491300), _1491304), _1491306)))], (5206 ^ _779203) ^ [_858626, _858628, _858630, _858632, _858634, _858636, _858638, _858640, _858642, _858644] : [-(c_New__DSequence_Opos__map(_858644, _858640, _858636, _858632, _858628) = c_New__DSequence_Opos__map(_858642, _858638, _858634, _858630, _858626)), _858644 = _858642, _858640 = _858638, _858636 = _858634, _858632 = _858630, _858628 = _858626], (42116 ^ _779203) ^ [_1617637, _1617639, _1617641] : [-(_1617637 = _1617639), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617641)), _1617637) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1617641)), _1617639), 42122 ^ _779203 : [(42125 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1617641, _1617641, tc_HOL_Obool), c_fequal), 42121 ^ [_1617637, _1617639, _1617641]))], (42123 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1617641, _1617641)), 42121 ^ [_1617637, _1617639, _1617641]), hAPP(c_List_Oset(tc_prod(_1617641, _1617641)), hAPP(hAPP(c_List_Ozip(_1617641, _1617641), _1617637), _1617639)))))]]], (27688 ^ _779203) ^ [_1267212, _1267214] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267212, tc_HOL_Obool)), _1267214), c_Orderings_Obot__class_Obot(tc_fun(_1267212, tc_HOL_Obool))) = _1267214)], (24221 ^ _779203) ^ [_1205749, _1205751, _1205753] : [class_Int_Onumber__ring(_1205749), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1205749), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1205749), _1205751), _1205753)), 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(_1205749), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1205749), hAPP(hAPP(c_Power_Opower__class_Opower(_1205749), _1205751), 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(_1205749), _1205753), 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(_1205749), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1205749), hAPP(c_Int_Onumber__class_Onumber__of(_1205749), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1205751)), _1205753)))], (15170 ^ _779203) ^ [_1044493] : [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), _1044493))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1044493) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1044493)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (1390 ^ _779203) ^ [_799538, _799540] : [-(class_Orderings_Owellorder(_799538)), _799540 = _799538, class_Orderings_Owellorder(_799540)], (7953 ^ _779203) ^ [_910162, _910164, _910166, _910168, _910170] : [class_Groups_Oab__group__add(_910162), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_910162), _910164), _910166) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_910162), _910168), _910170), 7960 ^ _779203 : [(7967 ^ _779203) ^ [] : [_910168 = _910170, -(_910164 = _910166)], (7961 ^ _779203) ^ [] : [_910164 = _910166, -(_910168 = _910170)]]], (25050 ^ _779203) ^ [_1220692, _1220694, _1220696] : [class_Rings_Olinordered__semidom(_1220692), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220692), c_Groups_Oone__class_Oone(_1220692)), _1220694)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220692), c_Groups_Oone__class_Oone(_1220692)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220692), _1220694), _1220696))))], (41072 ^ _779203) ^ [_1586429, _1586431] : [-(c_Transitive__Closure_Ortrancl(_1586429, _1586431) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1586429, _1586429), 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(_1586429, _1586429), tc_HOL_Obool), tc_fun(tc_prod(_1586429, _1586429), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1586429, _1586429), tc_HOL_Obool)), _1586431)))], (43530 ^ _779203) ^ [_1649436, _1649438, _1649440, _1649442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1649436), _1649438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1649440, tc_HOL_Obool)), hAPP(c_List_Oset(_1649440), hAPP(hAPP(c_List_Odrop(_1649440), _1649438), _1649442))), hAPP(c_List_Oset(_1649440), hAPP(hAPP(c_List_Odrop(_1649440), _1649436), _1649442)))))], (6349 ^ _779203) ^ [_881466, _881468] : [v_P(hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, _881466)), _881468), hAPP(hAPP(c_Set_Oinsert(t_a), v_mgt(c_Option_Othe(tc_Com_Ocom, c_Com_Obody(_881466)))), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), -(v_P(_881468, hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, _881466)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))))], (12997 ^ _779203) ^ [_1003917, _1003919, _1003921] : [-(hBOOL(hAPP(_1003917, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003919), _1003921)))), 13000 ^ _779203 : [(13003 ^ _779203) ^ [] : [hBOOL(hAPP(_1003917, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13001 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1003919), _1003921)))]], 13005 ^ _779203 : [(13008 ^ _779203) ^ [] : [hBOOL(hAPP(_1003917, 13004 ^ [_1003917, _1003919, _1003921]))], (13006 ^ _779203) ^ [] : [-(_1003919 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003921), 13004 ^ [_1003917, _1003919, _1003921]))]]], (8212 ^ _779203) ^ [_915588, _915590, _915592, _915594] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_915588, _915590, _915592, _915594, c_Orderings_Obot__class_Obot(tc_fun(_915588, tc_HOL_Obool))), _915594)))], (17112 ^ _779203) ^ [_1080597, _1080599, _1080601] : [class_Orderings_Olinorder(_1080597), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080597), _1080599)), -(hBOOL(hAPP(hAPP(c_member(_1080597), _1080601), _1080599))), -(c_Big__Operators_Olinorder__class_OMin(_1080597, hAPP(hAPP(c_Set_Oinsert(_1080597), _1080601), _1080599)) = hAPP(hAPP(c_Finite__Set_Ofold(_1080597, _1080597, c_Orderings_Oord__class_Omin(_1080597)), _1080601), _1080599))], (11344 ^ _779203) ^ [_974468, _974470, _974472, _974474] : [class_Groups_Oordered__comm__monoid__add(_974468), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974468), c_Groups_Ozero__class_Ozero(_974468)), _974470)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974468), _974472), _974474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974468), _974472), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974468), _974474), _974470))))], (4370 ^ _779203) ^ [_845480, _845482, _845484, _845486, _845488, _845490, _845492, _845494, _845496, _845498] : [-(c_Option_Ooption_Ooption__case(_845498, _845494, _845490, _845486, _845482) = c_Option_Ooption_Ooption__case(_845496, _845492, _845488, _845484, _845480)), _845498 = _845496, _845494 = _845492, _845490 = _845488, _845486 = _845484, _845482 = _845480], (8871 ^ _779203) ^ [_929128, _929130, _929132] : [class_Groups_Ogroup__add(_929128), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_929128), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929128), _929130), _929132)), _929132) = _929130)], (42722 ^ _779203) ^ [_1630719, _1630721] : [_1630721 = c_List_Olist_ONil(_1630719), -(c_Orderings_Obot__class_Obot(tc_fun(_1630719, tc_HOL_Obool)) = hAPP(c_List_Oset(_1630719), _1630721))], (36183 ^ _779203) ^ [_1459762, _1459764, _1459766] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1459762, _1459762)), _1459764), c_Relation_OId__on(_1459762, _1459766))), 36187 ^ _779203 : [(36190 ^ _779203) ^ [] : [-(_1459764 = hAPP(hAPP(c_Product__Type_OPair(_1459762, _1459762), 36186 ^ [_1459762, _1459764, _1459766]), 36186 ^ [_1459762, _1459764, _1459766]))], (36188 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1459762), 36186 ^ [_1459762, _1459764, _1459766]), _1459766)))]]], (39395 ^ _779203) ^ [_1545612, _1545614, _1545616] : [-(c_Hilbert__Choice_OEps(tc_prod(_1545612, _1545614), hAPP(c_Product__Type_Oprod_Oprod__case(_1545612, _1545614, tc_HOL_Obool), _1545616)) = c_Hilbert__Choice_OEps(tc_prod(_1545612, _1545614), hAPP(hAPP(c_COMBS(tc_prod(_1545612, _1545614), _1545614, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1545612, tc_fun(_1545614, tc_HOL_Obool), tc_prod(_1545612, _1545614)), _1545616), c_Product__Type_Ofst(_1545612, _1545614))), c_Product__Type_Osnd(_1545612, _1545614))))], (42862 ^ _779203) ^ [_1633498, _1633500, _1633502] : [hBOOL(hAPP(hAPP(c_member(_1633498), _1633500), hAPP(c_List_Oset(_1633498), _1633502))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633498)), c_List_Oremove1(_1633498, _1633500, _1633502)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633498)), _1633502)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (52681 ^ _779203) ^ [_1836735, _1836737] : [-(hAPP(c_COMBI(_1836735), _1836737) = _1836737)], (21941 ^ _779203) ^ [_1165932, _1165934, _1165936] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1165932), _1165934)), _1165936) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1165932), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1165934), _1165936))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1165932), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1165934, _1165936))), _1165936)))], (37481 ^ _779203) ^ [_1488722, _1488724] : [-(hAPP(c_Set_OCollect(_1488722), _1488724) = _1488724)], (32697 ^ _779203) ^ [_1377651] : [-(c_Divides_Oadjust(_1377651) = 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)), _1377651))))), 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)), _1377651))))), 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))))))))], (36270 ^ _779203) ^ [_1461450, _1461452] : [-(c_Fun_Oinj__on(_1461450, _1461450, c_COMBI(_1461450), _1461452))], (17722 ^ _779203) ^ [_1091567, _1091569, _1091571] : [class_Orderings_Olinorder(_1091567), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091567), _1091569)), -(hBOOL(hAPP(hAPP(c_member(_1091567), _1091571), _1091569))), -(_1091569 = c_Orderings_Obot__class_Obot(tc_fun(_1091567, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1091567, c_Orderings_Oord__class_Omin(_1091567), hAPP(hAPP(c_Set_Oinsert(_1091567), _1091571), _1091569)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1091567), _1091571), c_Big__Operators_Olattice_OInf__fin(_1091567, c_Orderings_Oord__class_Omin(_1091567), _1091569)))], (33006 ^ _779203) ^ [_1383948, _1383950] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1383948, _1383948)), hAPP(hAPP(c_Product__Type_OPair(_1383948, _1383948), 33007 ^ [_1383948, _1383950]), 33007 ^ [_1383948, _1383950])), _1383950)), -(c_Nitpick_Orefl_H(_1383948, _1383950))], (6685 ^ _779203) ^ [_887309, _887311, _887313, _887315, _887317] : [c_Finite__Set_Ofolding__one(_887309, _887311, _887313), hBOOL(hAPP(c_Finite__Set_Ofinite(_887309), _887315)), hBOOL(hAPP(hAPP(c_member(_887309), _887317), _887315)), 6696 ^ _779203 : [(6703 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887309, tc_HOL_Obool)), _887315), hAPP(hAPP(c_Set_Oinsert(_887309), _887317), c_Orderings_Obot__class_Obot(tc_fun(_887309, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_887309, tc_HOL_Obool))), -(hAPP(_887313, _887315) = hAPP(hAPP(_887311, _887317), hAPP(_887313, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887309, tc_HOL_Obool)), _887315), hAPP(hAPP(c_Set_Oinsert(_887309), _887317), c_Orderings_Obot__class_Obot(tc_fun(_887309, tc_HOL_Obool)))))))], (6697 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_887309, tc_HOL_Obool)), _887315), hAPP(hAPP(c_Set_Oinsert(_887309), _887317), c_Orderings_Obot__class_Obot(tc_fun(_887309, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_887309, tc_HOL_Obool)), -(hAPP(_887313, _887315) = _887317)]]], (27344 ^ _779203) ^ [_1260780, _1260782, _1260784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1260780, tc_HOL_Obool)), _1260782), _1260784)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260780, tc_HOL_Obool)), _1260782), _1260784) = _1260784)], (3264 ^ _779203) ^ [_827815, _827817, _827819, _827821] : [-(c_List_Olists(_827821, _827817) = c_List_Olists(_827819, _827815)), _827821 = _827819, _827817 = _827815], (39041 ^ _779203) ^ [_1536366, _1536368] : [-(c_List_Olex(_1536366, _1536368) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1536366), tc_List_Olist(_1536366)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1536366, _1536368)))], (12284 ^ _779203) ^ [_991098, _991100] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_991098), _991100))), -(hAPP(c_Finite__Set_Ocard(_991098), _991100) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40907 ^ _779203) ^ [_1582362] : [-(c_Relation_Osingle__valued(_1582362, _1582362, c_Relation_OId(_1582362)))], (32837 ^ _779203) ^ [_1380491, _1380493, _1380495, _1380497, _1380499, _1380501] : [hBOOL(hAPP(hAPP(_1380491, _1380493), _1380495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1380497, tc_fun(_1380499, tc_HOL_Obool))), _1380491), _1380501)), -(hBOOL(hAPP(hAPP(_1380501, _1380493), _1380495)))], (27596 ^ _779203) ^ [_1265566] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1265566), c_Orderings_Otop__class_Otop(tc_fun(_1265566, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1265566)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1265566), tc_HOL_Obool)))))], (50859 ^ _779203) ^ [_1809392] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809392, _1809392) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1809392), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (408 ^ _779203) ^ [_785339, _785341, _785343, _785345] : [-(c_Relation_Oirrefl(_785343, _785339)), c_Relation_Oirrefl(_785345, _785341), _785345 = _785343, _785341 = _785339], (5771 ^ _779203) ^ [_870491, _870493, _870495, _870497] : [_870491 = _870493, 5774 ^ _779203 : [(5781 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870495), _870493), _870497)), -(hBOOL(hAPP(hAPP(c_member(_870495), _870491), _870497)))], (5775 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870495), _870491), _870497)), -(hBOOL(hAPP(hAPP(c_member(_870495), _870493), _870497)))]]], (45853 ^ _779203) ^ [_1702093, _1702095] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1702093, _1702095)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1702093), _1702095))], (20092 ^ _779203) ^ [_1133639, _1133641, _1133643] : [class_Rings_Odivision__ring(_1133639), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1133639), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133639), _1133641), _1133643)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1133639), hAPP(c_Groups_Ouminus__class_Ouminus(_1133639), _1133641)), _1133643))], (33589 ^ _779203) ^ [_1393967, _1393969, _1393971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1393967, tc_fun(_1393967, tc_HOL_Obool))), _1393969), _1393971)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1393967, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1393967, _1393971)), c_Wellfounded_Oaccp(_1393967, _1393969))))], (7863 ^ _779203) ^ [_908500, _908502, _908504, _908506] : [class_Orderings_Oorder(_908500), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908500), _908502), _908504)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908500), _908506), _908502)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_908500), _908506), _908504)))], (5879 ^ _779203) ^ [_872343, _872345, _872347] : [_872343 = _872345, 5882 ^ _779203 : [(5885 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872347, tc_HOL_Obool)), _872345), _872343)))], (5883 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_872347, tc_HOL_Obool)), _872343), _872345)))]]], (24420 ^ _779203) ^ [_1209418, _1209420] : [c_Nat__Transfer_Onat__set(_1209418), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1209420), _1209418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1209420)))], (40719 ^ _779203) ^ [_1577606, _1577608, _1577610, _1577612] : [-(hAPP(c_Relation_Oconverse(_1577606, _1577608), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1577606, _1577608), tc_HOL_Obool)), _1577610), _1577612)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1577608, _1577606), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1577606, _1577608), _1577610)), hAPP(c_Relation_Oconverse(_1577606, _1577608), _1577612)))], (15336 ^ _779203) ^ [_1047958, _1047960, _1047962] : [class_Orderings_Olinorder(_1047958), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1047958), _1047960), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1047958), _1047960), _1047962)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1047958), _1047960), _1047962))], (2850 ^ _779203) ^ [_821396, _821398, _821400, _821402, _821404, _821406] : [-(c_Nitpick_Oof__frac(_821406, _821402, _821398) = c_Nitpick_Oof__frac(_821404, _821400, _821396)), _821406 = _821404, _821402 = _821400, _821398 = _821396], (41195 ^ _779203) ^ [_1590035, _1590037, _1590039, _1590041] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590035, _1590035)), hAPP(hAPP(c_Product__Type_OPair(_1590035, _1590035), _1590037), _1590039)), c_Transitive__Closure_Otrancl(_1590035, _1590041))), 41199 ^ _779203 : [(41202 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590035, _1590035)), hAPP(hAPP(c_Product__Type_OPair(_1590035, _1590035), 41198 ^ [_1590035, _1590037, _1590039, _1590041]), _1590039)), c_Transitive__Closure_Ortrancl(_1590035, _1590041))))], (41200 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590035, _1590035)), hAPP(hAPP(c_Product__Type_OPair(_1590035, _1590035), _1590037), 41198 ^ [_1590035, _1590037, _1590039, _1590041])), _1590041)))]]], (21573 ^ _779203) ^ [_1158977] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1158977)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1158977)))], (37116 ^ _779203) ^ [_1479501, _1479503, _1479505, _1479507] : [-(c_HOL_OThe(tc_prod(_1479501, _1479503), hAPP(c_Product__Type_Oprod_Oprod__case(_1479501, _1479503, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1479501, tc_fun(_1479503, tc_HOL_Obool), tc_fun(_1479503, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1479503, tc_HOL_Obool), tc_fun(_1479503, tc_HOL_Obool)), _1479501), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1479503)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1479501), c_fconj), hAPP(c_fequal, _1479505)))), hAPP(c_fequal, _1479507)))) = hAPP(hAPP(c_Product__Type_OPair(_1479501, _1479503), _1479505), _1479507))], (33939 ^ _779203) ^ [_1401106, _1401108, _1401110, _1401112, _1401114] : [hBOOL(hAPP(hAPP(_1401106, _1401108), _1401110)), -(hBOOL(hAPP(hAPP(_1401106, hAPP(c_Product__Type_Osnd(_1401112, _1401114), hAPP(hAPP(c_Product__Type_OPair(_1401112, _1401114), _1401110), _1401108))), hAPP(c_Product__Type_Ofst(_1401112, _1401114), hAPP(hAPP(c_Product__Type_OPair(_1401112, _1401114), _1401110), _1401108)))))], (33925 ^ _779203) ^ [_1400792, _1400794, _1400796, _1400798, _1400800] : [-(c_Product__Type_Oprod_Oprod__size(_1400792, _1400794, _1400796, _1400798, _1400800) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1400796, hAPP(c_Product__Type_Ofst(_1400792, _1400794), _1400800))), hAPP(_1400798, hAPP(c_Product__Type_Osnd(_1400792, _1400794), _1400800)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27630 ^ _779203) ^ [_1266139, _1266141] : [class_Lattices_Obounded__lattice__bot(_1266139), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1266139), _1266141), c_Orderings_Obot__class_Obot(_1266139)) = _1266141)], (48648 ^ _779203) ^ [_1760963, _1760965, _1760967] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1760963, _1760965, _1760967) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1760963)], (23038 ^ _779203) ^ [_1184807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1184807))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184807)))], (16572 ^ _779203) ^ [_1070607, _1070609, _1070611] : [class_Orderings_Olinorder(_1070607), hBOOL(hAPP(c_Finite__Set_Ofinite(_1070607), _1070609)), -(_1070609 = c_Orderings_Obot__class_Obot(tc_fun(_1070607, tc_HOL_Obool))), 16583 ^ _779203 : [(16593 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070607), hAPP(c_Finite__Set_Ofold1(_1070607, c_Orderings_Oord__class_Omin(_1070607)), _1070609)), _1070611))), 16594 ^ _779203 : [(16595 ^ _779203) ^ [_1070996] : [hBOOL(hAPP(hAPP(c_member(_1070607), _1070996), _1070609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070607), _1070996), _1070611))]]], (16584 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070607), hAPP(c_Finite__Set_Ofold1(_1070607, c_Orderings_Oord__class_Omin(_1070607)), _1070609)), _1070611)), 16588 ^ _779203 : [(16591 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070607), 16587 ^ [_1070607, _1070609, _1070611]), _1070611)))], (16589 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1070607), 16587 ^ [_1070607, _1070609, _1070611]), _1070609)))]]]]], (9534 ^ _779203) ^ [_941931, _941933, _941935] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _941931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _941933), _941935)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _941931), _941933)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _941931), _941935)))], (34464 ^ _779203) ^ [_1414479, _1414481, _1414483, _1414485] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414479, tc_fun(_1414481, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1414479, tc_HOL_Obool), _1414483)), _1414485) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1414479, tc_HOL_Obool), tc_fun(_1414481, tc_HOL_Obool)), _1414483), hAPP(hAPP(c_COMBC(tc_fun(_1414479, tc_HOL_Obool), tc_fun(_1414479, tc_fun(_1414481, tc_HOL_Obool)), tc_fun(_1414481, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414479, tc_fun(_1414481, tc_HOL_Obool))), _1414485)))], (48168 ^ _779203) ^ [_1750848, _1750850, _1750852, _1750854] : [-(hAPP(hAPP(c_List_Odrop(_1750848), _1750850), c_List_Oreplicate(_1750848, _1750852, _1750854)) = c_List_Oreplicate(_1750848, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1750852), _1750850), _1750854))], (268 ^ _779203) ^ [_783361, _783363] : [-(class_Fields_Ofield__inverse__zero(_783361)), _783363 = _783361, class_Fields_Ofield__inverse__zero(_783363)], (12667 ^ _779203) ^ [_997823, _997825, _997827, _997829, _997831] : [class_Rings_Olinordered__semiring__strict(_997823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997823), _997825), _997827)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997823), _997829), _997831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997823), c_Groups_Ozero__class_Ozero(_997823)), _997825)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_997823), c_Groups_Ozero__class_Ozero(_997823)), _997829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997823), _997825), _997829)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_997823), _997827), _997831))))], (33685 ^ _779203) ^ [_1395791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1395791)), 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), _1395791)) = 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), _1395791))))))], (38653 ^ _779203) ^ [_1527618] : [-(c_Wellfounded_Owf(tc_fun(_1527618, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1527618)))], (24153 ^ _779203) ^ [_1204589] : [_1204589 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1204589) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20550 ^ _779203) ^ [_1141600, _1141602, _1141604] : [class_Int_Onumber__ring(_1141600), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1141600), hAPP(c_Int_Onumber__class_Onumber__of(_1141600), _1141602)), hAPP(c_Int_Onumber__class_Onumber__of(_1141600), _1141604)) = hAPP(c_Int_Onumber__class_Onumber__of(_1141600), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1141602), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1141604))))], (46202 ^ _779203) ^ [_1708354, _1708356] : [class_Orderings_Olinorder(_1708354), c_List_Olinorder__class_Osorted(_1708354, _1708356), -(c_List_Olinorder__class_Osorted(_1708354, c_List_Oremdups(_1708354, _1708356)))], (9715 ^ _779203) ^ [_945148, _945150, _945152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945148), _945150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _945150), _945152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _945148)), _945152)))], (48842 ^ _779203) ^ [_1765458, _1765460] : [c_Relation_Otrans(_1765458, _1765460), -(c_Relation_Otrans(tc_List_Olist(_1765458), c_List_Olistrel(_1765458, _1765460)))], (13907 ^ _779203) ^ [_1020980, _1020982, _1020984, _1020986, _1020988] : [class_Fields_Ofield__inverse__zero(_1020980), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020980), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1020980), _1020982), _1020984)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1020980), _1020986), _1020988)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1020980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020980), _1020982), _1020986)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1020980), _1020984), _1020988)))], (41657 ^ _779203) ^ [_1604522, _1604524, _1604526, _1604528, _1604530] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604522), tc_List_Olist(_1604522))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604522), tc_List_Olist(_1604522)), hAPP(hAPP(c_List_Olist_OCons(_1604522), _1604524), _1604526)), _1604528)), c_List_Olistrel(_1604522, _1604530))), 41662 ^ _779203 : [(41667 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1604522), tc_List_Olist(_1604522))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1604522), tc_List_Olist(_1604522)), _1604526), 41661 ^ [_1604522, _1604524, _1604526, _1604528, _1604530])), c_List_Olistrel(_1604522, _1604530))))], (41665 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604522, _1604522)), hAPP(hAPP(c_Product__Type_OPair(_1604522, _1604522), _1604524), 41660 ^ [_1604522, _1604524, _1604526, _1604528, _1604530])), _1604530)))], (41663 ^ _779203) ^ [] : [-(_1604528 = hAPP(hAPP(c_List_Olist_OCons(_1604522), 41660 ^ [_1604522, _1604524, _1604526, _1604528, _1604530]), 41661 ^ [_1604522, _1604524, _1604526, _1604528, _1604530]))]]], (24592 ^ _779203) ^ [_1212350, _1212352] : [class_Rings_Oring__1__no__zero__divisors(_1212350), 24595 ^ _779203 : [(24596 ^ _779203) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1212350), _1212352), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1212350), -(_1212352 = c_Groups_Oone__class_Oone(_1212350)), -(_1212352 = hAPP(c_Groups_Ouminus__class_Ouminus(_1212350), c_Groups_Oone__class_Oone(_1212350)))], (24606 ^ _779203) ^ [] : [24607 ^ _779203 : [(24610 ^ _779203) ^ [] : [_1212352 = hAPP(c_Groups_Ouminus__class_Ouminus(_1212350), c_Groups_Oone__class_Oone(_1212350))], (24608 ^ _779203) ^ [] : [_1212352 = c_Groups_Oone__class_Oone(_1212350)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1212350), _1212352), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1212350))]]], (46604 ^ _779203) ^ [_1716260, _1716262, _1716264] : [_1716264 = hAPP(hAPP(c_List_Olist_OCons(_1716260), _1716262), c_List_Olist_ONil(_1716260)), -(hAPP(hAPP(c_List_Olist_OCons(_1716260), _1716262), c_List_Olist_ONil(_1716260)) = hAPP(c_List_Orev(_1716260), _1716264))], (19978 ^ _779203) ^ [_1131375, _1131377, _1131379] : [class_Groups_Ogroup__add(_1131375), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1131375), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131375), _1131377), _1131379)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131375), hAPP(c_Groups_Ouminus__class_Ouminus(_1131375), _1131379)), hAPP(c_Groups_Ouminus__class_Ouminus(_1131375), _1131377)))], (41248 ^ _779203) ^ [_1591475, _1591477, _1591479, _1591481] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591475, _1591477)), _1591479), hAPP(c_Relation_Oconverse(_1591477, _1591475), _1591481))), 41253 ^ _779203 : [(41256 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591477, _1591475)), hAPP(hAPP(c_Product__Type_OPair(_1591477, _1591475), 41251 ^ [_1591475, _1591477, _1591479, _1591481]), 41252 ^ [_1591475, _1591477, _1591479, _1591481])), _1591481)))], (41254 ^ _779203) ^ [] : [-(_1591479 = hAPP(hAPP(c_Product__Type_OPair(_1591475, _1591477), 41252 ^ [_1591475, _1591477, _1591479, _1591481]), 41251 ^ [_1591475, _1591477, _1591479, _1591481]))]]], (33000 ^ _779203) ^ [_1383828, _1383830] : [c_Nitpick_Orefl_H(_1383828, _1383830), 33003 ^ _779203 : [(33004 ^ _779203) ^ [_1383906] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1383828, _1383828)), hAPP(hAPP(c_Product__Type_OPair(_1383828, _1383828), _1383906), _1383906)), _1383830)))]]], (27660 ^ _779203) ^ [_1266673, _1266675, _1266677] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1266673), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1266673, tc_HOL_Obool)), _1266675), _1266677)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266673), _1266675)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1266673), _1266677))], (49725 ^ _779203) ^ [_1784367, _1784369, _1784371, _1784373, _1784375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1784367, tc_HOL_Obool)), _1784369), hAPP(c_Set_Oimage(_1784371, _1784367, _1784373), _1784375))), -(c_Fun_Oinj__on(_1784367, _1784371, c_Hilbert__Choice_Oinv__into(_1784371, _1784367, _1784375, _1784373), _1784369))], (48374 ^ _779203) ^ [_1754706, _1754708, _1754710] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754706)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1754706, _1754708, _1754710)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1754706)), _1754710)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10051 ^ _779203) ^ [_951023, _951025, _951027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951023), _951025)), 10054 ^ _779203 : [(10061 ^ _779203) ^ [] : [_951025 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951027), _951023), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _951025), _951023) = _951027)], (10055 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _951025), _951023) = _951027, -(_951025 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951027), _951023))]]], (51447 ^ _779203) ^ [_1819111, _1819113, _1819115] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819111), _1819113)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819113), _1819111))), _1819113 = _1819115, 51458 ^ _779203 : [(51461 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819115), _1819111))], (51459 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819111), _1819115)))]]], (38212 ^ _779203) ^ [_1514576, _1514578] : [-(c_Fun_Oinj__on(_1514576, _1514576, c_Fun_Oid(_1514576), _1514578))], (9943 ^ _779203) ^ [_948976, _948978, _948980] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _948976), _948978)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _948976), _948980)), 9950 ^ _779203 : [(9957 ^ _779203) ^ [] : [_948978 = _948980, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948978), _948976) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948980), _948976))], (9951 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948978), _948976) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948980), _948976), -(_948978 = _948980)]]], (26992 ^ _779203) ^ [_1254651, _1254653] : [26993 ^ _779203 : [(26996 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1254653), _1254651))], (26994 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1254651), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1254651, _1254653) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (21945 ^ _779203) ^ [_1166052, _1166054] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1166052), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1166054), _1166052)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1166054), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1166054, _1166052)))], (25994 ^ _779203) ^ [_1236296, _1236298] : [class_Rings_Oring__1(_1236296), -(hAPP(c_Int_Oring__1__class_Oof__int(_1236296), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1236298)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1236296), hAPP(c_Int_Oring__1__class_Oof__int(_1236296), _1236298)))], (1360 ^ _779203) ^ [_799163, _799165] : [-(class_Rings_Oring(_799163)), _799165 = _799163, class_Rings_Oring(_799165)], (16603 ^ _779203) ^ [_1071157, _1071159, _1071161] : [class_Orderings_Olinorder(_1071157), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071157), _1071159)), -(_1071159 = c_Orderings_Obot__class_Obot(tc_fun(_1071157, tc_HOL_Obool))), 16614 ^ _779203 : [(16615 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071157), _1071161), hAPP(c_Finite__Set_Ofold1(_1071157, c_Orderings_Oord__class_Omin(_1071157)), _1071159))), 16618 ^ _779203 : [(16619 ^ _779203) ^ [_1071450] : [hBOOL(hAPP(hAPP(c_member(_1071157), _1071450), _1071159)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071157), _1071161), _1071450)))]]], (16625 ^ _779203) ^ [] : [16627 ^ _779203 : [(16630 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071157), _1071161), 16626 ^ [_1071157, _1071159, _1071161]))], (16628 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071157), 16626 ^ [_1071157, _1071159, _1071161]), _1071159)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1071157), _1071161), hAPP(c_Finite__Set_Ofold1(_1071157, c_Orderings_Oord__class_Omin(_1071157)), _1071159))))]]], (40939 ^ _779203) ^ [_1582994, _1582996, _1582998, _1583000, _1583002] : [c_Relation_Osingle__valued(_1582994, _1582996, _1582998), c_Relation_Osingle__valued(_1582996, _1583000, _1583002), -(c_Relation_Osingle__valued(_1582994, _1583000, hAPP(hAPP(c_Relation_Orel__comp(_1582994, _1582996, _1583000), _1582998), _1583002)))], (8653 ^ _779203) ^ [_925032, _925034, _925036, _925038] : [class_Groups_Ocancel__semigroup__add(_925032), 8656 ^ _779203 : [(8663 ^ _779203) ^ [] : [_925034 = _925038, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925032), _925034), _925036) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925032), _925038), _925036))], (8657 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925032), _925034), _925036) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925032), _925038), _925036), -(_925034 = _925038)]]], (46626 ^ _779203) ^ [_1716858, _1716860, _1716862, _1716864, _1716866] : [c_List_Olist__all2(_1716858, _1716860, _1716862, hAPP(c_List_Orev(_1716858), _1716864), _1716866), -(c_List_Olist__all2(_1716858, _1716860, _1716862, _1716864, hAPP(c_List_Orev(_1716860), _1716866)))], (18897 ^ _779203) ^ [_1112134] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1112134)), -(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)), _1112134))))], (47712 ^ _779203) ^ [_1740575, _1740577, _1740579] : [c_List_Olist__ex(_1740575, _1740577, _1740579), -(c_List_Olist__ex(_1740575, _1740577, hAPP(c_List_Orev(_1740575), _1740579)))], (21897 ^ _779203) ^ [_1164858, _1164860] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1164858, _1164860)), _1164860) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (33357 ^ _779203) ^ [_1389794, _1389796, _1389798] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1389794), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1389796)), _1389798)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389794, _1389796), hAPP(c_Divides_OnegateSnd, _1389798))))], (47860 ^ _779203) ^ [_1743638, _1743640, _1743642] : [c_List_Olist__all(_1743638, _1743640, hAPP(c_List_Orev(_1743638), _1743642)), -(c_List_Olist__all(_1743638, _1743640, _1743642))], (42860 ^ _779203) ^ [_1633411, _1633413] : [-(c_List_Oset__Cons(_1633411, _1633413, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633411)), c_List_Olist_ONil(_1633411)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633411), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1633411, tc_List_Olist(_1633411), hAPP(hAPP(c_COMBC(_1633411, tc_List_Olist(_1633411), tc_List_Olist(_1633411)), c_List_Olist_OCons(_1633411)), c_List_Olist_ONil(_1633411))), _1633413))], (52667 ^ _779203) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (52445 ^ _779203) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (27958 ^ _779203) ^ [_1272724, _1272726, _1272728, _1272730, _1272732] : [-(hAPP(c_Set_Oimage(_1272724, _1272726, _1272728), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272724, tc_HOL_Obool)), _1272730), _1272732)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1272726, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1272724, _1272726, _1272728), _1272730)), hAPP(c_Set_Oimage(_1272724, _1272726, _1272728), _1272732)))], (22758 ^ _779203) ^ [_1180203, _1180205, _1180207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180203), 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)), _1180205)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180205), _1180207)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180203), _1180205)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180203), _1180207))))], (39720 ^ _779203) ^ [_1552811, _1552813, _1552815, _1552817, _1552819, _1552821] : [c_Finite__Set_Ofolding(_1552811, _1552813, _1552815, _1552817), -(hAPP(c_Fun_Ocomp(_1552813, _1552813, _1552813, hAPP(_1552815, _1552819)), hAPP(_1552815, _1552821)) = hAPP(c_Fun_Ocomp(_1552813, _1552813, _1552813, hAPP(_1552815, _1552821)), hAPP(_1552815, _1552819)))], (31165 ^ _779203) ^ [_1337151, _1337153, _1337155, _1337157, _1337159] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1337151, _1337153, _1337155), _1337157), _1337159), c_Orderings_Obot__class_Obot(tc_fun(_1337153, tc_HOL_Obool))) = _1337159)], (21809 ^ _779203) ^ [_1163190, _1163192] : [class_Int_Onumber__ring(_1163190), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163190), _1163192), hAPP(c_Int_Onumber__class_Onumber__of(_1163190), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163190), _1163192), _1163192))], (18300 ^ _779203) ^ [_1102012, _1102014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1102012), _1102014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1102012)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1102014))))], (21169 ^ _779203) ^ [_1152541] : [c_Int_OPls = c_Int_OBit1(_1152541)], (10079 ^ _779203) ^ [_951556, _951558, _951560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _951556), _951558)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _951558), _951560)), _951556) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _951558), _951556)), _951560))], (21623 ^ _779203) ^ [_1159848, _1159850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1159848)), c_Int_OBit1(_1159850))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1159848), _1159850)))], (35629 ^ _779203) ^ [_1446674, _1446676, _1446678] : [_1446676 = c_Orderings_Obot__class_Obot(tc_fun(_1446674, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1446674, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1446674), _1446676), _1446678))], (9249 ^ _779203) ^ [_937019, _937021] : [_937019 = _937021, -(hAPP(c_Nat_OSuc, _937019) = hAPP(c_Nat_OSuc, _937021))], (42545 ^ _779203) ^ [_1627454, _1627456, _1627458, _1627460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1627454), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627456)), _1627458))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1627454), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627456)), _1627460))), 42555 ^ _779203 : [(42558 ^ _779203) ^ [] : [hAPP(hAPP(c_List_Onth(_1627456), _1627458), 42554 ^ [_1627454, _1627456, _1627458, _1627460]) = hAPP(hAPP(c_List_Onth(_1627456), _1627460), 42554 ^ [_1627454, _1627456, _1627458, _1627460])], (42556 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 42554 ^ [_1627454, _1627456, _1627458, _1627460]), _1627454)))]], -(hAPP(hAPP(c_List_Otake(_1627456), _1627454), _1627458) = hAPP(hAPP(c_List_Otake(_1627456), _1627454), _1627460))], (40370 ^ _779203) ^ [_1569223, _1569225] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1569223, _1569223), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1569223, _1569225)), c_Relation_OId(_1569223)) = c_Transitive__Closure_Ortrancl(_1569223, _1569225))], (17974 ^ _779203) ^ [_1096169, _1096171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096169)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1096171)), -(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), _1096169), _1096171))))], (28350 ^ _779203) ^ [_1280516] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1280516)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1280516))], (20556 ^ _779203) ^ [_1141756, _1141758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1141756)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1141758)))), 20559 ^ _779203 : [(20562 ^ _779203) ^ [] : [-(_1141758 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20560 ^ _779203) ^ [] : [-(_1141756 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22474 ^ _779203) ^ [_1175519, _1175521, _1175523] : [class_Divides_Osemiring__div(_1175519), -(_1175521 = c_Groups_Ozero__class_Ozero(_1175519)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1175519), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1175519), _1175521), _1175523)), _1175521) = _1175523)], (43490 ^ _779203) ^ [_1648506, _1648508, _1648510] : [-(c_List_Obutlast(_1648506, hAPP(hAPP(c_List_Odrop(_1648506), _1648508), _1648510)) = hAPP(hAPP(c_List_Odrop(_1648506), _1648508), c_List_Obutlast(_1648506, _1648510)))], (15662 ^ _779203) ^ [_1053784, _1053786, _1053788] : [class_Orderings_Olinorder(_1053784), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1053784), _1053786), _1053788)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1053784), _1053788), _1053786) = _1053786)], (9641 ^ _779203) ^ [_943881, _943883] : [9642 ^ _779203 : [(9645 ^ _779203) ^ [] : [_943881 = _943883], (9643 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943881), _943883))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _943881), hAPP(c_Nat_OSuc, _943883))))], (44841 ^ _779203) ^ [_1677655] : [-(hAPP(c_Code__Numeral_Onat__of, _1677655) = c_Code__Numeral_Onat__of__aux(_1677655, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37124 ^ _779203) ^ [_1479835, _1479837] : [-(c_Divides_Odivmod__nat(_1479835, _1479837) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1479835, _1479837)))], (39397 ^ _779203) ^ [_1545693, _1545695, _1545697] : [39398 ^ _779203 : [(39399 ^ _779203) ^ [_1545747] : [hBOOL(hAPP(_1545693, _1545747))]], _1545695 = c_Hilbert__Choice_OEps(_1545697, _1545693), -(hBOOL(hAPP(_1545693, _1545695)))], (12945 ^ _779203) ^ [_1003047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1003047)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003047), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1003047)], (11838 ^ _779203) ^ [_983515, _983517, _983519] : [class_Rings_Olinordered__semiring__strict(_983515), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983515), c_Groups_Ozero__class_Ozero(_983515)), _983517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983515), c_Groups_Ozero__class_Ozero(_983515)), _983519)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983515), c_Groups_Ozero__class_Ozero(_983515)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_983515), _983517), _983519))))], (36798 ^ _779203) ^ [_1472721] : [class_Nat_Osemiring__char__0(_1472721), -(c_Fun_Oinj__on(tc_Nat_Onat, _1472721, c_Nat_Osemiring__1__class_Oof__nat(_1472721), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (12761 ^ _779203) ^ [_999630, _999632, _999634, _999636] : [class_Rings_Olinordered__semiring(_999630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999630), _999632), _999634)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_999630), _999632), _999636))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_999630), c_Groups_Ozero__class_Ozero(_999630)), _999632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999630), _999634), _999636)))], (45368 ^ _779203) ^ [_1689875, _1689877] : [-(hAPP(c_List_Oset(_1689875), c_List_Oremdups(_1689875, _1689877)) = hAPP(c_List_Oset(_1689875), _1689877))], (28568 ^ _779203) ^ [_1284503, _1284505] : [class_Groups_Oordered__ab__group__add(_1284503), -(hAPP(c_Set_Oimage(_1284503, _1284503, c_Groups_Ouminus__class_Ouminus(_1284503)), hAPP(c_SetInterval_Oord__class_OatLeast(_1284503), _1284505)) = hAPP(c_SetInterval_Oord__class_OatMost(_1284503), hAPP(c_Groups_Ouminus__class_Ouminus(_1284503), _1284505)))], (52525 ^ _779203) ^ [_1835094, _1835096] : [-(class_Enum_Oenum(tc_sum(_1835094, _1835096))), class_Enum_Oenum(_1835094), class_Enum_Oenum(_1835096)], (20694 ^ _779203) ^ [_1144400, _1144402, _1144404, _1144406, _1144408] : [hBOOL(hAPP(hAPP(c_member(_1144400), _1144402), c_SetInterval_Oord_OgreaterThanLessThan(_1144400, _1144404, _1144406, _1144408))), 20697 ^ _779203 : [(20700 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1144404, _1144402), _1144408)))], (20698 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1144404, _1144406), _1144402)))]]], (49610 ^ _779203) ^ [_1781825] : [-(c_Hilbert__Choice_Oinv__into(_1781825, _1781825, c_Orderings_Otop__class_Otop(tc_fun(_1781825, tc_HOL_Obool)), c_Fun_Oid(_1781825)) = c_Fun_Oid(_1781825))], (15264 ^ _779203) ^ [_1046246, _1046248, _1046250, _1046252] : [class_Orderings_Olinorder(_1046246), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046246), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046246), _1046248), _1046250)), _1046252) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046246), _1046248), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046246), _1046250), _1046252)))], (35308 ^ _779203) ^ [_1437139] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1437139)), -(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))), _1437139)), c_FunDef_Omax__weak)))], (28994 ^ _779203) ^ [_1292107, _1292109, _1292111] : [class_Lattices_Olattice(_1292107), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292107), _1292109)), -(hBOOL(hAPP(hAPP(c_member(_1292107), _1292111), _1292109))), -(_1292109 = c_Orderings_Obot__class_Obot(tc_fun(_1292107, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1292107, hAPP(hAPP(c_Set_Oinsert(_1292107), _1292111), _1292109)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292107), _1292111), c_Big__Operators_Olattice__class_OSup__fin(_1292107, _1292109)))], (18762 ^ _779203) ^ [_1109863, _1109865, _1109867] : [hBOOL(hAPP(_1109863, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109865), _1109867)))), 18765 ^ _779203 : [(18772 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1109865), _1109867)), -(hBOOL(hAPP(_1109863, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (18766 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109867), _1109865)), -(hBOOL(hAPP(_1109863, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1109865)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1109867)))))]]], (36160 ^ _779203) ^ [_1459233, _1459235, _1459237, _1459239, _1459241, _1459243, _1459245] : [c_Equiv__Relations_Oequiv(_1459233, _1459235, _1459237), c_Equiv__Relations_Ocongruent(_1459233, tc_fun(_1459239, tc_HOL_Obool), _1459237, _1459241), hBOOL(hAPP(hAPP(c_member(tc_fun(_1459233, tc_HOL_Obool)), _1459243), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1459233), _1459235), _1459237))), 36174 ^ _779203 : [(36177 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1459239, tc_HOL_Obool)), hAPP(_1459241, 36173 ^ [_1459233, _1459235, _1459237, _1459239, _1459241, _1459243, _1459245])), _1459245))], (36175 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1459233), 36173 ^ [_1459233, _1459235, _1459237, _1459239, _1459241, _1459243, _1459245]), _1459235)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1459239, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1459233, tc_fun(_1459239, tc_HOL_Obool)), _1459243), _1459241)), _1459245)))], (29946 ^ _779203) ^ [_1312185, _1312187, _1312189, _1312191] : [class_Orderings_Olinorder(_1312185), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312185, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1312185), _1312187)), c_SetInterval_Oord__class_OatLeastAtMost(_1312185, _1312189, _1312191)) = c_SetInterval_Oord__class_OatLeastAtMost(_1312185, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1312185), _1312187), _1312189), _1312191))], (23760 ^ _779203) ^ [_1197413, _1197415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197413), _1197415)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1197413, _1197415) = _1197413)], (43664 ^ _779203) ^ [_1652777, _1652779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652777)), _1652779)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1652777), _1652779) = _1652779)], (12026 ^ _779203) ^ [_987026, _987028, _987030] : [class_Groups_Oordered__ab__group__add(_987026), 12029 ^ _779203 : [(12036 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987026), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_987026), _987028), _987030)), c_Groups_Ozero__class_Ozero(_987026))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987026), _987028), _987030)))], (12030 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987026), _987028), _987030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_987026), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_987026), _987028), _987030)), c_Groups_Ozero__class_Ozero(_987026))))]]], (44444 ^ _779203) ^ [_1669241, _1669243, _1669245, _1669247] : [-(hAPP(c_List_Oset(_1669241), hAPP(hAPP(c_List_Omap(_1669243, _1669241), _1669245), _1669247)) = hAPP(c_Set_Oimage(_1669243, _1669241, _1669245), hAPP(c_List_Oset(_1669243), _1669247)))], (29702 ^ _779203) ^ [_1306499, _1306501, _1306503, _1306505] : [hBOOL(hAPP(hAPP(c_member(_1306499), _1306501), _1306503)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306499, tc_HOL_Obool)), _1306503), hAPP(hAPP(c_Set_Oinsert(_1306499), _1306501), _1306505)) = hAPP(hAPP(c_Set_Oinsert(_1306499), _1306501), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1306499, tc_HOL_Obool)), _1306503), _1306505)))], (24924 ^ _779203) ^ [_1218342, _1218344, _1218346] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218342)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1218342), _1218344)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1218342), _1218346))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1218344), _1218346)))], (18367 ^ _779203) ^ [_1103246, _1103248] : [class_Int_Onumber__ring(_1103246), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103246), _1103248), hAPP(c_Int_Onumber__class_Onumber__of(_1103246), c_Int_OPls)) = _1103248)], (51493 ^ _779203) ^ [_1819883, _1819885, _1819887] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819883), _1819885)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819885), _1819883))), 51508 ^ _779203 : [(51511 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819887), _1819883))], (51509 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819883), _1819887)))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819885), _1819887)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819887), _1819885)))], (45764 ^ _779203) ^ [_1698976, _1698978, _1698980] : [hBOOL(hAPP(c_List_Odistinct(_1698976), _1698978)), -(hAPP(c_List_Ofilter(_1698976, hAPP(hAPP(c_COMBC(_1698976, tc_fun(_1698976, tc_HOL_Obool), tc_HOL_Obool), c_member(_1698976)), hAPP(c_List_Oset(_1698976), c_List_Osublist(_1698976, _1698978, _1698980)))), _1698978) = c_List_Osublist(_1698976, _1698978, _1698980))], (35192 ^ _779203) ^ [_1434684, _1434686, _1434688, _1434690, _1434692, _1434694, _1434696] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1434684, tc_fun(_1434686, tc_fun(_1434688, tc_HOL_Obool))), _1434690), _1434692), _1434694), _1434696)), 35196 ^ _779203 : [(35199 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_1434692, 35195 ^ [_1434684, _1434686, _1434688, _1434690, _1434692, _1434694, _1434696]), _1434694), _1434696)))], (35197 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1434684), 35195 ^ [_1434684, _1434686, _1434688, _1434690, _1434692, _1434694, _1434696]), _1434690)))]]], (41735 ^ _779203) ^ [_1606513, _1606515, _1606517, _1606519] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606513)), hAPP(hAPP(c_List_Olist_OCons(_1606513), _1606515), _1606517)), c_List_Olists(_1606513, _1606519))), 41738 ^ _779203 : [(41741 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606513)), _1606517), c_List_Olists(_1606513, _1606519))))], (41739 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1606513), _1606515), _1606519)))]]], (31488 ^ _779203) ^ [_1343867, _1343869, _1343871] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1343867, tc_HOL_Obool)), _1343869), _1343871) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1343867, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1343867, tc_HOL_Obool)), _1343869), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1343867, tc_HOL_Obool)), _1343871), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1343867, tc_HOL_Obool), tc_HOL_Obool))))))], (21125 ^ _779203) ^ [_1151722, _1151724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1151722), _1151724)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1151722)), c_Int_OBit1(_1151724))))], (29390 ^ _779203) ^ [_1300409, _1300411, _1300413, _1300415] : [-(hBOOL(hAPP(hAPP(c_member(_1300409), _1300411), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300409, tc_HOL_Obool)), _1300413), _1300415)))), hBOOL(hAPP(hAPP(c_member(_1300409), _1300411), _1300413)), hBOOL(hAPP(hAPP(c_member(_1300409), _1300411), _1300415))], (28552 ^ _779203) ^ [_1284185, _1284187, _1284189] : [class_Orderings_Olinorder(_1284185), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284185), _1284187), _1284189)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1284185, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1284185), _1284187)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1284185, _1284187, _1284189)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1284185), _1284189))], (1998 ^ _779203) ^ [_807986, _807988, _807990, _807992] : [-(c_Int_Onat__aux(_807992, _807988) = c_Int_Onat__aux(_807990, _807986)), _807992 = _807990, _807988 = _807986], (22085 ^ _779203) ^ [_1168982, _1168984, _1168986, _1168988] : [class_Divides_Oring__div(_1168982), -(c_Divides_Odiv__class_Omod(_1168982, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168982), _1168984), _1168986), _1168988) = c_Divides_Odiv__class_Omod(_1168982, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168982), c_Divides_Odiv__class_Omod(_1168982, _1168984, _1168988)), c_Divides_Odiv__class_Omod(_1168982, _1168986, _1168988)), _1168988))], (10517 ^ _779203) ^ [_961042, _961044, _961046, _961048] : [class_Rings_Ocomm__semiring__1(_961042), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961042), _961044), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961042), _961046), _961048)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_961042), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961042), _961044), _961046)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_961042), _961044), _961048)))], (46462 ^ _779203) ^ [_1713096, _1713098] : [class_Orderings_Olinorder(_1713096), 46465 ^ _779203 : [(46466 ^ _779203) ^ [] : [c_List_Olinorder__class_Osorted(_1713096, _1713098), 46469 ^ _779203 : [(46470 ^ _779203) ^ [_1713267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1713267), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713096)), _1713098))), 46473 ^ _779203 : [(46474 ^ _779203) ^ [_1713384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1713384), _1713267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1713096), hAPP(hAPP(c_List_Onth(_1713096), _1713098), _1713384)), hAPP(hAPP(c_List_Onth(_1713096), _1713098), _1713267))))]]]]], (46480 ^ _779203) ^ [] : [46482 ^ _779203 : [(46488 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1713096), hAPP(hAPP(c_List_Onth(_1713096), _1713098), 46484 ^ [_1713096, _1713098])), hAPP(hAPP(c_List_Onth(_1713096), _1713098), 46481 ^ [_1713096, _1713098])))], (46486 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 46484 ^ [_1713096, _1713098]), 46481 ^ [_1713096, _1713098])))], (46483 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46481 ^ [_1713096, _1713098]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1713096)), _1713098))))]], -(c_List_Olinorder__class_Osorted(_1713096, _1713098))]]], (16948 ^ _779203) ^ [_1077529, _1077531, _1077533, _1077535] : [class_Fields_Olinordered__field__inverse__zero(_1077529), class_Int_Onumber(_1077529), 16955 ^ _779203 : [(16956 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077529), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1077529), _1077531), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533))), _1077535)), 16959 ^ _779203 : [(16966 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077529), c_Groups_Ozero__class_Ozero(_1077529)), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533)))), 16969 ^ _779203 : [(16976 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077529), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533)), c_Groups_Ozero__class_Ozero(_1077529)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077529), c_Groups_Ozero__class_Ozero(_1077529)), _1077535)))], (16970 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077529), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533)), c_Groups_Ozero__class_Ozero(_1077529))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077529), _1077535), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533))), _1077531)))]]], (16960 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077529), c_Groups_Ozero__class_Ozero(_1077529)), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077529), _1077531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077529), _1077535), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533)))))]]], (16982 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077529), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1077529), _1077531), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533))), _1077535))), 16985 ^ _779203 : [(16988 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077529), _1077531), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077529), _1077535), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533))))], (16986 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077529), c_Groups_Ozero__class_Ozero(_1077529)), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533))))]], 16989 ^ _779203 : [(16992 ^ _779203) ^ [] : [16993 ^ _779203 : [(16996 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077529), _1077535), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533))), _1077531))], (16994 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077529), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533)), c_Groups_Ozero__class_Ozero(_1077529))))]], 16997 ^ _779203 : [(17000 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077529), c_Groups_Ozero__class_Ozero(_1077529)), _1077535))], (16998 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077529), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533)), c_Groups_Ozero__class_Ozero(_1077529)))]]], (16990 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1077529), c_Groups_Ozero__class_Ozero(_1077529)), hAPP(c_Int_Onumber__class_Onumber__of(_1077529), _1077533)))]]]]], (50069 ^ _779203) ^ [_1791902, _1791904, _1791906] : [c_Fun_Obij__betw(_1791902, _1791904, _1791906, c_Orderings_Otop__class_Otop(tc_fun(_1791902, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1791904, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1791902, _1791904, _1791906, c_Orderings_Otop__class_Otop(tc_fun(_1791902, tc_HOL_Obool))))], (34947 ^ _779203) ^ [_1428307, _1428309, _1428311, _1428313] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1428307, tc_fun(_1428309, tc_HOL_Obool)), _1428311), _1428313) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1428309, tc_HOL_Obool), hAPP(c_Set_Oimage(_1428307, tc_fun(_1428309, tc_HOL_Obool), _1428313), _1428311)))], (10961 ^ _779203) ^ [_968394] : [class_Rings_Ozero__neq__one(_968394), c_Groups_Ozero__class_Ozero(_968394) = c_Groups_Oone__class_Oone(_968394)], (44394 ^ _779203) ^ [_1667986, _1667988, _1667990, _1667992, _1667994] : [class_Rings_Osemiring__0(_1667986), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667986), hAPP(hAPP(c_List_Omap(_1667988, _1667986), hAPP(hAPP(c_COMBB(_1667986, _1667986, _1667988), hAPP(c_Groups_Otimes__class_Otimes(_1667986), _1667990)), _1667992)), _1667994)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1667986), _1667990), hAPP(c_List_Omonoid__add__class_Olistsum(_1667986), hAPP(hAPP(c_List_Omap(_1667988, _1667986), _1667992), _1667994))))], (10251 ^ _779203) ^ [_955383, _955385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _955383)), _955385)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _955383), _955385)))], (51095 ^ _779203) ^ [_1813423, _1813425, _1813427] : [class_Divides_Oring__div(_1813423), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1813423), _1813425), _1813427)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813423), _1813427), hAPP(c_Groups_Ouminus__class_Ouminus(_1813423), _1813425)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1813423), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1813423), _1813427), _1813425)))], (38969 ^ _779203) ^ [_1534511, _1534513] : [c_Relation_Orefl__on(_1534511, c_Orderings_Otop__class_Otop(tc_fun(_1534511, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1534511, _1534511)), hAPP(c_Product__Type_Oprod_Oprod__case(_1534511, _1534511, tc_HOL_Obool), _1534513))), -(c_Predicate_Oreflp(_1534511, _1534513))], (43265 ^ _779203) ^ [_1642439, _1642441, _1642443, _1642445] : [-(hAPP(hAPP(c_List_Otake(_1642439), _1642441), hAPP(hAPP(c_List_Oappend(_1642439), _1642443), _1642445)) = hAPP(hAPP(c_List_Oappend(_1642439), hAPP(hAPP(c_List_Otake(_1642439), _1642441), _1642443)), hAPP(hAPP(c_List_Otake(_1642439), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1642441), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642439)), _1642443))), _1642445)))], (41563 ^ _779203) ^ [_1601290, _1601292, _1601294, _1601296] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1601290), tc_List_Olist(_1601290), c_List_Olistrel(_1601290, _1601292)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1601290)), hAPP(hAPP(c_List_Olist_OCons(_1601290), _1601294), _1601296)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1601290), tc_HOL_Obool)))) = c_List_Oset__Cons(_1601290, hAPP(c_Relation_OImage(_1601290, _1601290, _1601292), hAPP(hAPP(c_Set_Oinsert(_1601290), _1601294), c_Orderings_Obot__class_Obot(tc_fun(_1601290, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1601290), tc_List_Olist(_1601290), c_List_Olistrel(_1601290, _1601292)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1601290)), _1601296), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1601290), tc_HOL_Obool))))))], (48475 ^ _779203) ^ [_1756958, _1756960, _1756962] : [hBOOL(hAPP(hAPP(c_member(_1756958), _1756962), hAPP(c_List_Oset(_1756958), _1756960))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1756958), _1756960), _1756962)))], (44498 ^ _779203) ^ [_1670515, _1670517, _1670519, _1670521, _1670523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1670515), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670517)), _1670519))), -(hAPP(hAPP(c_List_Onth(_1670521), hAPP(hAPP(c_List_Omap(_1670517, _1670521), _1670523), _1670519)), _1670515) = hAPP(_1670523, hAPP(hAPP(c_List_Onth(_1670517), _1670519), _1670515)))], (8679 ^ _779203) ^ [_925464, _925466, _925468, _925470] : [class_Groups_Ocancel__ab__semigroup__add(_925464), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925464), _925466), _925468) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925464), _925466), _925470), -(_925468 = _925470)], (19676 ^ _779203) ^ [_1126363, _1126365] : [class_Int_Onumber__ring(_1126363), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1126363), hAPP(c_Int_Onumber__class_Onumber__of(_1126363), _1126365)) = hAPP(c_Int_Onumber__class_Onumber__of(_1126363), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1126365)))], (11137 ^ _779203) ^ [_970916] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _970916), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42760 ^ _779203) ^ [_1631373, _1631375, _1631377, _1631379] : [-(_1631373 = _1631375), 42763 ^ _779203 : [(42770 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1631377), _1631373), hAPP(c_List_Oset(_1631377), _1631379))), -(hBOOL(hAPP(hAPP(c_member(_1631377), _1631373), hAPP(c_List_Oset(_1631377), c_List_Oremove1(_1631377, _1631375, _1631379)))))], (42764 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1631377), _1631373), hAPP(c_List_Oset(_1631377), c_List_Oremove1(_1631377, _1631375, _1631379)))), -(hBOOL(hAPP(hAPP(c_member(_1631377), _1631373), hAPP(c_List_Oset(_1631377), _1631379))))]]], (22504 ^ _779203) ^ [_1175971, _1175973] : [class_Divides_Osemiring__div(_1175971), -(_1175973 = c_Groups_Ozero__class_Ozero(_1175971)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1175971), _1175973), _1175973) = c_Groups_Oone__class_Oone(_1175971))], (6025 ^ _779203) ^ [_874892, _874894, _874896, _874898, _874900] : [hBOOL(hAPP(hAPP(c_member(_874892), _874894), _874896)), -(hBOOL(hAPP(hAPP(c_member(_874898), hAPP(_874900, _874894)), hAPP(c_Set_Oimage(_874892, _874898, _874900), _874896))))], (39862 ^ _779203) ^ [_1556075, _1556077, _1556079, _1556081, _1556083, _1556085] : [class_Groups_Ocomm__monoid__add(_1556075), hBOOL(hAPP(c_Finite__Set_Ofinite(_1556077), _1556079)), 39872 ^ _779203 : [(39873 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1556077), 39871 ^ [_1556075, _1556077, _1556079, _1556081, _1556083, _1556085]), _1556079)))], (39878 ^ _779203) ^ [] : [39871 ^ [_1556075, _1556077, _1556079, _1556081, _1556083, _1556085] = 39874 ^ [_1556075, _1556077, _1556079, _1556081, _1556083, _1556085]], (39882 ^ _779203) ^ [] : [hAPP(_1556083, hAPP(_1556081, 39871 ^ [_1556075, _1556077, _1556079, _1556081, _1556083, _1556085])) = c_Groups_Ozero__class_Ozero(_1556075)], (39880 ^ _779203) ^ [] : [-(hAPP(_1556081, 39871 ^ [_1556075, _1556077, _1556079, _1556081, _1556083, _1556085]) = hAPP(_1556081, 39874 ^ [_1556075, _1556077, _1556079, _1556081, _1556083, _1556085]))], (39876 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1556077), 39874 ^ [_1556075, _1556077, _1556079, _1556081, _1556083, _1556085]), _1556079)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1556085, _1556075), _1556083), hAPP(c_Set_Oimage(_1556077, _1556085, _1556081), _1556079)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1556077, _1556075), hAPP(c_Fun_Ocomp(_1556085, _1556075, _1556077, _1556083), _1556081)), _1556079))], (52277 ^ _779203) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (25760 ^ _779203) ^ [_1232462, _1232464, _1232466, _1232468, _1232470] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1232462, _1232464, _1232466), _1232468), hAPP(c_Nat_OSuc, _1232470)) = hAPP(hAPP(_1232466, _1232468), hAPP(hAPP(c_Power_Opower_Opower(_1232462, _1232464, _1232466), _1232468), _1232470)))], (10981 ^ _779203) ^ [_968729] : [-(_968729 = 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)), _968729)))], (41098 ^ _779203) ^ [_1587073] : [-(c_Nat_Ofunpow(_1587073) = c_Nat_Ocompow(_1587073, _1587073))], (40972 ^ _779203) ^ [_1583745, _1583747, _1583749] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583745, _1583745), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1583747)), _1583749) = hAPP(hAPP(c_Relation_Orel__comp(_1583745, _1583745, _1583745), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1583745, _1583745), tc_HOL_Obool), _1583747), _1583749)), _1583749))], (40795 ^ _779203) ^ [_1579208, _1579210, _1579212, _1579214] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1579208, _1579208)), hAPP(hAPP(c_Product__Type_OPair(_1579208, _1579208), _1579210), _1579212)), c_Transitive__Closure_Ortrancl(_1579208, hAPP(c_Relation_Oconverse(_1579208, _1579208), _1579214)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579208, _1579208)), hAPP(hAPP(c_Product__Type_OPair(_1579208, _1579208), _1579212), _1579210)), c_Transitive__Closure_Ortrancl(_1579208, _1579214))))], (8138 ^ _779203) ^ [_914380, _914382, _914384, _914386, _914388] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_914380, _914380, _914382, _914384, _914386), _914388)), -(hBOOL(hAPP(hAPP(c_member(_914380), _914384), _914386))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_914380, _914382, hAPP(hAPP(c_Set_Oinsert(_914380), _914384), _914386)), _914388)))], (27836 ^ _779203) ^ [_1270040, _1270042, _1270044, _1270046] : [27838 ^ _779203 : [(27841 ^ _779203) ^ [] : [hBOOL(hAPP(_1270046, 27837 ^ [_1270040, _1270042, _1270044, _1270046]))], (27839 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1270040), 27837 ^ [_1270040, _1270042, _1270044, _1270046]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270040, tc_HOL_Obool)), _1270042), _1270044))))]], 27842 ^ _779203 : [(27849 ^ _779203) ^ [_1270357] : [hBOOL(hAPP(hAPP(c_member(_1270040), _1270357), _1270044)), -(hBOOL(hAPP(_1270046, _1270357)))], (27843 ^ _779203) ^ [_1270260] : [hBOOL(hAPP(hAPP(c_member(_1270040), _1270260), _1270042)), -(hBOOL(hAPP(_1270046, _1270260)))]]], (8342 ^ _779203) ^ [_918338, _918340, _918342, _918344] : [hBOOL(hAPP(hAPP(c_member(_918338), _918340), _918342)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918338, tc_Nat_Onat), _918344), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918338, tc_HOL_Obool)), _918342), hAPP(hAPP(c_Set_Oinsert(_918338), _918340), c_Orderings_Obot__class_Obot(tc_fun(_918338, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_918338, tc_Nat_Onat), _918344), _918342)), hAPP(_918344, _918340)))], (8877 ^ _779203) ^ [_929237, _929239, _929241] : [class_Groups_Ogroup__add(_929237), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_929237), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_929237), _929239), _929241)), _929241) = _929239)], (20564 ^ _779203) ^ [_1141883, _1141885] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1141883)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1141885))))), _1141883 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1141885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (33833 ^ _779203) ^ [_1398935, _1398937, _1398939, _1398941] : [_1398935 = _1398937, 33836 ^ _779203 : [(33839 ^ _779203) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1398939, _1398941), _1398935) = hAPP(c_Product__Type_Osnd(_1398939, _1398941), _1398937))], (33837 ^ _779203) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1398939, _1398941), _1398935) = hAPP(c_Product__Type_Ofst(_1398939, _1398941), _1398937))]]], (41593 ^ _779203) ^ [_1602171, _1602173] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1602171), tc_List_Olist(_1602171)), tc_HOL_Obool)), c_List_Olistrel(_1602171, _1602173)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1602171), c_List_Olistrel1(_1602171, _1602173)))))], (5655 ^ _779203) ^ [_868412, _868414] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), _868412), _868414)), -(v_P(_868414, _868412))], (8785 ^ _779203) ^ [_927463, _927465, _927467, _927469] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_927463), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927463), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927463), _927465), _927467)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_927463), _927465), _927469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927463), _927467), _927469)))], (36804 ^ _779203) ^ [] : [-(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))))], (41471 ^ _779203) ^ [_1598434, _1598436, _1598438, _1598440] : [hBOOL(hAPP(hAPP(c_member(_1598434), _1598436), c_Wellfounded_Oacc(_1598434, _1598438))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1598434)), _1598440), c_Wellfounded_Oacc(tc_List_Olist(_1598434), c_List_Olistrel1(_1598434, _1598438)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1598434)), hAPP(hAPP(c_List_Olist_OCons(_1598434), _1598436), _1598440)), c_Wellfounded_Oacc(tc_List_Olist(_1598434), c_List_Olistrel1(_1598434, _1598438)))))], (34320 ^ _779203) ^ [_1410176, _1410178, _1410180, _1410182, _1410184] : [_1410176 = c_Orderings_Obot__class_Obot(tc_fun(_1410178, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1410178, tc_fun(_1410180, tc_HOL_Obool)), _1410176), hAPP(hAPP(c_COMBB(tc_fun(_1410180, tc_HOL_Obool), tc_fun(_1410180, tc_HOL_Obool), _1410178), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1410180, tc_HOL_Obool)), _1410182)), _1410184)) = c_Orderings_Otop__class_Otop(tc_fun(_1410180, tc_HOL_Obool)))], (23607 ^ _779203) ^ [_1194848, _1194850] : [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), _1194848))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1194850))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1194848))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194850)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1194848)))], (6755 ^ _779203) ^ [_888816, _888818, _888820, _888822, _888824, _888826, _888828, _888830] : [c_Finite__Set_Ofolding__image__simple__idem(_888816, _888818, _888820, _888822, _888824, _888826), hBOOL(hAPP(c_Finite__Set_Ofinite(_888818), _888828)), hBOOL(hAPP(hAPP(c_member(_888818), _888830), _888828)), -(hAPP(hAPP(_888820, hAPP(_888824, _888830)), hAPP(_888826, _888828)) = hAPP(_888826, _888828))], (6178 ^ _779203) ^ [_878088, _878090, _878092, _878094, _878096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878088, tc_HOL_Obool)), _878090), _878092)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878094, tc_HOL_Obool)), hAPP(c_Set_Oimage(_878088, _878094, _878096), _878090)), hAPP(c_Set_Oimage(_878088, _878094, _878096), _878092))))], (37509 ^ _779203) ^ [_1489443, _1489445, _1489447, _1489449, _1489451, _1489453] : [class_Groups_Ocomm__monoid__add(_1489443), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489445, _1489443), hAPP(hAPP(c_COMBC(_1489445, tc_fun(_1489447, tc_HOL_Obool), _1489443), hAPP(hAPP(c_COMBB(tc_fun(_1489447, _1489443), tc_fun(tc_fun(_1489447, tc_HOL_Obool), _1489443), _1489445), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1489447, _1489443)), _1489449)), _1489451)), _1489453) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1489445, _1489447), _1489443), hAPP(c_Product__Type_Oprod_Oprod__case(_1489445, _1489447, _1489443), _1489449)), hAPP(hAPP(c_Product__Type_OSigma(_1489445, _1489447), _1489453), hAPP(c_COMBK(tc_fun(_1489447, tc_HOL_Obool), _1489445), _1489451))))], (46716 ^ _779203) ^ [_1718592, _1718594] : [-(hAPP(c_List_Orev(_1718592), _1718594) = hAPP(c_List_Ofoldl(tc_List_Olist(_1718592), _1718592, hAPP(c_COMBC(_1718592, tc_List_Olist(_1718592), tc_List_Olist(_1718592)), c_List_Olist_OCons(_1718592)), c_List_Olist_ONil(_1718592)), _1718594))], (37637 ^ _779203) ^ [_1492995, _1492997] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1492995, tc_HOL_Obool)), _1492997) = hAPP(c_Set_OCollect(_1492995), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1492995), c_fNot), hAPP(hAPP(c_COMBC(_1492995, tc_fun(_1492995, tc_HOL_Obool), tc_HOL_Obool), c_member(_1492995)), _1492997))))], (24081 ^ _779203) ^ [_1203318] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1203318))), 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), _1203318), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (29580 ^ _779203) ^ [_1303984, _1303986, _1303988] : [class_Lattices_Osemilattice__inf(_1303984), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303984), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1303984), _1303986), _1303988)), _1303988)))], (8053 ^ _779203) ^ [_912415, _912417, _912419] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_912415, tc_HOL_Obool)), _912417), _912419)), -(hBOOL(hAPP(hAPP(c_member(_912415), 8056 ^ [_912415, _912417, _912419]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912415, tc_HOL_Obool)), _912419), _912417))))], (12521 ^ _779203) ^ [_995112, _995114, _995116] : [class_Groups_Oordered__comm__monoid__add(_995112), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995112), c_Groups_Ozero__class_Ozero(_995112)), _995114)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995112), c_Groups_Ozero__class_Ozero(_995112)), _995116)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995112), c_Groups_Ozero__class_Ozero(_995112)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_995112), _995114), _995116))))], (37575 ^ _779203) ^ [_1491491, _1491493, _1491495, _1491497, _1491499] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1491491, _1491493), _1491495), hAPP(hAPP(c_COMBS(_1491491, tc_fun(_1491493, tc_HOL_Obool), tc_fun(_1491493, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1491493, tc_HOL_Obool), tc_fun(tc_fun(_1491493, tc_HOL_Obool), tc_fun(_1491493, tc_HOL_Obool)), _1491491), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1491493, tc_HOL_Obool))), _1491497)), _1491499)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1491491, _1491493), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1491491, _1491493), _1491495), _1491497)), hAPP(hAPP(c_Product__Type_OSigma(_1491491, _1491493), _1491495), _1491499)))], (10023 ^ _779203) ^ [_950486, _950488, _950490] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _950486), _950488)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _950490), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _950488), _950486)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _950490), _950488)), _950486))], (35826 ^ _779203) ^ [_1451044, _1451046, _1451048, _1451050, _1451052] : [hAPP(c_Relation_OImage(_1451044, _1451044, _1451046), hAPP(hAPP(c_Set_Oinsert(_1451044), _1451048), c_Orderings_Obot__class_Obot(tc_fun(_1451044, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1451044, _1451044, _1451046), hAPP(hAPP(c_Set_Oinsert(_1451044), _1451050), c_Orderings_Obot__class_Obot(tc_fun(_1451044, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1451044, _1451052, _1451046), hBOOL(hAPP(hAPP(c_member(_1451044), _1451050), _1451052)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1451044, _1451044)), hAPP(hAPP(c_Product__Type_OPair(_1451044, _1451044), _1451048), _1451050)), _1451046)))], (10939 ^ _779203) ^ [_968071, _968073, _968075] : [class_Groups_Ogroup__add(_968071), 10942 ^ _779203 : [(10949 ^ _779203) ^ [] : [_968073 = _968075, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_968071), _968073), _968075) = c_Groups_Ozero__class_Ozero(_968071))], (10943 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_968071), _968073), _968075) = c_Groups_Ozero__class_Ozero(_968071), -(_968073 = _968075)]]], (9461 ^ _779203) ^ [_940539, _940541] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _940539), _940541)), -(_940541 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _940539), 9464 ^ [_940539, _940541]))], (1250 ^ _779203) ^ [_797788, _797790] : [-(class_Groups_Oab__group__add(_797788)), _797790 = _797788, class_Groups_Oab__group__add(_797790)], (35649 ^ _779203) ^ [_1447149] : [-(c_Relation_OId__on(_1447149, c_Orderings_Obot__class_Obot(tc_fun(_1447149, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1447149, _1447149), tc_HOL_Obool)))], (18130 ^ _779203) ^ [_1099022, _1099024, _1099026, _1099028] : [class_Orderings_Olinorder(_1099022), hBOOL(hAPP(c_Finite__Set_Ofinite(_1099022), _1099024)), 18140 ^ _779203 : [(18143 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099022), 18139 ^ [_1099022, _1099024, _1099026, _1099028]), _1099026))], (18141 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1099022), 18139 ^ [_1099022, _1099024, _1099026, _1099028]), _1099024)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099022), hAPP(hAPP(c_Finite__Set_Ofold(_1099022, _1099022, c_Orderings_Oord__class_Omax(_1099022)), _1099028), _1099024)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1099022), _1099026), _1099028))))], (19478 ^ _779203) ^ [_1122614, _1122616, _1122618] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122614)))), 19481 ^ _779203 : [(19488 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122616)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1122614)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1122616)), _1122618)) = 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), _1122614), _1122616))), _1122618))], (19482 ^ _779203) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1122616))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1122614)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1122616)), _1122618)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1122614)), _1122618))]]], (38669 ^ _779203) ^ [_1527860, _1527862, _1527864] : [c_Wellfounded_Owf(_1527860, _1527862), -(c_Wellfounded_Owf(_1527860, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1527860, _1527860), tc_HOL_Obool)), _1527862), _1527864)))], (19009 ^ _779203) ^ [_1114070, _1114072] : [class_Int_Onumber__ring(_1114070), -(hAPP(c_Int_Onumber__class_Onumber__of(_1114070), c_Int_Osucc(_1114072)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1114070), c_Groups_Oone__class_Oone(_1114070)), hAPP(c_Int_Onumber__class_Onumber__of(_1114070), _1114072)))], (33351 ^ _779203) ^ [_1389755] : [-(_1389755 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1389755), 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)))))], (17202 ^ _779203) ^ [_1082397, _1082399, _1082401] : [class_Orderings_Olinorder(_1082397), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082397), _1082399)), hBOOL(hAPP(hAPP(c_member(_1082397), _1082401), _1082399)), 17213 ^ _779203 : [(17220 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1082397, tc_HOL_Obool)), _1082399), hAPP(hAPP(c_Set_Oinsert(_1082397), _1082401), c_Orderings_Obot__class_Obot(tc_fun(_1082397, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1082397, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1082397, c_Orderings_Oord__class_Omin(_1082397), _1082399) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1082397), _1082401), c_Big__Operators_Olattice_OInf__fin(_1082397, c_Orderings_Oord__class_Omin(_1082397), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1082397, tc_HOL_Obool)), _1082399), hAPP(hAPP(c_Set_Oinsert(_1082397), _1082401), c_Orderings_Obot__class_Obot(tc_fun(_1082397, tc_HOL_Obool)))))))], (17214 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1082397, tc_HOL_Obool)), _1082399), hAPP(hAPP(c_Set_Oinsert(_1082397), _1082401), c_Orderings_Obot__class_Obot(tc_fun(_1082397, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1082397, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1082397, c_Orderings_Oord__class_Omin(_1082397), _1082399) = _1082401)]]], (27366 ^ _779203) ^ [_1261241, _1261243, _1261245, _1261247, _1261249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261241, tc_HOL_Obool)), _1261243), _1261245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261241, tc_HOL_Obool)), _1261247), _1261249)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261241, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261241, tc_HOL_Obool)), _1261243), _1261247)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261241, tc_HOL_Obool)), _1261245), _1261249))))], (14607 ^ _779203) ^ [_1033631, _1033633, _1033635, _1033637] : [class_Fields_Olinordered__field(_1033631), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033631), _1033633), _1033635)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033631), c_Groups_Ozero__class_Ozero(_1033631)), _1033637)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033631), c_Groups_Ozero__class_Ozero(_1033631)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1033631), _1033635), _1033633))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1033631), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033631), _1033637), _1033635)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1033631), _1033637), _1033633))))], (39137 ^ _779203) ^ [_1538759, _1538761] : [c_Wellfounded_OwfP(_1538759, _1538761), -(c_Wellfounded_Oacyclic(_1538759, hAPP(c_Set_OCollect(tc_prod(_1538759, _1538759)), hAPP(c_Product__Type_Oprod_Oprod__case(_1538759, _1538759, tc_HOL_Obool), _1538761))))], (26386 ^ _779203) ^ [_1243213, _1243215] : [-(_1243213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1243215, _1243213) = c_Nitpick_Onat__gcd(_1243213, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1243215, _1243213)))], (10495 ^ _779203) ^ [_960624, _960626, _960628, _960630, _960632] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_960624), 10498 ^ _779203 : [(10499 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960624), _960626), _960630)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960624), _960628), _960632)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960624), _960626), _960632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960624), _960628), _960630)), -(_960626 = _960628), -(_960630 = _960632)], (10509 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960624), _960626), _960630)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960624), _960628), _960632)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_960624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960624), _960626), _960632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_960624), _960628), _960630))), 10512 ^ _779203 : [(10515 ^ _779203) ^ [] : [_960630 = _960632], (10513 ^ _779203) ^ [] : [_960626 = _960628]]]]], (48340 ^ _779203) ^ [_1753929, _1753931, _1753933] : [-(_1753929 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1753931), c_List_Oreplicate(_1753931, _1753929, _1753933)) = hAPP(hAPP(c_Set_Oinsert(_1753931), _1753933), c_Orderings_Obot__class_Obot(tc_fun(_1753931, tc_HOL_Obool))))], (29592 ^ _779203) ^ [_1304198, _1304200, _1304202] : [class_Lattices_Osemilattice__inf(_1304198), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304198), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1304198), _1304200), _1304202)), _1304200)))], (27800 ^ _779203) ^ [_1269433, _1269435, _1269437] : [class_Lattices_Osemilattice__sup(_1269433), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269433), _1269435), _1269437) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269433), _1269437), _1269435))], (29788 ^ _779203) ^ [_1308616, _1308618] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308616, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308616, tc_HOL_Obool)), _1308618)), _1308618) = c_Orderings_Obot__class_Obot(tc_fun(_1308616, tc_HOL_Obool)))], (6631 ^ _779203) ^ [_886144, _886146, _886148, _886150] : [c_Finite__Set_Ofolding__one(_886144, _886146, _886148), hBOOL(hAPP(c_Finite__Set_Ofinite(_886144), _886150)), -(_886150 = c_Orderings_Obot__class_Obot(tc_fun(_886144, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_886144), hAPP(hAPP(_886146, 6644 ^ [_886144, _886146, _886148, _886150]), 6645 ^ [_886144, _886146, _886148, _886150])), hAPP(hAPP(c_Set_Oinsert(_886144), 6644 ^ [_886144, _886146, _886148, _886150]), hAPP(hAPP(c_Set_Oinsert(_886144), 6645 ^ [_886144, _886146, _886148, _886150]), c_Orderings_Obot__class_Obot(tc_fun(_886144, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_886144), hAPP(_886148, _886150)), _886150)))], (34797 ^ _779203) ^ [_1424402, _1424404, _1424406, _1424408] : [_1424402 = c_Orderings_Obot__class_Obot(tc_fun(_1424404, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424404, tc_fun(_1424406, tc_HOL_Obool)), _1424402), hAPP(c_COMBK(tc_fun(_1424406, tc_HOL_Obool), _1424404), _1424408)) = c_Orderings_Otop__class_Otop(tc_fun(_1424406, tc_HOL_Obool)))], (33013 ^ _779203) ^ [_1384115] : [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), _1384115))), 33016 ^ _779203 : [(33023 ^ _779203) ^ [] : [-(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), _1384115)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384115)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384115)), 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), _1384115)))))], (33017 ^ _779203) ^ [] : [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), _1384115))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1384115)) = 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)))]]], (42918 ^ _779203) ^ [_1634854, _1634856, _1634858] : [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), _1634854), _1634856))), -(hBOOL(hAPP(hAPP(_1634858, _1634854), _1634856))), 42925 ^ _779203 : [(42928 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 42923 ^ [_1634854, _1634856, _1634858]), 42924 ^ [_1634854, _1634856, _1634858])), -(hBOOL(hAPP(hAPP(_1634858, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 42923 ^ [_1634854, _1634856, _1634858]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 42924 ^ [_1634854, _1634856, _1634858])))], (42934 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1634858, 42923 ^ [_1634854, _1634856, _1634858]), 42924 ^ [_1634854, _1634856, _1634858]))], (42926 ^ _779203) ^ [] : [-(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), 42923 ^ [_1634854, _1634856, _1634858]), 42924 ^ [_1634854, _1634856, _1634858]))))]]], (21283 ^ _779203) ^ [_1154413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1154413), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1154413)), c_Int_OPls)))], (48360 ^ _779203) ^ [_1754460, _1754462] : [-(c_Predicate_Opred__comp(_1754460, _1754460, _1754460, c_fequal, c_Predicate_Opred__comp(_1754460, _1754460, _1754460, _1754462, c_fequal)) = _1754462)], (6306 ^ _779203) ^ [_880657, _880659, _880661, _880663, _880665] : [class_Orderings_Oord(_880657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880659, _880657)), _880661), _880663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880657), hAPP(_880661, _880665)), hAPP(_880663, _880665))))], (42309 ^ _779203) ^ [_1622108, _1622110, _1622112, _1622114, _1622116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622108, tc_HOL_Obool)), hAPP(c_List_Oset(_1622108), _1622110)), _1622112)), hBOOL(hAPP(hAPP(c_member(_1622108), _1622114), _1622112)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1622108, tc_HOL_Obool)), hAPP(c_List_Oset(_1622108), hAPP(hAPP(c_List_Olist__update(_1622108, _1622110), _1622116), _1622114))), _1622112)))], (32175 ^ _779203) ^ [_1360720, _1360722, _1360724] : [class_Groups_Ocomm__monoid__add(_1360720), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1360720), _1360722), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1360724))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1360720), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1360720), _1360722), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1360724))), hAPP(_1360722, hAPP(c_Nat_OSuc, _1360724))))], (29200 ^ _779203) ^ [_1296254, _1296256] : [class_Lattices_Obounded__lattice__top(_1296254), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1296254), c_Orderings_Otop__class_Otop(_1296254)), _1296256) = _1296256)], (18419 ^ _779203) ^ [_1104097, _1104099, _1104101] : [class_Rings_Olinordered__semidom(_1104097), 18422 ^ _779203 : [(18429 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104099), _1104101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104097), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104097), _1104099)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104097), _1104101))))], (18423 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1104097), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104097), _1104099)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1104097), _1104101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1104099), _1104101)))]]], (32585 ^ _779203) ^ [_1370589, _1370591] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1370589)), _1370591) = 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), _1370589)), _1370591))], (45196 ^ _779203) ^ [_1686050, _1686052, _1686054, _1686056, _1686058, _1686060] : [c_List_Olist__all2(_1686050, _1686052, _1686054, _1686056, _1686058), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1686060), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686050)), _1686056))), -(hBOOL(hAPP(hAPP(_1686054, hAPP(hAPP(c_List_Onth(_1686050), _1686056), _1686060)), hAPP(hAPP(c_List_Onth(_1686052), _1686058), _1686060))))], (42039 ^ _779203) ^ [_1614175, _1614177, _1614179] : [-(hBOOL(hAPP(hAPP(c_member(_1614175), _1614177), hAPP(c_List_Oset(_1614175), _1614179)))), 42040 ^ _779203 : [(42041 ^ _779203) ^ [_1614249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1614249), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614175)), _1614179))), hAPP(hAPP(c_List_Onth(_1614175), _1614179), _1614249) = _1614177]]], (51575 ^ _779203) ^ [_1821293, _1821295, _1821297, _1821299] : [class_Divides_Osemiring__div(_1821293), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821293), _1821295), _1821297)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821293), _1821295), _1821299)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1821293), _1821295), c_Divides_Odiv__class_Omod(_1821293, _1821297, _1821299))))], (24261 ^ _779203) ^ [_1206701, _1206703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1206701)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1206701)), _1206703) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1206701), _1206703)))], (2568 ^ _779203) ^ [_816991, _816993] : [_816993 = _816991, -(c_Equiv__Relations_Oquotient(_816993) = c_Equiv__Relations_Oquotient(_816991))], (13197 ^ _779203) ^ [_1007409, _1007411, _1007413] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1007409), _1007411)), 13200 ^ _779203 : [(13220 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1007409, tc_Nat_Onat), _1007413), _1007411) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 13221 ^ _779203 : [(13222 ^ _779203) ^ [_1007890] : [hBOOL(hAPP(hAPP(c_member(_1007409), _1007890), _1007411)), hAPP(_1007413, _1007890) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 13230 ^ _779203 : [(13235 ^ _779203) ^ [] : [hAPP(_1007413, 13229 ^ [_1007409, _1007411, _1007413, _1007890]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (13233 ^ _779203) ^ [] : [_1007890 = 13229 ^ [_1007409, _1007411, _1007413, _1007890]], (13231 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1007409), 13229 ^ [_1007409, _1007411, _1007413, _1007890]), _1007411)))]]]]], (13201 ^ _779203) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1007409, tc_Nat_Onat), _1007413), _1007411) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 13205 ^ _779203 : [(13210 ^ _779203) ^ [_1007729] : [hBOOL(hAPP(hAPP(c_member(_1007409), _1007729), _1007411)), -(13204 ^ [_1007409, _1007411, _1007413] = _1007729), -(hAPP(_1007413, _1007729) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13208 ^ _779203) ^ [] : [-(hAPP(_1007413, 13204 ^ [_1007409, _1007411, _1007413]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (13206 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1007409), 13204 ^ [_1007409, _1007411, _1007413]), _1007411)))]]]]], (48398 ^ _779203) ^ [_1755168, _1755170, _1755172, _1755174] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755168, _1755170), c_Lazy__Sequence_Olazy__sequence_OInsert(_1755168, _1755172, _1755174)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1755170, _1755172)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1755168, _1755170), _1755174))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37549 ^ _779203) ^ [_1490721, _1490723, _1490725] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1490721, tc_HOL_Obool)), _1490723), _1490725) = hAPP(c_Set_OCollect(_1490721), hAPP(hAPP(c_COMBS(_1490721, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1490721), c_fdisj), hAPP(hAPP(c_COMBC(_1490721, tc_fun(_1490721, tc_HOL_Obool), tc_HOL_Obool), c_member(_1490721)), _1490723))), hAPP(hAPP(c_COMBC(_1490721, tc_fun(_1490721, tc_HOL_Obool), tc_HOL_Obool), c_member(_1490721)), _1490725))))], (36860 ^ _779203) ^ [_1473862, _1473864, _1473866, _1473868, _1473870] : [c_Typedef_Otype__definition(_1473862, _1473864, _1473866, _1473868, _1473870), -(hAPP(c_Set_Oimage(_1473864, _1473862, _1473868), _1473870) = c_Orderings_Otop__class_Otop(tc_fun(_1473862, tc_HOL_Obool)))], (30117 ^ _779203) ^ [_1315839, _1315841, _1315843] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1315839), _1315841)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315839), _1315843)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1315839), _1315841)), hAPP(c_Finite__Set_Ocard(_1315839), _1315843)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1315839), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315839, tc_HOL_Obool)), _1315841), _1315843))), hAPP(c_Finite__Set_Ocard(_1315839), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315839, tc_HOL_Obool)), _1315841), _1315843))))], (41799 ^ _779203) ^ [_1608307, _1608309, _1608311] : [_1608307 = _1608309, 41802 ^ _779203 : [(41805 ^ _779203) ^ [_1608455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1608455), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608311)), _1608307))), -(hAPP(hAPP(c_List_Onth(_1608311), _1608307), _1608455) = hAPP(hAPP(c_List_Onth(_1608311), _1608309), _1608455))], (41803 ^ _779203) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608311)), _1608307) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1608311)), _1608309))]]], (34851 ^ _779203) ^ [_1425756, _1425758, _1425760, _1425762, _1425764] : [hBOOL(hAPP(hAPP(c_member(_1425756), _1425758), _1425760)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1425762, tc_HOL_Obool)), hAPP(_1425764, _1425758)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425756, tc_fun(_1425762, tc_HOL_Obool)), _1425760), _1425764)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425756, tc_fun(_1425762, tc_HOL_Obool)), _1425760), _1425764))], (9279 ^ _779203) ^ [_937587, _937589] : [-(_937587 = _937589), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _937587), _937589))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _937589), _937587)))], (30587 ^ _779203) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (31825 ^ _779203) ^ [_1351686, _1351688, _1351690, _1351692] : [class_Fields_Olinordered__field(_1351686), -(hAPP(c_Groups_Oabs__class_Oabs(_1351686), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351688, _1351686), _1351690), _1351692)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1351688, _1351686), hAPP(hAPP(c_COMBB(_1351686, _1351686, _1351688), c_Groups_Oabs__class_Oabs(_1351686)), _1351690)), _1351692))], (2950 ^ _779203) ^ [_822880, _822882, _822884, _822886] : [-(c_List_Olenlex(_822886, _822882) = c_List_Olenlex(_822884, _822880)), _822886 = _822884, _822882 = _822880], (47966 ^ _779203) ^ [_1745630, _1745632, _1745634] : [c_List_Olist__ex1(_1745630, _1745632, _1745634), 47970 ^ _779203 : [(47975 ^ _779203) ^ [_1745876] : [-(_1745876 = 47969 ^ [_1745630, _1745632, _1745634]), hBOOL(hAPP(hAPP(c_member(_1745630), _1745876), hAPP(c_List_Oset(_1745630), _1745634))), hBOOL(hAPP(_1745632, _1745876))], (47973 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1745632, 47969 ^ [_1745630, _1745632, _1745634])))], (47971 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745630), 47969 ^ [_1745630, _1745632, _1745634]), hAPP(c_List_Oset(_1745630), _1745634))))]]], (38362 ^ _779203) ^ [_1518725, _1518727] : [-(hAPP(c_Relation_ORange(_1518725, _1518725), c_Relation_OId__on(_1518725, _1518727)) = _1518727)], (34865 ^ _779203) ^ [_1426187, _1426189, _1426191, _1426193, _1426195] : [-(_1426187 = c_Orderings_Obot__class_Obot(tc_fun(_1426189, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426189, tc_fun(_1426191, tc_HOL_Obool)), _1426187), hAPP(hAPP(c_COMBB(tc_fun(_1426191, tc_HOL_Obool), tc_fun(_1426191, tc_HOL_Obool), _1426189), hAPP(c_Set_Oinsert(_1426191), _1426193)), _1426195)) = hAPP(hAPP(c_Set_Oinsert(_1426191), _1426193), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1426189, tc_fun(_1426191, tc_HOL_Obool)), _1426187), _1426195)))], (38027 ^ _779203) ^ [_1506373, _1506375, _1506377, _1506379] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506373), hAPP(c_Set_OCollect(_1506373), _1506375))), 38030 ^ _779203 : [(38031 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506377), hAPP(c_Set_OCollect(_1506377), hAPP(hAPP(c_COMBB(tc_fun(_1506373, tc_HOL_Obool), tc_HOL_Obool, _1506377), c_HOL_OEx(_1506373)), hAPP(hAPP(c_COMBB(tc_fun(_1506373, tc_HOL_Obool), tc_fun(_1506373, tc_HOL_Obool), _1506377), hAPP(c_COMBS(_1506373, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506373), c_fconj), _1506375))), _1506379))))), 38034 ^ _779203 : [(38035 ^ _779203) ^ [_1506656] : [hBOOL(hAPP(_1506375, _1506656)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506377), hAPP(c_Set_OCollect(_1506377), hAPP(hAPP(c_COMBC(_1506377, _1506373, tc_HOL_Obool), _1506379), _1506656)))))]]], (38041 ^ _779203) ^ [] : [38043 ^ _779203 : [(38046 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506377), hAPP(c_Set_OCollect(_1506377), hAPP(hAPP(c_COMBC(_1506377, _1506373, tc_HOL_Obool), _1506379), 38042 ^ [_1506373, _1506375, _1506377, _1506379]))))], (38044 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1506375, 38042 ^ [_1506373, _1506375, _1506377, _1506379])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506377), hAPP(c_Set_OCollect(_1506377), hAPP(hAPP(c_COMBB(tc_fun(_1506373, tc_HOL_Obool), tc_HOL_Obool, _1506377), c_HOL_OEx(_1506373)), hAPP(hAPP(c_COMBB(tc_fun(_1506373, tc_HOL_Obool), tc_fun(_1506373, tc_HOL_Obool), _1506377), hAPP(c_COMBS(_1506373, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1506373), c_fconj), _1506375))), _1506379))))))]]], (38756 ^ _779203) ^ [_1529519, _1529521, _1529523] : [c_Wellfounded_Owf(_1529519, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529519, _1529519), tc_HOL_Obool)), _1529521), _1529523)), -(c_Wellfounded_Owf(_1529519, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529519, _1529519), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1529519, _1529519), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1529519, _1529519, _1529519), _1529521), _1529521)), hAPP(hAPP(c_Relation_Orel__comp(_1529519, _1529519, _1529519), _1529523), _1529521))), _1529523)))], (11055 ^ _779203) ^ [_969702, _969704] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _969702), _969704) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _969704), _969702) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_969702 = _969704)], (44321 ^ _779203) ^ [_1665858, _1665860, _1665862, _1665864, _1665866, _1665868, _1665870, _1665872] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1665858, _1665860), _1665862), _1665864), hAPP(hAPP(c_List_Ozip(_1665858, _1665860), hAPP(hAPP(c_List_Omap(_1665866, _1665858), _1665868), _1665870)), _1665872)) = hAPP(hAPP(c_List_Omap(tc_prod(_1665866, _1665860), _1665862), hAPP(c_Product__Type_Oprod_Oprod__case(_1665866, _1665860, _1665862), hAPP(hAPP(c_COMBB(tc_fun(_1665860, tc_prod(_1665858, _1665860)), tc_fun(_1665860, _1665862), _1665866), hAPP(c_COMBB(tc_prod(_1665858, _1665860), _1665862, _1665860), _1665864)), hAPP(hAPP(c_COMBB(_1665858, tc_fun(_1665860, tc_prod(_1665858, _1665860)), _1665866), c_Product__Type_OPair(_1665858, _1665860)), _1665868)))), hAPP(hAPP(c_List_Ozip(_1665866, _1665860), _1665870), _1665872)))], (45560 ^ _779203) ^ [_1693601, _1693603] : [-(hAPP(c_List_Oset(_1693601), c_List_Oconcat(_1693601, _1693603)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1693601), tc_fun(_1693601, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1693601)), _1693603)), c_List_Oset(_1693601)))], (48082 ^ _779203) ^ [_1748537, _1748539, _1748541] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748537, _1748537, hAPP(hAPP(c_COMBB(tc_fun(_1748537, tc_HOL_Obool), tc_fun(_1748537, tc_HOL_Obool), _1748537), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1748537), c_fNot)), c_fequal)), _1748539), _1748541)), _1748539 = _1748541], (37443 ^ _779203) ^ [_1487878, _1487880, _1487882, _1487884] : [-(hAPP(c_Set_OCollect(tc_prod(_1487878, _1487880)), hAPP(c_Product__Type_Oprod_Oprod__case(_1487878, _1487880, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1487878, tc_fun(_1487880, tc_HOL_Obool), tc_fun(_1487880, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1487880, tc_HOL_Obool), tc_fun(_1487880, tc_HOL_Obool)), _1487878), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1487880)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1487878), c_fconj), _1487882))), _1487884))) = hAPP(hAPP(c_Product__Type_OSigma(_1487878, _1487880), hAPP(c_Set_OCollect(_1487878), _1487882)), hAPP(c_COMBK(tc_fun(_1487880, tc_HOL_Obool), _1487878), hAPP(c_Set_OCollect(_1487880), _1487884))))], (5110 ^ _779203) ^ [_857130, _857132, _857134, _857136, _857138, _857140] : [-(c_Lazy__Sequence_Oappend(_857140, _857136, _857132) = c_Lazy__Sequence_Oappend(_857138, _857134, _857130)), _857140 = _857138, _857136 = _857134, _857132 = _857130], (26006 ^ _779203) ^ [_1236510, _1236512, _1236514] : [class_Rings_Oring__1(_1236510), -(hAPP(c_Int_Oring__1__class_Oof__int(_1236510), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1236512), _1236514)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1236510), hAPP(c_Int_Oring__1__class_Oof__int(_1236510), _1236512)), _1236514))], (23223 ^ _779203) ^ [_1187767, _1187769] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1187767) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1187769)), _1187767 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1187769)), 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), _1187769)))], (1480 ^ _779203) ^ [_800663, _800665] : [-(class_Orderings_Otop(_800663)), _800665 = _800663, class_Orderings_Otop(_800665)], (22904 ^ _779203) ^ [_1182588] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182588)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1182588)) = _1182588)], (1770 ^ _779203) ^ [_804288, _804290] : [-(class_Nat_Osemiring__char__0(_804288)), _804290 = _804288, class_Nat_Osemiring__char__0(_804290)], (33595 ^ _779203) ^ [_1394104, _1394106, _1394108, _1394110] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1394104, _1394106), _1394108)), hBOOL(hAPP(hAPP(_1394106, _1394110), _1394108)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1394104, _1394106), _1394110)))], (6517 ^ _779203) ^ [_884335, _884337, _884339, _884341] : [class_Orderings_Oorder(_884335), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884335), _884337), _884339)), _884337 = _884341, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884335), _884341), _884339)))], (8506 ^ _779203) ^ [_922155, _922157, _922159, _922161, _922163] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_922155, _922157, hAPP(hAPP(c_Set_Oinsert(_922155), _922159), _922161)), _922163)), 8511 ^ _779203 : [(8516 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_922155), 8509 ^ [_922155, _922157, _922159, _922161, _922163]), 8510 ^ [_922155, _922157, _922159, _922161, _922163]))], (8514 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_922155, _922155, _922157, 8509 ^ [_922155, _922157, _922159, _922161, _922163], 8510 ^ [_922155, _922157, _922159, _922161, _922163]), _922163)))], (8512 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_922155), _922159), _922161) = hAPP(hAPP(c_Set_Oinsert(_922155), 8509 ^ [_922155, _922157, _922159, _922161, _922163]), 8510 ^ [_922155, _922157, _922159, _922161, _922163]))]]], (45382 ^ _779203) ^ [_1690160, _1690162] : [-(c_List_Oremdups(_1690160, c_List_Oremdups(_1690160, _1690162)) = c_List_Oremdups(_1690160, _1690162))], (32932 ^ _779203) ^ [_1382514] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1382514) = 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), _1382514), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (43772 ^ _779203) ^ [_1654867, _1654869, _1654871] : [-(hAPP(c_List_Oset(_1654867), hAPP(c_List_Orotate(_1654867, _1654869), _1654871)) = hAPP(c_List_Oset(_1654867), _1654871))], (28054 ^ _779203) ^ [_1274574, _1274576] : [28062 ^ _779203 : [(28065 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1274576, 28061 ^ [_1274574, _1274576])))], (28063 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 28061 ^ [_1274574, _1274576]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1274574))))]], 28055 ^ _779203 : [(28056 ^ _779203) ^ [_1274642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1274642), _1274574)), hBOOL(hAPP(_1274576, _1274642))]]], (31648 ^ _779203) ^ [_1347292, _1347294, _1347296] : [class_Fields_Olinordered__field(_1347292), 31654 ^ _779203 : [(31657 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347292), _1347294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347292), _1347296), 31653 ^ [_1347292, _1347294, _1347296])))], (31655 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347292), c_Groups_Ozero__class_Ozero(_1347292)), 31653 ^ [_1347292, _1347294, _1347296])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347292), _1347294), _1347296)))], (26794 ^ _779203) ^ [_1251151, _1251153, _1251155] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251151)), 26797 ^ _779203 : [(26798 ^ _779203) ^ [_1251285] : [26800 ^ _779203 : [(26806 ^ _779203) ^ [] : [-(_1251285 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 26802 ^ [_1251151, _1251153, _1251155, _1251285]), 26799 ^ [_1251151, _1251153, _1251155, _1251285]))], (26804 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26802 ^ [_1251151, _1251153, _1251155, _1251285]), _1251153)))], (26801 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26799 ^ [_1251151, _1251153, _1251155, _1251285]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1251151))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251285), _1251155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1251285), _1251151)), _1251155)))]]], (48088 ^ _779203) ^ [_1748675, _1748677, _1748679] : [-(_1748677 = _1748679), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1748675, _1748675, hAPP(hAPP(c_COMBB(tc_fun(_1748675, tc_HOL_Obool), tc_fun(_1748675, tc_HOL_Obool), _1748675), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1748675), c_fNot)), c_fequal)), _1748677), _1748679)))], (9867 ^ _779203) ^ [_947593, _947595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _947593), _947595)), 9870 ^ _779203 : [(9873 ^ _779203) ^ [] : [_947593 = _947595], (9871 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _947593), _947595)))]]], (15956 ^ _779203) ^ [_1059090, _1059092, _1059094] : [class_Int_Onumber__ring(_1059090), -(hAPP(c_Int_Onumber__class_Onumber__of(_1059090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1059092), _1059094)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1059090), hAPP(c_Int_Onumber__class_Onumber__of(_1059090), _1059092)), hAPP(c_Int_Onumber__class_Onumber__of(_1059090), _1059094)))], (40661 ^ _779203) ^ [_1576152, _1576154, _1576156] : [c_Relation_Ototal__on(_1576152, _1576154, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1576152, _1576152), tc_HOL_Obool)), _1576156), c_Relation_OId(_1576152))), -(c_Relation_Ototal__on(_1576152, _1576154, _1576156))], (52129 ^ _779203) ^ [_1831061, _1831063] : [class_Lattices_Obounded__lattice(_1831061), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1831063, _1831061)))], (5939 ^ _779203) ^ [_873313, _873315, _873317, _873319] : [hBOOL(hAPP(hAPP(c_member(_873313), _873315), _873317)), -(hBOOL(hAPP(hAPP(c_member(_873313), _873315), hAPP(hAPP(c_Set_Oinsert(_873313), _873319), _873317))))], (44197 ^ _779203) ^ [_1663414, _1663416, _1663418] : [-(_1663414 = c_List_Olist_ONil(_1663416)), -(c_List_Olast(_1663416, hAPP(hAPP(c_List_Oappend(_1663416), _1663418), _1663414)) = c_List_Olast(_1663416, _1663414))], (32701 ^ _779203) ^ [_1377730, _1377732, _1377734, _1377736, _1377738, _1377740, _1377742] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1377730, _1377732)), hAPP(hAPP(c_Product__Type_OPair(_1377730, _1377732), _1377734), _1377736)), _1377738)), -(hBOOL(hAPP(hAPP(c_member(_1377740), hAPP(hAPP(_1377742, _1377734), _1377736)), hAPP(c_Set_Oimage(tc_prod(_1377730, _1377732), _1377740, hAPP(c_Product__Type_Oprod_Oprod__case(_1377730, _1377732, _1377740), _1377742)), _1377738))))], (48818 ^ _779203) ^ [_1765074, _1765076] : [c_Relation_Otrans(_1765074, _1765076), -(c_Relation_Otrans(tc_List_Olist(_1765074), c_List_Olexord(_1765074, _1765076)))], (42826 ^ _779203) ^ [_1632794, _1632796, _1632798] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1632794))), -(c_List_Osublist(_1632796, hAPP(hAPP(c_List_Olist_OCons(_1632796), _1632798), c_List_Olist_ONil(_1632796)), _1632794) = c_List_Olist_ONil(_1632796))], (49887 ^ _779203) ^ [_1788092, _1788094, _1788096] : [c_Fun_Obij__betw(_1788092, _1788094, _1788096, c_Orderings_Otop__class_Otop(tc_fun(_1788092, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1788094, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1788094, _1788092, c_Orderings_Otop__class_Otop(tc_fun(_1788094, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1788092, _1788094, c_Orderings_Otop__class_Otop(tc_fun(_1788092, tc_HOL_Obool)), _1788096)) = _1788096)], (27248 ^ _779203) ^ [_1258914, _1258916] : [_1258914 = _1258916, -(c_Random_Oinc__shift(_1258914, _1258916) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (52273 ^ _779203) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (15236 ^ _779203) ^ [_1045687, _1045689, _1045691] : [class_Int_Onumber(_1045687), 15239 ^ _779203 : [(15246 ^ _779203) ^ [] : [_1045691 = hAPP(c_Int_Onumber__class_Onumber__of(_1045687), _1045689), -(hAPP(c_Int_Onumber__class_Onumber__of(_1045687), _1045689) = _1045691)], (15240 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1045687), _1045689) = _1045691, -(_1045691 = hAPP(c_Int_Onumber__class_Onumber__of(_1045687), _1045689))]]], (18636 ^ _779203) ^ [_1107834, _1107836] : [class_Int_Onumber__ring(_1107834), class_Rings_Olinordered__idom(_1107834), 18643 ^ _779203 : [(18650 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1107836)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107834), c_Groups_Ozero__class_Ozero(_1107834)), hAPP(c_Int_Onumber__class_Onumber__of(_1107834), _1107836))))], (18644 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107834), c_Groups_Ozero__class_Ozero(_1107834)), hAPP(c_Int_Onumber__class_Onumber__of(_1107834), _1107836))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1107836)))]]], (48134 ^ _779203) ^ [_1749519, _1749521, _1749523, _1749525, _1749527] : [-(c_Predicate_Oconversep(_1749519, _1749521, c_Predicate_Opred__comp(_1749519, _1749523, _1749521, _1749525, _1749527)) = c_Predicate_Opred__comp(_1749521, _1749523, _1749519, c_Predicate_Oconversep(_1749523, _1749521, _1749527), c_Predicate_Oconversep(_1749519, _1749523, _1749525)))], (34803 ^ _779203) ^ [_1424539, _1424541, _1424543, _1424545] : [-(_1424539 = c_Orderings_Obot__class_Obot(tc_fun(_1424541, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1424541, tc_fun(_1424543, tc_HOL_Obool)), _1424539), hAPP(c_COMBK(tc_fun(_1424543, tc_HOL_Obool), _1424541), _1424545)) = _1424545)], (28354 ^ _779203) ^ [_1280630, _1280632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1280630), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1280632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1280632), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1280630))))), -(_1280630 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1280632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1280632), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1280630))))], (45350 ^ _779203) ^ [_1689584, _1689586] : [hBOOL(hAPP(c_List_Odistinct(_1689584), _1689586)), -(c_List_Oremdups(_1689584, _1689586) = _1689586)], (20354 ^ _779203) ^ [_1138176, _1138178, _1138180] : [class_Rings_Odivision__ring(_1138176), -(_1138178 = c_Groups_Ozero__class_Ozero(_1138176)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138176), hAPP(c_Groups_Ouminus__class_Ouminus(_1138176), _1138180)), hAPP(c_Groups_Ouminus__class_Ouminus(_1138176), _1138178)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1138176), _1138180), _1138178))], (42574 ^ _779203) ^ [_1628172, _1628174, _1628176, _1628178] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628172) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1628174), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628172)), hAPP(hAPP(c_List_Olist_OCons(_1628174), _1628176), _1628178)) = hAPP(hAPP(c_List_Olist_OCons(_1628174), _1628176), hAPP(hAPP(c_List_Otake(_1628174), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1628172)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1628178)))], (33979 ^ _779203) ^ [_1401860, _1401862, _1401864] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1401860, _1401862), _1401864))), _1401860 = 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), _1401864)), _1401862)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401864)), 33986 ^ _779203 : [(33989 ^ _779203) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1401864) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (33987 ^ _779203) ^ [] : [-(_1401862 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 33990 ^ _779203 : [(33993 ^ _779203) ^ [] : [33994 ^ _779203 : [(33997 ^ _779203) ^ [] : [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), _1401864))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401864)), _1401862))], (33995 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1401862)))]], 34002 ^ _779203 : [(34005 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1401862), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401864))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1401864)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (34003 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1401862))]]], (33991 ^ _779203) ^ [] : [_1401862 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (51479 ^ _779203) ^ [_1819653, _1819655] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819653), _1819655)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819655), _1819653))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819655), _1819653)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1819653), _1819655)))], (38222 ^ _779203) ^ [_1514739, _1514741] : [-(hAPP(c_Set_Ovimage(_1514739, _1514739, c_Fun_Oid(_1514739)), _1514741) = _1514741)], (21709 ^ _779203) ^ [_1161367, _1161369] : [class_Int_Onumber__ring(_1161367), class_Int_Oring__char__0(_1161367), 21716 ^ _779203 : [(21723 ^ _779203) ^ [] : [c_Int_Oiszero(_1161367, hAPP(c_Int_Onumber__class_Onumber__of(_1161367), _1161369)), -(c_Int_Oiszero(_1161367, hAPP(c_Int_Onumber__class_Onumber__of(_1161367), c_Int_OBit0(_1161369))))], (21717 ^ _779203) ^ [] : [c_Int_Oiszero(_1161367, hAPP(c_Int_Onumber__class_Onumber__of(_1161367), c_Int_OBit0(_1161369))), -(c_Int_Oiszero(_1161367, hAPP(c_Int_Onumber__class_Onumber__of(_1161367), _1161369)))]]], (32691 ^ _779203) ^ [_1376988, _1376990, _1376992, _1376994, _1376996, _1376998] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1376988, _1376990)), hAPP(hAPP(c_Product__Type_OPair(_1376988, _1376990), _1376996), _1376998)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool)), _1376992), _1376994))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1376988, tc_fun(_1376990, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1376988, tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_fun(_1376990, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376990, tc_fun(tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_fun(_1376990, tc_HOL_Obool)), _1376988), c_COMBC(_1376990, tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376990, tc_prod(_1376988, _1376990)), tc_fun(_1376990, tc_fun(tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_HOL_Obool)), _1376988), hAPP(c_COMBB(tc_prod(_1376988, _1376990), tc_fun(tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_HOL_Obool), _1376990), c_member(tc_prod(_1376988, _1376990)))), c_Product__Type_OPair(_1376988, _1376990)))), _1376992)), hAPP(hAPP(c_COMBC(_1376988, tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_fun(_1376990, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376990, tc_fun(tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_fun(_1376990, tc_HOL_Obool)), _1376988), c_COMBC(_1376990, tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1376990, tc_prod(_1376988, _1376990)), tc_fun(_1376990, tc_fun(tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_HOL_Obool)), _1376988), hAPP(c_COMBB(tc_prod(_1376988, _1376990), tc_fun(tc_fun(tc_prod(_1376988, _1376990), tc_HOL_Obool), tc_HOL_Obool), _1376990), c_member(tc_prod(_1376988, _1376990)))), c_Product__Type_OPair(_1376988, _1376990)))), _1376994)), _1376996), _1376998)))], (52489 ^ _779203) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (840 ^ _779203) ^ [_791753, _791755, _791757, _791759] : [-(c_Predicate_Osymp(_791757, _791753)), c_Predicate_Osymp(_791759, _791755), _791759 = _791757, _791755 = _791753], (22998 ^ _779203) ^ [_1184111, _1184113, _1184115, _1184117] : [class_Divides_Osemiring__div(_1184111), -(_1184113 = c_Groups_Ozero__class_Ozero(_1184111)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1184111), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184111), _1184115), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184111), _1184113), _1184117))), _1184113) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1184111), _1184117), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1184111), _1184115), _1184113)))], (2598 ^ _779203) ^ [_817462, _817464, _817466, _817468] : [-(c_Wellfounded_Omin__ext(_817468, _817464) = c_Wellfounded_Omin__ext(_817466, _817462)), _817468 = _817466, _817464 = _817462], (18818 ^ _779203) ^ [_1110758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1110758), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1110758)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38697 ^ _779203) ^ [_1528386, _1528388, _1528390, _1528392] : [c_Wellfounded_Owf(_1528386, _1528388), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528386, _1528386)), hAPP(hAPP(c_Product__Type_OPair(_1528386, _1528386), _1528390), _1528392)), _1528388)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1528386, _1528386)), hAPP(hAPP(c_Product__Type_OPair(_1528386, _1528386), _1528392), _1528390)), _1528388))], (34065 ^ _779203) ^ [] : [-(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))], (22023 ^ _779203) ^ [_1167595, _1167597, _1167599, _1167601] : [class_Divides_Osemiring__div(_1167595), -(c_Divides_Odiv__class_Omod(_1167595, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167595), _1167597), _1167599), _1167601) = c_Divides_Odiv__class_Omod(_1167595, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167595), _1167597), c_Divides_Odiv__class_Omod(_1167595, _1167599, _1167601)), _1167601))], (47634 ^ _779203) ^ [_1739057, _1739059, _1739061] : [c_List_Olist__ex(_1739057, _1739059, _1739061), 47638 ^ _779203 : [(47641 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1739059, hAPP(hAPP(c_List_Onth(_1739057), _1739061), 47637 ^ [_1739057, _1739059, _1739061]))))], (47639 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47637 ^ [_1739057, _1739059, _1739061]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1739057)), _1739061))))]]], (26320 ^ _779203) ^ [_1242154, _1242156, _1242158, _1242160, _1242162] : [class_Orderings_Oorder(_1242154), 26323 ^ _779203 : [(26344 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1242154, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1242154, _1242156, _1242158)), c_SetInterval_Oord__class_OatLeastAtMost(_1242154, _1242160, _1242162)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242154), _1242160), _1242162)), 26347 ^ _779203 : [(26350 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242154), _1242160), _1242156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242154), _1242158), _1242162)), 26357 ^ _779203 : [(26360 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1242154), _1242158), _1242162))], (26358 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1242154), _1242160), _1242156))]]], (26348 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242154), _1242156), _1242158)))]]], (26324 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1242154, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1242154, _1242156, _1242158)), c_SetInterval_Oord__class_OatLeastAtMost(_1242154, _1242160, _1242162))), 26327 ^ _779203 : [(26328 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242154), _1242156), _1242158)), 26331 ^ _779203 : [(26336 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1242154), _1242160), _1242156))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1242154), _1242158), _1242162)))], (26334 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242154), _1242158), _1242162)))], (26332 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242154), _1242160), _1242156)))]]], (26342 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242154), _1242160), _1242162)))]]]]], (6733 ^ _779203) ^ [_888329, _888331, _888333] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_888329), _888331)), hBOOL(hAPP(_888333, c_Orderings_Obot__class_Obot(tc_fun(_888329, tc_HOL_Obool)))), 6744 ^ _779203 : [(6747 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_888329), 6742 ^ [_888329, _888331, _888333]), 6743 ^ [_888329, _888331, _888333]))], (6749 ^ _779203) ^ [] : [-(hBOOL(hAPP(_888333, 6743 ^ [_888329, _888331, _888333])))], (6751 ^ _779203) ^ [] : [hBOOL(hAPP(_888333, hAPP(hAPP(c_Set_Oinsert(_888329), 6742 ^ [_888329, _888331, _888333]), 6743 ^ [_888329, _888331, _888333])))], (6745 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_888329), 6743 ^ [_888329, _888331, _888333])))]], -(hBOOL(hAPP(_888333, _888331)))], (46808 ^ _779203) ^ [_1720709, _1720711, _1720713] : [class_Orderings_Olinorder(_1720709), c_List_Olinorder__class_Osorted(_1720709, _1720711), -(c_List_Olinorder__class_Osorted(_1720709, c_List_OtakeWhile(_1720709, _1720713, _1720711)))], (50805 ^ _779203) ^ [_1808067, _1808069, _1808071, _1808073] : [class_Rings_Ocomm__ring(_1808067), class_Rings_Odvd(_1808067), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808067), _1808069), _1808071)), 50816 ^ _779203 : [(50823 ^ _779203) ^ [_1808493, _1808495] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808067), _1808069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808067), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1808067), _1808495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1808067), _1808493), _1808071))), _1808073))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808067), _1808069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808067), _1808495), _1808073))))], (50817 ^ _779203) ^ [_1808320, _1808322] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808067), _1808069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808067), _1808322), _1808073))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1808067), _1808069), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1808067), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1808067), _1808322), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1808067), _1808320), _1808071))), _1808073))))]]], (48631 ^ _779203) ^ [_1760612, _1760614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1760612)), _1760614)), 48635 ^ _779203 : [(48636 ^ _779203) ^ [_1760713] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1760612)), _1760713), _1760614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760612)), _1760713)), 48634 ^ [_1760612, _1760614])))]]], (46302 ^ _779203) ^ [_1710119, _1710121, _1710123] : [class_Orderings_Olinorder(_1710119), 46305 ^ _779203 : [(46318 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710119, hAPP(hAPP(c_List_Olist_OCons(_1710119), _1710121), _1710123))), c_List_Olinorder__class_Osorted(_1710119, _1710123), 46324 ^ _779203 : [(46327 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710119), _1710121), 46323 ^ [_1710119, _1710121, _1710123]))], (46325 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1710119), 46323 ^ [_1710119, _1710121, _1710123]), hAPP(c_List_Oset(_1710119), _1710123))))]]], (46306 ^ _779203) ^ [] : [c_List_Olinorder__class_Osorted(_1710119, hAPP(hAPP(c_List_Olist_OCons(_1710119), _1710121), _1710123)), 46309 ^ _779203 : [(46312 ^ _779203) ^ [_1710305] : [hBOOL(hAPP(hAPP(c_member(_1710119), _1710305), hAPP(c_List_Oset(_1710119), _1710123))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1710119), _1710121), _1710305)))], (46310 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1710119, _1710123))]]]]], (40197 ^ _779203) ^ [_1564194, _1564196] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1564194, _1564194), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1564194, _1564196)), hAPP(hAPP(c_Product__Type_OSigma(_1564194, _1564194), hAPP(c_Relation_OField(_1564194), _1564196)), hAPP(c_COMBK(tc_fun(_1564194, tc_HOL_Obool), _1564194), hAPP(c_Relation_OField(_1564194), _1564196))))))], (35571 ^ _779203) ^ [_1445229, _1445231] : [c_Relation_Oirrefl(_1445229, _1445231), 35574 ^ _779203 : [(35575 ^ _779203) ^ [_1445311] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1445229, _1445229)), hAPP(hAPP(c_Product__Type_OPair(_1445229, _1445229), _1445311), _1445311)), _1445231))]]], (33199 ^ _779203) ^ [_1387225, _1387227] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1387225), _1387227)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1387225), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1387227)))], (29240 ^ _779203) ^ [_1297430, _1297432] : [class_Lattices_Osemilattice__inf(_1297430), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1297430), _1297432), _1297432) = _1297432)], (18196 ^ _779203) ^ [] : [-(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))], (34633 ^ _779203) ^ [_1420362, _1420364, _1420366, _1420368, _1420370, _1420372] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1420364, _1420366)), hAPP(hAPP(c_Product__Type_OPair(_1420364, _1420366), _1420370), _1420372)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1420362, tc_fun(tc_prod(_1420364, _1420366), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1420362, tc_HOL_Obool))), _1420368))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1420362, tc_fun(_1420364, tc_fun(_1420366, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1420362, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1420364, _1420366), tc_HOL_Obool), tc_fun(_1420364, tc_fun(_1420366, tc_HOL_Obool)), _1420362), hAPP(c_COMBC(_1420364, tc_fun(tc_prod(_1420364, _1420366), tc_HOL_Obool), tc_fun(_1420366, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1420366, tc_fun(tc_fun(tc_prod(_1420364, _1420366), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1420364, _1420366), tc_HOL_Obool), tc_fun(_1420366, tc_HOL_Obool)), _1420364), c_COMBC(_1420366, tc_fun(tc_prod(_1420364, _1420366), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1420366, tc_prod(_1420364, _1420366)), tc_fun(_1420366, tc_fun(tc_fun(tc_prod(_1420364, _1420366), tc_HOL_Obool), tc_HOL_Obool)), _1420364), hAPP(c_COMBB(tc_prod(_1420364, _1420366), tc_fun(tc_fun(tc_prod(_1420364, _1420366), tc_HOL_Obool), tc_HOL_Obool), _1420366), c_member(tc_prod(_1420364, _1420366)))), c_Product__Type_OPair(_1420364, _1420366))))), _1420368)), _1420370), _1420372)))], (26526 ^ _779203) ^ [_1245887, _1245889, _1245891, _1245893, _1245895] : [class_Groups_Ocomm__monoid__add(_1245887), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1245889), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1245891), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245887), _1245893), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1245889, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1245891), _1245895))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1245887), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245887), _1245893), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1245889, _1245891))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1245887), _1245893), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1245891), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1245891), _1245895)))))], (50168 ^ _779203) ^ [_1793689, _1793691, _1793693, _1793695, _1793697, _1793699, _1793701] : [c_Fun_Obij__betw(_1793689, _1793691, _1793693, _1793695, _1793697), c_Fun_Obij__betw(_1793689, _1793691, _1793693, _1793699, _1793701), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1793691, tc_HOL_Obool)), _1793697), _1793701) = c_Orderings_Obot__class_Obot(tc_fun(_1793691, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1793689, _1793691, _1793693, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793689, tc_HOL_Obool)), _1793695), _1793699), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1793691, tc_HOL_Obool)), _1793697), _1793701)))], (32944 ^ _779203) ^ [_1382785, _1382787] : [-(c_Divides_OnegDivAlg(_1382785, _1382787) = hAPP(c_Divides_Oadjust(_1382787), c_Divides_OnegDivAlg(_1382785, 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)))), _1382787)))), -(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), _1382785), _1382787)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1382787), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (29790 ^ _779203) ^ [_1308665, _1308667, _1308669] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308665, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308665, tc_HOL_Obool)), _1308667), _1308669)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308665, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308665, tc_HOL_Obool)), _1308667)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308665, tc_HOL_Obool)), _1308669)))], (29970 ^ _779203) ^ [_1312725, _1312727, _1312729] : [class_Orderings_Oorder(_1312725), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1312725, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1312725), _1312727)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1312725, _1312727, _1312729)) = c_Orderings_Obot__class_Obot(tc_fun(_1312725, tc_HOL_Obool)))], (20084 ^ _779203) ^ [_1133470, _1133472, _1133474] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133470, tc_HOL_Obool)), _1133472), _1133474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1133470, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1133470, tc_HOL_Obool)), _1133474)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1133470, tc_HOL_Obool)), _1133472))))], (24958 ^ _779203) ^ [_1219047, _1219049, _1219051, _1219053] : [class_Groups_Omonoid__mult(_1219047), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1219047), _1219049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1219051), _1219053)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1219047), hAPP(hAPP(c_Power_Opower__class_Opower(_1219047), _1219049), _1219051)), _1219053))], (7065 ^ _779203) ^ [_895797, _895799, _895801, _895803, _895805] : [class_Groups_Ominus(_895797), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_895799, _895797)), _895801), _895803), _895805) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_895797), hAPP(_895801, _895805)), hAPP(_895803, _895805)))], (45835 ^ _779203) ^ [_1701472, _1701474, _1701476] : [class_Groups_Omonoid__add(_1701472), -(hAPP(c_List_Ofoldl(_1701472, _1701472, c_Groups_Oplus__class_Oplus(_1701472), _1701474), _1701476) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1701472), _1701474), c_List_Ofoldr(_1701472, _1701472, c_Groups_Oplus__class_Oplus(_1701472), _1701476, c_Groups_Ozero__class_Ozero(_1701472))))], (9303 ^ _779203) ^ [_937911, _937913, _937915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _937913), _937915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937911), _937913)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _937911), _937915))))], (50551 ^ _779203) ^ [_1803485, _1803487, _1803489] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1803485), _1803487)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1803485), _1803489))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1803485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1803487), _1803489)))], (37021 ^ _779203) ^ [_1477393, _1477395, _1477397, _1477399] : [hBOOL(hAPP(hAPP(c_member(_1477393), _1477395), c_Wellfounded_Oacc(_1477393, _1477397))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1477393, _1477393)), hAPP(hAPP(c_Product__Type_OPair(_1477393, _1477393), _1477399), _1477395)), _1477397)), -(hBOOL(hAPP(hAPP(c_member(_1477393), _1477399), c_Wellfounded_Oacc(_1477393, _1477397))))], (29796 ^ _779203) ^ [_1308868, _1308870, _1308872] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1308868, tc_HOL_Obool)), _1308870), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308868, tc_HOL_Obool)), _1308872)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308868, tc_HOL_Obool)), _1308870), _1308872))], (22644 ^ _779203) ^ [_1178404, _1178406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178404)), 22647 ^ _779203 : [(22654 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178406)), -(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), _1178406), _1178404))))], (22648 ^ _779203) ^ [] : [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), _1178406), _1178404))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1178406)))]]], (30983 ^ _779203) ^ [_1333337, _1333339, _1333341] : [class_Lattices_Olattice(_1333337), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333337), _1333339)), -(c_Big__Operators_Olattice__class_OInf__fin(_1333337, hAPP(hAPP(c_Set_Oinsert(_1333337), _1333341), _1333339)) = hAPP(hAPP(c_Finite__Set_Ofold(_1333337, _1333337, c_Lattices_Osemilattice__inf__class_Oinf(_1333337)), _1333341), _1333339))], (45691 ^ _779203) ^ [_1697368] : [-(c_List_Otranspose(_1697368, c_List_Olist_ONil(tc_List_Olist(_1697368))) = c_List_Olist_ONil(tc_List_Olist(_1697368)))], (25976 ^ _779203) ^ [_1235973] : [class_Rings_Oring__1(_1235973), -(hAPP(c_Int_Oring__1__class_Oof__int(_1235973), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1235973))], (23970 ^ _779203) ^ [_1201222, _1201224, _1201226, _1201228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1201222)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1201224), _1201226)), -(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), _1201226), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1201228, _1201222))), _1201224)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1201226), _1201222))))], (29032 ^ _779203) ^ [_1292814, _1292816] : [class_Lattices_Olattice(_1292814), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292814), _1292816)), -(_1292816 = c_Orderings_Obot__class_Obot(tc_fun(_1292814, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1292814), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1292814), 29045 ^ [_1292814, _1292816]), 29046 ^ [_1292814, _1292816])), hAPP(hAPP(c_Set_Oinsert(_1292814), 29045 ^ [_1292814, _1292816]), hAPP(hAPP(c_Set_Oinsert(_1292814), 29046 ^ [_1292814, _1292816]), c_Orderings_Obot__class_Obot(tc_fun(_1292814, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1292814), c_Big__Operators_Olattice__class_OSup__fin(_1292814, _1292816)), _1292816)))], (52437 ^ _779203) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (45851 ^ _779203) ^ [_1701888, _1701890, _1701892, _1701894] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1701888, tc_Nat_Onat), _1701888), c_Product__Type_Ofst(_1701888, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701888, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701888, 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(_1701888, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1701888, tc_Nat_Onat))), _1701890)), hAPP(hAPP(c_List_Ozip(_1701888, tc_Nat_Onat), _1701892), c_List_Oupt(_1701894, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1701894), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701888)), _1701892)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1701888, tc_Nat_Onat), _1701888), c_Product__Type_Ofst(_1701888, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1701888, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1701888, 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(_1701888, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1701888, 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(_1701888, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1701888, tc_Nat_Onat))), _1701894))), _1701890)), hAPP(hAPP(c_List_Ozip(_1701888, tc_Nat_Onat), _1701892), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701888)), _1701892))))))], (50751 ^ _779203) ^ [_1806966, _1806968, _1806970, _1806972, _1806974] : [class_Divides_Osemiring__div(_1806966), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806966), _1806968), _1806970)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1806966), _1806972), _1806974)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806966), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1806966), _1806970), _1806968)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1806966), _1806974), _1806972)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1806966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806966), _1806970), _1806974)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1806966), _1806968), _1806972)))], (47825 ^ _779203) ^ [_1742946, _1742948] : [-(c_FunDef_Ois__measure(_1742946, _1742948))], (48224 ^ _779203) ^ [_1751832, _1751834, _1751836, _1751838] : [48225 ^ _779203 : [(48228 ^ _779203) ^ [] : [_1751834 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48226 ^ _779203) ^ [] : [hBOOL(hAPP(_1751838, _1751836))]], 48229 ^ _779203 : [(48230 ^ _779203) ^ [_1751957] : [hBOOL(hAPP(hAPP(c_member(_1751832), _1751957), hAPP(c_List_Oset(_1751832), c_List_Oreplicate(_1751832, _1751834, _1751836)))), -(hBOOL(hAPP(_1751838, _1751957)))]]], (18395 ^ _779203) ^ [_1103711, _1103713, _1103715] : [class_Rings_Olinordered__semidom(_1103711), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1103713), _1103715)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103711), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103711), _1103713)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1103711), _1103715))))], (26380 ^ _779203) ^ [_1243136, _1243138] : [_1243136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1243138, _1243136) = _1243138)], (37247 ^ _779203) ^ [_1482887, _1482889, _1482891, _1482893, _1482895] : [hAPP(_1482893, _1482889) = _1482895, -(hBOOL(hAPP(hAPP(c_member(_1482887), _1482889), hAPP(c_Set_Ovimage(_1482887, _1482891, _1482893), hAPP(hAPP(c_Set_Oinsert(_1482891), _1482895), c_Orderings_Obot__class_Obot(tc_fun(_1482891, tc_HOL_Obool)))))))], (3572 ^ _779203) ^ [_832633, _832635, _832637, _832639, _832641, _832643, _832645, _832647, _832649, _832651] : [-(c_List_Ofoldr(_832651, _832647, _832643, _832639, _832635) = c_List_Ofoldr(_832649, _832645, _832641, _832637, _832633)), _832651 = _832649, _832647 = _832645, _832643 = _832641, _832639 = _832637, _832635 = _832633], (31775 ^ _779203) ^ [_1350390, _1350392] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1350390, tc_HOL_Obool)), _1350392)), -(hBOOL(hAPP(hAPP(c_member(_1350390), _1350392), c_Orderings_Obot__class_Obot(tc_fun(_1350390, tc_HOL_Obool)))))], (21015 ^ _779203) ^ [_1149744] : [-(_1149744 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21018 ^ _779203 : [(21025 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1149744))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1149744) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (21019 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1149744)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1149744) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (20993 ^ _779203) ^ [_1149379, _1149381, _1149383] : [class_Int_Onumber__ring(_1149379), 20996 ^ _779203 : [(21003 ^ _779203) ^ [] : [c_Int_Oiszero(_1149379, hAPP(c_Int_Onumber__class_Onumber__of(_1149379), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1149381), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1149383)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1149379), _1149381) = hAPP(c_Int_Onumber__class_Onumber__of(_1149379), _1149383))], (20997 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1149379), _1149381) = hAPP(c_Int_Onumber__class_Onumber__of(_1149379), _1149383), -(c_Int_Oiszero(_1149379, hAPP(c_Int_Onumber__class_Onumber__of(_1149379), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1149381), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1149383)))))]]], (45294 ^ _779203) ^ [_1688250, _1688252, _1688254] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1688250))), c_Enum_On__lists(_1688250, _1688252, _1688254)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688250)), _1688254)), _1688252))], (22391 ^ _779203) ^ [_1174211, _1174213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1174211), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1174211), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1174213, _1174211))))], (46560 ^ _779203) ^ [_1715405] : [-(hAPP(c_List_Orev(_1715405), c_List_Olist_ONil(_1715405)) = c_List_Olist_ONil(_1715405))], (2836 ^ _779203) ^ [_821175, _821177, _821179, _821181, _821183, _821185] : [-(c_Nitpick_Otimes__frac(_821185, _821181, _821177) = c_Nitpick_Otimes__frac(_821183, _821179, _821175)), _821185 = _821183, _821181 = _821179, _821177 = _821175], (14707 ^ _779203) ^ [_1035486, _1035488, _1035490, _1035492] : [class_Fields_Ofield(_1035486), -(_1035488 = c_Groups_Ozero__class_Ozero(_1035486)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035486), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035486), _1035490), _1035488)), _1035492) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1035486), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1035486), _1035490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035486), _1035488), _1035492))), _1035488))], (5100 ^ _779203) ^ [_856981, _856983, _856985, _856987] : [-(c_Product__Type_OPair(_856987, _856983) = c_Product__Type_OPair(_856985, _856981)), _856987 = _856985, _856983 = _856981], (47248 ^ _779203) ^ [_1730115, _1730117] : [-(c_List_Omeasures(_1730115, _1730117) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1730115), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1730115, tc_List_Olist(tc_fun(_1730115, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1730115, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1730115, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1730115), c_List_Omap(tc_fun(_1730115, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1730115, tc_Nat_Onat), _1730115, tc_Nat_Onat), c_COMBI(tc_fun(_1730115, tc_Nat_Onat))))), _1730117)))], (37265 ^ _779203) ^ [_1483317, _1483319, _1483321, _1483323, _1483325] : [hAPP(c_Set_Oimage(_1483317, _1483319, _1483321), c_Orderings_Otop__class_Otop(tc_fun(_1483317, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1483319, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483317, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1483317, _1483319, _1483321), _1483323)), _1483325)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1483319, tc_HOL_Obool)), _1483323), hAPP(c_Set_Oimage(_1483317, _1483319, _1483321), _1483325))))], (32807 ^ _779203) ^ [_1379824, _1379826, _1379828, _1379830, _1379832] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1379824, _1379826, tc_HOL_Obool), _1379828), hAPP(hAPP(c_Product__Type_OPair(_1379824, _1379826), _1379830), _1379832))), -(hBOOL(hAPP(hAPP(_1379828, _1379830), _1379832)))], (1740 ^ _779203) ^ [_803913, _803915] : [-(class_Groups_Osemigroup__add(_803913)), _803915 = _803913, class_Groups_Osemigroup__add(_803915)], (7263 ^ _779203) ^ [_899766, _899768, _899770] : [class_Orderings_Olinorder(_899766), 7266 ^ _779203 : [(7267 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899766), _899768), _899770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899766), _899770), _899768))), -(_899768 = _899770)], (7277 ^ _779203) ^ [] : [7278 ^ _779203 : [(7281 ^ _779203) ^ [] : [_899768 = _899770], (7279 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899766), _899770), _899768))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_899766), _899768), _899770))]]], (41891 ^ _779203) ^ [_1610694, _1610696, _1610698] : [-(hAPP(c_List_Oset(_1610694), c_List_Osublist(_1610694, _1610696, _1610698)) = hAPP(c_Set_OCollect(_1610694), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1610694), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1610694, 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)), _1610694), 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)), _1610694), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1610694, tc_fun(tc_Nat_Onat, _1610694), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1610694, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1610694), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1610694), c_COMBB(_1610694, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1610694), _1610696))))), 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(_1610694)), _1610696)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1610698))))))], (25842 ^ _779203) ^ [] : [-(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))], (44958 ^ _779203) ^ [_1680606, _1680608, _1680610] : [-(c_List_Olistsp(_1680606, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680606, tc_HOL_Obool)), _1680608), _1680610)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1680606), tc_HOL_Obool)), c_List_Olistsp(_1680606, _1680608)), c_List_Olistsp(_1680606, _1680610)))], (10437 ^ _779203) ^ [_959356, _959358, _959360, _959362] : [class_Rings_Ocomm__semiring__1(_959356), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959356), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959356), _959358), _959360)), _959362) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959356), _959358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_959356), _959360), _959362)))], (31011 ^ _779203) ^ [_1333759, _1333761, _1333763] : [class_Lattices_Olattice(_1333759), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333759), _1333761)), 31018 ^ _779203 : [(31025 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333759, tc_HOL_Obool)), _1333761), hAPP(hAPP(c_Set_Oinsert(_1333759), _1333763), c_Orderings_Obot__class_Obot(tc_fun(_1333759, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1333759, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1333759, hAPP(hAPP(c_Set_Oinsert(_1333759), _1333763), _1333761)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1333759), _1333763), c_Big__Operators_Olattice__class_OInf__fin(_1333759, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333759, tc_HOL_Obool)), _1333761), hAPP(hAPP(c_Set_Oinsert(_1333759), _1333763), c_Orderings_Obot__class_Obot(tc_fun(_1333759, tc_HOL_Obool)))))))], (31019 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1333759, tc_HOL_Obool)), _1333761), hAPP(hAPP(c_Set_Oinsert(_1333759), _1333763), c_Orderings_Obot__class_Obot(tc_fun(_1333759, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1333759, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1333759, hAPP(hAPP(c_Set_Oinsert(_1333759), _1333763), _1333761)) = _1333763)]]], (37090 ^ _779203) ^ [_1479038] : [-(c_Nitpick_Oone__frac(_1479038) = c_Nitpick_OAbs__Frac(_1479038, 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))))], (4508 ^ _779203) ^ [_847657, _847659, _847661, _847663] : [-(c_List_Oupto(_847663, _847659) = c_List_Oupto(_847661, _847657)), _847663 = _847661, _847659 = _847657], (9433 ^ _779203) ^ [_939975] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _939975), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _939975), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _939975), _939975)))))], (5532 ^ _779203) ^ [_863757, _863759, _863761, _863763] : [-(c_COMBK(_863763, _863759) = c_COMBK(_863761, _863757)), _863763 = _863761, _863759 = _863757], (38871 ^ _779203) ^ [_1532125] : [class_Orderings_Owellorder(_1532125), -(c_Wellfounded_Owf(_1532125, hAPP(c_Set_OCollect(tc_prod(_1532125, _1532125)), hAPP(c_Product__Type_Oprod_Oprod__case(_1532125, _1532125, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1532125)))))], (9649 ^ _779203) ^ [_944039, _944041] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _944039)), hAPP(c_Nat_OSuc, _944041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _944039), _944041)))], (49737 ^ _779203) ^ [_1784647, _1784649, _1784651, _1784653, _1784655, _1784657, _1784659] : [c_Fun_Oinj__on(_1784647, _1784649, _1784651, hAPP(c_Set_Oimage(_1784653, _1784647, _1784655), _1784657)), c_Fun_Oinj__on(_1784653, _1784647, _1784655, _1784657), hBOOL(hAPP(hAPP(c_member(_1784649), _1784659), hAPP(c_Set_Oimage(_1784647, _1784649, _1784651), hAPP(c_Set_Oimage(_1784653, _1784647, _1784655), _1784657)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1784653, _1784649, _1784657, hAPP(c_Fun_Ocomp(_1784647, _1784649, _1784653, _1784651), _1784655)), _1784659) = hAPP(hAPP(c_Fun_Ocomp(_1784647, _1784653, _1784649, c_Hilbert__Choice_Oinv__into(_1784653, _1784647, _1784657, _1784655)), c_Hilbert__Choice_Oinv__into(_1784647, _1784649, hAPP(c_Set_Oimage(_1784653, _1784647, _1784655), _1784657), _1784651)), _1784659))], (2216 ^ _779203) ^ [_811495, _811497, _811499, _811501, _811503, _811505, _811507, _811509] : [-(c_Nitpick_Opair__box_OPairBox(_811509, _811505, _811501, _811497) = c_Nitpick_Opair__box_OPairBox(_811507, _811503, _811499, _811495)), _811509 = _811507, _811505 = _811503, _811501 = _811499, _811497 = _811495], (52409 ^ _779203) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (5314 ^ _779203) ^ [_860480, _860482] : [_860482 = _860480, -(c_Groups_Oabs__class_Oabs(_860482) = c_Groups_Oabs__class_Oabs(_860480))], (42626 ^ _779203) ^ [_1629100, _1629102, _1629104, _1629106] : [_1629100 = _1629102, -(c_List_Oremove1(_1629104, _1629100, hAPP(hAPP(c_List_Olist_OCons(_1629104), _1629102), _1629106)) = _1629106)], (17322 ^ _779203) ^ [_1084626, _1084628] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084626), _1084628)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084628), _1084626)), -(_1084626 = _1084628)], (26022 ^ _779203) ^ [_1236798, _1236800, _1236802] : [class_Groups_Oordered__ab__group__add(_1236798), -(hAPP(c_Set_Oimage(_1236798, _1236798, c_Groups_Ouminus__class_Ouminus(_1236798)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1236798, _1236800, _1236802)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1236798, hAPP(c_Groups_Ouminus__class_Ouminus(_1236798), _1236802), hAPP(c_Groups_Ouminus__class_Ouminus(_1236798), _1236800)))], (32297 ^ _779203) ^ [_1363481, _1363483, _1363485] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1363481), _1363483)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1363481, tc_HOL_Obool)), _1363485), _1363483) = hAPP(hAPP(c_Finite__Set_Ofold(_1363481, tc_fun(_1363481, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1363481, tc_HOL_Obool), tc_fun(tc_fun(_1363481, tc_HOL_Obool), tc_fun(_1363481, tc_HOL_Obool)), _1363481), hAPP(c_COMBC(tc_fun(_1363481, tc_HOL_Obool), tc_fun(_1363481, tc_HOL_Obool), tc_fun(_1363481, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1363481, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1363481, tc_fun(_1363481, tc_HOL_Obool), tc_fun(_1363481, tc_HOL_Obool)), c_Set_Oinsert(_1363481)), c_Orderings_Obot__class_Obot(tc_fun(_1363481, tc_HOL_Obool))))), _1363485), _1363483))], (1310 ^ _779203) ^ [_798538, _798540] : [-(class_Int_Oring__char__0(_798538)), _798540 = _798538, class_Int_Oring__char__0(_798540)], (37801 ^ _779203) ^ [_1497828, _1497830, _1497832, _1497834, _1497836, _1497838] : [class_Groups_Ocomm__monoid__add(_1497828), hBOOL(hAPP(c_Finite__Set_Ofinite(_1497830), _1497832)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497830, _1497828), _1497834), _1497832) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497836, _1497828), hAPP(hAPP(c_COMBB(tc_fun(_1497830, tc_HOL_Obool), _1497828, _1497836), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1497830, _1497828), _1497834)), hAPP(hAPP(c_COMBB(tc_fun(_1497830, tc_HOL_Obool), tc_fun(_1497830, tc_HOL_Obool), _1497836), c_Set_OCollect(_1497830)), hAPP(hAPP(c_COMBB(tc_fun(_1497830, tc_HOL_Obool), tc_fun(_1497830, tc_HOL_Obool), _1497836), hAPP(c_COMBS(_1497830, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1497830), c_fconj), hAPP(hAPP(c_COMBC(_1497830, tc_fun(_1497830, tc_HOL_Obool), tc_HOL_Obool), c_member(_1497830)), _1497832)))), hAPP(c_COMBC(_1497830, _1497836, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1497836, tc_fun(_1497836, tc_HOL_Obool), _1497830), c_fequal), _1497838)))))), hAPP(c_Set_Oimage(_1497830, _1497836, _1497838), _1497832)))], (26774 ^ _779203) ^ [_1250743, _1250745, _1250747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250743)), 26777 ^ _779203 : [(26778 ^ _779203) ^ [_1250877] : [26780 ^ _779203 : [(26786 ^ _779203) ^ [] : [-(_1250877 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26782 ^ [_1250743, _1250745, _1250747, _1250877]), 26779 ^ [_1250743, _1250745, _1250747, _1250877]))], (26784 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26782 ^ [_1250743, _1250745, _1250747, _1250877]), _1250745)))], (26781 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26779 ^ [_1250743, _1250745, _1250747, _1250877]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1250743))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250747), _1250877)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250747), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1250877), _1250743))))]]], (22946 ^ _779203) ^ [_1183291, _1183293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183291), 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, _1183293, _1183291)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31849 ^ _779203) ^ [_1352266, _1352268, _1352270, _1352272, _1352274] : [c_Finite__Set_Ofun__left__comm__idem(_1352266, _1352268, _1352270), -(c_Finite__Set_Ofun__left__comm__idem(_1352272, _1352268, hAPP(hAPP(c_COMBB(_1352266, tc_fun(_1352268, _1352268), _1352272), _1352270), _1352274)))], (4838 ^ _779203) ^ [_852866, _852868] : [_852868 = _852866, -(c_HOL_OEx(_852868) = c_HOL_OEx(_852866))], (28834 ^ _779203) ^ [_1289240, _1289242, _1289244] : [class_Orderings_Olinorder(_1289240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289240), _1289242), _1289244)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1289240, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1289240), _1289242), c_Orderings_Obot__class_Obot(tc_fun(_1289240, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1289240, _1289242, _1289244)) = c_SetInterval_Oord__class_OatLeastAtMost(_1289240, _1289242, _1289244))], (26818 ^ _779203) ^ [_1251633, _1251635, _1251637] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1251633, _1251635) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1251637, _1251635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1251637), _1251633)), -(_1251633 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1251637), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1251635), 26825 ^ [_1251633, _1251635, _1251637])))], (14904 ^ _779203) ^ [_1039391, _1039393, _1039395, _1039397, _1039399] : [class_Groups_Ocomm__monoid__add(_1039391), hBOOL(hAPP(c_Finite__Set_Ofinite(_1039393), _1039395)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1039393, tc_HOL_Obool)), _1039397), _1039395)), 14918 ^ _779203 : [(14921 ^ _779203) ^ [] : [hAPP(_1039399, 14917 ^ [_1039391, _1039393, _1039395, _1039397, _1039399]) = c_Groups_Ozero__class_Ozero(_1039391)], (14919 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1039393), 14917 ^ [_1039391, _1039393, _1039395, _1039397, _1039399]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1039393, tc_HOL_Obool)), _1039395), _1039397))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1039393, _1039391), _1039399), _1039397) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1039393, _1039391), _1039399), _1039395))], (3318 ^ _779203) ^ [_828648, _828650, _828652, _828654] : [-(c_Enum_Osublists(_828654, _828650) = c_Enum_Osublists(_828652, _828648)), _828654 = _828652, _828650 = _828648], (20140 ^ _779203) ^ [_1134547, _1134549] : [class_Groups_Olinordered__ab__group__add(_1134547), 20143 ^ _779203 : [(20150 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134547), _1134549), c_Groups_Ozero__class_Ozero(_1134547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134547), _1134549), hAPP(c_Groups_Ouminus__class_Ouminus(_1134547), _1134549))))], (20144 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134547), _1134549), hAPP(c_Groups_Ouminus__class_Ouminus(_1134547), _1134549))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134547), _1134549), c_Groups_Ozero__class_Ozero(_1134547))))]]], (11998 ^ _779203) ^ [_986488, _986490, _986492, _986494] : [class_Rings_Olinordered__ring__strict(_986488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986488), _986490), _986492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986488), _986494), c_Groups_Ozero__class_Ozero(_986488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986488), _986492), _986494)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_986488), _986490), _986494))))], (19396 ^ _779203) ^ [_1121179, _1121181, _1121183] : [class_Fields_Olinordered__field__inverse__zero(_1121179), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1121179), c_Groups_Ozero__class_Ozero(_1121179)), _1121181)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121179), hAPP(c_Groups_Oabs__class_Oabs(_1121179), _1121183)), _1121181) = hAPP(c_Groups_Oabs__class_Oabs(_1121179), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1121179), _1121183), _1121181)))], (45392 ^ _779203) ^ [_1690326, _1690328] : [_1690328 = c_List_Olist_ONil(_1690326), -(c_List_Olist_ONil(_1690326) = c_List_Oremdups(_1690326, _1690328))], (17442 ^ _779203) ^ [_1086823, _1086825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1086823), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1086825), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1086823), _1086825)))], (20670 ^ _779203) ^ [_1143901, _1143903, _1143905, _1143907] : [hBOOL(hAPP(hAPP(_1143905, _1143907), _1143903)), -(hBOOL(hAPP(hAPP(c_member(_1143901), _1143903), c_SetInterval_Oord_OgreaterThan(_1143901, _1143905, _1143907))))], (37050 ^ _779203) ^ [_1478119, _1478121, _1478123, _1478125] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1478119), _1478121)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1478119), _1478123)), -(_1478123 = c_Orderings_Obot__class_Obot(tc_fun(_1478119, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1478119, tc_HOL_Obool), tc_fun(_1478119, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1478119, tc_HOL_Obool), tc_fun(_1478119, tc_HOL_Obool)), _1478121), _1478123)), c_Wellfounded_Omax__ext(_1478119, _1478125)))), 37064 ^ _779203 : [(37067 ^ _779203) ^ [_1478524] : [hBOOL(hAPP(hAPP(c_member(_1478119), _1478524), _1478123)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1478119, _1478119)), hAPP(hAPP(c_Product__Type_OPair(_1478119, _1478119), 37063 ^ [_1478119, _1478121, _1478123, _1478125]), _1478524)), _1478125))], (37065 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1478119), 37063 ^ [_1478119, _1478121, _1478123, _1478125]), _1478121)))]]], (25614 ^ _779203) ^ [_1230292] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1230292), c_Int_OMin) = c_Int_Opred(_1230292))], (47016 ^ _779203) ^ [_1724958, _1724960, _1724962, _1724964, _1724966] : [hBOOL(hAPP(hAPP(c_member(_1724958), _1724960), hAPP(c_List_Oset(_1724958), _1724962))), -(hBOOL(hAPP(_1724964, _1724960))), -(c_List_OdropWhile(_1724958, _1724964, hAPP(hAPP(c_List_Oappend(_1724958), _1724962), _1724966)) = hAPP(hAPP(c_List_Oappend(_1724958), c_List_OdropWhile(_1724958, _1724964, _1724962)), _1724966))], (19033 ^ _779203) ^ [_1114502, _1114504, _1114506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114502)), 19039 ^ _779203 : [(19042 ^ _779203) ^ [] : [hBOOL(hAPP(_1114504, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 19038 ^ [_1114502, _1114504, _1114506]), _1114502)))], (19040 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1114504, 19038 ^ [_1114502, _1114504, _1114506])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1114506)), 19047 ^ _779203 : [(19048 ^ _779203) ^ [_1114791] : [hBOOL(hAPP(_1114504, _1114791)), -(hBOOL(hAPP(_1114504, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1114791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1114506), _1114502)))))]]], (9546 ^ _779203) ^ [_942221, _942223, _942225] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942221), _942223)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942221), _942225)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _942223), _942225))], (32389 ^ _779203) ^ [_1365708, _1365710] : [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(_1365710))), 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), _1365708)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1365708)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1365710))))], (20746 ^ _779203) ^ [_1145417, _1145419] : [class_Int_Onumber__ring(_1145417), 20749 ^ _779203 : [(20756 ^ _779203) ^ [] : [c_Int_Oiszero(_1145417, hAPP(c_Int_Onumber__class_Onumber__of(_1145417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1145419)))), -(c_Groups_Ozero__class_Ozero(_1145417) = hAPP(c_Int_Onumber__class_Onumber__of(_1145417), _1145419))], (20750 ^ _779203) ^ [] : [c_Groups_Ozero__class_Ozero(_1145417) = hAPP(c_Int_Onumber__class_Onumber__of(_1145417), _1145419), -(c_Int_Oiszero(_1145417, hAPP(c_Int_Onumber__class_Onumber__of(_1145417), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1145419)))))]]], (43868 ^ _779203) ^ [_1656887, _1656889, _1656891, _1656893, _1656895, _1656897] : [-(hAPP(c_List_Ofoldl(_1656887, _1656889, _1656891, _1656893), hAPP(hAPP(c_List_Olist_OCons(_1656889), _1656895), _1656897)) = hAPP(c_List_Ofoldl(_1656887, _1656889, _1656891, hAPP(hAPP(_1656891, _1656893), _1656895)), _1656897))], (40068 ^ _779203) ^ [_1561158, _1561160, _1561162, _1561164, _1561166] : [-(_1561158 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1561160, _1561162, _1561158, _1561164), _1561166) = hAPP(hAPP(c_Product__Type_Oscomp(_1561162, _1561160, _1561162, tc_prod(_1561160, _1561162)), hAPP(_1561164, _1561166)), c_Random_Oiterate(_1561160, _1561162, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1561158), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1561164)))], (39358 ^ _779203) ^ [_1544464, _1544466, _1544468] : [c_Wellfounded_OwfP(_1544464, hAPP(_1544466, 39359 ^ [_1544464, _1544466, _1544468])), 39366 ^ _779203 : [(39369 ^ _779203) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1544464, tc_HOL_Obool)), c_Predicate_ODomainP(_1544464, _1544464, hAPP(_1544466, 39364 ^ [_1544464, _1544466, _1544468]))), c_Predicate_ORangeP(_1544464, _1544464, hAPP(_1544466, 39365 ^ [_1544464, _1544466, _1544468]))) = c_Orderings_Obot__class_Obot(tc_fun(_1544464, tc_HOL_Obool))], (39367 ^ _779203) ^ [] : [hAPP(_1544466, 39364 ^ [_1544464, _1544466, _1544468]) = hAPP(_1544466, 39365 ^ [_1544464, _1544466, _1544468])]], -(c_Wellfounded_OwfP(_1544464, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1544468, tc_fun(_1544464, tc_fun(_1544464, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1544468, tc_HOL_Obool))), _1544466)))], (47669 ^ _779203) ^ [_1739845, _1739847, _1739849, _1739851] : [c_List_Olist__ex(_1739845, _1739847, hAPP(hAPP(c_List_Oappend(_1739845), _1739849), _1739851)), -(c_List_Olist__ex(_1739845, _1739847, _1739849)), -(c_List_Olist__ex(_1739845, _1739847, _1739851))], (23239 ^ _779203) ^ [_1188055, _1188057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188055)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188057)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1188055)), hAPP(c_Int_Onat, _1188057)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1188055), _1188057)))], (20326 ^ _779203) ^ [_1137754, _1137756] : [class_Rings_Ocomm__ring__1(_1137754), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1137754), _1137756) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137754), hAPP(c_Groups_Ouminus__class_Ouminus(_1137754), c_Groups_Oone__class_Oone(_1137754))), _1137756))], (45398 ^ _779203) ^ [_1690419, _1690421] : [-(hAPP(c_List_OremoveAll(_1690419, _1690421), c_List_Olist_ONil(_1690419)) = c_List_Olist_ONil(_1690419))], (34216 ^ _779203) ^ [_1407392, _1407394, _1407396, _1407398, _1407400, _1407402] : [hBOOL(hAPP(hAPP(c_member(_1407392), _1407394), _1407396)), hBOOL(hAPP(hAPP(c_member(_1407398), _1407400), hAPP(_1407402, _1407394))), -(hBOOL(hAPP(hAPP(c_member(_1407398), _1407400), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1407392, tc_fun(_1407398, tc_HOL_Obool)), _1407396), _1407402))))], (5857 ^ _779203) ^ [_871930, _871932, _871934, _871936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871930, tc_HOL_Obool)), _871932), _871934)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871930, tc_HOL_Obool)), _871934), _871936)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_871930, tc_HOL_Obool)), _871932), _871936)))], (48808 ^ _779203) ^ [_1764938, _1764940] : [-(c_Relation_Otrans(_1764938, c_Transitive__Closure_Otrancl(_1764938, _1764940)))], (30089 ^ _779203) ^ [_1315117, _1315119, _1315121, _1315123, _1315125] : [class_Groups_Ocomm__monoid__mult(_1315117), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315119), _1315121)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315119), _1315123)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315117), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315119, _1315117), _1315125), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315119, tc_HOL_Obool)), _1315121), _1315123))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315119, _1315117), _1315125), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315119, tc_HOL_Obool)), _1315121), _1315123))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1315117), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315119, _1315117), _1315125), _1315121)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1315119, _1315117), _1315125), _1315123)))], (30235 ^ _779203) ^ [_1318294, _1318296, _1318298, _1318300, _1318302] : [class_Groups_Ocomm__monoid__add(_1318294), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318296), _1318298)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318296), _1318300)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318296, tc_HOL_Obool)), _1318298), _1318300) = c_Orderings_Obot__class_Obot(tc_fun(_1318296, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318296, _1318294), _1318302), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1318296, tc_HOL_Obool)), _1318298), _1318300)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1318294), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318296, _1318294), _1318302), _1318298)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1318296, _1318294), _1318302), _1318300)))], (29276 ^ _779203) ^ [_1298064, _1298066, _1298068] : [class_Lattices_Olattice(_1298064), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298064), _1298066), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298064), _1298066), _1298068)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1298064), _1298066), _1298068))], (12248 ^ _779203) ^ [_990577, _990579] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _990577), _990579) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 12249 ^ _779203 : [(12256 ^ _779203) ^ [] : [_990577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _990579 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12250 ^ _779203) ^ [] : [_990577 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _990579 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (52371 ^ _779203) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (44738 ^ _779203) ^ [_1675500, _1675502, _1675504, _1675506] : [class_Groups_Ocomm__monoid__add(_1675500), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1675500), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1675500), _1675502), c_List_Oupto(_1675504, _1675506))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1675500), _1675502), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1675504, _1675506))))], (31867 ^ _779203) ^ [_1352555, _1352557, _1352559] : [class_Groups_Ocomm__monoid__mult(_1352555), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1352557, _1352555), hAPP(c_COMBK(_1352555, _1352557), c_Groups_Oone__class_Oone(_1352555))), _1352559) = c_Groups_Oone__class_Oone(_1352555))], (16696 ^ _779203) ^ [_1072863, _1072865, _1072867] : [class_Orderings_Olinorder(_1072863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1072863), _1072865)), -(_1072865 = c_Orderings_Obot__class_Obot(tc_fun(_1072863, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1072863, hAPP(hAPP(c_Set_Oinsert(_1072863), _1072867), _1072865)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1072863), _1072867), c_Big__Operators_Olinorder__class_OMax(_1072863, _1072865)))], (29102 ^ _779203) ^ [_1294294, _1294296, _1294298, _1294300] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1294294, tc_HOL_Obool)), _1294296), _1294298), _1294300)), 29105 ^ _779203 : [(29108 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1294298, _1294300)))], (29106 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1294296, _1294300)))]]], (13399 ^ _779203) ^ [_1011260, _1011262, _1011264, _1011266, _1011268] : [class_Groups_Oordered__comm__monoid__add(_1011260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1011262), _1011264)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1011262, tc_HOL_Obool)), _1011266), _1011264)), 13413 ^ _779203 : [(13416 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1011260), c_Groups_Ozero__class_Ozero(_1011260)), hAPP(_1011268, 13412 ^ [_1011260, _1011262, _1011264, _1011266, _1011268])))], (13414 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1011262), 13412 ^ [_1011260, _1011262, _1011264, _1011266, _1011268]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1011262, tc_HOL_Obool)), _1011264), _1011266))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1011260), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1011262, _1011260), _1011268), _1011266)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1011262, _1011260), _1011268), _1011264))))], (32505 ^ _779203) ^ [_1368730, _1368732, _1368734] : [class_Int_Onumber__ring(_1368730), 32508 ^ _779203 : [(32515 ^ _779203) ^ [] : [-(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), _1368732)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1368730), hAPP(c_Int_Onumber__class_Onumber__of(_1368730), _1368734)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1368732))) = c_Groups_Oone__class_Oone(_1368730))], (32509 ^ _779203) ^ [] : [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), _1368732))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1368730), hAPP(c_Int_Onumber__class_Onumber__of(_1368730), _1368734)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1368732))) = hAPP(hAPP(c_HOL_OLet(_1368730, _1368730), hAPP(hAPP(c_Power_Opower__class_Opower(_1368730), hAPP(c_Int_Onumber__class_Onumber__of(_1368730), _1368734)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1368732))), hAPP(hAPP(c_COMBS(_1368730, _1368730, _1368730), hAPP(hAPP(c_COMBB(_1368730, tc_fun(_1368730, _1368730), _1368730), c_Groups_Otimes__class_Otimes(_1368730)), hAPP(c_Groups_Otimes__class_Otimes(_1368730), hAPP(c_Int_Onumber__class_Onumber__of(_1368730), _1368734)))), c_COMBI(_1368730))))]]], (48672 ^ _779203) ^ [_1761383, _1761385, _1761387] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1761383), _1761385, _1761387)), -(c_List_Olist__ex(tc_Int_Oint, _1761383, c_List_Oupto(_1761385, _1761387)))], (38013 ^ _779203) ^ [_1505875, _1505877, _1505879] : [class_Orderings_Olinorder(_1505875), hBOOL(hAPP(c_Finite__Set_Ofinite(_1505875), _1505877)), -(_1505877 = c_Orderings_Obot__class_Obot(tc_fun(_1505875, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1505875), _1505879), c_Big__Operators_Olattice_OSup__fin(_1505875, c_Orderings_Oord__class_Omax(_1505875), _1505877)) = c_Big__Operators_Olattice_OSup__fin(_1505875, c_Orderings_Oord__class_Omax(_1505875), hAPP(c_Set_OCollect(_1505875), hAPP(hAPP(c_COMBB(tc_fun(_1505875, tc_HOL_Obool), tc_HOL_Obool, _1505875), c_HOL_OEx(_1505875)), hAPP(hAPP(c_COMBC(_1505875, tc_fun(_1505875, tc_HOL_Obool), tc_fun(_1505875, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505875, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1505875, tc_HOL_Obool), tc_fun(_1505875, tc_HOL_Obool)), _1505875), c_COMBS(_1505875, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505875, tc_HOL_Obool), tc_fun(_1505875, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1505875), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1505875), c_fconj)), hAPP(hAPP(c_COMBC(_1505875, tc_fun(_1505875, _1505875), tc_fun(_1505875, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1505875, tc_HOL_Obool), tc_fun(tc_fun(_1505875, _1505875), tc_fun(_1505875, tc_HOL_Obool)), _1505875), c_COMBB(_1505875, tc_HOL_Obool, _1505875)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1505875), _1505879))))), hAPP(hAPP(c_COMBC(_1505875, tc_fun(_1505875, tc_HOL_Obool), tc_HOL_Obool), c_member(_1505875)), _1505877))))))], (25696 ^ _779203) ^ [_1231556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1231556)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1231556), c_Int_OMin)))], (7563 ^ _779203) ^ [_904204, _904206, _904208] : [class_Orderings_Olinorder(_904204), 7566 ^ _779203 : [(7573 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904204), _904208), _904206)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904204), _904206), _904208))], (7567 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_904204), _904206), _904208))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_904204), _904208), _904206)))]]], (9119 ^ _779203) ^ [_934424] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _934424)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _934424)], (51973 ^ _779203) ^ [_1828497, _1828499, _1828501] : [class_Divides_Osemiring__div(_1828497), class_Int_Onumber(_1828497), 51980 ^ _779203 : [(51987 ^ _779203) ^ [] : [c_Divides_Odiv__class_Omod(_1828497, hAPP(c_Int_Onumber__class_Onumber__of(_1828497), _1828501), hAPP(c_Int_Onumber__class_Onumber__of(_1828497), _1828499)) = c_Groups_Ozero__class_Ozero(_1828497), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828497), hAPP(c_Int_Onumber__class_Onumber__of(_1828497), _1828499)), hAPP(c_Int_Onumber__class_Onumber__of(_1828497), _1828501))))], (51981 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1828497), hAPP(c_Int_Onumber__class_Onumber__of(_1828497), _1828499)), hAPP(c_Int_Onumber__class_Onumber__of(_1828497), _1828501))), -(c_Divides_Odiv__class_Omod(_1828497, hAPP(c_Int_Onumber__class_Onumber__of(_1828497), _1828501), hAPP(c_Int_Onumber__class_Onumber__of(_1828497), _1828499)) = c_Groups_Ozero__class_Ozero(_1828497))]]], (40767 ^ _779203) ^ [_1578598, _1578600] : [-(c_Transitive__Closure_Otrancl(_1578598, hAPP(c_Relation_Oconverse(_1578598, _1578598), _1578600)) = hAPP(c_Relation_Oconverse(_1578598, _1578598), c_Transitive__Closure_Otrancl(_1578598, _1578600)))], (2864 ^ _779203) ^ [_821617, _821619] : [_821619 = _821617, -(c_Rings_Oinverse__class_Odivide(_821619) = c_Rings_Oinverse__class_Odivide(_821617))], (22416 ^ _779203) ^ [_1174652, _1174654] : [22417 ^ _779203 : [(22418 ^ _779203) ^ [_1174701] : [_1174652 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1174654), _1174701)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1174652, _1174654) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21889 ^ _779203) ^ [_1164724] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1164724, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1164724)], (21871 ^ _779203) ^ [_1164376, _1164378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1164376)), -(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)))), _1164378))), 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)))), _1164376)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1164378), _1164376))], (49678 ^ _779203) ^ [_1783169, _1783171, _1783173, _1783175] : [hAPP(c_Set_Oimage(_1783169, _1783171, _1783173), c_Orderings_Otop__class_Otop(tc_fun(_1783169, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1783171, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1783169, _1783171, _1783173), hAPP(c_Set_Oimage(_1783171, _1783169, c_Hilbert__Choice_Oinv__into(_1783169, _1783171, c_Orderings_Otop__class_Otop(tc_fun(_1783169, tc_HOL_Obool)), _1783173)), _1783175)) = _1783175)], (52595 ^ _779203) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (41341 ^ _779203) ^ [_1594385, _1594387, _1594389, _1594391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594385)), _1594387)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1594385)), _1594389))), _1594387 = hAPP(hAPP(c_List_Olist_OCons(_1594385), _1594391), _1594389)], (42337 ^ _779203) ^ [_1622703, _1622705, _1622707, _1622709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1622703), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622705)), _1622707))), 42340 ^ _779203 : [(42347 ^ _779203) ^ [] : [hAPP(hAPP(c_List_Onth(_1622705), _1622707), _1622703) = _1622709, -(hAPP(hAPP(c_List_Olist__update(_1622705, _1622707), _1622703), _1622709) = _1622707)], (42341 ^ _779203) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1622705, _1622707), _1622703), _1622709) = _1622707, -(hAPP(hAPP(c_List_Onth(_1622705), _1622707), _1622703) = _1622709)]]], (12338 ^ _779203) ^ [_991928, _991930] : [-(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), _991928), _991930)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _991928)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _991930))], (1400 ^ _779203) ^ [_799663, _799665] : [-(class_Complete__Lattice_Ocomplete__lattice(_799663)), _799665 = _799663, class_Complete__Lattice_Ocomplete__lattice(_799665)], (18258 ^ _779203) ^ [_1101214, _1101216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101214)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101216))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101214), _1101216)))], (48042 ^ _779203) ^ [_1747423, _1747425, _1747427, _1747429] : [-(c_New__Random__Sequence_Oneg__map(_1747423, _1747425, _1747427, _1747429) = c_New__Random__Sequence_Oneg__bind(_1747423, _1747425, _1747429, hAPP(c_Fun_Ocomp(_1747425, 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(_1747425)))))), _1747423, c_New__Random__Sequence_Oneg__single(_1747425)), _1747427)))], (45939 ^ _779203) ^ [_1703545, _1703547, _1703549] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1703545), c_List_Oupt(_1703547, _1703549)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1703547), _1703545), _1703549))], (10287 ^ _779203) ^ [_956025, _956027] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956025), _956027)), hAPP(c_Nat_OSuc, _956025))))], (6122 ^ _779203) ^ [_876941, _876943, _876945, _876947] : [_876947 = c_Orderings_Obot__class_Obot(tc_fun(_876941, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_876941, _876943, _876945), _876947) = c_Orderings_Obot__class_Obot(tc_fun(_876943, tc_HOL_Obool)))], (34488 ^ _779203) ^ [_1415497, _1415499, _1415501, _1415503, _1415505, _1415507] : [class_Complete__Lattice_Ocomplete__lattice(_1415497), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415499, _1415497), _1415501), hAPP(hAPP(c_COMBB(tc_fun(_1415503, _1415497), _1415497, _1415499), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415503, _1415497), _1415505)), _1415507)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415503, _1415497), _1415505), hAPP(hAPP(c_COMBB(tc_fun(_1415499, _1415497), _1415497, _1415503), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1415499, _1415497), _1415501)), hAPP(c_COMBC(_1415499, _1415503, _1415497), _1415507))))], (32229 ^ _779203) ^ [_1362000, _1362002, _1362004, _1362006] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362000), _1362002)), -(hAPP(c_Set_Oimage(_1362000, _1362004, _1362006), _1362002) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1362004, tc_HOL_Obool), _1362000, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1362004, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1362000, tc_fun(_1362004, tc_HOL_Obool), tc_fun(_1362004, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1362004, tc_fun(tc_fun(_1362004, tc_HOL_Obool), tc_fun(_1362004, tc_HOL_Obool)), _1362000), c_Set_Oinsert(_1362004)), _1362006)), c_Orderings_Obot__class_Obot(tc_fun(_1362004, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1362004, tc_HOL_Obool))), _1362002))], (38302 ^ _779203) ^ [_1516597, _1516599, _1516601] : [-(hAPP(c_Product__Type_Omap__pair(_1516597, _1516597, _1516599, _1516599, c_COMBI(_1516597), c_COMBI(_1516599)), _1516601) = _1516601)], (25362 ^ _779203) ^ [_1226569, _1226571, _1226573, _1226575] : [class_Rings_Olinordered__semidom(_1226569), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1226571), _1226573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226569), c_Groups_Ozero__class_Ozero(_1226569)), _1226575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226569), _1226575), c_Groups_Oone__class_Oone(_1226569))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1226569), hAPP(hAPP(c_Power_Opower__class_Opower(_1226569), _1226575), _1226573)), hAPP(hAPP(c_Power_Opower__class_Opower(_1226569), _1226575), _1226571))))], (29916 ^ _779203) ^ [_1311482, _1311484, _1311486, _1311488, _1311490] : [class_Orderings_Olinorder(_1311482), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311482, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1311482, _1311484, _1311486)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1311482, _1311488, _1311490)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1311482, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1311482), _1311484), _1311488), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311482), _1311486), _1311490)))], (9825 ^ _779203) ^ [_946976, _946978] : [9826 ^ _779203 : [(9829 ^ _779203) ^ [] : [_946976 = _946978], (9827 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _946976), _946978))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946976), _946978)))], (22590 ^ _779203) ^ [_1177580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177580), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1177580) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (28360 ^ _779203) ^ [_1280777, _1280779, _1280781, _1280783] : [class_Lattices_Osemilattice__sup(_1280777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1280777), _1280779)), hBOOL(hAPP(hAPP(c_member(_1280777), _1280781), _1280779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280777), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1280777), _1280781), _1280783)), hAPP(hAPP(c_Finite__Set_Ofold(_1280777, _1280777, c_Lattices_Osemilattice__sup__class_Osup(_1280777)), _1280783), _1280779))))], (26736 ^ _779203) ^ [_1250049, _1250051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250049)), 26745 ^ _779203 : [(26748 ^ _779203) ^ [] : [hBOOL(hAPP(_1250051, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26741 ^ [_1250049, _1250051]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 26742 ^ [_1250049, _1250051]), _1250049))))], (26746 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1250051, 26741 ^ [_1250049, _1250051])))]], 26749 ^ _779203 : [(26752 ^ _779203) ^ [] : [hBOOL(hAPP(_1250051, 26741 ^ [_1250049, _1250051]))], (26750 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1250051, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26741 ^ [_1250049, _1250051]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 26742 ^ [_1250049, _1250051]), _1250049)))))]], 26753 ^ _779203 : [(26763 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1250051, 26770 ^ [_1250049, _1250051]))), 26764 ^ _779203 : [(26765 ^ _779203) ^ [_1250596] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1250596), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1250049))), hBOOL(hAPP(_1250051, _1250596))]]], (26754 ^ _779203) ^ [] : [26755 ^ _779203 : [(26756 ^ _779203) ^ [_1250481] : [hBOOL(hAPP(_1250051, _1250481))]], 26758 ^ _779203 : [(26761 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1250051, 26757 ^ [_1250049, _1250051])))], (26759 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26757 ^ [_1250049, _1250051]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1250049))))]]]]], (9548 ^ _779203) ^ [_942272, _942274, _942276] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942272), _942274)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _942276), _942274)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _942272), _942276))], (26538 ^ _779203) ^ [_1246220, _1246222] : [c_Nat__Transfer_Ois__nat(_1246220), c_Nat__Transfer_Ois__nat(_1246222), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1246220, _1246222) = 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, _1246220), hAPP(c_Int_Onat, _1246222))))], (10401 ^ _779203) ^ [_958430, _958432, _958434, _958436] : [class_Rings_Ocomm__semiring__1(_958430), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958430), _958432), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958430), _958434), _958436)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958430), _958434), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_958430), _958432), _958436)))], (38463 ^ _779203) ^ [_1521695, _1521697, _1521699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1521695, _1521695), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1521695, _1521695, _1521695), _1521697), _1521699)), _1521697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1521695, tc_HOL_Obool), tc_fun(_1521695, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1521695, tc_HOL_Obool), tc_fun(_1521695, tc_HOL_Obool), tc_fun(_1521695, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1521695, _1521697)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1521695, tc_HOL_Obool), tc_fun(_1521695, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1521695, _1521699)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1521695, tc_HOL_Obool), tc_fun(_1521695, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1521695, tc_HOL_Obool), tc_fun(_1521695, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1521695, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1521695, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1521695, tc_HOL_Obool), tc_fun(_1521695, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1521695, _1521697))))], (25528 ^ _779203) ^ [_1229006] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1229006)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1229006), c_Int_OMin)))], (34833 ^ _779203) ^ [_1425144, _1425146, _1425148, _1425150, _1425152] : [hBOOL(hAPP(hAPP(c_member(_1425144), _1425146), _1425148)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1425150, tc_HOL_Obool)), hAPP(_1425152, _1425146)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1425144, tc_fun(_1425150, tc_HOL_Obool)), _1425148), _1425152))))], (52299 ^ _779203) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (52549 ^ _779203) ^ [_1835400] : [-(class_Nat_Osize(tc_Option_Ooption(_1835400)))], (20949 ^ _779203) ^ [_1148680, _1148682] : [class_Rings_Olinordered__idom(_1148680), -(hAPP(c_Groups_Oabs__class_Oabs(_1148680), _1148682) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148680), _1148682), c_Groups_Osgn__class_Osgn(_1148680, _1148682)))], (12400 ^ _779203) ^ [_993036, _993038, _993040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _993036)), 12403 ^ _779203 : [(12410 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993038), _993040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993036), _993038)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993036), _993040))))], (12404 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993036), _993038)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _993036), _993040))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _993038), _993040)))]]], (6983 ^ _779203) ^ [_893840, _893842, _893844, _893846] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893840, tc_HOL_Obool)), _893842), hAPP(hAPP(c_Set_Oinsert(_893840), _893844), _893846)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893840, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_893840, tc_HOL_Obool)), _893842), _893846)), hAPP(hAPP(c_Set_Oinsert(_893840), _893844), c_Orderings_Obot__class_Obot(tc_fun(_893840, tc_HOL_Obool)))))], (17512 ^ _779203) ^ [_1087955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1087955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1087955)))], (5460 ^ _779203) ^ [_862715, _862717] : [_862717 = _862715, -(c_Groups_Oone__class_Oone(_862717) = c_Groups_Oone__class_Oone(_862715))], (7363 ^ _779203) ^ [_901011, _901013, _901015] : [class_Orderings_Oorder(_901011), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901011), _901013), _901015)), _901013 = _901015], (44005 ^ _779203) ^ [_1659921, _1659923, _1659925, _1659927, _1659929, _1659931] : [class_Orderings_Olinorder(_1659921), 44008 ^ _779203 : [(44015 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659921), hAPP(_1659923, _1659925)), hAPP(_1659923, _1659927)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659929, _1659921, _1659923), _1659925), hAPP(hAPP(c_List_Olist_OCons(_1659929), _1659927), _1659931)) = hAPP(hAPP(c_List_Olist_OCons(_1659929), _1659927), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659929, _1659921, _1659923), _1659925), _1659931)))], (44009 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1659921), hAPP(_1659923, _1659925)), hAPP(_1659923, _1659927))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659929, _1659921, _1659923), _1659925), hAPP(hAPP(c_List_Olist_OCons(_1659929), _1659927), _1659931)) = hAPP(hAPP(c_List_Olist_OCons(_1659929), _1659925), hAPP(hAPP(c_List_Olist_OCons(_1659929), _1659927), _1659931)))]]], (25618 ^ _779203) ^ [_1230341] : [class_Int_Onumber__ring(_1230341), c_Int_Oiszero(_1230341, hAPP(c_Int_Onumber__class_Onumber__of(_1230341), c_Int_OMin))], (4974 ^ _779203) ^ [_855022, _855024, _855026, _855028, _855030, _855032] : [-(c_Set_Ovimage(_855032, _855028, _855024) = c_Set_Ovimage(_855030, _855026, _855022)), _855032 = _855030, _855028 = _855026, _855024 = _855022], (2360 ^ _779203) ^ [_813701, _813703, _813705, _813707] : [-(c_Divides_Odivmod__int(_813707, _813703) = c_Divides_Odivmod__int(_813705, _813701)), _813707 = _813705, _813703 = _813701], (43048 ^ _779203) ^ [_1637913, _1637915, _1637917, _1637919] : [-(hAPP(hAPP(c_List_Oappend(_1637913), hAPP(hAPP(c_List_Olist_OCons(_1637913), _1637915), _1637917)), _1637919) = hAPP(hAPP(c_List_Olist_OCons(_1637913), _1637915), hAPP(hAPP(c_List_Oappend(_1637913), _1637917), _1637919)))], (35244 ^ _779203) ^ [_1436056] : [-(_1436056 = 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)), _1436056), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (38230 ^ _779203) ^ [_1514867, _1514869] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1514867, _1514869, tc_prod(_1514867, _1514869)), c_Product__Type_OPair(_1514867, _1514869)) = c_Fun_Oid(tc_prod(_1514867, _1514869)))], (21535 ^ _779203) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (6184 ^ _779203) ^ [_878263, _878265, _878267, _878269, _878271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878263, tc_HOL_Obool)), _878265), hAPP(c_Set_Oimage(_878267, _878263, _878269), _878271))), 6188 ^ _779203 : [(6191 ^ _779203) ^ [] : [-(_878265 = hAPP(c_Set_Oimage(_878267, _878263, _878269), 6187 ^ [_878263, _878265, _878267, _878269, _878271]))], (6189 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878267, tc_HOL_Obool)), 6187 ^ [_878263, _878265, _878267, _878269, _878271]), _878271)))]]], (38214 ^ _779203) ^ [_1514605, _1514607] : [-(hAPP(c_Fun_Oid(_1514605), _1514607) = _1514607)], (24195 ^ _779203) ^ [_1205228, _1205230] : [class_Rings_Oring__1(_1205228), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1205228), hAPP(c_Groups_Ouminus__class_Ouminus(_1205228), c_Groups_Oone__class_Oone(_1205228))), 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)))), _1205230))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1205228), c_Groups_Oone__class_Oone(_1205228)))], (20720 ^ _779203) ^ [_1144916, _1144918, _1144920, _1144922, _1144924, _1144926] : [-(hBOOL(hAPP(hAPP(c_member(_1144916), _1144918), c_SetInterval_Oord_OatLeastLessThan(_1144916, _1144920, _1144922, _1144924, _1144926)))), hBOOL(hAPP(hAPP(_1144920, _1144924), _1144918)), hBOOL(hAPP(hAPP(_1144922, _1144918), _1144926))], (27968 ^ _779203) ^ [_1272978, _1272980] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1272978, _1272980)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1272978, _1272980), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272978), c_Orderings_Otop__class_Otop(tc_fun(_1272978, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1272980), c_Orderings_Otop__class_Otop(tc_fun(_1272980, tc_HOL_Obool))))], (42858 ^ _779203) ^ [_1633334, _1633336] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1633334), tc_List_Olist(_1633334), c_List_Olistrel(_1633334, _1633336)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633334)), c_List_Olist_ONil(_1633334)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633334), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1633334)), c_List_Olist_ONil(_1633334)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1633334), tc_HOL_Obool))))], (5246 ^ _779203) ^ [_859316, _859318, _859320, _859322, _859324, _859326, _859328, _859330, _859332, _859334] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_859334, _859330, _859326, _859322, _859318) = c_SetInterval_Oord_OgreaterThanAtMost(_859332, _859328, _859324, _859320, _859316)), _859334 = _859332, _859330 = _859328, _859326 = _859324, _859322 = _859320, _859318 = _859316], (9237 ^ _779203) ^ [_936787, _936789] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _936787)), _936789) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936787), _936789)))], (28820 ^ _779203) ^ [_1288975, _1288977, _1288979, _1288981] : [class_Orderings_Olinorder(_1288975), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288975), _1288977), _1288979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288975), _1288979), _1288981)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1288975, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1288975, _1288977, _1288979)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1288975, _1288979, _1288981)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1288975, _1288977, _1288981))], (48058 ^ _779203) ^ [_1747929, _1747931] : [-(c_List_Osplice(_1747929, _1747931, c_List_Olist_ONil(_1747929)) = _1747931)], (46568 ^ _779203) ^ [_1715543, _1715545] : [_1715545 = c_List_Olist_ONil(_1715543), -(c_List_Olist_ONil(_1715543) = hAPP(c_List_Orev(_1715543), _1715545))], (16558 ^ _779203) ^ [_1070370, _1070372, _1070374] : [class_Orderings_Olinorder(_1070370), hBOOL(hAPP(c_Finite__Set_Ofinite(_1070370), _1070372)), hBOOL(hAPP(hAPP(c_member(_1070370), _1070374), _1070372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070370), hAPP(c_Finite__Set_Ofold1(_1070370, c_Orderings_Oord__class_Omin(_1070370)), _1070372)), _1070374)))], (52399 ^ _779203) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (29632 ^ _779203) ^ [_1305095, _1305097] : [c_Nat__Transfer_Onat__set(_1305095), c_Nat__Transfer_Onat__set(_1305097), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1305095), _1305097)))], (52135 ^ _779203) ^ [_1831140, _1831142] : [class_Lattices_Olattice(_1831140), -(class_Lattices_Osemilattice__sup(tc_fun(_1831142, _1831140)))], (34314 ^ _779203) ^ [_1409838, _1409840, _1409842, _1409844, _1409846] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409838, tc_fun(_1409840, tc_HOL_Obool)), _1409842), hAPP(hAPP(c_COMBS(_1409838, tc_fun(_1409840, tc_HOL_Obool), tc_fun(_1409840, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1409840, tc_HOL_Obool), tc_fun(tc_fun(_1409840, tc_HOL_Obool), tc_fun(_1409840, tc_HOL_Obool)), _1409838), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409840, tc_HOL_Obool))), _1409844)), _1409846)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1409840, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409838, tc_fun(_1409840, tc_HOL_Obool)), _1409842), _1409844)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1409838, tc_fun(_1409840, tc_HOL_Obool)), _1409842), _1409846)))], (32643 ^ _779203) ^ [_1372946, _1372948, _1372950, _1372952, _1372954, _1372956] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1372946, _1372948)), hAPP(hAPP(c_Product__Type_OPair(_1372946, _1372948), _1372954), _1372956)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool)), _1372950), _1372952))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1372946, tc_fun(_1372948, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1372946, tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_fun(_1372948, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372948, tc_fun(tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_fun(_1372948, tc_HOL_Obool)), _1372946), c_COMBC(_1372948, tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372948, tc_prod(_1372946, _1372948)), tc_fun(_1372948, tc_fun(tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_HOL_Obool)), _1372946), hAPP(c_COMBB(tc_prod(_1372946, _1372948), tc_fun(tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_HOL_Obool), _1372948), c_member(tc_prod(_1372946, _1372948)))), c_Product__Type_OPair(_1372946, _1372948)))), _1372950)), hAPP(hAPP(c_COMBC(_1372946, tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_fun(_1372948, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372948, tc_fun(tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_fun(_1372948, tc_HOL_Obool)), _1372946), c_COMBC(_1372948, tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1372948, tc_prod(_1372946, _1372948)), tc_fun(_1372948, tc_fun(tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_HOL_Obool)), _1372946), hAPP(c_COMBB(tc_prod(_1372946, _1372948), tc_fun(tc_fun(tc_prod(_1372946, _1372948), tc_HOL_Obool), tc_HOL_Obool), _1372948), c_member(tc_prod(_1372946, _1372948)))), c_Product__Type_OPair(_1372946, _1372948)))), _1372952)), _1372954), _1372956)))], (50520 ^ _779203) ^ [_1802853, _1802855, _1802857] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1802853), _1802855, _1802857)), -(c_List_Olist__ex(tc_Nat_Onat, _1802853, c_List_Oupt(_1802855, _1802857)))], (12384 ^ _779203) ^ [_992783, _992785, _992787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _992783)), 12387 ^ _779203 : [(12394 ^ _779203) ^ [] : [_992785 = _992787, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992783), _992785) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992783), _992787))], (12388 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992783), _992785) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _992783), _992787), -(_992785 = _992787)]]], (34452 ^ _779203) ^ [_1414036, _1414038, _1414040, _1414042, _1414044, _1414046] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414036, tc_fun(_1414038, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1414040, _1414036, _1414042), _1414044)), _1414046) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1414040, tc_fun(_1414038, tc_HOL_Obool)), _1414044), hAPP(hAPP(c_COMBB(_1414036, tc_fun(_1414038, tc_HOL_Obool), _1414040), _1414046), _1414042)))], (14643 ^ _779203) ^ [_1034349, _1034351, _1034353, _1034355] : [class_Fields_Ofield__inverse__zero(_1034349), -(_1034351 = c_Groups_Ozero__class_Ozero(_1034349)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034349), _1034353), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034349), _1034355), _1034351)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1034349), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1034349), _1034355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1034349), _1034353), _1034351))), _1034351))], (40318 ^ _779203) ^ [_1567872, _1567874, _1567876] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567872, _1567872)), hAPP(hAPP(c_Product__Type_OPair(_1567872, _1567872), _1567874), _1567874)), c_Transitive__Closure_Ortrancl(_1567872, _1567876))))], (35320 ^ _779203) ^ [_1437304, _1437306, _1437308, _1437310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437304, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1437304, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 35321 ^ [_1437304, _1437306, _1437308, _1437310])), _1437306)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1437304, 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), 35321 ^ [_1437304, _1437306, _1437308, _1437310]), _1437308))), _1437310))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1437304, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1437304, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1437306)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1437304, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1437310))))], (22792 ^ _779203) ^ [_1180790, _1180792, _1180794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180790), _1180792)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180794), 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), _1180792), _1180794)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1180790), _1180794))))], (39067 ^ _779203) ^ [_1536904, _1536906, _1536908, _1536910] : [39069 ^ _779203 : [(39072 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1536906, hAPP(_1536908, 39068 ^ [_1536904, _1536906, _1536908, _1536910]))), hAPP(_1536906, 39068 ^ [_1536904, _1536906, _1536908, _1536910])))], (39070 ^ _779203) ^ [] : [-(hBOOL(hAPP(_1536904, 39068 ^ [_1536904, _1536906, _1536908, _1536910])))]], -(c_Wellfounded_Owf(_1536910, hAPP(c_Set_OCollect(tc_prod(_1536910, _1536910)), hAPP(c_Product__Type_Oprod_Oprod__case(_1536910, _1536910, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1536910, tc_HOL_Obool), tc_fun(_1536910, tc_HOL_Obool), _1536910), hAPP(c_COMBS(_1536910, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1536910), c_fconj), _1536904))), hAPP(hAPP(c_COMBC(_1536910, tc_fun(_1536910, _1536910), tc_fun(_1536910, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1536910, tc_HOL_Obool), tc_fun(tc_fun(_1536910, _1536910), tc_fun(_1536910, tc_HOL_Obool)), _1536910), c_COMBB(_1536910, tc_HOL_Obool, _1536910)), c_fequal)), _1536908))))))], (42271 ^ _779203) ^ [_1621175, _1621177, _1621179, _1621181] : [_1621175 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1621177)), _1621179)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1621177, hAPP(hAPP(c_List_Olist__update(_1621177, _1621179), _1621175), _1621181)) = c_List_Obutlast(_1621177, _1621179))], (45933 ^ _779203) ^ [_1703446, _1703448] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1703446), _1703448)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1703446, _1703448)) = _1703446)], (45576 ^ _779203) ^ [_1693995, _1693997, _1693999] : [45578 ^ _779203 : [(45581 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1693995), tc_List_Olist(_1693995), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1693995), tc_fun(tc_List_Olist(_1693995), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693995), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1693995), tc_Nat_Onat), tc_fun(tc_List_Olist(_1693995), tc_HOL_Obool)), tc_List_Olist(_1693995)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1693995))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1693995)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1693995))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1693995)))), 45577 ^ [_1693995, _1693997, _1693999]))], (45579 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1693995), tc_List_Olist(_1693995))), 45577 ^ [_1693995, _1693997, _1693999]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1693995), tc_List_Olist(_1693995))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1693995), tc_List_Olist(_1693995)), _1693997), _1693999)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693995))), _1693997) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1693995))), _1693999), 45586 ^ _779203 : [(45593 ^ _779203) ^ [] : [_1693997 = _1693999, -(c_List_Oconcat(_1693995, _1693997) = c_List_Oconcat(_1693995, _1693999))], (45587 ^ _779203) ^ [] : [c_List_Oconcat(_1693995, _1693997) = c_List_Oconcat(_1693995, _1693999), -(_1693997 = _1693999)]]], (11456 ^ _779203) ^ [_976574, _976576, _976578, _976580] : [class_Rings_Oordered__ring(_976574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976574), _976576), _976578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976574), _976580), c_Groups_Ozero__class_Ozero(_976574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_976574), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976574), _976580), _976578)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_976574), _976580), _976576))))], (22960 ^ _779203) ^ [_1183545, _1183547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1183545), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183547), _1183545)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183545, _1183547) = _1183545)], (47171 ^ _779203) ^ [_1728369, _1728371, _1728373] : [-(hBOOL(hAPP(hAPP(c_member(_1728369), _1728371), hAPP(c_List_Oset(_1728369), _1728373)))), -(c_List_Oinsert(_1728369, _1728371, _1728373) = hAPP(hAPP(c_List_Olist_OCons(_1728369), _1728371), _1728373))], (45728 ^ _779203) ^ [_1698054, _1698056, _1698058, _1698060, _1698062] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698054)), hAPP(c_List_Ofilter(_1698054, _1698056), hAPP(hAPP(c_List_Omap(_1698058, _1698054), _1698060), _1698062))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698058)), hAPP(c_List_Ofilter(_1698058, hAPP(c_Fun_Ocomp(_1698054, tc_HOL_Obool, _1698058, _1698056), _1698060)), _1698062)))], (40062 ^ _779203) ^ [_1561053, _1561055, _1561057, _1561059, _1561061] : [_1561053 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1561055, _1561057, _1561053, _1561059), _1561061) = hAPP(c_Product__Type_OPair(_1561055, _1561057), _1561061))], (7299 ^ _779203) ^ [_900151, _900153, _900155] : [class_Orderings_Olinorder(_900151), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900151), _900153), _900155))), 7306 ^ _779203 : [(7313 ^ _779203) ^ [] : [_900155 = _900153, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900151), _900155), _900153))], (7307 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_900151), _900155), _900153))), -(_900155 = _900153)]]], (42189 ^ _779203) ^ [_1619544] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1619544) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 42192 ^ _779203 : [(42193 ^ _779203) ^ [_1619619] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1619619), hAPP(c_List_Oset(tc_Nat_Onat), _1619544))), -(_1619619 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (5787 ^ _779203) ^ [_870752, _870754, _870756, _870758] : [_870752 = _870754, 5790 ^ _779203 : [(5797 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870756), _870758), _870754)), -(hBOOL(hAPP(hAPP(c_member(_870756), _870758), _870752)))], (5791 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_870756), _870758), _870752)), -(hBOOL(hAPP(hAPP(c_member(_870756), _870758), _870754)))]]], (45460 ^ _779203) ^ [_1691498, _1691500, _1691502, _1691504, _1691506] : [c_Fun_Oinj__on(_1691498, _1691500, _1691502, c_Orderings_Otop__class_Otop(tc_fun(_1691498, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1691498, _1691500), _1691502), hAPP(c_List_OremoveAll(_1691498, _1691504), _1691506)) = hAPP(c_List_OremoveAll(_1691500, hAPP(_1691502, _1691504)), hAPP(hAPP(c_List_Omap(_1691498, _1691500), _1691502), _1691506)))], (32679 ^ _779203) ^ [_1375749, _1375751, _1375753, _1375755] : [_1375753 = _1375755, -(hAPP(hAPP(c_COMBC(_1375749, tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_fun(_1375751, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1375751, tc_fun(tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_fun(_1375751, tc_HOL_Obool)), _1375749), c_COMBC(_1375751, tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1375751, tc_prod(_1375749, _1375751)), tc_fun(_1375751, tc_fun(tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_HOL_Obool)), _1375749), hAPP(c_COMBB(tc_prod(_1375749, _1375751), tc_fun(tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_HOL_Obool), _1375751), c_member(tc_prod(_1375749, _1375751)))), c_Product__Type_OPair(_1375749, _1375751)))), _1375753) = hAPP(hAPP(c_COMBC(_1375749, tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_fun(_1375751, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1375751, tc_fun(tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_fun(_1375751, tc_HOL_Obool)), _1375749), c_COMBC(_1375751, tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1375751, tc_prod(_1375749, _1375751)), tc_fun(_1375751, tc_fun(tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_HOL_Obool)), _1375749), hAPP(c_COMBB(tc_prod(_1375749, _1375751), tc_fun(tc_fun(tc_prod(_1375749, _1375751), tc_HOL_Obool), tc_HOL_Obool), _1375751), c_member(tc_prod(_1375749, _1375751)))), c_Product__Type_OPair(_1375749, _1375751)))), _1375755))], (36794 ^ _779203) ^ [_1472666, _1472668] : [-(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)), _1472666), _1472668))], (43646 ^ _779203) ^ [_1652352, _1652354, _1652356, _1652358] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652352) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1652354), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1652352)), hAPP(hAPP(c_List_Olist_OCons(_1652354), _1652356), _1652358)) = hAPP(hAPP(c_List_Olist_OCons(_1652354), _1652356), _1652358))], (25970 ^ _779203) ^ [_1235838, _1235840, _1235842] : [class_Rings_Oring__1(_1235838), -(hAPP(c_Int_Oring__1__class_Oof__int(_1235838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235840), _1235842)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1235838), hAPP(c_Int_Oring__1__class_Oof__int(_1235838), _1235840)), hAPP(c_Int_Oring__1__class_Oof__int(_1235838), _1235842)))], (26182 ^ _779203) ^ [_1239785, _1239787, _1239789, _1239791, _1239793] : [hAPP(c_Set_Oimage(_1239785, _1239787, _1239789), _1239791) = _1239793, -(hAPP(c_Set_Oimage(tc_fun(_1239785, tc_HOL_Obool), tc_fun(_1239787, tc_HOL_Obool), c_Set_Oimage(_1239785, _1239787, _1239789)), hAPP(c_Set_OPow(_1239785), _1239791)) = hAPP(c_Set_OPow(_1239787), _1239793))], (15506 ^ _779203) ^ [_1051074, _1051076, _1051078] : [class_Orderings_Olinorder(_1051074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1051074), _1051076), _1051078)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1051074), _1051076), _1051078) = _1051078)], (38158 ^ _779203) ^ [_1511804, _1511806, _1511808] : [class_Orderings_Olinorder(_1511804), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511804), _1511806)), -(_1511806 = c_Orderings_Obot__class_Obot(tc_fun(_1511804, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1511804), _1511808), c_Big__Operators_Olattice_OInf__fin(_1511804, c_Orderings_Oord__class_Omin(_1511804), _1511806)) = c_Big__Operators_Olattice_OInf__fin(_1511804, c_Orderings_Oord__class_Omin(_1511804), hAPP(c_Set_OCollect(_1511804), hAPP(hAPP(c_COMBB(tc_fun(_1511804, tc_HOL_Obool), tc_HOL_Obool, _1511804), c_HOL_OEx(_1511804)), hAPP(hAPP(c_COMBC(_1511804, tc_fun(_1511804, tc_HOL_Obool), tc_fun(_1511804, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511804, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1511804, tc_HOL_Obool), tc_fun(_1511804, tc_HOL_Obool)), _1511804), c_COMBS(_1511804, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511804, tc_HOL_Obool), tc_fun(_1511804, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1511804), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1511804), c_fconj)), hAPP(hAPP(c_COMBC(_1511804, tc_fun(_1511804, _1511804), tc_fun(_1511804, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1511804, tc_HOL_Obool), tc_fun(tc_fun(_1511804, _1511804), tc_fun(_1511804, tc_HOL_Obool)), _1511804), c_COMBB(_1511804, tc_HOL_Obool, _1511804)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1511804), _1511808))))), hAPP(hAPP(c_COMBC(_1511804, tc_fun(_1511804, tc_HOL_Obool), tc_HOL_Obool), c_member(_1511804)), _1511806))))))], (486 ^ _779203) ^ [_786464, _786466, _786468, _786470, _786472, _786474] : [-(c_Nitpick_Oless__eq__frac(_786472, _786468, _786464)), c_Nitpick_Oless__eq__frac(_786474, _786470, _786466), _786474 = _786472, _786470 = _786468, _786466 = _786464], (50303 ^ _779203) ^ [_1796497, _1796499, _1796501] : [hBOOL(hAPP(hAPP(c_member(_1796497), _1796499), c_Quotient_ORespects(_1796497, _1796501))), -(hBOOL(hAPP(hAPP(_1796501, _1796499), _1796499)))], (13767 ^ _779203) ^ [_1018346, _1018348, _1018350, _1018352] : [class_Fields_Olinordered__field(_1018346), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1018346), _1018348), c_Groups_Ozero__class_Ozero(_1018346))), 13774 ^ _779203 : [(13781 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018346), _1018352), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018346), _1018350), _1018348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018346), _1018350), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1018346), _1018352), _1018348))))], (13775 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018346), _1018350), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1018346), _1018352), _1018348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1018346), _1018352), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1018346), _1018350), _1018348))))]]], (52705 ^ _779203) ^ [] : [-(hBOOL(c_fTrue))], (25452 ^ _779203) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (18270 ^ _779203) ^ [_1101445, _1101447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101445)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101445), _1101447)))], (17138 ^ _779203) ^ [_1080985, _1080987] : [class_Orderings_Olinorder(_1080985), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080985), _1080987)), -(_1080987 = c_Orderings_Obot__class_Obot(tc_fun(_1080985, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1080985), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1080985), 17151 ^ [_1080985, _1080987]), 17152 ^ [_1080985, _1080987])), hAPP(hAPP(c_Set_Oinsert(_1080985), 17151 ^ [_1080985, _1080987]), hAPP(hAPP(c_Set_Oinsert(_1080985), 17152 ^ [_1080985, _1080987]), c_Orderings_Obot__class_Obot(tc_fun(_1080985, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1080985), c_Big__Operators_Olinorder__class_OMax(_1080985, _1080987)), _1080987)))], (30905 ^ _779203) ^ [_1332123, _1332125] : [class_Lattices_Olattice(_1332123), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332123), _1332125)), -(c_Big__Operators_Olattice__class_OInf__fin(_1332123, _1332125) = hAPP(c_Finite__Set_Ofold1(_1332123, c_Lattices_Osemilattice__inf__class_Oinf(_1332123)), _1332125))], (36272 ^ _779203) ^ [_1461500, _1461502, _1461504, _1461506] : [c_Fun_Oinj__on(_1461500, _1461502, _1461504, _1461506), 36275 ^ _779203 : [(36276 ^ _779203) ^ [_1461608] : [hBOOL(hAPP(hAPP(c_member(_1461500), _1461608), _1461506)), 36279 ^ _779203 : [(36280 ^ _779203) ^ [_1461710] : [hBOOL(hAPP(hAPP(c_member(_1461500), _1461710), _1461506)), hAPP(_1461504, _1461608) = hAPP(_1461504, _1461710), -(_1461608 = _1461710)]]]]], (27752 ^ _779203) ^ [_1268411, _1268413, _1268415, _1268417] : [class_Lattices_Osemilattice__sup(_1268411), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268411), _1268413), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268411), _1268415), _1268417)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268411), _1268415), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1268411), _1268413), _1268417)))], (22358 ^ _779203) ^ [_1173748] : [-(hBOOL(hAPP(_1173748, 22365 ^ [_1173748]))), 22359 ^ _779203 : [(22360 ^ _779203) ^ [_1173800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1173800)), hBOOL(hAPP(_1173748, hAPP(c_Int_Onat, _1173800)))]]], (20308 ^ _779203) ^ [_1137397, _1137399, _1137401] : [class_Groups_Ogroup__add(_1137397), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1137397), _1137399), _1137401) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1137397), _1137399), hAPP(c_Groups_Ouminus__class_Ouminus(_1137397), _1137401)))], (15330 ^ _779203) ^ [_1047833, _1047835, _1047837] : [class_Orderings_Olinorder(_1047833), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047833), _1047835), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047833), _1047835), _1047837)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1047833), _1047835), _1047837))], (21707 ^ _779203) ^ [_1161338] : [-(c_Int_Opred(c_Int_OBit1(_1161338)) = c_Int_OBit0(_1161338))], (46058 ^ _779203) ^ [_1706165] : [class_Orderings_Olinorder(_1706165), -(c_List_Olinorder__class_Osorted(_1706165, c_List_Olist_ONil(_1706165)))], (10523 ^ _779203) ^ [_961201, _961203, _961205] : [class_Groups_Oab__semigroup__mult(_961201), hBOOL(hAPP(c_Finite__Set_Ofinite(_961201), _961203)), -(hBOOL(hAPP(hAPP(c_member(_961201), _961205), _961203))), -(hAPP(c_Finite__Set_Ofold1(_961201, c_Groups_Otimes__class_Otimes(_961201)), hAPP(hAPP(c_Set_Oinsert(_961201), _961205), _961203)) = hAPP(hAPP(c_Finite__Set_Ofold(_961201, _961201, c_Groups_Otimes__class_Otimes(_961201)), _961205), _961203))], (45121 ^ _779203) ^ [_1684461, _1684463, _1684465, _1684467, _1684469, _1684471] : [c_List_Olist__all2(_1684461, _1684463, _1684465, _1684467, _1684469), -(c_List_Olist__all2(_1684461, _1684463, _1684465, hAPP(hAPP(c_List_Otake(_1684461), _1684471), _1684467), hAPP(hAPP(c_List_Otake(_1684463), _1684471), _1684469)))], (27710 ^ _779203) ^ [_1267556, _1267558, _1267560] : [class_Orderings_Olinorder(_1267556), 27713 ^ _779203 : [(27720 ^ _779203) ^ [] : [_1267558 = _1267560, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1267556), _1267558) = hAPP(c_SetInterval_Oord__class_OatLeast(_1267556), _1267560))], (27714 ^ _779203) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1267556), _1267558) = hAPP(c_SetInterval_Oord__class_OatLeast(_1267556), _1267560), -(_1267558 = _1267560)]]], (34929 ^ _779203) ^ [_1427768, _1427770, _1427772, _1427774, _1427776] : [-(_1427768 = c_Orderings_Obot__class_Obot(tc_fun(_1427770, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427772, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427770, tc_fun(_1427772, tc_HOL_Obool)), _1427768), _1427774)), _1427776) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1427770, tc_fun(_1427772, tc_HOL_Obool)), _1427768), hAPP(hAPP(c_COMBC(_1427770, tc_fun(_1427772, tc_HOL_Obool), tc_fun(_1427772, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1427772, tc_HOL_Obool), tc_fun(tc_fun(_1427772, tc_HOL_Obool), tc_fun(_1427772, tc_HOL_Obool)), _1427770), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1427772, tc_HOL_Obool))), _1427774)), _1427776)))], (35405 ^ _779203) ^ [_1440153, _1440155] : [-(c_FunDef_Orp__inv__image(_1440153, _1440155) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1440153, _1440153), tc_HOL_Obool), tc_fun(tc_prod(_1440153, _1440153), tc_HOL_Obool), tc_fun(tc_fun(_1440155, _1440153), tc_prod(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1440153, _1440153), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1440153, _1440153), tc_HOL_Obool), tc_fun(tc_fun(_1440155, _1440153), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1440153, _1440153), tc_HOL_Obool), tc_fun(tc_fun(_1440155, _1440153), tc_prod(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1440155, _1440153), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool)), tc_fun(tc_fun(_1440155, _1440153), tc_prod(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1440153, _1440153), tc_HOL_Obool), tc_fun(tc_fun(_1440155, _1440153), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1440153, _1440153), tc_HOL_Obool), tc_fun(tc_fun(_1440155, _1440153), tc_prod(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool))))), tc_fun(tc_prod(_1440153, _1440153), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1440155, _1440153), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool)), tc_fun(tc_fun(_1440155, _1440153), tc_prod(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool))), tc_fun(tc_prod(_1440153, _1440153), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1440155, _1440153), tc_fun(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1440155, _1440153), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool)), tc_fun(tc_fun(_1440155, _1440153), tc_prod(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool)))), tc_fun(tc_prod(_1440153, _1440153), tc_HOL_Obool)), c_COMBS(tc_fun(_1440155, _1440153), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1440155, _1440153), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool)), tc_fun(tc_fun(_1440155, _1440153), tc_fun(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool)))), tc_fun(tc_prod(_1440153, _1440153), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool))), tc_fun(_1440155, _1440153)), c_Product__Type_OPair(tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool), tc_fun(tc_prod(_1440155, _1440155), tc_HOL_Obool)))), c_Relation_Oinv__image(_1440153, _1440155))))), c_Relation_Oinv__image(_1440153, _1440155))))], (24934 ^ _779203) ^ [_1218523, _1218525, _1218527, _1218529] : [class_Groups_Ocomm__monoid__mult(_1218523), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1218523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218523), _1218525), _1218527)), _1218529) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1218523), hAPP(hAPP(c_Power_Opower__class_Opower(_1218523), _1218525), _1218529)), hAPP(hAPP(c_Power_Opower__class_Opower(_1218523), _1218527), _1218529)))], (52635 ^ _779203) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (50508 ^ _779203) ^ [_1802654, _1802656, _1802658] : [c_List_Oall__interval__nat(_1802654, _1802656, _1802658), -(c_List_Olist__all(tc_Nat_Onat, _1802654, c_List_Oupt(_1802656, _1802658)))], (25652 ^ _779203) ^ [_1230860] : [class_Int_Onumber__ring(_1230860), -(hAPP(c_Int_Onumber__class_Onumber__of(_1230860), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1230860), c_Groups_Oone__class_Oone(_1230860)))], (39005 ^ _779203) ^ [_1535663, _1535665, _1535667, _1535669] : [hBOOL(hAPP(c_Predicate_ODomainP(_1535663, _1535665, _1535667), _1535669)), -(hBOOL(hAPP(hAPP(_1535667, _1535669), 39008 ^ [_1535663, _1535665, _1535667, _1535669])))], (37547 ^ _779203) ^ [_1490636, _1490638, _1490640] : [-(hAPP(hAPP(c_Set_Oinsert(_1490636), _1490638), _1490640) = hAPP(c_Set_OCollect(_1490636), hAPP(hAPP(c_COMBS(_1490636, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1490636), c_fdisj), hAPP(hAPP(c_COMBC(_1490636, _1490636, tc_HOL_Obool), c_fequal), _1490638))), hAPP(hAPP(c_COMBC(_1490636, tc_fun(_1490636, tc_HOL_Obool), tc_HOL_Obool), c_member(_1490636)), _1490640))))], (29904 ^ _779203) ^ [_1311192, _1311194, _1311196, _1311198, _1311200] : [class_Orderings_Olinorder(_1311192), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311192, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1311192, _1311194, _1311196)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1311192, _1311198, _1311200)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1311192, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1311192), _1311194), _1311198), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311192), _1311196), _1311200)))], (47823 ^ _779203) ^ [_1742921, _1742923] : [-(c_FunDef_Ois__measure(_1742921, _1742923))], (40178 ^ _779203) ^ [_1563829, _1563831] : [c_Wellfounded_Oacyclic(_1563829, _1563831), 40181 ^ _779203 : [(40182 ^ _779203) ^ [_1563914] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563829, _1563829)), hAPP(hAPP(c_Product__Type_OPair(_1563829, _1563829), _1563914), _1563914)), c_Transitive__Closure_Otrancl(_1563829, _1563831)))]]], (3302 ^ _779203) ^ [_828414, _828416] : [_828416 = _828414, -(c_Set_OPow(_828416) = c_Set_OPow(_828414))], (29792 ^ _779203) ^ [_1308738, _1308740, _1308742] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308738, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308738, tc_HOL_Obool)), _1308740), _1308742)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308738, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308738, tc_HOL_Obool)), _1308740)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1308738, tc_HOL_Obool)), _1308742)))], (20384 ^ _779203) ^ [_1138651, _1138653, _1138655] : [class_Groups_Oordered__ab__group__add__abs(_1138651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138651), _1138653), _1138655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138651), hAPP(c_Groups_Ouminus__class_Ouminus(_1138651), _1138653)), _1138655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138651), hAPP(c_Groups_Oabs__class_Oabs(_1138651), _1138653)), _1138655)))], (45270 ^ _779203) ^ [_1687750, _1687752, _1687754] : [-(hAPP(c_List_Oset(tc_List_Olist(_1687750)), c_Enum_On__lists(_1687750, _1687752, _1687754)) = hAPP(c_Set_OCollect(tc_List_Olist(_1687750)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1687750), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1687750)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687750), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1687750)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1687750)))), _1687752))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687750), tc_fun(_1687750, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1687750, tc_HOL_Obool), tc_fun(tc_fun(_1687750, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1687750)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1687750, tc_HOL_Obool))), c_List_Oset(_1687750))), hAPP(c_List_Oset(_1687750), _1687754)))))], (33879 ^ _779203) ^ [_1399973, _1399975] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1399973), 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)), _1399975)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1399973), _1399975) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1399973, _1399975)))], (52395 ^ _779203) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (43594 ^ _779203) ^ [_1650968, _1650970, _1650972, _1650974, _1650976] : [hAPP(hAPP(c_List_Oappend(_1650968), _1650970), _1650972) = hAPP(hAPP(c_List_Oappend(_1650968), _1650974), _1650976), 43597 ^ _779203 : [(43606 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650968)), _1650970)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650968)), _1650974)))), 43609 ^ _779203 : [(43612 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1650968), hAPP(hAPP(c_List_Odrop(_1650968), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650968)), _1650974)), _1650970)), _1650972) = _1650976)], (43610 ^ _779203) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1650968), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650968)), _1650974)), _1650970) = _1650974)]]], (43598 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650968)), _1650970)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650968)), _1650974))), 43601 ^ _779203 : [(43604 ^ _779203) ^ [] : [-(_1650972 = hAPP(hAPP(c_List_Oappend(_1650968), hAPP(hAPP(c_List_Odrop(_1650968), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650968)), _1650970)), _1650974)), _1650976))], (43602 ^ _779203) ^ [] : [-(_1650970 = hAPP(hAPP(c_List_Otake(_1650968), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650968)), _1650970)), _1650974))]]]]], (20518 ^ _779203) ^ [_1141082, _1141084] : [class_Groups_Oordered__ab__group__add__abs(_1141082), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1141082), hAPP(c_Groups_Ouminus__class_Ouminus(_1141082), hAPP(c_Groups_Oabs__class_Oabs(_1141082), _1141084))), c_Groups_Ozero__class_Ozero(_1141082))))], (34508 ^ _779203) ^ [_1416090, _1416092, _1416094, _1416096] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1416090, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1416092, tc_fun(_1416090, tc_HOL_Obool)), _1416094), _1416096)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1416092, tc_fun(_1416090, tc_HOL_Obool)), _1416094), hAPP(hAPP(c_COMBB(tc_fun(_1416090, tc_HOL_Obool), tc_fun(_1416090, tc_HOL_Obool), _1416092), c_Groups_Ouminus__class_Ouminus(tc_fun(_1416090, tc_HOL_Obool))), _1416096)))], (44891 ^ _779203) ^ [_1678668, _1678670] : [-(c_List_Opartition(_1678668, _1678670, c_List_Olist_ONil(_1678668)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1678668), tc_List_Olist(_1678668)), c_List_Olist_ONil(_1678668)), c_List_Olist_ONil(_1678668)))], (39824 ^ _779203) ^ [_1555259, _1555261, _1555263, _1555265, _1555267, _1555269] : [c_Finite__Set_Ofolding(_1555259, _1555261, _1555263, _1555265), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555259), _1555267)), -(hBOOL(hAPP(hAPP(c_member(_1555259), _1555269), _1555267))), -(hAPP(_1555265, hAPP(hAPP(c_Set_Oinsert(_1555259), _1555269), _1555267)) = hAPP(c_Fun_Ocomp(_1555261, _1555261, _1555261, hAPP(_1555265, _1555267)), hAPP(_1555263, _1555269)))], (50861 ^ _779203) ^ [_1809444, _1809446, _1809448] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1809444, _1809446) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1809448), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 50864 ^ _779203 : [(50867 ^ _779203) ^ [] : [-(_1809446 = _1809448)], (50865 ^ _779203) ^ [] : [-(_1809444 = _1809446)]]], (40889 ^ _779203) ^ [_1581749, _1581751, _1581753] : [-(hAPP(c_Relation_Oconverse(_1581749, _1581751), _1581753) = hAPP(c_Set_OCollect(tc_prod(_1581751, _1581749)), hAPP(c_Product__Type_Oprod_Oprod__case(_1581751, _1581749, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1581751, tc_fun(tc_prod(_1581749, _1581751), tc_HOL_Obool), tc_fun(_1581749, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581749, tc_fun(tc_fun(tc_prod(_1581749, _1581751), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1581749, _1581751), tc_HOL_Obool), tc_fun(_1581749, tc_HOL_Obool)), _1581751), c_COMBC(_1581749, tc_fun(tc_prod(_1581749, _1581751), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1581749, tc_prod(_1581749, _1581751)), tc_fun(_1581749, tc_fun(tc_fun(tc_prod(_1581749, _1581751), tc_HOL_Obool), tc_HOL_Obool)), _1581751), hAPP(c_COMBB(tc_prod(_1581749, _1581751), tc_fun(tc_fun(tc_prod(_1581749, _1581751), tc_HOL_Obool), tc_HOL_Obool), _1581749), c_member(tc_prod(_1581749, _1581751)))), hAPP(c_COMBC(_1581749, _1581751, tc_prod(_1581749, _1581751)), c_Product__Type_OPair(_1581749, _1581751))))), _1581753))))], (27700 ^ _779203) ^ [_1267427] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1267427) = c_Orderings_Oord__class_Omax(_1267427)), class_Lattices_Osemilattice__sup(_1267427), class_Orderings_Olinorder(_1267427)], (37455 ^ _779203) ^ [_1488286, _1488288] : [-(hBOOL(hAPP(_1488288, 37456 ^ [_1488286, _1488288]))), -(hAPP(c_Set_OCollect(_1488286), _1488288) = c_Orderings_Obot__class_Obot(tc_fun(_1488286, tc_HOL_Obool)))], (23421 ^ _779203) ^ [_1191393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191393)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1191393)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1191393)))], (47377 ^ _779203) ^ [_1733235, _1733237, _1733239, _1733241] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1733235, _1733237, _1733239, _1733241) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1733235, _1733237), _1733239), _1733241)))], (38637 ^ _779203) ^ [_1527378, _1527380, _1527382] : [c_Wellfounded_Owf(_1527378, _1527380), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1527378, _1527378), tc_HOL_Obool)), _1527382), _1527380)), -(c_Wellfounded_Owf(_1527378, _1527382))], (42149 ^ _779203) ^ [_1618569, _1618571, _1618573, _1618575] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1618569, _1618569)), hAPP(hAPP(c_Product__Type_OPair(_1618569, _1618569), _1618571), _1618573)), hAPP(c_List_Oset(tc_prod(_1618569, _1618569)), hAPP(hAPP(c_List_Ozip(_1618569, _1618569), _1618575), _1618575)))), 42152 ^ _779203 : [(42155 ^ _779203) ^ [] : [-(_1618571 = _1618573)], (42153 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1618569), _1618571), hAPP(c_List_Oset(_1618569), _1618575))))]]], (39778 ^ _779203) ^ [_1554298, _1554300, _1554302, _1554304, _1554306, _1554308, _1554310, _1554312] : [c_Finite__Set_Ofolding(_1554298, _1554300, _1554302, _1554304), hBOOL(hAPP(c_Finite__Set_Ofinite(_1554298), _1554306)), -(hAPP(c_Fun_Ocomp(_1554300, _1554300, _1554308, hAPP(_1554302, _1554310)), hAPP(c_Fun_Ocomp(_1554300, _1554300, _1554308, hAPP(_1554304, _1554306)), _1554312)) = hAPP(c_Fun_Ocomp(_1554300, _1554300, _1554308, hAPP(_1554304, _1554306)), hAPP(c_Fun_Ocomp(_1554300, _1554300, _1554308, hAPP(_1554302, _1554310)), _1554312)))], (31991 ^ _779203) ^ [_1356033, _1356035, _1356037, _1356039] : [class_Rings_Osemiring__1(_1356033), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1356033), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356035, tc_Nat_Onat), _1356037), _1356039)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1356035, _1356033), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1356033, _1356035), c_Nat_Osemiring__1__class_Oof__nat(_1356033)), _1356037)), _1356039))], (33711 ^ _779203) ^ [_1396414, _1396416, _1396418, _1396420, _1396422] : [-(hAPP(c_Product__Type_Osnd(_1396414, _1396416), hAPP(c_Product__Type_Oapsnd(_1396418, _1396416, _1396414, _1396420), _1396422)) = hAPP(_1396420, hAPP(c_Product__Type_Osnd(_1396414, _1396418), _1396422)))], (23701 ^ _779203) ^ [_1196426, _1196428] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1196426, _1196428)), _1196426)))], (12324 ^ _779203) ^ [_991685, _991687] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _991687), _991685)), -(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), _991685), _991687))))], (38827 ^ _779203) ^ [_1531248, _1531250] : [38829 ^ _779203 : [(38830 ^ _779203) ^ [_1531273] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1531248, _1531248)), hAPP(hAPP(c_Product__Type_OPair(_1531248, _1531248), hAPP(38828 ^ [_1531248, _1531250], hAPP(c_Nat_OSuc, _1531273))), hAPP(38828 ^ [_1531248, _1531250], _1531273))), _1531250)))]], -(c_Wellfounded_Owf(_1531248, _1531250))], (44021 ^ _779203) ^ [_1660303, _1660305, _1660307, _1660309, _1660311] : [class_Orderings_Olinorder(_1660303), -(hAPP(c_List_Oset(_1660305), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1660305, _1660303, _1660307), _1660309), _1660311)) = hAPP(hAPP(c_Set_Oinsert(_1660305), _1660309), hAPP(c_List_Oset(_1660305), _1660311)))], (28482 ^ _779203) ^ [_1282910, _1282912, _1282914] : [class_Orderings_Olinorder(_1282910), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282910), _1282912)), -(_1282912 = c_Orderings_Obot__class_Obot(tc_fun(_1282910, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1282910), _1282914)), -(_1282914 = c_Orderings_Obot__class_Obot(tc_fun(_1282910, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1282910, c_Orderings_Oord__class_Omax(_1282910), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1282910, tc_HOL_Obool)), _1282912), _1282914)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282910), c_Big__Operators_Olattice_OSup__fin(_1282910, c_Orderings_Oord__class_Omax(_1282910), _1282912)), c_Big__Operators_Olattice_OSup__fin(_1282910, c_Orderings_Oord__class_Omax(_1282910), _1282914)))], (28284 ^ _779203) ^ [_1279228, _1279230, _1279232, _1279234] : [class_Orderings_Olinorder(_1279228), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279228), _1279230), _1279232)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279228), _1279232), _1279234)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1279228, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1279228, _1279230), _1279232)), c_SetInterval_Oord__class_OatLeastAtMost(_1279228, _1279232, _1279234)) = c_SetInterval_Oord__class_OatLeastAtMost(_1279228, _1279230, _1279234))], (39626 ^ _779203) ^ [_1550724, _1550726, _1550728, _1550730, _1550732] : [class_Groups_Ocomm__monoid__mult(_1550724), hBOOL(hAPP(c_Finite__Set_Ofinite(_1550726), _1550728)), c_Fun_Oinj__on(_1550726, _1550726, _1550730, _1550728), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1550726, _1550724), _1550732), hAPP(c_Set_Oimage(_1550726, _1550726, _1550730), _1550728)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1550726, _1550724), hAPP(c_Fun_Ocomp(_1550726, _1550724, _1550726, _1550732), _1550730)), _1550728))], (34246 ^ _779203) ^ [_1408007, _1408009, _1408011, _1408013, _1408015, _1408017] : [hBOOL(hAPP(hAPP(c_member(_1408007), _1408009), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1408011, tc_fun(_1408007, tc_HOL_Obool)), _1408013), _1408015))), hBOOL(hAPP(hAPP(c_member(_1408011), _1408017), _1408013)), -(hBOOL(hAPP(hAPP(c_member(_1408007), _1408009), hAPP(_1408015, _1408017))))], (33871 ^ _779203) ^ [_1399719, _1399721] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399719, _1399721) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1399719, _1399721)))], (21047 ^ _779203) ^ [_1150195, _1150197] : [class_Int_Onumber__ring(_1150195), 21050 ^ _779203 : [(21057 ^ _779203) ^ [] : [c_Int_Oiszero(_1150195, hAPP(c_Int_Onumber__class_Onumber__of(_1150195), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1150197), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1150195), _1150197) = c_Groups_Oone__class_Oone(_1150195))], (21051 ^ _779203) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1150195), _1150197) = c_Groups_Oone__class_Oone(_1150195), -(c_Int_Oiszero(_1150195, hAPP(c_Int_Onumber__class_Onumber__of(_1150195), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1150197), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (27262 ^ _779203) ^ [] : [-(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))))], (38386 ^ _779203) ^ [_1519497, _1519499, _1519501, _1519503, _1519505, _1519507, _1519509] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1519497, _1519499, _1519501), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519503, tc_fun(tc_prod(_1519497, _1519499), tc_HOL_Obool)), _1519505), _1519507)), _1519509) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1519503, tc_fun(tc_prod(_1519497, _1519501), tc_HOL_Obool)), _1519505), hAPP(hAPP(c_COMBC(_1519503, tc_fun(tc_prod(_1519499, _1519501), tc_HOL_Obool), tc_fun(tc_prod(_1519497, _1519501), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1519497, _1519499), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1519499, _1519501), tc_HOL_Obool), tc_fun(tc_prod(_1519497, _1519501), tc_HOL_Obool)), _1519503), c_Relation_Orel__comp(_1519497, _1519499, _1519501)), _1519507)), _1519509)))], (32135 ^ _779203) ^ [_1359800, _1359802, _1359804, _1359806, _1359808] : [class_Groups_Ocomm__monoid__mult(_1359800), hBOOL(hAPP(c_Finite__Set_Ofinite(_1359802), _1359804)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1359800, _1359802, c_Groups_Otimes__class_Otimes(_1359800)), hAPP(hAPP(c_COMBS(_1359802, _1359800, _1359800), hAPP(hAPP(c_COMBB(_1359800, tc_fun(_1359800, _1359800), _1359802), c_Groups_Otimes__class_Otimes(_1359800)), _1359806)), _1359808)), c_Groups_Oone__class_Oone(_1359800)), _1359804) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359800), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1359800, _1359802, c_Groups_Otimes__class_Otimes(_1359800)), _1359806), c_Groups_Oone__class_Oone(_1359800)), _1359804)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1359800, _1359802, c_Groups_Otimes__class_Otimes(_1359800)), _1359808), c_Groups_Oone__class_Oone(_1359800)), _1359804)))], (31452 ^ _779203) ^ [_1343218, _1343220, _1343222] : [class_Complete__Lattice_Ocomplete__lattice(_1343218), hBOOL(hAPP(hAPP(c_member(_1343218), _1343220), _1343222)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343218), c_Complete__Lattice_OInf__class_OInf(_1343218, _1343222)), _1343220)))], (10335 ^ _779203) ^ [_957093, _957095, _957097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957093), _957095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _957093), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _957095), _957097))))], (32565 ^ _779203) ^ [_1370176, _1370178] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1370176)), _1370178) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1370176), 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), _1370176)), _1370178))], (12330 ^ _779203) ^ [_991805, _991807] : [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), _991805), _991807))), 12333 ^ _779203 : [(12336 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _991807)))], (12334 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _991805)))]]], (35948 ^ _779203) ^ [_1453943, _1453945, _1453947, _1453949, _1453951, _1453953] : [c_Equiv__Relations_Oequiv(_1453943, _1453945, _1453947), c_Equiv__Relations_Ocongruent(_1453943, tc_fun(_1453949, tc_HOL_Obool), _1453947, _1453951), hBOOL(hAPP(hAPP(c_member(_1453943), _1453953), _1453945)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1453943, tc_fun(_1453949, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1453943, _1453943, _1453947), hAPP(hAPP(c_Set_Oinsert(_1453943), _1453953), c_Orderings_Obot__class_Obot(tc_fun(_1453943, tc_HOL_Obool))))), _1453951) = hAPP(_1453951, _1453953))], (458 ^ _779203) ^ [_786070, _786072] : [-(class_Rings_Oinverse(_786070)), _786072 = _786070, class_Rings_Oinverse(_786072)], (17348 ^ _779203) ^ [_1084980] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1084980), _1084980)))], (35594 ^ _779203) ^ [_1445668, _1445670, _1445672] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1445668, _1445668), tc_HOL_Obool)), _1445670), _1445672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1445668, tc_HOL_Obool)), hAPP(c_Relation_OField(_1445668), _1445670)), hAPP(c_Relation_OField(_1445668), _1445672))))], (18939 ^ _779203) ^ [_1112872, _1112874] : [_1112872 = _1112874, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1112872) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1112874))], (21131 ^ _779203) ^ [_1151844, _1151846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1151844)), c_Int_OBit1(_1151846))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1151844), _1151846)))], (39423 ^ _779203) ^ [_1546161, _1546163, _1546165, _1546167, _1546169, _1546171] : [c_Fun_Oinj__on(_1546161, _1546163, hAPP(c_Fun_Ocomp(_1546165, _1546163, _1546161, _1546167), _1546169), _1546171), -(c_Fun_Oinj__on(_1546165, _1546163, _1546167, hAPP(c_Set_Oimage(_1546161, _1546165, _1546169), _1546171)))], (4566 ^ _779203) ^ [_848578, _848580, _848582, _848584, _848586, _848588, _848590, _848592] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_848592, _848588, _848584, _848580) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_848590, _848586, _848582, _848578)), _848592 = _848590, _848588 = _848586, _848584 = _848582, _848580 = _848578], (10679 ^ _779203) ^ [_963968, _963970, _963972, _963974] : [class_Rings_Ocomm__semiring__1(_963968), class_Rings_Ono__zero__divisors(_963968), hBOOL(hAPP(c_Finite__Set_Ofinite(_963970), _963972)), 10690 ^ _779203 : [(10700 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_963970, _963968), _963974), _963972) = c_Groups_Ozero__class_Ozero(_963968)), 10701 ^ _779203 : [(10702 ^ _779203) ^ [_964346] : [hBOOL(hAPP(hAPP(c_member(_963970), _964346), _963972)), hAPP(_963974, _964346) = c_Groups_Ozero__class_Ozero(_963968)]]], (10691 ^ _779203) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_963970, _963968), _963974), _963972) = c_Groups_Ozero__class_Ozero(_963968), 10695 ^ _779203 : [(10698 ^ _779203) ^ [] : [-(hAPP(_963974, 10694 ^ [_963968, _963970, _963972, _963974]) = c_Groups_Ozero__class_Ozero(_963968))], (10696 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_963970), 10694 ^ [_963968, _963970, _963972, _963974]), _963972)))]]]]], (8037 ^ _779203) ^ [_912155, _912157, _912159, _912161, _912163, _912165] : [-(hBOOL(hAPP(hAPP(c_member(_912155), _912157), _912159))), -(hAPP(c_Set_Oimage(_912155, _912161, c_Fun_Ofun__upd(_912155, _912161, _912163, _912157, _912165)), _912159) = hAPP(c_Set_Oimage(_912155, _912161, _912163), _912159))], (16544 ^ _779203) ^ [_1070103, _1070105, _1070107, _1070109] : [class_Orderings_Olinorder(_1070103), hBOOL(hAPP(c_Finite__Set_Ofinite(_1070103), _1070105)), hBOOL(hAPP(hAPP(c_member(_1070103), _1070107), _1070105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1070103), hAPP(hAPP(c_Finite__Set_Ofold(_1070103, _1070103, c_Orderings_Oord__class_Omin(_1070103)), _1070109), _1070105)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1070103), _1070107), _1070109))))], (22079 ^ _779203) ^ [_1168847, _1168849, _1168851, _1168853] : [class_Divides_Oring__div(_1168847), -(c_Divides_Odiv__class_Omod(_1168847, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168847), _1168849), _1168851), _1168853) = c_Divides_Odiv__class_Omod(_1168847, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1168847), c_Divides_Odiv__class_Omod(_1168847, _1168849, _1168853)), _1168851), _1168853))], (28136 ^ _779203) ^ [_1276326, _1276328] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1276326, tc_HOL_Obool)), _1276328), c_Orderings_Otop__class_Otop(tc_fun(_1276326, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1276326, tc_HOL_Obool)))], (25556 ^ _779203) ^ [_1229440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1229440)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229440), c_Int_OMin)))], (18479 ^ _779203) ^ [] : [-(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))], (13335 ^ _779203) ^ [_1010197, _1010199, _1010201] : [class_Lattices_Oab__semigroup__idem__mult(_1010197), -(_1010199 = c_Orderings_Obot__class_Obot(tc_fun(_1010197, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1010197), _1010199)), -(hAPP(c_Finite__Set_Ofold1(_1010197, c_Groups_Otimes__class_Otimes(_1010197)), hAPP(hAPP(c_Set_Oinsert(_1010197), _1010201), _1010199)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1010197), _1010201), hAPP(c_Finite__Set_Ofold1(_1010197, c_Groups_Otimes__class_Otimes(_1010197)), _1010199)))], (51855 ^ _779203) ^ [_1826328, _1826330, _1826332, _1826334] : [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), _1826328, _1826330)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826332, _1826334))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826328), _1826330)), 51862 ^ _779203 : [(51865 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826330), _1826334)))], (51863 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826332), _1826328)))]]], (44462 ^ _779203) ^ [_1669666, _1669668, _1669670, _1669672, _1669674, _1669676] : [-(hAPP(hAPP(c_List_Omap(_1669666, _1669668), _1669670), hAPP(hAPP(c_List_Omap(_1669672, _1669666), _1669674), _1669676)) = hAPP(hAPP(c_List_Omap(_1669672, _1669668), hAPP(c_Fun_Ocomp(_1669666, _1669668, _1669672, _1669670), _1669674)), _1669676))], (36076 ^ _779203) ^ [_1456834, _1456836, _1456838, _1456840, _1456842, _1456844, _1456846, _1456848, _1456850] : [c_Equiv__Relations_Oequiv(_1456834, _1456836, _1456838), c_Equiv__Relations_Oequiv(_1456840, _1456842, _1456844), c_Equiv__Relations_Ocongruent2(_1456834, _1456840, tc_fun(_1456846, tc_HOL_Obool), _1456838, _1456844, _1456848), hBOOL(hAPP(hAPP(c_member(_1456840), _1456850), _1456842)), -(c_Equiv__Relations_Ocongruent(_1456834, tc_fun(_1456846, tc_HOL_Obool), _1456838, hAPP(hAPP(c_COMBB(tc_fun(_1456840, tc_fun(_1456846, tc_HOL_Obool)), tc_fun(_1456846, tc_HOL_Obool), _1456834), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1456840, tc_fun(_1456846, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1456840, _1456840, _1456844), hAPP(hAPP(c_Set_Oinsert(_1456840), _1456850), c_Orderings_Obot__class_Obot(tc_fun(_1456840, tc_HOL_Obool)))))), _1456848)))], (17578 ^ _779203) ^ [_1089059, _1089061] : [class_Orderings_Olinorder(_1089059), -(c_Big__Operators_Olattice_OInf__fin(_1089059, c_Orderings_Oord__class_Omin(_1089059), hAPP(hAPP(c_Set_Oinsert(_1089059), _1089061), c_Orderings_Obot__class_Obot(tc_fun(_1089059, tc_HOL_Obool)))) = _1089061)], (41292 ^ _779203) ^ [_1592576, _1592578, _1592580] : [c_Nitpick_Oless__eq__frac(_1592576, _1592578, _1592580), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1592576), c_Nitpick_Oplus__frac(_1592576, _1592578, c_Nitpick_Ouminus__frac(_1592576, _1592580)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28706 ^ _779203) ^ [_1286847, _1286849, _1286851, _1286853] : [class_Orderings_Olinorder(_1286847), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286847), _1286849), _1286851)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1286847), _1286851), _1286853)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1286847, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1286847, _1286849, _1286851)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1286847, _1286851, _1286853)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1286847, _1286849, _1286853))], (37841 ^ _779203) ^ [_1499436, _1499438, _1499440, _1499442, _1499444, _1499446] : [class_Groups_Ocomm__monoid__add(_1499436), hBOOL(hAPP(c_Finite__Set_Ofinite(_1499438), _1499440)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1499438, _1499436), hAPP(hAPP(c_COMBS(_1499438, _1499436, _1499436), hAPP(hAPP(c_COMBS(_1499438, _1499436, tc_fun(_1499436, _1499436)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1499436, tc_fun(_1499436, _1499436)), _1499438), c_If(_1499436)), _1499442)), _1499444)), _1499446)), _1499440) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1499436), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1499438, _1499436), _1499444), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499438, tc_HOL_Obool)), _1499440), hAPP(c_Set_OCollect(_1499438), _1499442)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1499438, _1499436), _1499446), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1499438, tc_HOL_Obool)), _1499440), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1499438, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1499438), _1499442))))))], (44552 ^ _779203) ^ [_1671713, _1671715, _1671717] : [c_Fun_Oinj__on(_1671713, _1671715, _1671717, c_Orderings_Otop__class_Otop(tc_fun(_1671713, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1671713), tc_List_Olist(_1671715), hAPP(c_List_Omap(_1671713, _1671715), _1671717), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1671713), tc_HOL_Obool))))], (29654 ^ _779203) ^ [_1305452] : [class_Lattices_Osemilattice__inf(_1305452), -(c_Finite__Set_Ofun__left__comm__idem(_1305452, _1305452, c_Lattices_Osemilattice__inf__class_Oinf(_1305452)))], (19208 ^ _779203) ^ [_1117642] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1117642)))], (35590 ^ _779203) ^ [_1445564, _1445566] : [-(hAPP(c_Relation_OField(_1445564), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1445564, _1445564), tc_HOL_Obool), _1445566)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1445564, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1445564, _1445564), tc_HOL_Obool), tc_fun(_1445564, tc_HOL_Obool), c_Relation_OField(_1445564)), _1445566)))], (10365 ^ _779203) ^ [_957634, _957636] : [class_Rings_Ocomm__semiring__1(_957634), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_957634), c_Groups_Oone__class_Oone(_957634)), _957636) = _957636)], (27692 ^ _779203) ^ [_1267303] : [c_Orderings_Otop__class_Otop(tc_fun(_1267303, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1267303, tc_HOL_Obool))], (48110 ^ _779203) ^ [_1749077, _1749079, _1749081, _1749083, _1749085] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749077, _1749079, _1749081), _1749083), _1749085)), -(hBOOL(hAPP(hAPP(_1749081, _1749085), _1749083)))], (43462 ^ _779203) ^ [_1647953, _1647955, _1647957] : [-(hAPP(hAPP(c_List_Odrop(_1647953), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1647953), _1647955), _1647957)) = _1647957)], (8031 ^ _779203) ^ [_911958, _911960, _911962, _911964, _911966, _911968] : [hBOOL(hAPP(hAPP(c_member(_911958), _911960), _911962)), -(hAPP(c_Set_Oimage(_911958, _911964, c_Fun_Ofun__upd(_911958, _911964, _911966, _911960, _911968)), _911962) = hAPP(hAPP(c_Set_Oinsert(_911964), _911968), hAPP(c_Set_Oimage(_911958, _911964, _911966), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911958, tc_HOL_Obool)), _911962), hAPP(hAPP(c_Set_Oinsert(_911958), _911960), c_Orderings_Obot__class_Obot(tc_fun(_911958, tc_HOL_Obool)))))))], (6833 ^ _779203) ^ [_890514, _890516, _890518, _890520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890514, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_890514, tc_HOL_Obool)), _890516), hAPP(hAPP(c_Set_Oinsert(_890514), _890518), c_Orderings_Obot__class_Obot(tc_fun(_890514, tc_HOL_Obool))))), _890520)), hBOOL(hAPP(hAPP(c_member(_890514), _890518), _890516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890514, tc_HOL_Obool)), _890516), hAPP(hAPP(c_Set_Oinsert(_890514), _890518), _890520))))], (10710 ^ _779203) ^ [_964501, _964503, _964505, _964507] : [class_Rings_Ocomm__semiring__1(_964501), hBOOL(hAPP(c_Finite__Set_Ofinite(_964503), _964505)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_964503, _964501), _964507), _964505) = c_Groups_Ozero__class_Ozero(_964501)), 10719 ^ _779203 : [(10720 ^ _779203) ^ [_964682] : [hBOOL(hAPP(hAPP(c_member(_964503), _964682), _964505)), hAPP(_964507, _964682) = c_Groups_Ozero__class_Ozero(_964501)]]], (44400 ^ _779203) ^ [_1668169, _1668171, _1668173, _1668175, _1668177] : [class_Rings_Osemiring__0(_1668169), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1668169), hAPP(hAPP(c_List_Omap(_1668171, _1668169), hAPP(hAPP(c_COMBC(_1668171, _1668169, _1668169), hAPP(hAPP(c_COMBB(_1668169, tc_fun(_1668169, _1668169), _1668171), c_Groups_Otimes__class_Otimes(_1668169)), _1668173)), _1668175)), _1668177)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1668169), hAPP(c_List_Omonoid__add__class_Olistsum(_1668169), hAPP(hAPP(c_List_Omap(_1668171, _1668169), _1668173), _1668177))), _1668175))], (28662 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (6559 ^ _779203) ^ [_885000, _885002, _885004] : [class_Orderings_Oorder(_885000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885000), _885002), _885004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885000), _885004), _885002)), -(_885004 = _885002)], (6769 ^ _779203) ^ [_889093, _889095, _889097, _889099, _889101] : [c_Finite__Set_Ofolding__one(_889093, _889095, _889097), hBOOL(hAPP(c_Finite__Set_Ofinite(_889093), _889099)), 6776 ^ _779203 : [(6783 ^ _779203) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889093, tc_HOL_Obool)), _889099), hAPP(hAPP(c_Set_Oinsert(_889093), _889101), c_Orderings_Obot__class_Obot(tc_fun(_889093, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_889093, tc_HOL_Obool))), -(hAPP(_889097, hAPP(hAPP(c_Set_Oinsert(_889093), _889101), _889099)) = hAPP(hAPP(_889095, _889101), hAPP(_889097, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889093, tc_HOL_Obool)), _889099), hAPP(hAPP(c_Set_Oinsert(_889093), _889101), c_Orderings_Obot__class_Obot(tc_fun(_889093, tc_HOL_Obool)))))))], (6777 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_889093, tc_HOL_Obool)), _889099), hAPP(hAPP(c_Set_Oinsert(_889093), _889101), c_Orderings_Obot__class_Obot(tc_fun(_889093, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_889093, tc_HOL_Obool)), -(hAPP(_889097, hAPP(hAPP(c_Set_Oinsert(_889093), _889101), _889099)) = _889101)]]], (38927 ^ _779203) ^ [_1533509, _1533511, _1533513, _1533515] : [c_FunDef_Oreduction__pair(_1533509, _1533511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533509, _1533509), tc_HOL_Obool)), _1533513), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1533509, _1533509), tc_HOL_Obool), tc_fun(tc_prod(_1533509, _1533509), tc_HOL_Obool)), _1533511))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533509, _1533509), tc_HOL_Obool)), _1533515), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1533509, _1533509), tc_HOL_Obool), tc_fun(tc_prod(_1533509, _1533509), tc_HOL_Obool)), _1533511))), c_Wellfounded_Owf(_1533509, _1533515), -(c_Wellfounded_Owf(_1533509, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1533509, _1533509), tc_HOL_Obool)), _1533513), _1533515)))], (35031 ^ _779203) ^ [_1430445, _1430447, _1430449, _1430451, _1430453] : [class_Complete__Lattice_Ocomplete__lattice(_1430445), hBOOL(hAPP(hAPP(c_member(_1430447), _1430449), _1430451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1430445), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1430447, _1430445), _1430451), _1430453)), hAPP(_1430453, _1430449))))], (32575 ^ _779203) ^ [_1370390, _1370392] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1370390), _1370392)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1370390)), _1370392)))], (6913 ^ _779203) ^ [_892229, _892231, _892233] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_892229), _892231)), 6916 ^ _779203 : [(6923 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_892229), _892233)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_892229), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892229, tc_HOL_Obool)), _892233), _892231))))], (6917 ^ _779203) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_892229), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_892229, tc_HOL_Obool)), _892233), _892231))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_892229), _892233)))]]], (39321 ^ _779203) ^ [_1543642] : [-(_1543642 = hAPP(c_Int_OAbs__Integ, 39319 ^ [_1543642]))], (166 ^ _779203) ^ [_781708, _781710, _781712, _781714, _781716, _781718] : [-(c_Finite__Set_Ofolding__one__idem(_781716, _781712, _781708)), c_Finite__Set_Ofolding__one__idem(_781718, _781714, _781710), _781718 = _781716, _781714 = _781712, _781710 = _781708], (9937 ^ _779203) ^ [_948865, _948867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _948865), _948867)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948867), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948867), _948865)) = _948865)], (48142 ^ _779203) ^ [_1749981, _1749983, _1749985, _1749987, _1749989] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1749983, _1749981)), hAPP(hAPP(c_Product__Type_OPair(_1749983, _1749981), _1749987), _1749989)), hAPP(c_Relation_Oconverse(_1749981, _1749983), _1749985))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1749981, _1749983, hAPP(hAPP(c_COMBC(_1749981, tc_fun(tc_prod(_1749981, _1749983), tc_HOL_Obool), tc_fun(_1749983, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749983, tc_fun(tc_fun(tc_prod(_1749981, _1749983), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1749981, _1749983), tc_HOL_Obool), tc_fun(_1749983, tc_HOL_Obool)), _1749981), c_COMBC(_1749983, tc_fun(tc_prod(_1749981, _1749983), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1749983, tc_prod(_1749981, _1749983)), tc_fun(_1749983, tc_fun(tc_fun(tc_prod(_1749981, _1749983), tc_HOL_Obool), tc_HOL_Obool)), _1749981), hAPP(c_COMBB(tc_prod(_1749981, _1749983), tc_fun(tc_fun(tc_prod(_1749981, _1749983), tc_HOL_Obool), tc_HOL_Obool), _1749983), c_member(tc_prod(_1749981, _1749983)))), c_Product__Type_OPair(_1749981, _1749983)))), _1749985)), _1749987), _1749989)))], (30947 ^ _779203) ^ [_1332802, _1332804, _1332806] : [class_Lattices_Olattice(_1332802), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332802), _1332804)), -(_1332804 = c_Orderings_Obot__class_Obot(tc_fun(_1332802, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1332802), _1332806)), -(_1332806 = c_Orderings_Obot__class_Obot(tc_fun(_1332802, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1332802, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1332802, tc_HOL_Obool)), _1332804), _1332806)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1332802), c_Big__Operators_Olattice__class_OInf__fin(_1332802, _1332804)), c_Big__Operators_Olattice__class_OInf__fin(_1332802, _1332806)))], (12116 ^ _779203) ^ [_988592] : [class_Rings_Olinordered__semidom(_988592), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988592), c_Groups_Ozero__class_Ozero(_988592)), c_Groups_Oone__class_Oone(_988592))))], (52563 ^ _779203) ^ [_1835580, _1835582] : [-(class_Finite__Set_Ofinite(tc_prod(_1835580, _1835582))), class_Finite__Set_Ofinite(_1835580), class_Finite__Set_Ofinite(_1835582)], (17352 ^ _779203) ^ [_1085065, _1085067, _1085069] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1085065), _1085067)), _1085069) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085065), _1085069)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1085067), _1085069)))], (42222 ^ _779203) ^ [_1620161, _1620163] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1620161, _1620163) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1620161), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1620163)))], (51667 ^ _779203) ^ [_1822924, _1822926, _1822928, _1822930] : [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), _1822924, _1822926)), c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822928, _1822930))), 51670 ^ _779203 : [(51671 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822924), _1822926)), 51674 ^ _779203 : [(51679 ^ _779203) ^ [] : [51680 ^ _779203 : [(51683 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822924), _1822928))], (51681 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822928), _1822924)))]], 51684 ^ _779203 : [(51687 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822930), _1822926))], (51685 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822926), _1822930)))]]], (51677 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822926), _1822930)))], (51675 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822928), _1822924)))]]], (51689 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1822928), _1822930)))]]], (8829 ^ _779203) ^ [_928319, _928321, _928323, _928325] : [class_Groups_Oordered__cancel__ab__semigroup__add(_928319), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928319), _928321), _928323)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_928319), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928319), _928321), _928325)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_928319), _928323), _928325))))], (1320 ^ _779203) ^ [_798663, _798665] : [-(class_Int_Onumber__ring(_798663)), _798665 = _798663, class_Int_Onumber__ring(_798665)], (13645 ^ _779203) ^ [_1016281, _1016283, _1016285, _1016287] : [class_Rings_Odivision__ring(_1016281), -(_1016283 = c_Groups_Ozero__class_Ozero(_1016281)), 13652 ^ _779203 : [(13659 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016281), _1016285), _1016283) = _1016287, -(_1016285 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1016281), _1016287), _1016283))], (13653 ^ _779203) ^ [] : [_1016285 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1016281), _1016287), _1016283), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1016281), _1016285), _1016283) = _1016287)]]], (21161 ^ _779203) ^ [_1152391, _1152393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1152391), _1152393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1152391)), c_Int_OBit1(_1152393))))], (904 ^ _779203) ^ [_792685, _792687, _792689, _792691, _792693, _792695, _792697, _792699, _792701, _792703] : [-(c_Fun_Obij__betw(_792701, _792697, _792693, _792689, _792685)), c_Fun_Obij__betw(_792703, _792699, _792695, _792691, _792687), _792703 = _792701, _792699 = _792697, _792695 = _792693, _792691 = _792689, _792687 = _792685], (52639 ^ _779203) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (18276 ^ _779203) ^ [_1101550, _1101552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1101550), _1101552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101550)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1101552))))], (46720 ^ _779203) ^ [_1718713, _1718715, _1718717] : [-(hAPP(c_List_Orev(_1718713), hAPP(hAPP(c_List_Otake(_1718713), _1718715), _1718717)) = hAPP(hAPP(c_List_Odrop(_1718713), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718713)), _1718717)), _1718715)), hAPP(c_List_Orev(_1718713), _1718717)))], (22340 ^ _779203) ^ [_1173427] : [22342 ^ _779203 : [(22345 ^ _779203) ^ [] : [hBOOL(hAPP(_1173427, hAPP(c_Int_Onat, 22341 ^ [_1173427])))], (22343 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 22341 ^ [_1173427])))]], 22346 ^ _779203 : [(22347 ^ _779203) ^ [_1173560] : [-(hBOOL(hAPP(_1173427, _1173560)))]]], (35133 ^ _779203) ^ [_1433097, _1433099, _1433101, _1433103, _1433105, _1433107] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433097, tc_fun(_1433099, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433101, tc_fun(_1433097, tc_HOL_Obool)), _1433103), _1433105)), _1433107) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433101, tc_fun(_1433099, tc_HOL_Obool)), _1433103), hAPP(hAPP(c_COMBC(_1433101, tc_fun(_1433097, tc_fun(_1433099, tc_HOL_Obool)), tc_fun(_1433099, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1433097, tc_HOL_Obool), tc_fun(tc_fun(_1433097, tc_fun(_1433099, tc_HOL_Obool)), tc_fun(_1433099, tc_HOL_Obool)), _1433101), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1433097, tc_fun(_1433099, tc_HOL_Obool))), _1433105)), _1433107)))], (1800 ^ _779203) ^ [_804663, _804665] : [-(class_Orderings_Olinorder(_804663)), _804665 = _804663, class_Orderings_Olinorder(_804665)], (10969 ^ _779203) ^ [_968520] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _968520)], (7887 ^ _779203) ^ [_908930, _908932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_908930, tc_HOL_Obool)), _908932), c_Orderings_Obot__class_Obot(tc_fun(_908930, tc_HOL_Obool))))], (17454 ^ _779203) ^ [_1087039, _1087041, _1087043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1087039), _1087041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1087043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1087043), _1087039)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1087043), _1087041))))], (6193 ^ _779203) ^ [_878467, _878469, _878471, _878473, _878475] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878467, tc_HOL_Obool)), _878469), hAPP(c_Set_Oimage(_878471, _878467, _878473), _878475)))), 6194 ^ _779203 : [(6195 ^ _779203) ^ [_878547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878471, tc_HOL_Obool)), _878547), _878475)), _878469 = hAPP(c_Set_Oimage(_878471, _878467, _878473), _878547)]]], (41262 ^ _779203) ^ [_1591894, _1591896, _1591898, _1591900, _1591902, _1591904] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1591894, _1591896, _1591898), _1591900), hAPP(hAPP(c_Product__Type_OPair(_1591894, _1591896), _1591902), _1591904)) = hAPP(hAPP(_1591900, _1591902), _1591904))], (33643 ^ _779203) ^ [_1395051, _1395053, _1395055] : [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), _1395051), _1395053))), -(hBOOL(hAPP(hAPP(_1395055, _1395051), _1395053))), 33650 ^ _779203 : [(33653 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1395055, 33648 ^ [_1395051, _1395053, _1395055]), 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)))), 33649 ^ [_1395051, _1395053, _1395055])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 33648 ^ [_1395051, _1395053, _1395055]), 33649 ^ [_1395051, _1395053, _1395055]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 33649 ^ [_1395051, _1395053, _1395055]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33663 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1395055, 33648 ^ [_1395051, _1395053, _1395055]), 33649 ^ [_1395051, _1395053, _1395055]))], (33651 ^ _779203) ^ [] : [-(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), 33648 ^ [_1395051, _1395053, _1395055]), 33649 ^ [_1395051, _1395053, _1395055]))))]]], (46708 ^ _779203) ^ [_1718495, _1718497] : [-(_1718495 = c_List_Olist_ONil(_1718497)), -(hAPP(c_List_Ohd(_1718497), hAPP(c_List_Orev(_1718497), _1718495)) = c_List_Olast(_1718497, _1718495))], (41723 ^ _779203) ^ [_1606294, _1606296, _1606298] : [c_Equiv__Relations_Oequiv(_1606294, _1606296, _1606298), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1606294), c_List_Olists(_1606294, _1606296), c_List_Olistrel(_1606294, _1606298)))], (18895 ^ _779203) ^ [] : [-(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))))], (37545 ^ _779203) ^ [_1490551, _1490553, _1490555] : [-(hAPP(hAPP(c_Set_Oinsert(_1490551), _1490553), _1490555) = hAPP(c_Set_OCollect(_1490551), hAPP(hAPP(c_COMBS(_1490551, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1490551), c_fdisj), hAPP(hAPP(c_COMBC(_1490551, _1490551, tc_HOL_Obool), c_fequal), _1490553))), hAPP(hAPP(c_COMBC(_1490551, tc_fun(_1490551, tc_HOL_Obool), tc_HOL_Obool), c_member(_1490551)), _1490555))))], (33363 ^ _779203) ^ [_1389907, _1389909] : [-(_1389907 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1389909, _1389907), c_Divides_Odivmod__int(_1389909, _1389907))))], (23675 ^ _779203) ^ [_1195874, _1195876, _1195878] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1195874, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195876), _1195878)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195876), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1195874), _1195876), _1195878))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1195874, _1195876)))], (5927 ^ _779203) ^ [_873088, _873090] : [_873090 = c_Orderings_Obot__class_Obot(tc_fun(_873088, tc_HOL_Obool)), 5930 ^ _779203 : [(5931 ^ _779203) ^ [_873168] : [hBOOL(hAPP(hAPP(c_member(_873088), _873168), _873090))]]], (29738 ^ _779203) ^ [_1307148, _1307150, _1307152, _1307154] : [hBOOL(hAPP(hAPP(c_member(_1307148), _1307150), _1307152)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307148, tc_HOL_Obool)), _1307152), hAPP(hAPP(c_Set_Oinsert(_1307148), _1307150), _1307154)) = hAPP(hAPP(c_Set_Oinsert(_1307148), _1307150), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307148, tc_HOL_Obool)), _1307152), _1307154)))], (32587 ^ _779203) ^ [_1370634, _1370636, _1370638, _1370640] : [-(hAPP(c_Nat_Onat_Onat__rec(_1370634, _1370636, _1370638), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1370640)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1370634), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1370640))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1370634, _1370634), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1370634, tc_fun(_1370634, _1370634)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1370634, tc_fun(_1370634, _1370634)), tc_Int_Oint), c_If(_1370634)), c_Nat__Numeral_Oneg)), _1370636)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1370634, _1370634), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1370634, _1370634), tc_Int_Oint), _1370638), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1370634, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1370634, _1370636, _1370638)), c_Int_Onat)))))], (41008 ^ _779203) ^ [_1584812, _1584814, _1584816, _1584818] : [-(hAPP(hAPP(c_Nat_Ocompow(_1584812, _1584812), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1584814), _1584816)), _1584818) = hAPP(c_Fun_Ocomp(_1584812, _1584812, _1584812, hAPP(hAPP(c_Nat_Ocompow(_1584812, _1584812), _1584814), _1584818)), hAPP(hAPP(c_Nat_Ocompow(_1584812, _1584812), _1584816), _1584818)))], (9807 ^ _779203) ^ [_946587, _946589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _946587)), _946589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _946587), _946589)))], (6142 ^ _779203) ^ [_877351, _877353, _877355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_877351, tc_HOL_Obool)), _877353), _877355)), hBOOL(hAPP(c_Finite__Set_Ofinite(_877351), _877355)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_877351), _877353)))], (40378 ^ _779203) ^ [_1569419, _1569421, _1569423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569419, _1569419), tc_HOL_Obool)), _1569421), _1569423)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569419, _1569419), tc_HOL_Obool)), _1569423), c_Transitive__Closure_Ortrancl(_1569419, _1569421))), -(c_Transitive__Closure_Ortrancl(_1569419, _1569423) = c_Transitive__Closure_Ortrancl(_1569419, _1569421))], (1992 ^ _779203) ^ [_807901, _807903] : [_807903 = _807901, -(c_Nat_Osemiring__1__class_ONats(_807903) = c_Nat_Osemiring__1__class_ONats(_807901))], (47439 ^ _779203) ^ [_1734647, _1734649, _1734651, _1734653, _1734655] : [class_Orderings_Olinorder(_1734647), 47445 ^ _779203 : [(47448 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1734647), hAPP(_1734653, _1734655)), hAPP(_1734653, 47444 ^ [_1734647, _1734649, _1734651, _1734653, _1734655])))], (47446 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734649), 47444 ^ [_1734647, _1734649, _1734651, _1734653, _1734655]), hAPP(c_List_Oset(_1734649), _1734651))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1734649, _1734647, _1734653), _1734655), _1734651) = hAPP(hAPP(c_List_Olist_OCons(_1734649), _1734655), _1734651))], (8518 ^ _779203) ^ [_922546, _922548, _922550, _922552, _922554] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_922546, _922548, hAPP(hAPP(c_Set_Oinsert(_922546), _922550), _922552)), _922554))), 8519 ^ _779203 : [(8520 ^ _779203) ^ [_922650, _922652] : [hAPP(hAPP(c_Set_Oinsert(_922546), _922550), _922552) = hAPP(hAPP(c_Set_Oinsert(_922546), _922652), _922650), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_922546, _922546, _922548, _922652, _922650), _922554)), -(hBOOL(hAPP(hAPP(c_member(_922546), _922652), _922650)))]]], (38613 ^ _779203) ^ [_1526935, _1526937, _1526939, _1526941, _1526943] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1526935, _1526937)), hAPP(hAPP(c_Product__Type_OPair(_1526935, _1526937), _1526939), _1526941)), _1526943)), -(hBOOL(hAPP(hAPP(c_member(_1526935), _1526939), hAPP(c_Relation_ODomain(_1526935, _1526937), _1526943))))], (45386 ^ _779203) ^ [_1690239, _1690241] : [c_List_Olist_ONil(_1690239) = c_List_Oremdups(_1690239, _1690241), -(_1690241 = c_List_Olist_ONil(_1690239))], (29220 ^ _779203) ^ [_1296906, _1296908, _1296910, _1296912] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296906, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1296906), _1296908), _1296910)), hAPP(hAPP(c_Set_Oinsert(_1296906), _1296908), _1296912)) = hAPP(hAPP(c_Set_Oinsert(_1296906), _1296908), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1296906, tc_HOL_Obool)), _1296910), _1296912)))], (29194 ^ _779203) ^ [_1296159, _1296161] : [class_Lattices_Obounded__lattice__top(_1296159), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1296159), _1296161), c_Orderings_Otop__class_Otop(_1296159)) = _1296161)], (46586 ^ _779203) ^ [_1715861, _1715863, _1715865] : [hAPP(c_List_Orev(_1715861), _1715863) = hAPP(hAPP(c_List_Olist_OCons(_1715861), _1715865), c_List_Olist_ONil(_1715861)), -(_1715863 = hAPP(hAPP(c_List_Olist_OCons(_1715861), _1715865), c_List_Olist_ONil(_1715861)))], (41871 ^ _779203) ^ [_1610033, _1610035, _1610037, _1610039] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1610033), tc_List_Olist(_1610033))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1610033), tc_List_Olist(_1610033)), _1610035), _1610037)), c_List_Olexord(_1610033, _1610039)))), 41872 ^ _779203 : [(41879 ^ _779203) ^ [_1610340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1610340), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610033)), _1610035)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610033)), _1610037)))), hAPP(hAPP(c_List_Otake(_1610033), _1610340), _1610035) = hAPP(hAPP(c_List_Otake(_1610033), _1610340), _1610037), hBOOL(hAPP(hAPP(c_member(tc_prod(_1610033, _1610033)), hAPP(hAPP(c_Product__Type_OPair(_1610033, _1610033), hAPP(hAPP(c_List_Onth(_1610033), _1610035), _1610340)), hAPP(hAPP(c_List_Onth(_1610033), _1610037), _1610340))), _1610039))], (41873 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610033)), _1610035)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610033)), _1610037))), hAPP(hAPP(c_List_Otake(_1610033), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1610033)), _1610035)), _1610037) = _1610035]]], (50087 ^ _779203) ^ [_1792235, _1792237, _1792239, _1792241] : [c_Fun_Obij__betw(_1792235, _1792237, _1792239, _1792241, c_Orderings_Obot__class_Obot(tc_fun(_1792237, tc_HOL_Obool))), -(_1792241 = c_Orderings_Obot__class_Obot(tc_fun(_1792235, tc_HOL_Obool)))], (11392 ^ _779203) ^ [_975352, _975354, _975356] : [class_Rings_Oordered__ring(_975352), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975352), c_Groups_Ozero__class_Ozero(_975352)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_975352), _975354), _975356)))), 11397 ^ _779203 : [(11404 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975352), _975354), c_Groups_Ozero__class_Ozero(_975352))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975352), _975356), c_Groups_Ozero__class_Ozero(_975352)))], (11398 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975352), c_Groups_Ozero__class_Ozero(_975352)), _975354)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_975352), c_Groups_Ozero__class_Ozero(_975352)), _975356))]]], (24488 ^ _779203) ^ [_1210573, _1210575] : [class_Rings_Olinordered__idom(_1210573), -(hAPP(c_Groups_Oabs__class_Oabs(_1210573), hAPP(hAPP(c_Power_Opower__class_Opower(_1210573), _1210575), 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(_1210573), _1210575), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (31663 ^ _779203) ^ [_1347588, _1347590] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1347588), _1347590) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1347588), _1347590))], (7403 ^ _779203) ^ [_901623, _901625, _901627, _901629] : [class_Orderings_Oord(_901623), _901625 = _901627, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901623), _901627), _901629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_901623), _901625), _901629)))], (13975 ^ _779203) ^ [_1022285, _1022287, _1022289] : [class_Fields_Olinordered__field__inverse__zero(_1022285), 13978 ^ _779203 : [(13993 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022285), c_Groups_Ozero__class_Ozero(_1022285)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1022285), _1022287), _1022289)))), 13994 ^ _779203 : [(14001 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022285), _1022287), c_Groups_Ozero__class_Ozero(_1022285))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022285), _1022289), c_Groups_Ozero__class_Ozero(_1022285)))], (13995 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022285), c_Groups_Ozero__class_Ozero(_1022285)), _1022287)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022285), c_Groups_Ozero__class_Ozero(_1022285)), _1022289))]]], (13979 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022285), c_Groups_Ozero__class_Ozero(_1022285)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1022285), _1022287), _1022289))), 13984 ^ _779203 : [(13987 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022285), c_Groups_Ozero__class_Ozero(_1022285)), _1022289)))], (13985 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022285), c_Groups_Ozero__class_Ozero(_1022285)), _1022287)))]], 13988 ^ _779203 : [(13991 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022285), _1022289), c_Groups_Ozero__class_Ozero(_1022285))))], (13989 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1022285), _1022287), c_Groups_Ozero__class_Ozero(_1022285))))]]]]], (45516 ^ _779203) ^ [_1692610, _1692612, _1692614] : [-(c_List_Oconcat(_1692610, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1692610)), _1692612), _1692614)) = hAPP(hAPP(c_List_Oappend(_1692610), _1692612), c_List_Oconcat(_1692610, _1692614)))], (7907 ^ _779203) ^ [_909333, _909335, _909337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_909333, tc_HOL_Obool)), _909335), _909337)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_909333, tc_HOL_Obool)), _909335), _909337))), -(_909335 = _909337)], (10615 ^ _779203) ^ [_962917, _962919, _962921] : [class_Lattices_Oab__semigroup__idem__mult(_962917), hBOOL(hAPP(c_Finite__Set_Ofinite(_962917), _962919)), -(hAPP(c_Finite__Set_Ofold1(_962917, c_Groups_Otimes__class_Otimes(_962917)), hAPP(hAPP(c_Set_Oinsert(_962917), _962921), _962919)) = hAPP(hAPP(c_Finite__Set_Ofold(_962917, _962917, c_Groups_Otimes__class_Otimes(_962917)), _962921), _962919))], (15586 ^ _779203) ^ [_1052443, _1052445, _1052447, _1052449] : [class_Orderings_Olinorder(_1052443), 15589 ^ _779203 : [(15590 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052443), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1052443), _1052445), _1052447)), _1052449)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052443), _1052445), _1052449))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052443), _1052447), _1052449)))], (15600 ^ _779203) ^ [] : [15601 ^ _779203 : [(15604 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052443), _1052447), _1052449))], (15602 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052443), _1052445), _1052449))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1052443), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1052443), _1052445), _1052447)), _1052449)))]]], (21677 ^ _779203) ^ [_1160787, _1160789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1160787), _1160789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1160787)), c_Int_OBit0(_1160789))))], (48761 ^ _779203) ^ [_1763679, _1763681] : [c_Relation_Otrans(_1763679, _1763681), 48764 ^ _779203 : [(48765 ^ _779203) ^ [_1763815, _1763817] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763679, _1763679)), hAPP(hAPP(c_Product__Type_OPair(_1763679, _1763679), _1763817), _1763815)), _1763681)), 48768 ^ _779203 : [(48769 ^ _779203) ^ [_1763958] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763679, _1763679)), hAPP(hAPP(c_Product__Type_OPair(_1763679, _1763679), _1763815), _1763958)), _1763681)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763679, _1763679)), hAPP(hAPP(c_Product__Type_OPair(_1763679, _1763679), _1763817), _1763958)), _1763681)))]]]]], (40542 ^ _779203) ^ [] : [-(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))))], (25616 ^ _779203) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (10993 ^ _779203) ^ [_968852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _968852), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31333 ^ _779203) ^ [_1340796, _1340798, _1340800, _1340802, _1340804, _1340806, _1340808, _1340810] : [c_Finite__Set_Ofolding__image__simple(_1340796, _1340798, _1340800, _1340802, _1340804, _1340806), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340798), _1340808)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340798), _1340810)), 31347 ^ _779203 : [(31350 ^ _779203) ^ [] : [hAPP(_1340804, 31346 ^ [_1340796, _1340798, _1340800, _1340802, _1340804, _1340806, _1340808, _1340810]) = _1340802], (31348 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1340798), 31346 ^ [_1340796, _1340798, _1340800, _1340802, _1340804, _1340806, _1340808, _1340810]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340798, tc_HOL_Obool)), _1340808), _1340810))))]], -(hAPP(_1340806, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340798, tc_HOL_Obool)), _1340808), _1340810)) = hAPP(hAPP(_1340800, hAPP(_1340806, _1340808)), hAPP(_1340806, _1340810)))], (27952 ^ _779203) ^ [_1272549] : [-(hAPP(c_Set_OPow(_1272549), c_Orderings_Otop__class_Otop(tc_fun(_1272549, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1272549, tc_HOL_Obool), tc_HOL_Obool)))], (33745 ^ _779203) ^ [_1397012, _1397014] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1397012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397014), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397012, _1397014) = 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), _1397012), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1397014)))))], (12915 ^ _779203) ^ [_1002540, _1002542] : [hAPP(c_Finite__Set_Ocard(_1002540), _1002542) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1002542 = c_Orderings_Obot__class_Obot(tc_fun(_1002540, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1002540), _1002542))], (17358 ^ _779203) ^ [_1085177, _1085179] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085177), _1085179) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1085179), _1085177))], (12104 ^ _779203) ^ [_988400] : [class_Rings_Olinordered__semidom(_988400), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_988400), c_Groups_Oone__class_Oone(_988400)), c_Groups_Ozero__class_Ozero(_988400)))], (25386 ^ _779203) ^ [_1227001, _1227003] : [class_Int_Onumber__ring(_1227001), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1227001), hAPP(c_Int_Onumber__class_Onumber__of(_1227001), 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)))), _1227003))) = hAPP(c_Int_Onumber__class_Onumber__of(_1227001), c_Int_OMin))], (9233 ^ _779203) ^ [_936698, _936700] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936698), hAPP(c_Nat_OSuc, _936700)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _936698), _936700)))], (31763 ^ _779203) ^ [_1350099, _1350101, _1350103] : [hAPP(hAPP(c_COMBC(_1350099, tc_fun(_1350099, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350099)), _1350101) = hAPP(hAPP(c_COMBC(_1350099, tc_fun(_1350099, tc_HOL_Obool), tc_HOL_Obool), c_member(_1350099)), _1350103), -(_1350101 = _1350103)], (12478 ^ _779203) ^ [_994425, _994427] : [_994425 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _994425), _994427), -(_994427 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_994425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3428 ^ _779203) ^ [_830357, _830359] : [_830359 = _830357, -(c_List_Otranspose__rel(_830359) = c_List_Otranspose__rel(_830357))], (51841 ^ _779203) ^ [_1826068, _1826070, _1826072] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826068), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1826070), _1826072))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826068), _1826072)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1826072), _1826070)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1826068), _1826070)))], (27556 ^ _779203) ^ [_1264753, _1264755, _1264757, _1264759] : [hBOOL(hAPP(hAPP(c_member(_1264753), _1264755), _1264757)), -(hBOOL(hAPP(hAPP(c_member(_1264753), _1264755), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264753, tc_HOL_Obool)), _1264757), _1264759))))], (22127 ^ _779203) ^ [_1169796] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169796)) = _1169796)], (6176 ^ _779203) ^ [_878024, _878026, _878028, _878030, _878032] : [-(hAPP(c_Set_Oimage(_878024, _878026, _878028), hAPP(hAPP(c_Set_Oinsert(_878024), _878030), _878032)) = hAPP(hAPP(c_Set_Oinsert(_878026), hAPP(_878028, _878030)), hAPP(c_Set_Oimage(_878024, _878026, _878028), _878032)))], (46280 ^ _779203) ^ [_1709654, _1709656, _1709658, _1709660, _1709662] : [class_Orderings_Olinorder(_1709654), c_List_Olinorder__class_Osorted(_1709654, hAPP(hAPP(c_List_Omap(_1709656, _1709654), _1709658), _1709660)), -(c_List_Olinorder__class_Osorted(_1709654, hAPP(hAPP(c_List_Omap(_1709656, _1709654), _1709658), hAPP(c_List_Ofilter(_1709656, _1709662), _1709660))))], (8895 ^ _779203) ^ [_929504, _929506, _929508] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_929504), _929506)), -(hBOOL(hAPP(hAPP(c_member(_929504), _929508), _929506))), -(hAPP(c_Finite__Set_Ocard(_929504), hAPP(hAPP(c_Set_Oinsert(_929504), _929508), _929506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_929504), _929506)))], (44325 ^ _779203) ^ [_1666182, _1666184, _1666186, _1666188, _1666190, _1666192] : [-(hAPP(hAPP(c_List_Ozip(_1666182, _1666184), _1666186), hAPP(hAPP(c_List_Omap(_1666188, _1666184), _1666190), _1666192)) = hAPP(hAPP(c_List_Omap(tc_prod(_1666182, _1666188), tc_prod(_1666182, _1666184)), hAPP(c_Product__Type_Oprod_Oprod__case(_1666182, _1666188, tc_prod(_1666182, _1666184)), hAPP(hAPP(c_COMBC(_1666182, tc_fun(_1666188, _1666184), tc_fun(_1666188, tc_prod(_1666182, _1666184))), hAPP(hAPP(c_COMBB(tc_fun(_1666184, tc_prod(_1666182, _1666184)), tc_fun(tc_fun(_1666188, _1666184), tc_fun(_1666188, tc_prod(_1666182, _1666184))), _1666182), c_COMBB(_1666184, tc_prod(_1666182, _1666184), _1666188)), c_Product__Type_OPair(_1666182, _1666184))), _1666190))), hAPP(hAPP(c_List_Ozip(_1666182, _1666188), _1666186), _1666192)))], (44574 ^ _779203) ^ [_1672176, _1672178, _1672180, _1672182] : [class_Rings_Osemiring__1(_1672176), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1672176), hAPP(hAPP(c_List_Omap(_1672178, _1672176), hAPP(c_COMBK(_1672176, _1672178), _1672180)), _1672182)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1672176), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1672176), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672178)), _1672182))), _1672180))], (35794 ^ _779203) ^ [_1450400, _1450402, _1450404, _1450406, _1450408, _1450410, _1450412] : [c_Equiv__Relations_Oequiv(_1450400, _1450402, _1450404), hBOOL(hAPP(hAPP(c_member(tc_fun(_1450400, tc_HOL_Obool)), _1450406), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1450400), _1450402), _1450404))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1450400, tc_HOL_Obool)), _1450408), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1450400), _1450402), _1450404))), hBOOL(hAPP(hAPP(c_member(_1450400), _1450410), _1450406)), hBOOL(hAPP(hAPP(c_member(_1450400), _1450412), _1450408)), 