TSTP Solution File: SWW387+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW387+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n031.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 12:26:05 EDT 2023

% Result   : Theorem 45.28s 44.00s
% Output   : Proof 45.35s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWW387+1 : TPTP v8.1.2. Released v5.2.0.
% 0.13/0.13  % Command  : nanocop.sh %s %d
% 0.14/0.34  % Computer : n031.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu May 18 22:43:10 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 45.28/44.00  
% 45.28/44.00  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 45.28/44.00  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 45.28/44.00  %-----------------------------------------------------
% 45.28/44.00  ncf(matrix, plain, [(51474 ^ _2056764) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, v_pn))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))], !, (18215 ^ _777959) ^ [_1125870, _1125872, _1125874] : [class_Orderings_Olinorder(_1125870), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125870), _1125872)), -(hBOOL(hAPP(hAPP(c_member(_1125870), _1125874), _1125872))), -(c_Big__Operators_Olattice_OSup__fin(_1125870, c_Orderings_Oord__class_Omax(_1125870), hAPP(hAPP(c_Set_Oinsert(_1125870), _1125874), _1125872)) = hAPP(hAPP(c_Finite__Set_Ofold(_1125870, _1125870, c_Orderings_Oord__class_Omax(_1125870)), _1125874), _1125872))], (2414 ^ _777959) ^ [_813689, _813691] : [_813691 = _813689, -(c_Int_Opred(_813691) = c_Int_Opred(_813689))], (42212 ^ _777959) ^ [_1610008, _1610010, _1610012, _1610014] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1610008, _1610010)), hAPP(hAPP(c_Product__Type_OSigma(_1610008, _1610010), hAPP(hAPP(c_Set_Oinsert(_1610008), _1610012), c_Orderings_Obot__class_Obot(tc_fun(_1610008, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1610010, tc_HOL_Obool), _1610008), _1610014))) = hAPP(c_Finite__Set_Ocard(_1610010), _1610014))], (38172 ^ _777959) ^ [_1509225, _1509227, _1509229, _1509231] : [-(_1509225 = c_Orderings_Obot__class_Obot(tc_fun(_1509227, tc_HOL_Obool))), 38175 ^ _777959 : [(38176 ^ _777959) ^ [] : [-(hAPP(c_Set_Oimage(_1509229, _1509227, 38183 ^ [_1509225, _1509227, _1509229, _1509231]), _1509231) = _1509225), 38177 ^ _777959 : [(38178 ^ _777959) ^ [_1509366] : [c_Fun_Oinj__on(_1509227, _1509229, _1509366, _1509225), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509229, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1509227, _1509229, _1509366), _1509225)), _1509231))]]], (38187 ^ _777959) ^ [] : [38188 ^ _777959 : [(38189 ^ _777959) ^ [_1509558] : [hAPP(c_Set_Oimage(_1509229, _1509227, _1509558), _1509231) = _1509225]], 38191 ^ _777959 : [(38194 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509229, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1509227, _1509229, 38190 ^ [_1509225, _1509227, _1509229, _1509231]), _1509225)), _1509231)))], (38192 ^ _777959) ^ [] : [-(c_Fun_Oinj__on(_1509227, _1509229, 38190 ^ [_1509225, _1509227, _1509229, _1509231], _1509225))]]]]], (50470 ^ _777959) ^ [_1801633, _1801635, _1801637, _1801639, _1801641] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1801633, _1801635, hAPP(hAPP(c_COMBC(_1801633, tc_fun(tc_prod(_1801633, _1801635), tc_HOL_Obool), tc_fun(_1801635, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1801635, tc_fun(tc_fun(tc_prod(_1801633, _1801635), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1801633, _1801635), tc_HOL_Obool), tc_fun(_1801635, tc_HOL_Obool)), _1801633), c_COMBC(_1801635, tc_fun(tc_prod(_1801633, _1801635), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1801635, tc_prod(_1801633, _1801635)), tc_fun(_1801635, tc_fun(tc_fun(tc_prod(_1801633, _1801635), tc_HOL_Obool), tc_HOL_Obool)), _1801633), hAPP(c_COMBB(tc_prod(_1801633, _1801635), tc_fun(tc_fun(tc_prod(_1801633, _1801635), tc_HOL_Obool), tc_HOL_Obool), _1801635), c_member(tc_prod(_1801633, _1801635)))), c_Product__Type_OPair(_1801633, _1801635)))), _1801637)), _1801639), _1801641)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1801635, _1801633)), hAPP(hAPP(c_Product__Type_OPair(_1801635, _1801633), _1801639), _1801641)), hAPP(c_Relation_Oconverse(_1801633, _1801635), _1801637))))], (16809 ^ _777959) ^ [_1099860, _1099862, _1099864, _1099866] : [class_Orderings_Olinorder(_1099860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099860), _1099862), _1099864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099860), _1099862), _1099866)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099860), _1099862), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099860), _1099864), _1099866))))], (43576 ^ _777959) ^ [_1644065, _1644067, _1644069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644065)), _1644067)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1644065, _1644069), _1644067) = _1644067)], (36670 ^ _777959) ^ [_1473589, _1473591, _1473593, _1473595] : [-(hAPP(c_Product__Type_Ofst(_1473589, _1473591), hAPP(hAPP(c_Product__Type_OPair(_1473589, _1473591), _1473593), _1473595)) = _1473593)], (9990 ^ _777959) ^ [_951580, _951582, _951584] : [class_Lattices_Olattice(_951580), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_951580), _951582), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951580), _951582), _951584)) = _951582)], (38756 ^ _777959) ^ [_1521965, _1521967, _1521969, _1521971] : [-(hAPP(c_Set_Ovimage(_1521965, _1521967, _1521969), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1521967, tc_HOL_Obool)), _1521971)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1521965, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1521965, _1521967, _1521969), _1521971)))], (50828 ^ _777959) ^ [_1808346, _1808348] : [class_Orderings_Obot(_1808346), -(class_Orderings_Obot(tc_fun(_1808348, _1808346)))], (38692 ^ _777959) ^ [_1520510, _1520512, _1520514] : [c_Fun_Oinj__on(tc_List_Olist(_1520510), tc_List_Olist(_1520512), hAPP(c_List_Omap(_1520510, _1520512), _1520514), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1520510), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1520510, _1520512, _1520514, c_Orderings_Otop__class_Otop(tc_fun(_1520510, tc_HOL_Obool))))], (29709 ^ _777959) ^ [_1338459, _1338461, _1338463] : [hAPP(c_Set_Oimage(_1338461, tc_fun(_1338461, tc_HOL_Obool), _1338459), _1338463) = hAPP(c_Set_OPow(_1338461), _1338463)], (10767 ^ _777959) ^ [_969039, _969041, _969043, _969045] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_969039), _969041)), 10770 ^ _777959 : [(10771 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_969043), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_969039, tc_fun(_969043, tc_HOL_Obool)), _969041), _969045))), 10774 ^ _777959 : [(10775 ^ _777959) ^ [_969223] : [hBOOL(hAPP(hAPP(c_member(_969039), _969223), _969041)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_969043), hAPP(_969045, _969223))))]]], (10781 ^ _777959) ^ [] : [10783 ^ _777959 : [(10786 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_969043), hAPP(_969045, 10782 ^ [_969039, _969041, _969043, _969045])))], (10784 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_969039), 10782 ^ [_969039, _969041, _969043, _969045]), _969041)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_969043), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_969039, tc_fun(_969043, tc_HOL_Obool)), _969041), _969045))))]]], (22052 ^ _777959) ^ [_1197468, _1197470, _1197472, _1197474, _1197476] : [class_Groups_Ocomm__monoid__mult(_1197468), hBOOL(hAPP(c_Finite__Set_Ofinite(_1197470), _1197472)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1197470), _1197474)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1197470, tc_HOL_Obool)), _1197472), _1197474) = c_Orderings_Obot__class_Obot(tc_fun(_1197470, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1197470, _1197468), _1197476), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1197470, tc_HOL_Obool)), _1197472), _1197474)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197468), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1197470, _1197468), _1197476), _1197472)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1197470, _1197468), _1197476), _1197474)))], (34521 ^ _777959) ^ [_1427716] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1427716)), 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, _1427716, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (21121 ^ _777959) ^ [_1179189, _1179191] : [_1179189 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1179189), _1179191), -(_1179191 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1179189 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3960 ^ _777959) ^ [_837946, _837948, _837950, _837952] : [-(c_Random_Oselect__weight(_837952, _837948) = c_Random_Oselect__weight(_837950, _837946)), _837952 = _837950, _837948 = _837946], (42036 ^ _777959) ^ [_1606324, _1606326, _1606328, _1606330] : [_1606330 = c_List_Olist_ONil(_1606324), -(hAPP(hAPP(c_List_Omap(_1606324, _1606326), _1606328), _1606330) = c_List_Olist_ONil(_1606326))], (22820 ^ _777959) ^ [_1213274, _1213276] : [class_Rings_Ocomm__semiring__1(_1213274), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1213274), _1213276), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1213274))], (19114 ^ _777959) ^ [_1145302, _1145304, _1145306] : [-(c_Nat_Onat_Onat__case(_1145302, _1145304, _1145306, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1145304)], (50567 ^ _777959) ^ [_1803811, _1803813, _1803815, _1803817] : [50574 ^ _777959 : [(50577 ^ _777959) ^ [] : [_1803813 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50575 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1803817, _1803815)))]], 50568 ^ _777959 : [(50569 ^ _777959) ^ [_1803883] : [hBOOL(hAPP(hAPP(c_member(_1803811), _1803883), hAPP(c_List_Oset(_1803811), c_List_Oreplicate(_1803811, _1803813, _1803815)))), hBOOL(hAPP(_1803817, _1803883))]]], (17267 ^ _777959) ^ [_1108108, _1108110, _1108112, _1108114] : [class_Orderings_Olinorder(_1108108), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108108), _1108110)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1108108, _1108108, c_Orderings_Oord__class_Omax(_1108108)), _1108112), hAPP(hAPP(c_Set_Oinsert(_1108108), _1108114), _1108110)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1108108), _1108114), hAPP(hAPP(c_Finite__Set_Ofold(_1108108, _1108108, c_Orderings_Oord__class_Omax(_1108108)), _1108112), _1108110)))], (50770 ^ _777959) ^ [_1807585, _1807587] : [class_Lattices_Olattice(_1807585), -(class_Lattices_Osemilattice__inf(tc_fun(_1807587, _1807585)))], (7916 ^ _777959) ^ [_912761, _912763, _912765, _912767] : [-(hBOOL(hAPP(hAPP(c_member(_912761), _912763), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912761, tc_HOL_Obool)), _912765), _912767)))), hBOOL(hAPP(hAPP(c_member(_912761), _912763), _912765)), -(hBOOL(hAPP(hAPP(c_member(_912761), _912763), _912767)))], (15727 ^ _777959) ^ [_1077171, _1077173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077171), _1077173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077171)), _1077173)))], (10394 ^ _777959) ^ [_961365, _961367, _961369, _961371, _961373, _961375] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_961365, tc_Option_Ooption(_961367)), c_Map_Orestrict__map(_961365, _961367, _961369, _961371)), _961373), _961375) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_961365, tc_Option_Ooption(_961367)), c_Map_Orestrict__map(_961365, _961367, _961369, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_961365, tc_HOL_Obool)), _961371), hAPP(hAPP(c_Set_Oinsert(_961365), _961373), c_Orderings_Obot__class_Obot(tc_fun(_961365, tc_HOL_Obool)))))), _961373), _961375))], (51356 ^ _777959) ^ [_1813620] : [-(class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(_1813620)))], (8286 ^ _777959) ^ [_921009, _921011, _921013] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_921009), _921011)), hBOOL(hAPP(_921013, _921011)), 8297 ^ _777959 : [(8300 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_921009), 8295 ^ [_921009, _921011, _921013]), 8296 ^ [_921009, _921011, _921013])))], (8302 ^ _777959) ^ [] : [-(hBOOL(hAPP(_921013, 8296 ^ [_921009, _921011, _921013])))], (8304 ^ _777959) ^ [] : [hBOOL(hAPP(_921013, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921009, tc_HOL_Obool)), 8296 ^ [_921009, _921011, _921013]), hAPP(hAPP(c_Set_Oinsert(_921009), 8295 ^ [_921009, _921011, _921013]), c_Orderings_Obot__class_Obot(tc_fun(_921009, tc_HOL_Obool))))))], (8298 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_921009), 8296 ^ [_921009, _921011, _921013])))]], -(hBOOL(hAPP(_921013, c_Orderings_Obot__class_Obot(tc_fun(_921009, tc_HOL_Obool)))))], (27784 ^ _777959) ^ [_1302857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302857)), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onat, _1302857)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1302857)))], (42798 ^ _777959) ^ [_1625884, _1625886, _1625888, _1625890] : [hAPP(hAPP(c_List_Oappend(_1625884), _1625886), _1625888) = hAPP(hAPP(c_List_Oappend(_1625884), _1625886), _1625890), -(_1625888 = _1625890)], (12996 ^ _777959) ^ [_1014422, _1014424, _1014426] : [class_Groups_Ogroup__add(_1014422), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014422), _1014424), _1014426) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014422), _1014424), hAPP(c_Groups_Ouminus__class_Ouminus(_1014422), _1014426)))], (41481 ^ _777959) ^ [_1591144, _1591146, _1591148] : [hAPP(hAPP(c_List_Olist_OCons(_1591144), _1591146), _1591148) = _1591148], (31024 ^ _777959) ^ [_1364042, _1364044] : [class_Groups_Oordered__ab__group__add__abs(_1364042), -(hAPP(c_Groups_Oabs__class_Oabs(_1364042), hAPP(c_Groups_Ouminus__class_Ouminus(_1364042), _1364044)) = hAPP(c_Groups_Oabs__class_Oabs(_1364042), _1364044))], (14007 ^ _777959) ^ [_1037825, _1037827, _1037829] : [hBOOL(hAPP(_1037825, _1037827)), -(hAPP(c_Set_OCollect(_1037829), hAPP(hAPP(c_COMBS(_1037829, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1037829), c_fconj), hAPP(hAPP(c_COMBC(_1037829, _1037829, tc_HOL_Obool), c_fequal), _1037827))), _1037825)) = hAPP(hAPP(c_Set_Oinsert(_1037829), _1037827), c_Orderings_Obot__class_Obot(tc_fun(_1037829, tc_HOL_Obool))))], (1972 ^ _777959) ^ [_806564, _806566, _806568, _806570, _806572, _806574] : [-(c_SetInterval_Oord_OatMost(_806574, _806570, _806566) = c_SetInterval_Oord_OatMost(_806572, _806568, _806564)), _806574 = _806572, _806570 = _806568, _806566 = _806564], (5280 ^ _777959) ^ [_858802, _858804] : [_858804 = _858802, -(c_List_Otake(_858804) = c_List_Otake(_858802))], (40970 ^ _777959) ^ [_1577542, _1577544, _1577546, _1577548] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1577542), tc_List_Olist(_1577542))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1577542), tc_List_Olist(_1577542)), _1577544), _1577546)), c_List_Olistrel(_1577542, _1577548)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577542)), _1577544) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1577542)), _1577546), 40976 ^ _777959 : [(40979 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1577542, _1577542, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1577542, tc_fun(tc_prod(_1577542, _1577542), tc_HOL_Obool), tc_fun(_1577542, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577542, tc_fun(tc_fun(tc_prod(_1577542, _1577542), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1577542, _1577542), tc_HOL_Obool), tc_fun(_1577542, tc_HOL_Obool)), _1577542), c_COMBC(_1577542, tc_fun(tc_prod(_1577542, _1577542), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1577542, tc_prod(_1577542, _1577542)), tc_fun(_1577542, tc_fun(tc_fun(tc_prod(_1577542, _1577542), tc_HOL_Obool), tc_HOL_Obool)), _1577542), hAPP(c_COMBB(tc_prod(_1577542, _1577542), tc_fun(tc_fun(tc_prod(_1577542, _1577542), tc_HOL_Obool), tc_HOL_Obool), _1577542), c_member(tc_prod(_1577542, _1577542)))), c_Product__Type_OPair(_1577542, _1577542)))), _1577548)), 40975 ^ [_1577542, _1577544, _1577546, _1577548]))], (40977 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577542, _1577542)), 40975 ^ [_1577542, _1577544, _1577546, _1577548]), hAPP(c_List_Oset(tc_prod(_1577542, _1577542)), hAPP(hAPP(c_List_Ozip(_1577542, _1577542), _1577544), _1577546)))))]]], (27339 ^ _777959) ^ [_1295283, _1295285, _1295287, _1295289] : [class_Orderings_Oorder(_1295283), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1295283, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1295283, _1295285, _1295287)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1295283, _1295287, _1295289)) = c_Orderings_Obot__class_Obot(tc_fun(_1295283, tc_HOL_Obool)))], (41057 ^ _777959) ^ [_1580664, _1580666, _1580668] : [-(_1580664 = _1580666), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1580668)), _1580664) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1580668)), _1580666), 41063 ^ _777959 : [(41066 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1580668, _1580668, tc_HOL_Obool), c_fequal), 41062 ^ [_1580664, _1580666, _1580668]))], (41064 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1580668, _1580668)), 41062 ^ [_1580664, _1580666, _1580668]), hAPP(c_List_Oset(tc_prod(_1580668, _1580668)), hAPP(hAPP(c_List_Ozip(_1580668, _1580668), _1580664), _1580666)))))]]], (37405 ^ _777959) ^ [_1492271, _1492273, _1492275, _1492277, _1492279] : [c_Equiv__Relations_Oequiv(_1492271, _1492273, _1492275), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1492271, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1492271, _1492271, _1492275), hAPP(hAPP(c_Set_Oinsert(_1492271), _1492277), c_Orderings_Obot__class_Obot(tc_fun(_1492271, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1492271, _1492271, _1492275), hAPP(hAPP(c_Set_Oinsert(_1492271), _1492279), c_Orderings_Obot__class_Obot(tc_fun(_1492271, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1492271), _1492277), _1492273)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1492271, _1492271)), hAPP(hAPP(c_Product__Type_OPair(_1492271, _1492271), _1492279), _1492277)), _1492275)))], (12476 ^ _777959) ^ [_1004625, _1004627, _1004629, _1004631, _1004633, _1004635, _1004637, _1004639] : [c_Finite__Set_Ofolding__image__simple(_1004625, _1004627, _1004629, _1004631, _1004633, _1004635), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004627), _1004637)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004627), _1004639)), 12490 ^ _777959 : [(12493 ^ _777959) ^ [] : [hAPP(_1004633, 12489 ^ [_1004625, _1004627, _1004629, _1004631, _1004633, _1004635, _1004637, _1004639]) = _1004631], (12491 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1004627), 12489 ^ [_1004625, _1004627, _1004629, _1004631, _1004633, _1004635, _1004637, _1004639]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1004627, tc_HOL_Obool)), _1004637), _1004639))))]], -(hAPP(_1004635, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1004627, tc_HOL_Obool)), _1004637), _1004639)) = hAPP(hAPP(_1004629, hAPP(_1004635, _1004637)), hAPP(_1004635, _1004639)))], (12840 ^ _777959) ^ [_1010924, _1010926, _1010928] : [class_Groups_Ogroup__add(_1010924), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1010924), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010924), _1010926), _1010928)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010924), hAPP(c_Groups_Ouminus__class_Ouminus(_1010924), _1010928)), hAPP(c_Groups_Ouminus__class_Ouminus(_1010924), _1010926)))], (35739 ^ _777959) ^ [_1455555, _1455557, _1455559, _1455561, _1455563, _1455565] : [hBOOL(hAPP(hAPP(_1455555, _1455557), _1455559)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1455561, tc_fun(_1455563, tc_HOL_Obool))), _1455565), _1455555), _1455557), _1455559)))], (5807 ^ _777959) ^ [_869957, _869959, _869961, _869963] : [5808 ^ _777959 : [(5811 ^ _777959) ^ [] : [hBOOL(hAPP(_869961, _869963))], (5809 ^ _777959) ^ [] : [_869959 = _869963]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_869957), _869959), _869961), _869963)))], (30685 ^ _777959) ^ [_1357844, _1357846] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1357844, _1357846)) = _1357846), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1357844), _1357846) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1357844, _1357846)))], (31975 ^ _777959) ^ [_1381676, _1381678, _1381680, _1381682, _1381684, _1381686] : [c_Com_Ocom_OCall(_1381676, _1381678, _1381680) = c_Com_Ocom_OLocal(_1381682, _1381684, _1381686)], (30788 ^ _777959) ^ [_1359640, _1359642] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1359640), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1359642), _1359640)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1359642), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1359642, _1359640)))], (49032 ^ _777959) ^ [_1768466, _1768468] : [-(hAPP(c_Relation_Oconverse(_1768466, _1768466), c_Relation_OId__on(_1768466, _1768468)) = c_Relation_OId__on(_1768466, _1768468))], (35397 ^ _777959) ^ [_1447701, _1447703, _1447705, _1447707] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(_1447703, _1447701)), _1447705), _1447707) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(_1447703), hAPP(hAPP(c_COMBC(_1447703, tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(hAPP(c_COMBB(tc_fun(_1447701, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1447703), c_Smallcheck_Osmall__class_Osmall(_1447701)), hAPP(hAPP(c_COMBB(tc_fun(_1447701, tc_prod(_1447703, _1447701)), tc_fun(_1447701, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), _1447703), hAPP(c_COMBB(tc_prod(_1447703, _1447701), tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), _1447701), _1447705)), c_Product__Type_OPair(_1447703, _1447701)))), _1447707)), _1447707)), class_Smallcheck_Osmall(_1447701), class_Smallcheck_Osmall(_1447703)], (49872 ^ _777959) ^ [_1789337, _1789339, _1789341] : [49874 ^ _777959 : [(49877 ^ _777959) ^ [] : [hBOOL(hAPP(_1789339, 49873 ^ [_1789337, _1789339, _1789341]))], (49875 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1789337), 49873 ^ [_1789337, _1789339, _1789341]), hAPP(c_List_Oset(_1789337), _1789341))))]], -(c_List_Olist__all(_1789337, _1789339, _1789341))], (9600 ^ _777959) ^ [_943822, _943824, _943826, _943828, _943830, _943832] : [hBOOL(hAPP(hAPP(c_member(_943822), _943824), _943826)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_943822, tc_Option_Ooption(_943828)), c_Map_Orestrict__map(_943822, _943828, _943830, _943826)), _943824), _943832) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_943822, tc_Option_Ooption(_943828)), c_Map_Orestrict__map(_943822, _943828, _943830, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_943822, tc_HOL_Obool)), _943826), hAPP(hAPP(c_Set_Oinsert(_943822), _943824), c_Orderings_Obot__class_Obot(tc_fun(_943822, tc_HOL_Obool)))))), _943824), _943832))], (23204 ^ _777959) ^ [_1220192, _1220194, _1220196] : [class_Rings_Olinordered__semidom(_1220192), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220192), c_Groups_Oone__class_Oone(_1220192)), _1220194)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1220196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220192), c_Groups_Oone__class_Oone(_1220192)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220192), _1220194), _1220196))))], (24205 ^ _777959) ^ [_1238083] : [-(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)))), _1238083)) = 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), _1238083), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (34963 ^ _777959) ^ [] : [-(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))], (5612 ^ _777959) ^ [_863722, _863724, _863726, _863728] : [-(hAPP(_863728, _863724) = hAPP(_863726, _863722)), _863728 = _863726, _863724 = _863722], (4210 ^ _777959) ^ [_841705, _841707] : [_841707 = _841705, -(c_New__DSequence_Opos__not__seq(_841707) = c_New__DSequence_Opos__not__seq(_841705))], (37237 ^ _777959) ^ [_1487819, _1487821, _1487823, _1487825] : [-(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), _1487819), _1487821)), 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), _1487823), _1487825)), 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), _1487819), _1487823)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1487821), _1487825))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1487819), _1487825)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1487821), _1487823)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (51156 ^ _777959) ^ [] : [-(class_Nat_Osize(tc_Com_Ovname))], (27746 ^ _777959) ^ [_1302237, _1302239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302239)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1302237)), hAPP(c_Int_Onat, _1302239)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1302237, _1302239)))], (43532 ^ _777959) ^ [_1643166, _1643168, _1643170] : [hBOOL(hAPP(c_List_Odistinct(_1643166), hAPP(c_List_Orotate(_1643166, _1643168), _1643170))), -(hBOOL(hAPP(c_List_Odistinct(_1643166), _1643170)))], (7784 ^ _777959) ^ [_910216, _910218, _910220, _910222, _910224, _910226, _910228, _910230] : [c_Finite__Set_Ofolding__image__simple__idem(_910216, _910218, _910220, _910222, _910224, _910226), hBOOL(hAPP(c_Finite__Set_Ofinite(_910218), _910228)), hBOOL(hAPP(c_Finite__Set_Ofinite(_910218), _910230)), -(hAPP(_910226, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910218, tc_HOL_Obool)), _910228), _910230)) = hAPP(hAPP(_910220, hAPP(_910226, _910228)), hAPP(_910226, _910230)))], (5825 ^ _777959) ^ [_870314, _870316] : [_870314 = _870316, -(hAPP(c_Com_Ocom_OBODY, _870314) = hAPP(c_Com_Ocom_OBODY, _870316))], (30619 ^ _777959) ^ [_1356733, _1356735] : [class_Rings_Olinordered__idom(_1356733), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356733), _1356735), c_Groups_Ozero__class_Ozero(_1356733))), -(c_Groups_Osgn__class_Osgn(_1356733, _1356735) = hAPP(c_Groups_Ouminus__class_Ouminus(_1356733), c_Groups_Oone__class_Oone(_1356733)))], (18921 ^ _777959) ^ [_1141181, _1141183, _1141185, _1141187] : [c_Big__Operators_Osemilattice__big(_1141181, _1141183, _1141185), hBOOL(hAPP(c_Finite__Set_Ofinite(_1141181), _1141187)), -(hAPP(_1141185, _1141187) = hAPP(c_Finite__Set_Ofold1(_1141181, _1141183), _1141187))], (36886 ^ _777959) ^ [_1477906] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1477906)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1477906)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42056 ^ _777959) ^ [_1606770, _1606772, _1606774] : [_1606770 = c_List_Olist_ONil(_1606772), -(c_List_Obutlast(_1606772, hAPP(hAPP(c_List_Olist_OCons(_1606772), _1606774), _1606770)) = c_List_Olist_ONil(_1606772))], (20685 ^ _777959) ^ [_1172142, _1172144] : [class_Groups_Oordered__ab__group__add(_1172142), 20688 ^ _777959 : [(20695 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172142), c_Groups_Ozero__class_Ozero(_1172142)), _1172144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172142), hAPP(c_Groups_Ouminus__class_Ouminus(_1172142), _1172144)), c_Groups_Ozero__class_Ozero(_1172142))))], (20689 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172142), hAPP(c_Groups_Ouminus__class_Ouminus(_1172142), _1172144)), c_Groups_Ozero__class_Ozero(_1172142))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172142), c_Groups_Ozero__class_Ozero(_1172142)), _1172144)))]]], (24686 ^ _777959) ^ [_1246333, _1246335, _1246337, _1246339] : [class_Divides_Osemiring__div(_1246333), 24689 ^ _777959 : [(24696 ^ _777959) ^ [] : [-(_1246335 = c_Groups_Ozero__class_Ozero(_1246333)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1246333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246333), _1246335), _1246337)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246333), _1246335), _1246339)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1246333), _1246337), _1246339))], (24690 ^ _777959) ^ [] : [_1246335 = c_Groups_Ozero__class_Ozero(_1246333), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1246333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246333), _1246335), _1246337)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246333), _1246335), _1246339)) = c_Groups_Ozero__class_Ozero(_1246333))]]], (38776 ^ _777959) ^ [_1522422, _1522424, _1522426, _1522428, _1522430] : [-(hAPP(c_Set_Ovimage(_1522422, _1522424, _1522426), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1522424, tc_HOL_Obool)), _1522428), _1522430)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1522422, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1522422, _1522424, _1522426), _1522428)), hAPP(c_Set_Ovimage(_1522422, _1522424, _1522426), _1522430)))], (31428 ^ _777959) ^ [_1371601, _1371603] : [-(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), _1371601)), _1371603))))], (24858 ^ _777959) ^ [_1249359, _1249361, _1249363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249359), _1249361)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1249363), 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), _1249361), _1249363)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1249359), _1249363))))], (50942 ^ _777959) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (48851 ^ _777959) ^ [_1763670, _1763672, _1763674, _1763676] : [c_Wellfounded_Oacyclic(_1763670, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1763670, _1763670)), hAPP(hAPP(c_Product__Type_OPair(_1763670, _1763670), _1763672), _1763674)), _1763676)), 48854 ^ _777959 : [(48857 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1763670, _1763670)), hAPP(hAPP(c_Product__Type_OPair(_1763670, _1763670), _1763674), _1763672)), c_Transitive__Closure_Ortrancl(_1763670, _1763676)))], (48855 ^ _777959) ^ [] : [-(c_Wellfounded_Oacyclic(_1763670, _1763676))]]], (23895 ^ _777959) ^ [_1232270, _1232272, _1232274, _1232276] : [class_Rings_Olinordered__semidom(_1232270), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232272), _1232274)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232270), c_Groups_Oone__class_Oone(_1232270)), _1232276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232270), hAPP(hAPP(c_Power_Opower__class_Opower(_1232270), _1232276), _1232272)), hAPP(hAPP(c_Power_Opower__class_Opower(_1232270), _1232276), _1232274))))], (40305 ^ _777959) ^ [_1560087, _1560089, _1560091] : [-(hBOOL(hAPP(hAPP(c_member(_1560087), _1560089), hAPP(c_List_Oset(_1560087), _1560091)))), 40306 ^ _777959 : [(40307 ^ _777959) ^ [_1560161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1560161), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1560087)), _1560091))), hAPP(hAPP(c_List_Onth(_1560087), _1560091), _1560161) = _1560089]]], (23865 ^ _777959) ^ [_1231807, _1231809] : [class_Power_Opower(_1231807), class_Rings_Osemiring__0(_1231807), 23872 ^ _777959 : [(23879 ^ _777959) ^ [] : [-(_1231809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1231807), c_Groups_Ozero__class_Ozero(_1231807)), _1231809) = c_Groups_Ozero__class_Ozero(_1231807))], (23873 ^ _777959) ^ [] : [_1231809 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1231807), c_Groups_Ozero__class_Ozero(_1231807)), _1231809) = c_Groups_Oone__class_Oone(_1231807))]]], (7526 ^ _777959) ^ [_904342, _904344, _904346, _904348, _904350] : [c_Finite__Set_Ofolding__one__idem(_904342, _904344, _904346), hBOOL(hAPP(c_Finite__Set_Ofinite(_904342), _904348)), -(_904348 = c_Orderings_Obot__class_Obot(tc_fun(_904342, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_904342), _904350)), -(_904350 = c_Orderings_Obot__class_Obot(tc_fun(_904342, tc_HOL_Obool))), -(hAPP(_904346, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_904342, tc_HOL_Obool)), _904348), _904350)) = hAPP(hAPP(_904344, hAPP(_904346, _904348)), hAPP(_904346, _904350)))], (11088 ^ _777959) ^ [_975192, _975194, _975196] : [_975196 = hAPP(c_COMBK(tc_Option_Ooption(_975194), _975192), c_Option_Ooption_ONone(_975194)), -(c_Map_Odom(_975192, _975194, _975196) = c_Orderings_Obot__class_Obot(tc_fun(_975192, tc_HOL_Obool)))], (25930 ^ _777959) ^ [_1269463, _1269465, _1269467, _1269469] : [class_Fields_Ofield(_1269463), -(_1269465 = c_Groups_Ozero__class_Ozero(_1269463)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1269467), _1269469)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1269463), _1269465), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1269469), _1269467)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1269463), hAPP(hAPP(c_Power_Opower__class_Opower(_1269463), _1269465), _1269469)), hAPP(hAPP(c_Power_Opower__class_Opower(_1269463), _1269465), _1269467)))], (8020 ^ _777959) ^ [_914929, _914931] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_914929, _914931))), 8023 ^ _777959 : [(8026 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _914931)))], (8024 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _914929)))]]], (42314 ^ _777959) ^ [_1612477, _1612479, _1612481, _1612483] : [-(hAPP(c_Set_Oimage(tc_prod(_1612477, _1612479), tc_prod(_1612479, _1612477), hAPP(c_Product__Type_Oprod_Oprod__case(_1612477, _1612479, tc_prod(_1612479, _1612477)), hAPP(c_COMBC(_1612479, _1612477, tc_prod(_1612479, _1612477)), c_Product__Type_OPair(_1612479, _1612477)))), hAPP(hAPP(c_Product__Type_OSigma(_1612477, _1612479), _1612481), hAPP(c_COMBK(tc_fun(_1612479, tc_HOL_Obool), _1612477), _1612483))) = hAPP(hAPP(c_Product__Type_OSigma(_1612479, _1612477), _1612483), hAPP(c_COMBK(tc_fun(_1612477, tc_HOL_Obool), _1612479), _1612481)))], (12584 ^ _777959) ^ [_1006505, _1006507] : [12585 ^ _777959 : [(12588 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006507), _1006505))], (12586 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006505), _1006507))]], _1006505 = _1006507], (16004 ^ _777959) ^ [_1082867, _1082869, _1082871] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1082867), _1082869)), 16007 ^ _777959 : [(16014 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1082867), _1082871), _1082869))), -(hAPP(c_Finite__Set_Ocard(_1082867), hAPP(hAPP(c_Set_Oinsert(_1082867), _1082871), _1082869)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1082867), _1082869)))], (16008 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1082867), _1082871), _1082869)), -(hAPP(c_Finite__Set_Ocard(_1082867), hAPP(hAPP(c_Set_Oinsert(_1082867), _1082871), _1082869)) = hAPP(c_Finite__Set_Ocard(_1082867), _1082869))]]], (51334 ^ _777959) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (50290 ^ _777959) ^ [_1797354, _1797356, _1797358, _1797360, _1797362, _1797364, _1797366] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1797354, _1797356, _1797358, _1797360, _1797362, _1797364, _1797366) = c_New__DSequence_Oneg__decr__bind(_1797354, _1797356, hAPP(hAPP(hAPP(_1797358, _1797362), _1797364), _1797366), hAPP(hAPP(c_COMBC(_1797354, 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(_1797356)))), hAPP(hAPP(c_COMBC(_1797354, 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(_1797356))))), hAPP(hAPP(c_COMBC(_1797354, 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(_1797356)))))), _1797360), _1797362)), _1797364)), _1797366)))], (32347 ^ _777959) ^ [_1388665, _1388667, _1388669, _1388671] : [class_Fields_Olinordered__field__inverse__zero(_1388665), class_Int_Onumber(_1388665), 32354 ^ _777959 : [(32355 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), _1388667), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388665), _1388669), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671)))), 32358 ^ _777959 : [(32365 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), c_Groups_Ozero__class_Ozero(_1388665)), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671)))), 32368 ^ _777959 : [(32375 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671)), c_Groups_Ozero__class_Ozero(_1388665)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), _1388667), c_Groups_Ozero__class_Ozero(_1388665))))], (32369 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671)), c_Groups_Ozero__class_Ozero(_1388665))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), _1388669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388665), _1388667), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671)))))]]], (32359 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), c_Groups_Ozero__class_Ozero(_1388665)), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388665), _1388667), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671))), _1388669)))]]], (32381 