35813 ^ _779203 : [(35820 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1450400, _1450400)), hAPP(hAPP(c_Product__Type_OPair(_1450400, _1450400), _1450410), _1450412)), _1450404)), -(_1450406 = _1450408)], (35814 ^ _779203) ^ [] : [_1450406 = _1450408, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1450400, _1450400)), hAPP(hAPP(c_Product__Type_OPair(_1450400, _1450400), _1450410), _1450412)), _1450404)))]]], (23641 ^ _779203) ^ [_1195358, _1195360] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1195358))), -(c_SMT_Oz3div(_1195360, _1195358) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1195360), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1195358))))], (23501 ^ _779203) ^ [_1192774, _1192776, _1192778, _1192780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1192776)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1192776), _1192778)), -(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), _1192778), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1192780, _1192774))), _1192776))))], (44119 ^ _779203) ^ [_1662143, _1662145, _1662147] : [class_Orderings_Olinorder(_1662143), hBOOL(hAPP(hAPP(c_member(_1662143), _1662145), hAPP(c_List_Oset(_1662143), _1662147))), -(c_List_Olinorder__class_Oinsort__insert__key(_1662143, _1662143, c_COMBI(_1662143), _1662145, _1662147) = _1662147)], (43915 ^ _779203) ^ [_1657822, _1657824] : [class_Complete__Lattice_Ocomplete__lattice(_1657822), -(c_Complete__Lattice_OInf__class_OInf(_1657822, hAPP(c_List_Oset(_1657822), _1657824)) = hAPP(c_List_Ofoldl(_1657822, _1657822, c_Lattices_Osemilattice__inf__class_Oinf(_1657822), c_Orderings_Otop__class_Otop(_1657822)), _1657824))], (47205 ^ _779203) ^ [_1728932, _1728934, _1728936] : [-(c_List_Omaps(_1728932, _1728934, _1728936, c_List_Olist_ONil(_1728932)) = c_List_Olist_ONil(_1728934))], (25988 ^ _779203) ^ [_1236195, _1236197] : [class_Rings_Oring__1(_1236195), -(hAPP(c_Int_Oring__1__class_Oof__int(_1236195), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1236197)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1236195), _1236197))], (49427 ^ _779203) ^ [_1778104, _1778106] : [-(c_Equiv__Relations_Opart__equivp(_1778104, _1778106)), 49430 ^ _779203 : [(49431 ^ _779203) ^ [_1778181] : [hBOOL(hAPP(hAPP(_1778106, _1778181), _1778181))]], c_Predicate_Osymp(_1778104, _1778106), c_Predicate_Otransp(_1778104, _1778106)], (52735 ^ _779203) ^ [_1837519, _1837521] : [hBOOL(hAPP(hAPP(c_fconj, _1837519), _1837521)), -(hBOOL(_1837521))], (19956 ^ _779203) ^ [_1130953, _1130955, _1130957] : [class_Groups_Oordered__ab__group__add(_1130953), 19959 ^ _779203 : [(19966 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130953), _1130957), hAPP(c_Groups_Ouminus__class_Ouminus(_1130953), _1130955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130953), _1130955), hAPP(c_Groups_Ouminus__class_Ouminus(_1130953), _1130957))))], (19960 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130953), _1130955), hAPP(c_Groups_Ouminus__class_Ouminus(_1130953), _1130957))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130953), _1130957), hAPP(c_Groups_Ouminus__class_Ouminus(_1130953), _1130955))))]]], (52279 ^ _779203) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (47866 ^ _779203) ^ [_1743727, _1743729, _1743731] : [c_List_Olist__all(_1743727, _1743729, _1743731), -(c_List_Olist__all(_1743727, _1743729, hAPP(c_List_Orev(_1743727), _1743731)))], (35864 ^ _779203) ^ [_1451925, _1451927, _1451929, _1451931, _1451933] : [c_Equiv__Relations_Oequiv(_1451925, _1451927, _1451929), 35867 ^ _779203 : [(35878 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1451925, _1451925)), hAPP(hAPP(c_Product__Type_OPair(_1451925, _1451925), _1451931), _1451933)), _1451929))), hAPP(c_Relation_OImage(_1451925, _1451925, _1451929), hAPP(hAPP(c_Set_Oinsert(_1451925), _1451931), c_Orderings_Obot__class_Obot(tc_fun(_1451925, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1451925, _1451925, _1451929), hAPP(hAPP(c_Set_Oinsert(_1451925), _1451933), c_Orderings_Obot__class_Obot(tc_fun(_1451925, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1451925), _1451931), _1451927)), hBOOL(hAPP(hAPP(c_member(_1451925), _1451933), _1451927))], (35868 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1451925, _1451925)), hAPP(hAPP(c_Product__Type_OPair(_1451925, _1451925), _1451931), _1451933)), _1451929)), 35871 ^ _779203 : [(35876 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451925), _1451933), _1451927)))], (35874 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1451925), _1451931), _1451927)))], (35872 ^ _779203) ^ [] : [-(hAPP(c_Relation_OImage(_1451925, _1451925, _1451929), hAPP(hAPP(c_Set_Oinsert(_1451925), _1451931), c_Orderings_Obot__class_Obot(tc_fun(_1451925, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1451925, _1451925, _1451929), hAPP(hAPP(c_Set_Oinsert(_1451925), _1451933), c_Orderings_Obot__class_Obot(tc_fun(_1451925, tc_HOL_Obool)))))]]]]], (9931 ^ _779203) ^ [_948742, _948744, _948746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _948742), _948744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948742), _948746)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _948744), _948746))))], (42938 ^ _779203) ^ [_1635345] : [class_Orderings_Olinorder(_1635345), -(c_List_Olinorder__class_Osorted__list__of__set(_1635345, c_Orderings_Obot__class_Obot(tc_fun(_1635345, tc_HOL_Obool))) = c_List_Olist_ONil(_1635345))], (33511 ^ _779203) ^ [_1392657, _1392659] : [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), _1392657), _1392659))), 33514 ^ _779203 : [(33523 ^ _779203) ^ [] : [-(c_Divides_OposDivAlg(_1392657, _1392659) = hAPP(c_Divides_Oadjust(_1392659), c_Divides_OposDivAlg(_1392657, 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)))), _1392659)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392657), _1392659))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1392659), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (33515 ^ _779203) ^ [] : [33516 ^ _779203 : [(33519 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1392659), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33517 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392657), _1392659))]], -(c_Divides_OposDivAlg(_1392657, _1392659) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392657))]]], (33667 ^ _779203) ^ [_1395537, _1395539] : [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), _1395537), _1395539))), 33670 ^ _779203 : [(33677 ^ _779203) ^ [] : [-(_1395539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1395537, _1395539) = c_Nitpick_Onat__gcd(_1395539, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1395537, _1395539)))], (33671 ^ _779203) ^ [] : [_1395539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1395537, _1395539) = _1395537)]]], (25006 ^ _779203) ^ [_1220017, _1220019, _1220021] : [class_Rings_Olinordered__semidom(_1220017), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220017), c_Groups_Ozero__class_Ozero(_1220017)), _1220019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220017), c_Groups_Ozero__class_Ozero(_1220017)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220017), _1220019), _1220021))))], (9211 ^ _779203) ^ [_936419, _936421] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936419), _936421) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _936421), _936419))], (4398 ^ _779203) ^ [_845954, _845956, _845958, _845960, _845962, _845964] : [-(c_Lazy__Sequence_Oanamorph(_845964, _845960, _845956) = c_Lazy__Sequence_Oanamorph(_845962, _845958, _845954)), _845964 = _845962, _845960 = _845958, _845956 = _845954], (20332 ^ _779203) ^ [_1137869, _1137871] : [class_Rings_Oring__1__no__zero__divisors(_1137869), 20335 ^ _779203 : [(20336 ^ _779203) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137869), _1137871), _1137871) = c_Groups_Oone__class_Oone(_1137869), -(_1137871 = c_Groups_Oone__class_Oone(_1137869)), -(_1137871 = hAPP(c_Groups_Ouminus__class_Ouminus(_1137869), c_Groups_Oone__class_Oone(_1137869)))], (20346 ^ _779203) ^ [] : [20347 ^ _779203 : [(20350 ^ _779203) ^ [] : [_1137871 = hAPP(c_Groups_Ouminus__class_Ouminus(_1137869), c_Groups_Oone__class_Oone(_1137869))], (20348 ^ _779203) ^ [] : [_1137871 = c_Groups_Oone__class_Oone(_1137869)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137869), _1137871), _1137871) = c_Groups_Oone__class_Oone(_1137869))]]], (7119 ^ _779203) ^ [_896793, _896795, _896797] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_896793), _896795)), hBOOL(hAPP(_896797, _896795)), 7130 ^ _779203 : [(7133 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_896793), 7128 ^ [_896793, _896795, _896797]), 7129 ^ [_896793, _896795, _896797])))], (7135 ^ _779203) ^ [] : [-(hBOOL(hAPP(_896797, 7129 ^ [_896793, _896795, _896797])))], (7137 ^ _779203) ^ [] : [hBOOL(hAPP(_896797, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_896793, tc_HOL_Obool)), 7129 ^ [_896793, _896795, _896797]), hAPP(hAPP(c_Set_Oinsert(_896793), 7128 ^ [_896793, _896795, _896797]), c_Orderings_Obot__class_Obot(tc_fun(_896793, tc_HOL_Obool))))))], (7131 ^ _779203) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_896793), 7129 ^ [_896793, _896795, _896797])))]], -(hBOOL(hAPP(_896797, c_Orderings_Obot__class_Obot(tc_fun(_896793, tc_HOL_Obool)))))], (48711 ^ _779203) ^ [_1762378, _1762380, _1762382] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1762378, _1762380, _1762382, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1762380)], (45296 ^ _779203) ^ [_1688303, _1688305, _1688307, _1688309] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1688303)), _1688305), hAPP(c_List_Oset(tc_List_Olist(_1688303)), c_Enum_On__lists(_1688303, _1688307, _1688309)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688303)), _1688305) = _1688307)], (26548 ^ _779203) ^ [_1246379, _1246381, _1246383] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246379)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1246381), _1246383)), 26555 ^ _779203 : [(26556 ^ _779203) ^ [_1246569] : [26558 ^ _779203 : [(26564 ^ _779203) ^ [] : [-(_1246569 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26560 ^ [_1246379, _1246381, _1246383, _1246569]), 26557 ^ [_1246379, _1246381, _1246383, _1246569]))], (26562 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26560 ^ [_1246379, _1246381, _1246383, _1246569]), _1246383)))], (26559 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26557 ^ [_1246379, _1246381, _1246383, _1246569]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1246379))))]], -(_1246569 = _1246381), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1246569), _1246379) = _1246381]]], (49608 ^ _779203) ^ [_1781757, _1781759, _1781761, _1781763] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1781757, _1781759, c_Orderings_Otop__class_Otop(tc_fun(_1781757, tc_HOL_Obool)), _1781761), _1781763) = c_Hilbert__Choice_OEps(_1781757, hAPP(hAPP(c_COMBC(_1781757, _1781759, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1781759, tc_fun(_1781759, tc_HOL_Obool), _1781757), c_fequal), _1781761)), _1781763)))], (19254 ^ _779203) ^ [_1118360, _1118362] : [class_Groups_Oordered__ab__group__add__abs(_1118360), 19257 ^ _779203 : [(19264 ^ _779203) ^ [] : [-(_1118362 = c_Groups_Ozero__class_Ozero(_1118360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118360), c_Groups_Ozero__class_Ozero(_1118360)), hAPP(c_Groups_Oabs__class_Oabs(_1118360), _1118362))))], (19258 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1118360), c_Groups_Ozero__class_Ozero(_1118360)), hAPP(c_Groups_Oabs__class_Oabs(_1118360), _1118362))), _1118362 = c_Groups_Ozero__class_Ozero(_1118360)]]], (38737 ^ _779203) ^ [_1529156, _1529158] : [hBOOL(hAPP(hAPP(c_member(_1529156), 38738 ^ [_1529156, _1529158]), c_Wellfounded_Oacc(_1529156, _1529158))), -(c_Wellfounded_Owf(_1529156, _1529158))], (32401 ^ _779203) ^ [_1366019, _1366021] : [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(_1366021))), 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), _1366019)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1366019)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1366021))))], (15900 ^ _779203) ^ [_1057819, _1057821, _1057823, _1057825] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1057819), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057819), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1057819), _1057821), _1057823)), _1057825) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1057819), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057819), _1057821), _1057825)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1057819), _1057823), _1057825)))], (48276 ^ _779203) ^ [_1752796, _1752798, _1752800, _1752802] : [-(hBOOL(hAPP(_1752796, _1752798))), -(hAPP(c_List_Ofilter(_1752800, _1752796), c_List_Oreplicate(_1752800, _1752802, _1752798)) = c_List_Olist_ONil(_1752800))], (47197 ^ _779203) ^ [_1728746, _1728748, _1728750] : [-(hAPP(c_List_Oset(_1728746), c_List_Oinsert(_1728746, _1728748, _1728750)) = hAPP(hAPP(c_Set_Oinsert(_1728746), _1728748), hAPP(c_List_Oset(_1728746), _1728750)))], (15288 ^ _779203) ^ [_1046818, _1046820, _1046822, _1046824] : [class_Orderings_Olinorder(_1046818), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046818), _1046820), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046818), _1046822), _1046824)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046818), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046818), _1046820), _1046822)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046818), _1046820), _1046824)))], (42049 ^ _779203) ^ [_1614411, _1614413, _1614415] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1614411), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1614413)), _1614415))), -(hBOOL(hAPP(hAPP(c_member(_1614413), hAPP(hAPP(c_List_Onth(_1614413), _1614415), _1614411)), hAPP(c_List_Oset(_1614413), _1614415))))], (15282 ^ _779203) ^ [_1046675, _1046677, _1046679, _1046681] : [class_Orderings_Olinorder(_1046675), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046675), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046675), _1046677), _1046679)), _1046681) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046675), _1046677), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046675), _1046679), _1046681)))], (19027 ^ _779203) ^ [_1114436, _1114438] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1114436)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1114436)), _1114438)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1114436))), _1114438))], (4164 ^ _779203) ^ [_842225, _842227] : [_842227 = _842225, -(c_List_Otake(_842227) = c_List_Otake(_842225))], (38304 ^ _779203) ^ [_1516638, _1516640, _1516642, _1516644, _1516646, _1516648, _1516650] : [-(hAPP(c_Product__Type_Ofst(_1516638, _1516640), hAPP(c_Product__Type_Omap__pair(_1516642, _1516638, _1516644, _1516640, _1516646, _1516648), _1516650)) = hAPP(_1516646, hAPP(c_Product__Type_Ofst(_1516642, _1516644), _1516650)))], (8699 ^ _779203) ^ [_925798, _925800, _925802, _925804] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_925798), 8702 ^ _779203 : [(8709 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925798), _925800), _925804)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925798), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925798), _925800), _925802)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925798), _925804), _925802))))], (8703 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925798), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925798), _925800), _925802)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_925798), _925804), _925802))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925798), _925800), _925804)))]]], (42742 ^ _779203) ^ [_1631090, _1631092, _1631094] : [-(hAPP(hAPP(c_List_Olist__update(_1631090, c_List_Olist_ONil(_1631090)), _1631092), _1631094) = c_List_Olist_ONil(_1631090))], (18508 ^ _779203) ^ [_1105667, _1105669] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1105667), _1105669), hAPP(c_Int_Onumber__class_Onumber__of(_1105667), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1105667)), class_Fields_Ofield__inverse__zero(_1105667), class_Int_Onumber__ring(_1105667)], (278 ^ _779203) ^ [_783486, _783488] : [-(class_Fields_Ofield(_783486)), _783488 = _783486, class_Fields_Ofield(_783488)], (48460 ^ _779203) ^ [_1756559, _1756561, _1756563, _1756565, _1756567] : [48462 ^ _779203 : [(48465 ^ _779203) ^ [] : [c_Relation_Orefl__on(_1756563, hAPP(_1756565, 48461 ^ [_1756559, _1756561, _1756563, _1756565, _1756567]), hAPP(_1756567, 48461 ^ [_1756559, _1756561, _1756563, _1756565, _1756567]))], (48463 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1756559), 48461 ^ [_1756559, _1756561, _1756563, _1756565, _1756567]), _1756561)))]], -(c_Relation_Orefl__on(_1756563, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1756559, tc_fun(_1756563, tc_HOL_Obool)), _1756561), _1756565), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1756559, tc_fun(tc_prod(_1756563, _1756563), tc_HOL_Obool)), _1756561), _1756567)))], (30589 ^ _779203) ^ [_1325378, _1325380] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1325378, tc_HOL_Obool), hAPP(c_Set_OPow(_1325378), _1325380)) = _1325380)], (35992 ^ _779203) ^ [_1455243, _1455245] : [-(c_Equiv__Relations_Oequivp(_1455243, _1455245)), 35997 ^ _779203 : [(36000 ^ _779203) ^ [] : [hAPP(_1455245, 35993 ^ [_1455243, _1455245]) = hAPP(_1455245, 35994 ^ [_1455243, _1455245])], (35998 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(_1455245, 35993 ^ [_1455243, _1455245]), 35994 ^ [_1455243, _1455245])))]], 36001 ^ _779203 : [(36004 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(_1455245, 35993 ^ [_1455243, _1455245]), 35994 ^ [_1455243, _1455245]))], (36002 ^ _779203) ^ [] : [-(hAPP(_1455245, 35993 ^ [_1455243, _1455245]) = hAPP(_1455245, 35994 ^ [_1455243, _1455245]))]]], (44161 ^ _779203) ^ [_1662923, _1662925] : [-(_1662923 = c_List_Olist_ONil(_1662925)), -(c_List_Olast(_1662925, _1662923) = hAPP(hAPP(c_List_Onth(_1662925), _1662923), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662925)), _1662923)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (33605 ^ _779203) ^ [_1394289, _1394291, _1394293] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1394289, _1394291), _1394293)), 33608 ^ _779203 : [(33609 ^ _779203) ^ [_1394374] : [hBOOL(hAPP(hAPP(_1394291, _1394374), _1394293)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1394289, _1394291), _1394374)))]]], (47274 ^ _779203) ^ [_1730838, _1730840, _1730842, _1730844, _1730846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1730838, _1730840)), hAPP(_1730838, _1730842))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730844, _1730844)), hAPP(hAPP(c_Product__Type_OPair(_1730844, _1730844), _1730840), _1730842)), c_List_Omeasures(_1730844, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1730844, tc_Nat_Onat)), _1730838), _1730846)))))], (14862 ^ _779203) ^ [_1038489, _1038491, _1038493, _1038495, _1038497] : [class_Groups_Ocomm__monoid__mult(_1038489), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038491), _1038493)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1038491, tc_HOL_Obool)), _1038495), _1038493)), 14876 ^ _779203 : [(14879 ^ _779203) ^ [] : [hAPP(_1038497, 14875 ^ [_1038489, _1038491, _1038493, _1038495, _1038497]) = c_Groups_Oone__class_Oone(_1038489)], (14877 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1038491), 14875 ^ [_1038489, _1038491, _1038493, _1038495, _1038497]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1038491, tc_HOL_Obool)), _1038493), _1038495))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038491, _1038489), _1038497), _1038495) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1038491, _1038489), _1038497), _1038493))], (14079 ^ _779203) ^ [_1024178, _1024180, _1024182] : [class_Fields_Olinordered__field(_1024178), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024178), c_Groups_Ozero__class_Ozero(_1024178)), _1024180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024178), c_Groups_Ozero__class_Ozero(_1024178)), _1024182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1024178), c_Groups_Ozero__class_Ozero(_1024178)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1024178), _1024180), _1024182))))], (31259 ^ _779203) ^ [_1338877, _1338879, _1338881, _1338883, _1338885] : [class_Groups_Ocomm__monoid__mult(_1338877), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338879), _1338881)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1338879), _1338883)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1338877), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1338877, _1338879, c_Groups_Otimes__class_Otimes(_1338877)), _1338885), c_Groups_Oone__class_Oone(_1338877)), _1338881)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1338877, _1338879, c_Groups_Otimes__class_Otimes(_1338877)), _1338885), c_Groups_Oone__class_Oone(_1338877)), _1338883)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1338877), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1338877, _1338879, c_Groups_Otimes__class_Otimes(_1338877)), _1338885), c_Groups_Oone__class_Oone(_1338877)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1338879, tc_HOL_Obool)), _1338881), _1338883))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1338877, _1338879, c_Groups_Otimes__class_Otimes(_1338877)), _1338885), c_Groups_Oone__class_Oone(_1338877)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1338879, tc_HOL_Obool)), _1338881), _1338883))))], (2150 ^ _779203) ^ [_810328, _810330, _810332, _810334, _810336, _810338, _810340, _810342, _810344, _810346] : [-(c_Nitpick_Opair__box_Opair__box__size(_810346, _810342, _810338, _810334, _810330) = c_Nitpick_Opair__box_Opair__box__size(_810344, _810340, _810336, _810332, _810328)), _810346 = _810344, _810342 = _810340, _810338 = _810336, _810334 = _810332, _810330 = _810328], (35085 ^ _779203) ^ [_1431784, _1431786, _1431788] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1431784, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1431786)), _1431788) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1431784, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1431784, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1431786)), _1431788)), hAPP(_1431788, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45514 ^ _779203) ^ [_1692578] : [-(c_List_Oconcat(_1692578, c_List_Olist_ONil(tc_List_Olist(_1692578))) = c_List_Olist_ONil(_1692578))], (15294 ^ _779203) ^ [_1046977, _1046979, _1046981, _1046983] : [class_Orderings_Olinorder(_1046977), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046977), _1046979), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046977), _1046981), _1046983)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1046977), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046977), _1046979), _1046981)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1046977), _1046979), _1046983)))], (39556 ^ _779203) ^ [_1549085, _1549087, _1549089, _1549091, _1549093, _1549095, _1549097, _1549099, _1549101, _1549103] : [-(c_Product__Type_Omap__pair(_1549085, _1549087, _1549089, _1549091, hAPP(c_Fun_Ocomp(_1549093, _1549087, _1549085, _1549095), _1549097), hAPP(c_Fun_Ocomp(_1549099, _1549091, _1549089, _1549101), _1549103)) = hAPP(c_Fun_Ocomp(tc_prod(_1549093, _1549099), tc_prod(_1549087, _1549091), tc_prod(_1549085, _1549089), c_Product__Type_Omap__pair(_1549093, _1549087, _1549099, _1549091, _1549095, _1549101)), c_Product__Type_Omap__pair(_1549085, _1549093, _1549089, _1549099, _1549097, _1549103)))], (41264 ^ _779203) ^ [_1591952, _1591954, _1591956] : [-(c_Nitpick_Otimes__frac(_1591952, _1591954, _1591956) = hAPP(hAPP(c_Nitpick_Ofrac(_1591952), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1591952), _1591954)), hAPP(c_Nitpick_Onum(_1591952), _1591956))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1591952), _1591954)), hAPP(c_Nitpick_Odenom(_1591952), _1591956))))], (46387 ^ _779203) ^ [_1711781, _1711783, _1711785] : [class_Orderings_Olinorder(_1711781), 46390 ^ _779203 : [(46403 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711781, hAPP(hAPP(c_List_Olist_OCons(_1711781), _1711783), _1711785))), 46407 ^ _779203 : [(46410 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711781), _1711783), 46406 ^ [_1711781, _1711783, _1711785]))], (46408 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1711781), 46406 ^ [_1711781, _1711783, _1711785]), hAPP(c_List_Oset(_1711781), _1711785))))]], c_List_Olinorder__class_Osorted(_1711781, _1711785)], (46391 ^ _779203) ^ [] : [c_List_Olinorder__class_Osorted(_1711781, hAPP(hAPP(c_List_Olist_OCons(_1711781), _1711783), _1711785)), 46394 ^ _779203 : [(46395 ^ _779203) ^ [_1711949] : [hBOOL(hAPP(hAPP(c_member(_1711781), _1711949), hAPP(c_List_Oset(_1711781), _1711785))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1711781), _1711783), _1711949)))], (46401 ^ _779203) ^ [] : [-(c_List_Olinorder__class_Osorted(_1711781, _1711785))]]]]], (27118 ^ _779203) ^ [_1256695, _1256697, _1256699] : [class_Orderings_Oorder(_1256695), 27121 ^ _779203 : [(27128 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256695), _1256697), _1256699))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256695, _1256697), _1256699) = c_Orderings_Obot__class_Obot(tc_fun(_1256695, tc_HOL_Obool)))], (27122 ^ _779203) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1256695, _1256697), _1256699) = c_Orderings_Obot__class_Obot(tc_fun(_1256695, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256695), _1256697), _1256699))]]], (8378 ^ _779203) ^ [_919162, _919164, _919166, _919168, _919170, _919172] : [c_Finite__Set_Ofun__left__comm(_919162, _919164, _919166), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_919162, _919164, _919166, _919168, _919170), _919172)), -(hAPP(hAPP(c_Finite__Set_Ofold(_919162, _919164, _919166), _919168), _919170) = _919172)], (22936 ^ _779203) ^ [_1183140, _1183142] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1183140)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1183140), _1183142)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1183140, _1183142) = _1183140)], (11173 ^ _779203) ^ [_971437, _971439, _971441] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_971437), _971439)), 11176 ^ _779203 : [(11177 ^ _779203) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_971437, tc_Nat_Onat), _971441), _971439) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 11180 ^ _779203 : [(11181 ^ _779203) ^ [_971599] : [hBOOL(hAPP(hAPP(c_member(_971437), _971599), _971439)), -(hAPP(_971441, _971599) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (11187 ^ _779203) ^ [] : [11189 ^ _779203 : [(11192 ^ _779203) ^ [] : [hAPP(_971441, 11188 ^ [_971437, _971439, _971441]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (11190 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_971437), 11188 ^ [_971437, _971439, _971441]), _971439)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_971437, tc_Nat_Onat), _971441), _971439) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (45742 ^ _779203) ^ [_1698316, _1698318, _1698320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1698316), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1698318))), c_List_Otranspose(_1698318, _1698320)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1698318)), c_List_Otranspose(_1698318, _1698320)), _1698316) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1698318), _1698318), hAPP(hAPP(c_COMBC(tc_List_Olist(_1698318), tc_Nat_Onat, _1698318), c_List_Onth(_1698318)), _1698316)), hAPP(c_List_Ofilter(tc_List_Olist(_1698318), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1698318)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1698316)), c_Nat_Osize__class_Osize(tc_List_Olist(_1698318)))), _1698320)))], (6413 ^ _779203) ^ [_882788, _882790, _882792] : [class_Orderings_Olinorder(_882788), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882788), _882790), _882792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882788), _882792), _882790)))], (41753 ^ _779203) ^ [_1606911, _1606913, _1606915] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606911)), _1606913), c_Wellfounded_Oacc(tc_List_Olist(_1606911), c_List_Olistrel1(_1606911, _1606915)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1606911)), _1606913), c_List_Olists(_1606911, c_Wellfounded_Oacc(_1606911, _1606915)))))], (43740 ^ _779203) ^ [_1654202, _1654204, _1654206] : [-(hAPP(c_List_Otl(_1654202), hAPP(hAPP(c_List_Odrop(_1654202), _1654204), _1654206)) = hAPP(hAPP(c_List_Odrop(_1654202), _1654204), hAPP(c_List_Otl(_1654202), _1654206)))], (25484 ^ _779203) ^ [_1228399, _1228401] : [c_Nat__Transfer_Ois__nat(_1228399), c_Nat__Transfer_Ois__nat(_1228401), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1228399, _1228401)))], (20262 ^ _779203) ^ [_1136602, _1136604] : [class_Groups_Oab__group__add(_1136602), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1136602), hAPP(c_Groups_Ouminus__class_Ouminus(_1136602), _1136604)), _1136604) = c_Groups_Ozero__class_Ozero(_1136602))], (8060 ^ _779203) ^ [_912564, _912566, _912568, _912570, _912572] : [class_Groups_Oab__group__add(_912564), hBOOL(hAPP(c_Finite__Set_Ofinite(_912566), _912568)), 8067 ^ _779203 : [(8074 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912566), _912570), _912568))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_912566, _912564), _912572), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912566, tc_HOL_Obool)), _912568), hAPP(hAPP(c_Set_Oinsert(_912566), _912570), c_Orderings_Obot__class_Obot(tc_fun(_912566, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_912566, _912564), _912572), _912568))], (8068 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_member(_912566), _912570), _912568)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_912566, _912564), _912572), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912566, tc_HOL_Obool)), _912568), hAPP(hAPP(c_Set_Oinsert(_912566), _912570), c_Orderings_Obot__class_Obot(tc_fun(_912566, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_912564), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_912566, _912564), _912572), _912568)), hAPP(_912572, _912570)))]]], (20624 ^ _779203) ^ [_1142965] : [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, _1142965)))))], (21841 ^ _779203) ^ [_1163728, _1163730] : [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), _1163728))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1163730)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1163728))) = 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), _1163730), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1163728)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (52637 ^ _779203) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (10307 ^ _779203) ^ [_956485, _956487, _956489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _956485), _956487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _956489), _956485)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956485), _956489)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _956487), _956489))))], (40105 ^ _779203) ^ [_1562078, _1562080, _1562082, _1562084, _1562086, _1562088, _1562090] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1562078, _1562080, _1562082, _1562084), _1562086), _1562088), _1562090) = hAPP(hAPP(_1562088, hAPP(c_Product__Type_Ofst(_1562080, _1562082), hAPP(_1562086, _1562090))), hAPP(c_Product__Type_Osnd(_1562080, _1562082), hAPP(_1562086, _1562090))))], (18064 ^ _779203) ^ [_1097934, _1097936] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1097934), _1097936))), -(c_Nat__Transfer_Otsub(_1097936, _1097934) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48160 ^ _779203) ^ [_1750638, _1750640, _1750642, _1750644] : [-(hAPP(hAPP(c_List_Omap(_1750638, _1750640), hAPP(c_COMBK(_1750640, _1750638), _1750642)), _1750644) = c_List_Oreplicate(_1750640, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750638)), _1750644), _1750642))], (50569 ^ _779203) ^ [_1803787] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1803787)))], (27356 ^ _779203) ^ [_1261022, _1261024, _1261026, _1261028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261022, tc_HOL_Obool)), _1261024), _1261026)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261022, tc_HOL_Obool)), _1261028), _1261026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1261022, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261022, tc_HOL_Obool)), _1261024), _1261028)), _1261026)))], (27824 ^ _779203) ^ [_1269823, _1269825] : [class_Lattices_Obounded__lattice__top(_1269823), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1269823), c_Orderings_Otop__class_Otop(_1269823)), _1269825) = c_Orderings_Otop__class_Otop(_1269823))], (31699 ^ _779203) ^ [_1348400, _1348402, _1348404, _1348406] : [class_Groups_Oordered__ab__group__add__abs(_1348400), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348400), c_Groups_Ozero__class_Ozero(_1348400)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1348402, _1348400), hAPP(hAPP(c_COMBB(_1348400, _1348400, _1348402), c_Groups_Oabs__class_Oabs(_1348400)), _1348404)), _1348406))))], (3148 ^ _779203) ^ [_825981, _825983, _825985, _825987, _825989, _825991] : [-(c_Big__Operators_Olattice_OSup__fin(_825991, _825987, _825983) = c_Big__Operators_Olattice_OSup__fin(_825989, _825985, _825981)), _825991 = _825989, _825987 = _825985, _825983 = _825981], (22802 ^ _779203) ^ [_1180977, _1180979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180977)), 22805 ^ _779203 : [(22812 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180979), _1180977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1180979)), hAPP(c_Int_Onat, _1180977))))], (22806 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1180979)), hAPP(c_Int_Onat, _1180977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180979), _1180977)))]]], (43792 ^ _779203) ^ [_1655244, _1655246, _1655248] : [-(_1655244 = c_List_Olist_ONil(_1655246)), -(hAPP(c_List_Otl(_1655246), hAPP(hAPP(c_List_Oappend(_1655246), _1655244), _1655248)) = hAPP(hAPP(c_List_Oappend(_1655246), hAPP(c_List_Otl(_1655246), _1655244)), _1655248))], (37092 ^ _779203) ^ [_1479066, _1479068] : [-(c_Nitpick_Onumber__of__frac(_1479066, _1479068) = c_Nitpick_OAbs__Frac(_1479066, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1479068), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (37239 ^ _779203) ^ [_1482663, _1482665, _1482667, _1482669] : [-(hAPP(c_Set_Ovimage(_1482663, _1482665, _1482667), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1482665, tc_HOL_Obool), _1482669)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1482665, tc_HOL_Obool), tc_fun(_1482663, tc_HOL_Obool)), _1482669), c_Set_Ovimage(_1482663, _1482665, _1482667)))], (28176 ^ _779203) ^ [_1277119, _1277121] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1277119)), _1277121) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1277119, _1277121))], (44732 ^ _779203) ^ [_1675418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1675418)), _1675418 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18166 ^ _779203) ^ [_1099793, _1099795, _1099797] : [class_Nat_Osemiring__char__0(_1099793), 18169 ^ _779203 : [(18176 ^ _779203) ^ [] : [_1099795 = _1099797, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1099793), _1099795) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1099793), _1099797))], (18170 ^ _779203) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1099793), _1099795) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1099793), _1099797), -(_1099795 = _1099797)]]], (50991 ^ _779203) ^ [_1811591, _1811593] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1811591), _1811593)), -(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)))), _1811593, _1811591) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (47262 ^ _779203) ^ [_1730515, _1730517, _1730519, _1730521, _1730523] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730515, _1730515)), hAPP(hAPP(c_Product__Type_OPair(_1730515, _1730515), _1730517), _1730519)), c_List_Omeasures(_1730515, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1730515, tc_Nat_Onat)), _1730521), _1730523))))), 47263 ^ _779203 : [(47266 ^ _779203) ^ [] : [hAPP(_1730521, _1730517) = hAPP(_1730521, _1730519), hBOOL(hAPP(hAPP(c_member(tc_prod(_1730515, _1730515)), hAPP(hAPP(c_Product__Type_OPair(_1730515, _1730515), _1730517), _1730519)), c_List_Omeasures(_1730515, _1730523)))], (47264 ^ _779203) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1730521, _1730517)), hAPP(_1730521, _1730519)))]]], (26620 ^ _779203) ^ [_1247751, _1247753, _1247755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247751)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1247753), _1247755)), 26627 ^ _779203 : [(26628 ^ _779203) ^ [_1247947] : [26630 ^ _779203 : [(26636 ^ _779203) ^ [] : [-(_1247947 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 26632 ^ [_1247751, _1247753, _1247755, _1247947]), 26629 ^ [_1247751, _1247753, _1247755, _1247947]))], (26634 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26632 ^ [_1247751, _1247753, _1247755, _1247947]), _1247755)))], (26631 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 26629 ^ [_1247751, _1247753, _1247755, _1247947]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1247751))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247947), _1247753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1247947), _1247751)), _1247753)))]]], (6895 ^ _779203) ^ [_891851, _891853, _891855, _891857] : [-(hBOOL(hAPP(hAPP(c_member(_891851), _891853), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_891851, tc_HOL_Obool)), _891855), _891857)))), hBOOL(hAPP(hAPP(c_member(_891851), _891853), _891855)), -(hBOOL(hAPP(hAPP(c_member(_891851), _891853), _891857)))], (49566 ^ _779203) ^ [_1780762, _1780764, _1780766] : [c_Fun_Oinj__on(_1780762, _1780764, _1780766, c_Orderings_Otop__class_Otop(tc_fun(_1780762, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1780764, _1780762, _1780762, c_Hilbert__Choice_Oinv__into(_1780762, _1780764, c_Orderings_Otop__class_Otop(tc_fun(_1780762, tc_HOL_Obool)), _1780766)), _1780766) = c_Fun_Oid(_1780762))], (43842 ^ _779203) ^ [_1656249, _1656251, _1656253, _1656255] : [43843 ^ _779203 : [(43844 ^ _779203) ^ [_1656346, _1656348] : [_1656249 = hAPP(hAPP(c_List_Olist_OCons(_1656251), _1656348), _1656346)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1656251), tc_List_Olist(_1656251))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1656251), tc_List_Olist(_1656251)), _1656253), hAPP(hAPP(c_List_Oappend(_1656251), _1656253), _1656249))), c_List_Olexord(_1656251, _1656255))))], (6261 ^ _779203) ^ [_879942, _879944] : [v_wt(_879942), 6267 ^ _779203 : [(6270 ^ _779203) ^ [] : [v_P(_879944, hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, 6266 ^ [_879942, _879944])), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))))], (6268 ^ _779203) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), 6266 ^ [_879942, _879944]), v_U)))]], -(v_P(_879944, hAPP(hAPP(c_Set_Oinsert(t_a), v_mgt(_879942)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))))], (39748 ^ _779203) ^ [_1553615, _1553617, _1553619, _1553621, _1553623, _1553625, _1553627] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1553615, _1553617, _1553619), hAPP(c_Fun_Ocomp(_1553621, tc_fun(_1553617, _1553619), _1553615, _1553623), _1553625)), _1553627) = hAPP(hAPP(_1553623, hAPP(_1553625, hAPP(c_Product__Type_Ofst(_1553615, _1553617), _1553627))), hAPP(c_Product__Type_Osnd(_1553615, _1553617), _1553627)))], (23693 ^ _779203) ^ [_1196280, _1196282, _1196284] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1196280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1196282), _1196284)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1196280), _1196282)), _1196284))]], input).
% 69.25/66.92  ncf('1',plain,[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))],start(52791 ^ 0)).
% 69.25/66.92  ncf('1.1',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(t_a), hAPP(v_mgt__call, v_pn)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)))), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))), hBOOL(hAPP(hAPP(c_member(t_a), hAPP(v_mgt__call, v_pn)), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))],extension(6245 ^ 1,bind([[_879586, _879588, _879590, _879592], [t_a, hAPP(v_mgt__call, v_pn), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)]]))).
% 69.25/66.92  ncf('1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(t_a), hAPP(v_mgt__call, v_pn)), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)))), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pn), v_U))],extension(6025 ^ 2,bind([[_874892, _874894, _874896, _874898, _874900], [tc_Com_Opname, v_pn, v_U, t_a, v_mgt__call]]))).
% 69.25/66.92  ncf('1.1.1.1',plain,[-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), v_pn), v_U)))],extension(52789 ^ 3)).
% 69.25/66.92  ncf('1.1.2',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(t_a, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(t_a, tc_HOL_Obool))), hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U))))],extension(5667 ^ 2,bind([[_868610, _868612], [t_a, hAPP(c_Set_Oimage(tc_Com_Opname, t_a, v_mgt__call), v_U)]]))).
% 69.25/66.92  %-----------------------------------------------------
% 69.25/66.92  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------