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), _1388667), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1388665), _1388669), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671))))), 32384 ^ _777959 : [(32387 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388665), _1388667), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671))), _1388669))], (32385 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), c_Groups_Ozero__class_Ozero(_1388665)), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671))))]], 32388 ^ _777959 : [(32391 ^ _777959) ^ [] : [32392 ^ _777959 : [(32395 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), _1388669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388665), _1388667), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671))))], (32393 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671)), c_Groups_Ozero__class_Ozero(_1388665))))]], 32396 ^ _777959 : [(32399 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), _1388667), c_Groups_Ozero__class_Ozero(_1388665)))], (32397 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671)), c_Groups_Ozero__class_Ozero(_1388665)))]]], (32389 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1388665), c_Groups_Ozero__class_Ozero(_1388665)), hAPP(c_Int_Onumber__class_Onumber__of(_1388665), _1388671)))]]]]], (9984 ^ _777959) ^ [_951471, _951473, _951475] : [class_Lattices_Olattice(_951471), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951471), _951473), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_951471), _951473), _951475)) = _951473)], (23923 ^ _777959) ^ [_1232800, _1232802, _1232804, _1232806] : [class_Rings_Olinordered__semidom(_1232800), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232800), c_Groups_Oone__class_Oone(_1232800)), _1232802)), 23930 ^ _777959 : [(23937 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232804), _1232806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232800), hAPP(hAPP(c_Power_Opower__class_Opower(_1232800), _1232802), _1232804)), hAPP(hAPP(c_Power_Opower__class_Opower(_1232800), _1232802), _1232806))))], (23931 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232800), hAPP(hAPP(c_Power_Opower__class_Opower(_1232800), _1232802), _1232804)), hAPP(hAPP(c_Power_Opower__class_Opower(_1232800), _1232802), _1232806))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232804), _1232806)))]]], (33285 ^ _777959) ^ [_1405932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1405932)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1405932), c_Int_OPls)))], (4886 ^ _777959) ^ [_852477, _852479] : [_852479 = _852477, -(c_New__Random__Sequence_Oneg__single(_852479) = c_New__Random__Sequence_Oneg__single(_852477))], (21280 ^ _777959) ^ [_1182325, _1182327, _1182329, _1182331] : [class_Rings_Olinordered__semiring__strict(_1182325), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182325), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182325), _1182327), _1182329)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182325), _1182327), _1182331))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182325), c_Groups_Ozero__class_Ozero(_1182325)), _1182327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182325), _1182329), _1182331)))], (16643 ^ _777959) ^ [_1096989, _1096991, _1096993, _1096995] : [class_Orderings_Olinorder(_1096989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096989), _1096991), _1096993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096989), _1096995), _1096993)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096989), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1096989), _1096991), _1096995)), _1096993)))], (11549 ^ _777959) ^ [_984274, _984276, _984278, _984280, _984282] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_984274, tc_fun(_984276, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_984274), _984278), _984280)), _984282) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984276, tc_HOL_Obool)), hAPP(_984282, _984278)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_984274, tc_fun(_984276, tc_HOL_Obool)), _984280), _984282)))], (30166 ^ _777959) ^ [_1348452, _1348454] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1348452, _1348454) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1348452 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1348454), 30169 ^ [_1348452, _1348454]))], (44905 ^ _777959) ^ [_1671207, _1671209, _1671211] : [-(c_List_Oconcat(_1671207, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1671207)), _1671209), _1671211)) = hAPP(hAPP(c_List_Oappend(_1671207), _1671209), c_List_Oconcat(_1671207, _1671211)))], (48705 ^ _777959) ^ [_1760025, _1760027] : [-(c_Transitive__Closure_Ortrancl(_1760025, _1760027) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1760025, _1760025), tc_HOL_Obool)), c_Relation_OId(_1760025)), hAPP(hAPP(c_Relation_Orel__comp(_1760025, _1760025, _1760025), c_Transitive__Closure_Ortrancl(_1760025, _1760027)), _1760027)))], (33441 ^ _777959) ^ [_1408365, _1408367] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408365)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408367))), 33444 ^ _777959 : [(33445 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408365), _1408367)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1408367)))], (33451 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408365), _1408367)))]]], (9508 ^ _777959) ^ [_941988, _941990, _941992, _941994, _941996] : [class_Groups_Oab__group__add(_941988), hBOOL(hAPP(c_Finite__Set_Ofinite(_941990), _941992)), 9515 ^ _777959 : [(9522 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_941990), _941994), _941992))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_941990, _941988), _941996), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941990, tc_HOL_Obool)), _941992), hAPP(hAPP(c_Set_Oinsert(_941990), _941994), c_Orderings_Obot__class_Obot(tc_fun(_941990, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_941990, _941988), _941996), _941992))], (9516 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_941990), _941994), _941992)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_941990, _941988), _941996), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_941990, tc_HOL_Obool)), _941992), hAPP(hAPP(c_Set_Oinsert(_941990), _941994), c_Orderings_Obot__class_Obot(tc_fun(_941990, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_941988), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_941990, _941988), _941996), _941992)), hAPP(_941996, _941994)))]]], (16443 ^ _777959) ^ [_1092702, _1092704, _1092706] : [class_Orderings_Olinorder(_1092702), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1092702), _1092704), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092702), _1092704), _1092706)) = _1092704)], (51166 ^ _777959) ^ [_1811568] : [-(class_Nat_Osize(tc_List_Olist(_1811568)))], (29202 ^ _777959) ^ [_1328476, _1328478, _1328480] : [class_Orderings_Olinorder(_1328476), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328476), _1328478), _1328480)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328476, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1328476), _1328478)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1328476, _1328478, _1328480)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1328476), _1328480))], (50579 ^ _777959) ^ [_1804053, _1804055, _1804057, _1804059] : [50587 ^ _777959 : [(50590 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1804059, 50586 ^ [_1804053, _1804055, _1804057, _1804059])))], (50588 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804053), 50586 ^ [_1804053, _1804055, _1804057, _1804059]), hAPP(c_List_Oset(_1804053), c_List_Oreplicate(_1804053, _1804055, _1804057)))))]], hBOOL(hAPP(_1804059, _1804057)), -(_1804055 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37560 ^ _777959) ^ [_1495546, _1495548, _1495550, _1495552, _1495554] : [hAPP(c_Relation_OImage(_1495546, _1495546, _1495548), hAPP(hAPP(c_Set_Oinsert(_1495546), _1495550), c_Orderings_Obot__class_Obot(tc_fun(_1495546, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1495546, _1495546, _1495548), hAPP(hAPP(c_Set_Oinsert(_1495546), _1495552), c_Orderings_Obot__class_Obot(tc_fun(_1495546, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1495546, _1495554, _1495548), hBOOL(hAPP(hAPP(c_member(_1495546), _1495552), _1495554)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1495546, _1495546)), hAPP(hAPP(c_Product__Type_OPair(_1495546, _1495546), _1495550), _1495552)), _1495548)))], (49229 ^ _777959) ^ [_1773111, _1773113, _1773115] : [49231 ^ _777959 : [(49232 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1773111), 49230 ^ [_1773111, _1773113, _1773115]), _1773113)))], (49237 ^ _777959) ^ [] : [49230 ^ [_1773111, _1773113, _1773115] = 49233 ^ [_1773111, _1773113, _1773115]], (49241 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773111, _1773111)), hAPP(hAPP(c_Product__Type_OPair(_1773111, _1773111), 49233 ^ [_1773111, _1773113, _1773115]), 49230 ^ [_1773111, _1773113, _1773115])), _1773115))], (49239 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1773111, _1773111)), hAPP(hAPP(c_Product__Type_OPair(_1773111, _1773111), 49230 ^ [_1773111, _1773113, _1773115]), 49233 ^ [_1773111, _1773113, _1773115])), _1773115))], (49235 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1773111), 49233 ^ [_1773111, _1773113, _1773115]), _1773113)))]], -(c_Relation_Ototal__on(_1773111, _1773113, _1773115))], (13939 ^ _777959) ^ [_1036092, _1036094, _1036096, _1036098, _1036100] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1036092, tc_fun(_1036094, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1036092, tc_HOL_Obool)), _1036096), _1036098)), _1036100) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1036094, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1036092, tc_fun(_1036094, tc_HOL_Obool)), _1036096), _1036100)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1036092, tc_fun(_1036094, tc_HOL_Obool)), _1036098), _1036100)))], (1810 ^ _777959) ^ [_803308, _803310] : [-(class_Groups_Oone(_803308)), _803310 = _803308, class_Groups_Oone(_803310)], (3652 ^ _777959) ^ [_833096, _833098] : [_833098 = _833096, -(c_Int_Oint__ge__less__than(_833098) = c_Int_Oint__ge__less__than(_833096))], (5336 ^ _777959) ^ [_859610, _859612] : [_859612 = _859610, -(c_List_Olist_ONil(_859612) = c_List_Olist_ONil(_859610))], (43556 ^ _777959) ^ [_1643576, _1643578, _1643580] : [-(hAPP(hAPP(c_List_Otake(_1643576), _1643578), hAPP(c_List_Otl(_1643576), _1643580)) = hAPP(c_List_Otl(_1643576), hAPP(hAPP(c_List_Otake(_1643576), hAPP(c_Nat_OSuc, _1643578)), _1643580)))], (35615 ^ _777959) ^ [_1453036, _1453038, _1453040, _1453042, _1453044, _1453046, _1453048] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1453036, _1453038)), hAPP(hAPP(c_Product__Type_OPair(_1453036, _1453038), _1453040), _1453042)), _1453044)), -(hBOOL(hAPP(hAPP(c_member(_1453046), hAPP(hAPP(_1453048, _1453040), _1453042)), hAPP(c_Set_Oimage(tc_prod(_1453036, _1453038), _1453046, hAPP(c_Product__Type_Oprod_Oprod__case(_1453036, _1453038, _1453046), _1453048)), _1453044))))], (40819 ^ _777959) ^ [_1571649, _1571651, _1571653, _1571655, _1571657] : [-(c_Map_Odom(_1571649, _1571651, c_Map_Omap__upds(_1571649, _1571651, _1571653, _1571655, _1571657)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1571649, tc_HOL_Obool)), hAPP(c_List_Oset(_1571649), hAPP(hAPP(c_List_Otake(_1571649), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1571651)), _1571657)), _1571655))), c_Map_Odom(_1571649, _1571651, _1571653)))], (33223 ^ _777959) ^ [_1405067] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1405067), c_Int_OPls) = _1405067)], (39366 ^ _777959) ^ [_1537188, _1537190, _1537192, _1537194, _1537196, _1537198, _1537200, _1537202] : [c_Finite__Set_Ofolding__image(_1537188, _1537190, _1537192, _1537194, _1537196), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537190), _1537198)), -(hAPP(hAPP(_1537196, hAPP(hAPP(c_COMBS(_1537190, _1537188, _1537188), hAPP(hAPP(c_COMBB(_1537188, tc_fun(_1537188, _1537188), _1537190), _1537192), _1537200)), _1537202)), _1537198) = hAPP(hAPP(_1537192, hAPP(hAPP(_1537196, _1537200), _1537198)), hAPP(hAPP(_1537196, _1537202), _1537198)))], (7029 ^ _777959) ^ [_894339, _894341, _894343, _894345, _894347, _894349, _894351, _894353, _894355] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_894339), _894341)), 7035 ^ _777959 : [(7038 ^ _777959) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_894343, _894345, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_894343)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_894343), hAPP(_894353, 7034 ^ [_894339, _894341, _894343, _894345, _894347, _894349, _894351, _894353, _894355])), hAPP(_894349, 7034 ^ [_894339, _894341, _894343, _894345, _894347, _894349, _894351, _894353, _894355])), hAPP(_894355, 7034 ^ [_894339, _894341, _894343, _894345, _894347, _894349, _894351, _894353, _894355]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_894343), tc_HOL_Obool))))], (7036 ^ _777959) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_894343, _894345, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_894343)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_894343), hAPP(_894347, 7034 ^ [_894339, _894341, _894343, _894345, _894347, _894349, _894351, _894353, _894355])), hAPP(_894349, 7034 ^ [_894339, _894341, _894343, _894345, _894347, _894349, _894351, _894353, _894355])), hAPP(_894351, 7034 ^ [_894339, _894341, _894343, _894345, _894347, _894349, _894351, _894353, _894355]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_894343), tc_HOL_Obool)))))]], c_Hoare__Mirabelle_Ohoare__derivs(_894343, _894345, hAPP(c_Set_Oimage(_894339, tc_Hoare__Mirabelle_Otriple(_894343), hAPP(hAPP(c_COMBS(_894339, tc_fun(_894343, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_894343)), hAPP(hAPP(c_COMBS(_894339, tc_Com_Ocom, tc_fun(tc_fun(_894343, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_894343))), hAPP(hAPP(c_COMBB(tc_fun(_894343, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_894343, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_894343))), _894339), c_Hoare__Mirabelle_Otriple_Otriple(_894343)), _894347)), _894349)), _894351)), _894341)), -(c_Hoare__Mirabelle_Ohoare__derivs(_894343, _894345, hAPP(c_Set_Oimage(_894339, tc_Hoare__Mirabelle_Otriple(_894343), hAPP(hAPP(c_COMBS(_894339, tc_fun(_894343, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_894343)), hAPP(hAPP(c_COMBS(_894339, tc_Com_Ocom, tc_fun(tc_fun(_894343, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_894343))), hAPP(hAPP(c_COMBB(tc_fun(_894343, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_894343, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_894343))), _894339), c_Hoare__Mirabelle_Otriple_Otriple(_894343)), _894353)), _894349)), _894355)), _894341)))], (15664 ^ _777959) ^ [_1076172, _1076174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076172), _1076174)), -(_1076174 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076172), 15667 ^ [_1076172, _1076174])))], (28570 ^ _777959) ^ [_1316161, _1316163, _1316165, _1316167] : [class_Orderings_Oorder(_1316161), 28573 ^ _777959 : [(28582 ^ _777959) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_1316161, _1316163, _1316165) = hAPP(hAPP(c_Set_Oinsert(_1316161), _1316167), c_Orderings_Obot__class_Obot(tc_fun(_1316161, tc_HOL_Obool)))), _1316163 = _1316165, _1316165 = _1316167], (28574 ^ _777959) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1316161, _1316163, _1316165) = hAPP(hAPP(c_Set_Oinsert(_1316161), _1316167), c_Orderings_Obot__class_Obot(tc_fun(_1316161, tc_HOL_Obool))), 28577 ^ _777959 : [(28580 ^ _777959) ^ [] : [-(_1316165 = _1316167)], (28578 ^ _777959) ^ [] : [-(_1316163 = _1316165)]]]]], (34275 ^ _777959) ^ [_1423228, _1423230] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1423228)), c_Int_OBit1(_1423230)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1423228), _1423230)))], (49156 ^ _777959) ^ [_1771392, _1771394, _1771396, _1771398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1771392, _1771394), tc_HOL_Obool)), _1771396), _1771398)), c_Relation_Osingle__valued(_1771392, _1771394, _1771398), -(c_Relation_Osingle__valued(_1771392, _1771394, _1771396))], (33237 ^ _777959) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44837 ^ _777959) ^ [_1669811, _1669813] : [hBOOL(hAPP(c_List_Odistinct(_1669811), hAPP(c_List_Orev(_1669811), _1669813))), -(hBOOL(hAPP(c_List_Odistinct(_1669811), _1669813)))], (25926 ^ _777959) ^ [_1269411, _1269413, _1269415] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCall(_1269411, _1269413, _1269415)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40093 ^ _777959) ^ [_1554827, _1554829, _1554831, _1554833] : [-(hAPP(c_List_Oset(tc_prod(_1554827, _1554829)), hAPP(hAPP(c_List_Ozip(_1554827, _1554829), _1554831), _1554833)) = hAPP(c_Set_OCollect(tc_prod(_1554827, _1554829)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1554827, _1554829)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1554827, _1554829), 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(_1554827, _1554829)), 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(_1554827, _1554829)), 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(_1554827, _1554829), tc_fun(tc_Nat_Onat, tc_prod(_1554827, _1554829)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1554827, _1554829), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1554827, _1554829)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1554827, _1554829)), c_COMBB(tc_prod(_1554827, _1554829), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1554829, tc_prod(_1554827, _1554829)), hAPP(hAPP(c_COMBB(_1554827, tc_fun(_1554829, tc_prod(_1554827, _1554829)), tc_Nat_Onat), c_Product__Type_OPair(_1554827, _1554829)), hAPP(c_List_Onth(_1554827), _1554831))), hAPP(c_List_Onth(_1554829), _1554833)))))), 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(_1554827)), _1554831)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554829)), _1554833)))))))], (37327 ^ _777959) ^ [_1490413, _1490415, _1490417] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490413), _1490415), _1490417) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1490413, tc_HOL_Obool), tc_HOL_Obool)), -(_1490415 = c_Orderings_Obot__class_Obot(tc_fun(_1490413, tc_HOL_Obool)))], (3568 ^ _777959) ^ [_831808, _831810, _831812, _831814] : [-(c_List_Olex(_831814, _831810) = c_List_Olex(_831812, _831808)), _831814 = _831812, _831810 = _831808], (42395 ^ _777959) ^ [_1615173, _1615175] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1615173), _1615175))), -(c_List_Oupto(_1615173, _1615175) = c_List_Olist_ONil(tc_Int_Oint))], (50764 ^ _777959) ^ [_1807506, _1807508] : [class_Lattices_Olattice(_1807506), -(class_Lattices_Osemilattice__sup(tc_fun(_1807508, _1807506)))], (29072 ^ _777959) ^ [] : [-(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))))], (6032 ^ _777959) ^ [_874326, _874328, _874330, _874332] : [6033 ^ _777959 : [(6036 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874326), _874328), _874332))], (6034 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_874326), _874328), _874330))]], -(hBOOL(hAPP(hAPP(c_member(_874326), _874328), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_874326, tc_HOL_Obool)), _874332), _874330))))], (7948 ^ _777959) ^ [_913373, _913375, _913377, _913379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913373, tc_HOL_Obool)), _913375), _913377)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913373, tc_HOL_Obool)), _913377), _913379)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913373, tc_HOL_Obool)), _913377), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913373, tc_HOL_Obool)), _913379), _913375)) = _913375)], (50342 ^ _777959) ^ [_1798846, _1798848] : [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), _1798846), _1798848))), 50345 ^ _777959 : [(50352 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1798846), _1798848))), -(c_Lazy__Sequence_Osmall__lazy_H(_1798846, _1798848) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1798848), c_Lazy__Sequence_Osmall__lazy_H(_1798846, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1798848), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50346 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1798846), _1798848)), -(c_Lazy__Sequence_Osmall__lazy_H(_1798846, _1798848) = c_Lazy__Sequence_Oempty(tc_Int_Oint))]]], (28291 ^ _777959) ^ [_1311324] : [-(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)))), _1311324))))], (33743 ^ _777959) ^ [_1413170, _1413172] : [class_Int_Onumber__ring(_1413170), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1413170), c_Groups_Oone__class_Oone(_1413170)), hAPP(c_Int_Onumber__class_Onumber__of(_1413170), _1413172)) = hAPP(c_Int_Onumber__class_Onumber__of(_1413170), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1413172)))], (42555 ^ _777959) ^ [_1619969, _1619971, _1619973, _1619975] : [c_Finite__Set_Ofolding(_1619969, _1619971, _1619973, _1619975), -(hAPP(_1619975, c_Orderings_Obot__class_Obot(tc_fun(_1619969, tc_HOL_Obool))) = c_Fun_Oid(_1619971))], (15050 ^ _777959) ^ [_1064230, _1064232] : [hAPP(c_Nat_OSuc, _1064230) = hAPP(c_Nat_OSuc, _1064232), -(_1064230 = _1064232)], (44196 ^ _777959) ^ [_1657230, _1657232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657230), _1657232)), -(c_List_Oupt(_1657230, _1657232) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1657230), c_List_Oupt(hAPP(c_Nat_OSuc, _1657230), _1657232)))], (24534 ^ _777959) ^ [_1243857, _1243859] : [class_Divides_Osemiring__div(_1243857), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1243857), _1243859), c_Groups_Ozero__class_Ozero(_1243857)) = c_Groups_Ozero__class_Ozero(_1243857))], (28113 ^ _777959) ^ [_1308352, _1308354, _1308356, _1308358] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1308352), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308354, tc_Int_Oint), _1308356), _1308358)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308354, _1308352), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1308352, _1308354), c_Int_Oring__1__class_Oof__int(_1308352)), _1308356)), _1308358)), class_Groups_Ocomm__monoid__mult(_1308352), class_Rings_Oring__1(_1308352)], (48073 ^ _777959) ^ [_1745952, _1745954, _1745956, _1745958, _1745960, _1745962, _1745964, _1745966] : [class_Groups_Ocomm__monoid__add(_1745952), class_Orderings_Oord(_1745954), _1745956 = _1745958, _1745960 = _1745962, 48091 ^ _777959 : [(48096 ^ _777959) ^ [] : [hAPP(_1745964, 48090 ^ [_1745952, _1745954, _1745956, _1745958, _1745960, _1745962, _1745964, _1745966]) = hAPP(_1745966, 48090 ^ [_1745952, _1745954, _1745956, _1745958, _1745960, _1745962, _1745964, _1745966])], (48094 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1745954), 48090 ^ [_1745952, _1745954, _1745956, _1745958, _1745960, _1745962, _1745964, _1745966]), _1745962)))], (48092 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1745954), _1745958), 48090 ^ [_1745952, _1745954, _1745956, _1745958, _1745960, _1745962, _1745964, _1745966])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1745954, _1745952), _1745964), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1745954, _1745956), _1745960)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1745954, _1745952), _1745966), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1745954, _1745958), _1745962)))], (50914 ^ _777959) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (43280 ^ _777959) ^ [_1637523, _1637525, _1637527] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637523)), hAPP(hAPP(c_List_Odrop(_1637523), _1637525), _1637527)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1637523)), _1637527)), _1637525))], (40588 ^ _777959) ^ [_1566335, _1566337] : [class_Groups_Ocomm__monoid__add(_1566335), hBOOL(hAPP(c_List_Odistinct(_1566335), _1566337)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1566335), _1566337) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566335, _1566335), c_COMBI(_1566335)), hAPP(c_List_Oset(_1566335), _1566337)))], (23561 ^ _777959) ^ [_1226378, _1226380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226378), _1226380)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226378), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1226380)))], (42302 ^ _777959) ^ [_1612117, _1612119] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612117), tc_List_Olist(_1612117))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612117), tc_List_Olist(_1612117)), c_List_Olist_ONil(_1612117)), c_List_Olist_ONil(_1612117))), c_List_Olistrel(_1612117, _1612119))))], (11106 ^ _777959) ^ [_975503, _975505, _975507, _975509] : [-(hAPP(c_Map_Orestrict__map(_975503, _975505, _975507, c_Orderings_Obot__class_Obot(tc_fun(_975503, tc_HOL_Obool))), _975509) = c_Option_Ooption_ONone(_975505))], (46978 ^ _777959) ^ [_1719914, _1719916] : [c_Wellfounded_Owf(_1719914, _1719916), -(c_Wellfounded_Owf(tc_fun(_1719914, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1719914, _1719916)))], (36666 ^ _777959) ^ [_1473492, _1473494, _1473496] : [-(hAPP(c_Product__Type_Ofst(_1473492, _1473494), _1473496) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1473492, _1473494, _1473492), c_COMBK(_1473492, _1473494)), _1473496))], (29270 ^ _777959) ^ [_1329834, _1329836, _1329838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329834)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1329836), _1329838)), 29277 ^ _777959 : [(29278 ^ _777959) ^ [_1330024] : [29280 ^ _777959 : [(29286 ^ _777959) ^ [] : [-(_1330024 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 29282 ^ [_1329834, _1329836, _1329838, _1330024]), 29279 ^ [_1329834, _1329836, _1329838, _1330024]))], (29284 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29282 ^ [_1329834, _1329836, _1329838, _1330024]), _1329838)))], (29281 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29279 ^ [_1329834, _1329836, _1329838, _1330024]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1329834))))]], -(_1330024 = _1329836), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1330024), _1329834) = _1329836]]], (51274 ^ _777959) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (50888 ^ _777959) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (2730 ^ _777959) ^ [_818637, _818639, _818641, _818643] : [-(c_Com_Ocom_OWhile(_818643, _818639) = c_Com_Ocom_OWhile(_818641, _818637)), _818643 = _818641, _818639 = _818637], (15082 ^ _777959) ^ [_1064787, _1064789] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1064787)), _1064789) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064787), _1064789)))], (14825 ^ _777959) ^ [_1056972, _1056974, _1056976] : [class_Lattices_Odistrib__lattice(_1056972), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056972), _1056974)), -(_1056974 = c_Orderings_Obot__class_Obot(tc_fun(_1056972, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1056972), _1056976), c_Big__Operators_Olattice__class_OSup__fin(_1056972, _1056974)) = c_Big__Operators_Olattice__class_OSup__fin(_1056972, hAPP(c_Set_OCollect(_1056972), hAPP(hAPP(c_COMBB(tc_fun(_1056972, tc_HOL_Obool), tc_HOL_Obool, _1056972), c_HOL_OEx(_1056972)), hAPP(hAPP(c_COMBC(_1056972, tc_fun(_1056972, tc_HOL_Obool), tc_fun(_1056972, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1056972, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1056972, tc_HOL_Obool), tc_fun(_1056972, tc_HOL_Obool)), _1056972), c_COMBS(_1056972, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1056972, tc_HOL_Obool), tc_fun(_1056972, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1056972), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1056972), c_fconj)), hAPP(hAPP(c_COMBC(_1056972, tc_fun(_1056972, _1056972), tc_fun(_1056972, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1056972, tc_HOL_Obool), tc_fun(tc_fun(_1056972, _1056972), tc_fun(_1056972, tc_HOL_Obool)), _1056972), c_COMBB(_1056972, tc_HOL_Obool, _1056972)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1056972), _1056976))))), hAPP(hAPP(c_COMBC(_1056972, tc_fun(_1056972, tc_HOL_Obool), tc_HOL_Obool), c_member(_1056972)), _1056974))))))], (5781 ^ _777959) ^ [_869474, _869476, _869478] : [-(hAPP(c_Set_Oimage(_869474, _869476, _869478), c_Orderings_Obot__class_Obot(tc_fun(_869474, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_869476, tc_HOL_Obool)))], (42475 ^ _777959) ^ [_1616903, _1616905, _1616907, _1616909, _1616911] : [-(hAPP(hAPP(c_List_Ozip(_1616903, _1616905), hAPP(hAPP(c_List_Olist_OCons(_1616903), _1616907), _1616909)), _1616911) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1616903, _1616905)), _1616905, c_List_Olist_ONil(tc_prod(_1616903, _1616905)), hAPP(hAPP(c_COMBC(_1616905, tc_fun(tc_List_Olist(_1616905), tc_List_Olist(tc_prod(_1616903, _1616905))), tc_fun(tc_List_Olist(_1616905), tc_List_Olist(tc_prod(_1616903, _1616905)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1616903, _1616905)), tc_List_Olist(tc_prod(_1616903, _1616905))), tc_fun(tc_fun(tc_List_Olist(_1616905), tc_List_Olist(tc_prod(_1616903, _1616905))), tc_fun(tc_List_Olist(_1616905), tc_List_Olist(tc_prod(_1616903, _1616905)))), _1616905), c_COMBB(tc_List_Olist(tc_prod(_1616903, _1616905)), tc_List_Olist(tc_prod(_1616903, _1616905)), tc_List_Olist(_1616905))), hAPP(hAPP(c_COMBB(tc_prod(_1616903, _1616905), tc_fun(tc_List_Olist(tc_prod(_1616903, _1616905)), tc_List_Olist(tc_prod(_1616903, _1616905))), _1616905), c_List_Olist_OCons(tc_prod(_1616903, _1616905))), hAPP(c_Product__Type_OPair(_1616903, _1616905), _1616907)))), hAPP(c_List_Ozip(_1616903, _1616905), _1616909))), _1616911))], (35713 ^ _777959) ^ [_1455052, _1455054, _1455056, _1455058, _1455060, _1455062] : [hBOOL(hAPP(hAPP(_1455052, _1455054), _1455056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1455058, tc_fun(_1455060, tc_HOL_Obool))), _1455052), _1455062)), -(hBOOL(hAPP(hAPP(_1455062, _1455054), _1455056)))], (12946 ^ _777959) ^ [_1013528, _1013530, _1013532] : [class_Complete__Lattice_Ocomplete__lattice(_1013528), 12949 ^ _777959 : [(12950 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013528), c_Complete__Lattice_OSup__class_OSup(_1013528, _1013530)), _1013532)), 12953 ^ _777959 : [(12954 ^ _777959) ^ [_1013686] : [hBOOL(hAPP(hAPP(c_member(_1013528), _1013686), _1013530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013528), _1013686), _1013532)))]]], (12960 ^ _777959) ^ [] : [12962 ^ _777959 : [(12965 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013528), 12961 ^ [_1013528, _1013530, _1013532]), _1013532))], (12963 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1013528), 12961 ^ [_1013528, _1013530, _1013532]), _1013530)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1013528), c_Complete__Lattice_OSup__class_OSup(_1013528, _1013530)), _1013532)))]]], (44416 ^ _777959) ^ [_1660768, _1660770, _1660772, _1660774, _1660776] : [class_Orderings_Olinorder(_1660768), c_List_Olinorder__class_Osorted(_1660768, hAPP(hAPP(c_List_Omap(_1660770, _1660768), _1660772), _1660774)), -(c_List_Olinorder__class_Osorted(_1660768, hAPP(hAPP(c_List_Omap(_1660770, _1660768), _1660772), c_List_Olinorder__class_Oinsort__insert__key(_1660770, _1660768, _1660772, _1660776, _1660774))))], (36526 ^ _777959) ^ [_1470677, _1470679, _1470681, _1470683, _1470685] : [hAPP(c_Product__Type_Osnd(_1470677, _1470679), hAPP(hAPP(c_Product__Type_OPair(_1470677, _1470679), _1470681), _1470683)) = _1470685, -(_1470683 = _1470685)], (47222 ^ _777959) ^ [_1725253, _1725255, _1725257] : [_1725257 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1725253, _1725255), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1725253, _1725255), _1725257) = c_Orderings_Obot__class_Obot(tc_fun(_1725255, tc_HOL_Obool)))], (9858 ^ _777959) ^ [_949243, _949245, _949247, _949249] : [class_Lattices_Osemilattice__inf(_949243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949243), _949245), _949247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949243), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949243), _949245), _949249)), _949247)))], (1120 ^ _777959) ^ [_794683, _794685] : [-(class_Rings_Olinordered__idom(_794683)), _794685 = _794683, class_Rings_Olinordered__idom(_794685)], (26220 ^ _777959) ^ [_1275041, _1275043, _1275045] : [class_Fields_Olinordered__field__inverse__zero(_1275041), 26223 ^ _777959 : [(26238 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275041), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275041), _1275043), _1275045)), c_Groups_Ozero__class_Ozero(_1275041)))), 26239 ^ _777959 : [(26246 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275041), _1275043), c_Groups_Ozero__class_Ozero(_1275041))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275041), c_Groups_Ozero__class_Ozero(_1275041)), _1275045))], (26240 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275041), c_Groups_Ozero__class_Ozero(_1275041)), _1275043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275041), _1275045), c_Groups_Ozero__class_Ozero(_1275041)))]]], (26224 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275041), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275041), _1275043), _1275045)), c_Groups_Ozero__class_Ozero(_1275041))), 26229 ^ _777959 : [(26232 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275041), _1275045), c_Groups_Ozero__class_Ozero(_1275041))))], (26230 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275041), c_Groups_Ozero__class_Ozero(_1275041)), _1275043)))]], 26233 ^ _777959 : [(26236 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275041), c_Groups_Ozero__class_Ozero(_1275041)), _1275045)))], (26234 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275041), _1275043), c_Groups_Ozero__class_Ozero(_1275041))))]]]]], (22408 ^ _777959) ^ [_1204995, _1204997, _1204999] : [hAPP(c_Finite__Set_Ocard(_1204995), _1204997) = hAPP(c_Nat_OSuc, _1204999), 22413 ^ _777959 : [(22416 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1204995), 22411 ^ [_1204995, _1204997, _1204999]), 22412 ^ [_1204995, _1204997, _1204999]))], (22418 ^ _777959) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1204995), 22412 ^ [_1204995, _1204997, _1204999]) = _1204999)], (22420 ^ _777959) ^ [] : [_1204999 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(22412 ^ [_1204995, _1204997, _1204999] = c_Orderings_Obot__class_Obot(tc_fun(_1204995, tc_HOL_Obool)))], (22414 ^ _777959) ^ [] : [-(_1204997 = hAPP(hAPP(c_Set_Oinsert(_1204995), 22411 ^ [_1204995, _1204997, _1204999]), 22412 ^ [_1204995, _1204997, _1204999]))]]], (49592 ^ _777959) ^ [_1783025, _1783027, _1783029] : [class_Divides_Osemiring__div(_1783025), -(_1783027 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1783025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1783025), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1783025), _1783027), _1783029)), _1783029)), c_Divides_Odiv__class_Omod(_1783025, _1783027, _1783029)))], (51076 ^ _777959) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (14021 ^ _777959) ^ [_1038183, _1038185, _1038187, _1038189] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038183, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1038185, tc_fun(_1038183, tc_HOL_Obool)), _1038187), _1038189)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038185, tc_fun(_1038183, tc_HOL_Obool)), _1038187), hAPP(hAPP(c_COMBB(tc_fun(_1038183, tc_HOL_Obool), tc_fun(_1038183, tc_HOL_Obool), _1038185), c_Groups_Ouminus__class_Ouminus(tc_fun(_1038183, tc_HOL_Obool))), _1038189)))], (23136 ^ _777959) ^ [_1218908, _1218910, _1218912, _1218914] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1218908), _1218910)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1218912), _1218914)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1218908, _1218912)), c_Sum__Type_OPlus(_1218908, _1218912, _1218910, _1218914))))], (7992 ^ _777959) ^ [_914380, _914382] : [hBOOL(hAPP(c_Com_OWT, _914382)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_914380, _914382))))], (24628 ^ _777959) ^ [_1245398, _1245400] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1245398), 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)), _1245400)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1245398), _1245400)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (2394 ^ _777959) ^ [_813383, _813385] : [_813385 = _813383, -(c_Com_Ocom_Ocom__size(_813385) = c_Com_Ocom_Ocom__size(_813383))], (13765 ^ _777959) ^ [_1032576, _1032578] : [class_Orderings_Otop(_1032576), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1032576), _1032578), c_Orderings_Otop__class_Otop(_1032576))))], (45756 ^ _777959) ^ [_1691003, _1691005] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1691003, _1691005)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1691005), tc_fun(_1691003, _1691005)), hAPP(hAPP(c_COMBB(tc_fun(_1691003, tc_Option_Ooption(_1691005)), tc_fun(_1691003, _1691005), tc_List_Olist(_1691005)), c_Fun_Ocomp(tc_Option_Ooption(_1691005), _1691005, _1691003, c_Option_Othe(_1691005))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1691003, _1691005)), tc_fun(_1691003, tc_Option_Ooption(_1691005)), tc_List_Olist(_1691005)), c_Map_Omap__of(_1691003, _1691005)), hAPP(c_List_Ozip(_1691003, _1691005), c_Enum_Oenum__class_Oenum(_1691003))))), c_Enum_On__lists(_1691005, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691003)), c_Enum_Oenum__class_Oenum(_1691003)), c_Enum_Oenum__class_Oenum(_1691005)))), class_Enum_Oenum(_1691003), class_Enum_Oenum(_1691005)], (49106 ^ _777959) ^ [_1770461, _1770463, _1770465, _1770467, _1770469, _1770471] : [c_Relation_Osingle__valued(_1770461, _1770463, hAPP(c_Relation_Oconverse(_1770463, _1770461), _1770465)), -(_1770467 = c_Orderings_Obot__class_Obot(tc_fun(_1770469, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1770463, _1770461, _1770465), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1770469, tc_fun(_1770463, tc_HOL_Obool)), _1770467), _1770471)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1770469, tc_fun(_1770461, tc_HOL_Obool)), _1770467), hAPP(hAPP(c_COMBB(tc_fun(_1770463, tc_HOL_Obool), tc_fun(_1770461, tc_HOL_Obool), _1770469), c_Relation_OImage(_1770463, _1770461, _1770465)), _1770471)))], (28956 ^ _777959) ^ [_1323764] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1323764)) = hAPP(c_Nat_OSuc, _1323764))], (1430 ^ _777959) ^ [_798558, _798560] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_798558)), _798560 = _798558, class_Groups_Oordered__ab__semigroup__add__imp__le(_798560)], (10930 ^ _777959) ^ [_972230, _972232, _972234, _972236] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_972230), 10933 ^ _777959 : [(10940 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972230), _972234), _972236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972230), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972230), _972232), _972234)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972230), _972232), _972236))))], (10934 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972230), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972230), _972232), _972234)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972230), _972232), _972236))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972230), _972234), _972236)))]]], (12054 ^ _777959) ^ [_996593, _996595] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996593), _996595) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996595), _996593))], (50146 ^ _777959) ^ [_1794388] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1794388)))], (32867 ^ _777959) ^ [_1398795, _1398797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398795)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398797))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1398795), _1398797)))], (36624 ^ _777959) ^ [_1472719] : [-(hAPP(c_Int_Onat, _1472719) = 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, _1472719)), 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)))))))], (44869 ^ _777959) ^ [_1670455, _1670457, _1670459] : [hAPP(c_List_Orev(_1670455), _1670457) = _1670459, -(_1670457 = hAPP(c_List_Orev(_1670455), _1670459))], (22473 ^ _777959) ^ [_1206407, _1206409, _1206411] : [class_Orderings_Olinorder(_1206407), 22476 ^ _777959 : [(22483 ^ _777959) ^ [] : [_1206409 = _1206411, -(hAPP(c_SetInterval_Oord__class_OlessThan(_1206407), _1206409) = hAPP(c_SetInterval_Oord__class_OlessThan(_1206407), _1206411))], (22477 ^ _777959) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_1206407), _1206409) = hAPP(c_SetInterval_Oord__class_OlessThan(_1206407), _1206411), -(_1206409 = _1206411)]]], (50258 ^ _777959) ^ [_1796816, _1796818, _1796820, _1796822, _1796824] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1796816, _1796818, _1796820) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1796816, _1796822, _1796824), 50261 ^ _777959 : [(50264 ^ _777959) ^ [] : [-(_1796820 = _1796824)], (50262 ^ _777959) ^ [] : [-(_1796818 = _1796822)]]], (2340 ^ _777959) ^ [_812558, _812560, _812562, _812564] : [-(c_Nitpick_Onat__lcm(_812564, _812560) = c_Nitpick_Onat__lcm(_812562, _812558)), _812564 = _812562, _812560 = _812558], (46850 ^ _777959) ^ [_1717428, _1717430, _1717432, _1717434, _1717436, _1717438, _1717440, _1717442] : [hBOOL(hAPP(hAPP(_1717428, _1717430), _1717432)), hBOOL(hAPP(hAPP(_1717434, _1717432), _1717436)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1717438, _1717440, _1717442, _1717428, _1717434), _1717430), _1717436)))], (48893 ^ _777959) ^ [_1764846, _1764848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1764846), _1764848)), -(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), _1764846), _1764848)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (15852 ^ _777959) ^ [_1079461, _1079463, _1079465, _1079467, _1079469, _1079471, _1079473] : [hAPP(_1079461, _1079463) = hAPP(c_Option_Ooption_OSome(_1079465), _1079467), -(c_Map_Omap__comp(_1079465, _1079469, _1079471, _1079473, _1079461, _1079463) = hAPP(_1079473, _1079467))], (33329 ^ _777959) ^ [_1406601, _1406603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406601), _1406603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1406601)), _1406603)))], (43300 ^ _777959) ^ [_1638022, _1638024, _1638026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638022)), _1638024)), _1638026)), -(hAPP(hAPP(c_List_Odrop(_1638022), _1638026), _1638024) = c_List_Olist_ONil(_1638022))], (49022 ^ _777959) ^ [_1768265, _1768267, _1768269] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1768267, _1768265)), _1768269)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1768265, _1768267)), hAPP(c_Relation_Oconverse(_1768267, _1768265), _1768269))))], (11533 ^ _777959) ^ [_983977, _983979, _983981, _983983, _983985] : [hAPP(_983977, _983979) = c_Option_Ooption_ONone(_983981), -(c_Map_Oran(_983983, _983981, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_983983, tc_Option_Ooption(_983981)), _983977), _983979), hAPP(c_Option_Ooption_OSome(_983981), _983985))) = hAPP(hAPP(c_Set_Oinsert(_983981), _983985), c_Map_Oran(_983983, _983981, _983977)))], (31344 ^ _777959) ^ [_1370208, _1370210] : [class_Groups_Oordered__ab__group__add__abs(_1370208), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370208), hAPP(c_Groups_Ouminus__class_Ouminus(_1370208), hAPP(c_Groups_Oabs__class_Oabs(_1370208), _1370210))), c_Groups_Ozero__class_Ozero(_1370208))))], (49720 ^ _777959) ^ [_1786332, _1786334, _1786336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1786332), c_Nitpick_Oplus__frac(_1786332, _1786334, c_Nitpick_Ouminus__frac(_1786332, _1786336)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1786332, _1786334, _1786336))], (19839 ^ _777959) ^ [_1156790, _1156792] : [class_Groups_Olinordered__ab__group__add(_1156790), 19842 ^ _777959 : [(19849 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156790), c_Groups_Ozero__class_Ozero(_1156790)), _1156792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156790), c_Groups_Ozero__class_Ozero(_1156790)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156790), _1156792), _1156792))))], (19843 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156790), c_Groups_Ozero__class_Ozero(_1156790)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156790), _1156792), _1156792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156790), c_Groups_Ozero__class_Ozero(_1156790)), _1156792)))]]], (19322 ^ _777959) ^ [_1148592, _1148594] : [class_Rings_Omult__zero(_1148592), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148592), _1148594), c_Groups_Ozero__class_Ozero(_1148592)) = c_Groups_Ozero__class_Ozero(_1148592))], (45234 ^ _777959) ^ [_1679616, _1679618, _1679620, _1679622, _1679624] : [-(c_Map_Omap__upds(_1679616, _1679618, _1679620, _1679622, _1679624) = c_Map_Omap__add(_1679616, _1679618, _1679620, hAPP(c_Map_Omap__of(_1679616, _1679618), hAPP(c_List_Orev(tc_prod(_1679616, _1679618)), hAPP(hAPP(c_List_Ozip(_1679616, _1679618), _1679622), _1679624)))))], (12626 ^ _777959) ^ [_1007162, _1007164, _1007166] : [class_Groups_Ogroup__add(_1007162), 12629 ^ _777959 : [(12636 ^ _777959) ^ [] : [_1007166 = hAPP(c_Groups_Ouminus__class_Ouminus(_1007162), _1007164), -(_1007164 = hAPP(c_Groups_Ouminus__class_Ouminus(_1007162), _1007166))], (12630 ^ _777959) ^ [] : [_1007164 = hAPP(c_Groups_Ouminus__class_Ouminus(_1007162), _1007166), -(_1007166 = hAPP(c_Groups_Ouminus__class_Ouminus(_1007162), _1007164))]]], (22096 ^ _777959) ^ [_1198414, _1198416] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1198414), _1198416)))), -(_1198416 = c_Orderings_Obot__class_Obot(tc_fun(_1198414, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1198414), _1198416))], (6777 ^ _777959) ^ [_888122, _888124, _888126, _888128] : [hBOOL(hAPP(hAPP(c_member(_888122), _888124), _888126)), -(hBOOL(hAPP(hAPP(c_member(_888122), _888124), hAPP(hAPP(c_Set_Oinsert(_888122), _888128), _888126))))], (41381 ^ _777959) ^ [_1588693, _1588695, _1588697, _1588699, _1588701, _1588703] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1588693), tc_List_Olist(_1588693))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1588693), tc_List_Olist(_1588693)), hAPP(hAPP(c_List_Olist_OCons(_1588693), _1588695), _1588697)), hAPP(hAPP(c_List_Olist_OCons(_1588693), _1588699), _1588701))), c_List_Olex(_1588693, _1588703))), 41386 ^ _777959 : [(41389 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588693)), _1588697) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588693)), _1588701))], (41387 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588693, _1588693)), hAPP(hAPP(c_Product__Type_OPair(_1588693, _1588693), _1588695), _1588699)), _1588703)))]], 41390 ^ _777959 : [(41393 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1588693), tc_List_Olist(_1588693))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1588693), tc_List_Olist(_1588693)), _1588697), _1588701)), c_List_Olex(_1588693, _1588703))))], (41391 ^ _777959) ^ [] : [-(_1588695 = _1588699)]]], (29763 ^ _777959) ^ [_1339783, _1339785, _1339787] : [-(hAPP(c_Set_OPow(_1339783), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1339783, tc_HOL_Obool)), _1339785), _1339787)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1339783, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1339783), _1339785)), hAPP(c_Set_OPow(_1339783), _1339787)))], (51190 ^ _777959) ^ [_1811877, _1811879] : [-(class_Nat_Osize(tc_sum(_1811877, _1811879)))], (5508 ^ _777959) ^ [_862128, _862130] : [_862130 = _862128, -(tc_Lazy__Sequence_Olazy__sequence(_862130) = tc_Lazy__Sequence_Olazy__sequence(_862128))], (5707 ^ _777959) ^ [_868039] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _868039))), -(hAPP(c_Com_Obody, _868039) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 5710 ^ [_868039]))], (50416 ^ _777959) ^ [_1800572, _1800574, _1800576] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1800572, _1800572, hAPP(hAPP(c_COMBB(tc_fun(_1800572, tc_HOL_Obool), tc_fun(_1800572, tc_HOL_Obool), _1800572), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1800572), c_fNot)), c_fequal)), _1800574), _1800576)), _1800574 = _1800576], (9482 ^ _777959) ^ [_941346, _941348, _941350] : [class_Lattices_Olattice(_941346), hAPP(_941348, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_941346), 9487 ^ [_941346, _941348, _941350]), 9488 ^ [_941346, _941348, _941350])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_941346), hAPP(_941348, 9487 ^ [_941346, _941348, _941350])), hAPP(_941348, 9488 ^ [_941346, _941348, _941350])), hBOOL(hAPP(c_Finite__Set_Ofinite(_941346), _941350)), -(_941350 = c_Orderings_Obot__class_Obot(tc_fun(_941346, tc_HOL_Obool))), -(hAPP(_941348, c_Big__Operators_Olattice__class_OSup__fin(_941346, _941350)) = c_Big__Operators_Olattice__class_OSup__fin(_941346, hAPP(c_Set_Oimage(_941346, _941346, _941348), _941350)))], (6789 ^ _777959) ^ [_888356, _888358, _888360] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888356, tc_HOL_Obool)), _888358), hAPP(hAPP(c_Set_Oinsert(_888356), _888360), _888358))))], (23399 ^ _777959) ^ [_1223588, _1223590, _1223592] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223588), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1223590), _1223592)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223588), _1223590)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223588), _1223592)))], (31414 ^ _777959) ^ [_1371411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371411), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1371411) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1371411))], (946 ^ _777959) ^ [_792368, _792370, _792372, _792374, _792376, _792378, _792380, _792382] : [-(c_Nat__Transfer_Otransfer__morphism(_792380, _792376, _792372, _792368)), c_Nat__Transfer_Otransfer__morphism(_792382, _792378, _792374, _792370), _792382 = _792380, _792378 = _792376, _792374 = _792372, _792370 = _792368], (50496 ^ _777959) ^ [_1802650, _1802652, _1802654, _1802656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1802650), _1802652)), -(hAPP(hAPP(c_List_Onth(_1802654), c_List_Oreplicate(_1802654, _1802652, _1802656)), _1802650) = _1802656)], (34091 ^ _777959) ^ [_1420070, _1420072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1420070)), c_Int_OBit0(_1420072))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420070), _1420072)))], (40576 ^ _777959) ^ [_1566029, _1566031] : [class_Groups_Oordered__ab__group__add__abs(_1566029), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1566029), hAPP(c_Groups_Oabs__class_Oabs(_1566029), hAPP(c_List_Omonoid__add__class_Olistsum(_1566029), _1566031))), hAPP(c_List_Omonoid__add__class_Olistsum(_1566029), hAPP(hAPP(c_List_Omap(_1566029, _1566029), c_Groups_Oabs__class_Oabs(_1566029)), _1566031)))))], (45270 ^ _777959) ^ [_1680406, _1680408] : [-(hAPP(c_List_Oset(_1680406), c_List_Oremdups(_1680406, _1680408)) = hAPP(c_List_Oset(_1680406), _1680408))], (46457 ^ _777959) ^ [_1705937, _1705939, _1705941, _1705943] : [_1705943 = c_List_Olist_ONil(_1705937), -(c_List_Olist__all2(_1705937, _1705939, _1705941, _1705943, c_List_Olist_ONil(_1705939)))], (48875 ^ _777959) ^ [_1764298, _1764300, _1764302, _1764304] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1764298), tc_List_Olist(_1764298))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1764298), tc_List_Olist(_1764298)), _1764300), _1764302)), c_List_Olistrel(_1764298, _1764304))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1764298), tc_List_Olist(_1764298))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1764298), tc_List_Olist(_1764298)), _1764300), _1764302)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1764298), c_List_Olistrel1(_1764298, _1764304)))))], (3330 ^ _777959) ^ [_828149, _828151, _828153, _828155, _828157, _828159] : [-(c_Finite__Set_Ofold(_828159, _828155, _828151) = c_Finite__Set_Ofold(_828157, _828153, _828149)), _828159 = _828157, _828155 = _828153, _828151 = _828149], (13327 ^ _777959) ^ [_1021695, _1021697, _1021699, _1021701, _1021703, _1021705, _1021707, _1021709] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1021695, tc_fun(_1021697, tc_fun(_1021699, tc_HOL_Obool))), _1021701), _1021703), _1021705), _1021707)), -(hBOOL(hAPP(hAPP(hAPP(_1021703, _1021709), _1021705), _1021707))), hBOOL(hAPP(hAPP(c_member(_1021695), _1021709), _1021701))], (40779 ^ _777959) ^ [_1570699, _1570701, _1570703] : [hBOOL(hAPP(c_List_Odistinct(_1570699), _1570701)), -(hBOOL(hAPP(c_List_Odistinct(_1570699), hAPP(hAPP(c_List_Otake(_1570699), _1570703), _1570701))))], (36201 ^ _777959) ^ [_1464223, _1464225, _1464227, _1464229, _1464231] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1464223, _1464225), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1464227), _1464229))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1464225)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1464231)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1464223, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1464225), _1464231)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1464227), _1464231)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1464225), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1464227, _1464231))), _1464229)))))], (19536 ^ _777959) ^ [_1151713] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1151713), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1151713)], (19358 ^ _777959) ^ [_1149178, _1149180, _1149182] : [class_Groups_Oab__group__add(_1149178), 19361 ^ _777959 : [(19368 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149178), _1149180), _1149182) = c_Groups_Ozero__class_Ozero(_1149178), -(_1149180 = _1149182)], (19362 ^ _777959) ^ [] : [_1149180 = _1149182, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149178), _1149180), _1149182) = c_Groups_Ozero__class_Ozero(_1149178))]]], (16923 ^ _777959) ^ [_1101818, _1101820, _1101822, _1101824] : [class_Orderings_Olinorder(_1101818), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101818), _1101820), _1101822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101818), _1101820), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1101818), _1101824), _1101822))))], (3070 ^ _777959) ^ [_823953, _823955, _823957, _823959] : [-(c_List_OremoveAll(_823959, _823955) = c_List_OremoveAll(_823957, _823953)), _823959 = _823957, _823955 = _823953], (7070 ^ _777959) ^ [_895983, _895985, _895987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895983, tc_HOL_Obool)), _895985), _895987)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895983, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_895983, tc_fun(_895983, tc_HOL_Obool), tc_HOL_Obool), c_member(_895983)), _895985)), hAPP(hAPP(c_COMBC(_895983, tc_fun(_895983, tc_HOL_Obool), tc_HOL_Obool), c_member(_895983)), _895987))))], (25140 ^ _777959) ^ [_1254227, _1254229, _1254231, _1254233, _1254235] : [class_Orderings_Olinorder(_1254227), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1254227, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1254227, _1254229), _1254231)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1254227, _1254233), _1254235)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1254227, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1254227), _1254229), _1254233)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1254227), _1254231), _1254235)))], (50206 ^ _777959) ^ [_1795472, _1795474] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1795472)), c_Int_OBit1(_1795474)))], (9912 ^ _777959) ^ [_950172, _950174, _950176, _950178] : [class_Lattices_Osemilattice__inf(_950172), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950172), _950174), _950176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950172), _950174), _950178)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950172), _950174), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950172), _950176), _950178))))], (41669 ^ _777959) ^ [_1595616, _1595618, _1595620, _1595622, _1595624, _1595626] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595616), tc_List_Olist(_1595616))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595616), tc_List_Olist(_1595616)), hAPP(hAPP(c_List_Olist_OCons(_1595616), _1595618), _1595620)), hAPP(hAPP(c_List_Olist_OCons(_1595616), _1595622), _1595624))), c_List_Olexord(_1595616, _1595626))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595616, _1595616)), hAPP(hAPP(c_Product__Type_OPair(_1595616, _1595616), _1595618), _1595622)), _1595626))), 41676 ^ _777959 : [(41679 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595616), tc_List_Olist(_1595616))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595616), tc_List_Olist(_1595616)), _1595620), _1595624)), c_List_Olexord(_1595616, _1595626))))], (41677 ^ _777959) ^ [] : [-(_1595618 = _1595622)]]], (28131 ^ _777959) ^ [_1308658, _1308660] : [c_Nat__Transfer_Onat__set(_1308658), c_Nat__Transfer_Onat__set(_1308660), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1308658), _1308660) = 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), _1308658)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1308660))))], (7136 ^ _777959) ^ [_897136, _897138, _897140] : [class_Lattices_Osemilattice__sup(_897136), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897136), _897138), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897136), _897138), _897140)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897136), _897138), _897140))], (50996 ^ _777959) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (27371 ^ _777959) ^ [_1295843, _1295845] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1295843)), hAPP(c_Int_Onat, _1295845)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1295845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1295843), _1295845))], (27732 ^ _777959) ^ [_1301935, _1301937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301935)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1301935), _1301937)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1301935)), _1301937))], (34375 ^ _777959) ^ [_1425031, _1425033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425031), _1425033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1425031)), c_Int_OBit1(_1425033))))], (6143 ^ _777959) ^ [_876360, _876362, _876364] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876360, tc_HOL_Obool)), _876362), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876360, tc_HOL_Obool)), _876362), _876364)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876360, tc_HOL_Obool)), _876362), _876364))], (48701 ^ _777959) ^ [_1759930, _1759932] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1759930, _1759930, _1759930), c_Transitive__Closure_Ortrancl(_1759930, _1759932)), c_Transitive__Closure_Ortrancl(_1759930, _1759932)) = c_Transitive__Closure_Ortrancl(_1759930, _1759932))], (42825 ^ _777959) ^ [_1626463, _1626465, _1626467, _1626469, _1626471] : [-(hAPP(hAPP(c_List_Oappend(_1626463), _1626465), _1626467) = hAPP(hAPP(c_List_Oappend(_1626463), _1626469), _1626471)), 42826 ^ _777959 : [(42833 ^ _777959) ^ [_1626687] : [hAPP(hAPP(c_List_Oappend(_1626463), _1626465), _1626687) = _1626469, _1626467 = hAPP(hAPP(c_List_Oappend(_1626463), _1626687), _1626471)], (42827 ^ _777959) ^ [_1626575] : [_1626465 = hAPP(hAPP(c_List_Oappend(_1626463), _1626469), _1626575), hAPP(hAPP(c_List_Oappend(_1626463), _1626575), _1626467) = _1626471]]], (15046 ^ _777959) ^ [_1064154] : [_1064154 = hAPP(c_Nat_OSuc, _1064154)], (48960 ^ _777959) ^ [_1766804, _1766806, _1766808, _1766810, _1766812] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1766804, _1766806)), hAPP(hAPP(c_Product__Type_OPair(_1766804, _1766806), _1766808), _1766810)), _1766812)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1766806, _1766804)), hAPP(hAPP(c_Product__Type_OPair(_1766806, _1766804), _1766810), _1766808)), hAPP(c_Relation_Oconverse(_1766804, _1766806), _1766812))))], (40359 ^ _777959) ^ [_1561241, _1561243, _1561245, _1561247] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1561241)), hAPP(hAPP(c_List_Olist__update(_1561241, _1561243), _1561245), _1561247)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1561241)), _1561243))], (31408 ^ _777959) ^ [_1371312] : [_1371312 = 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), _1371312)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (10946 ^ _777959) ^ [_972537, _972539, _972541, _972543] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_972537), 10949 ^ _777959 : [(10956 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972537), _972539), _972543)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972537), _972539), _972541)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972537), _972543), _972541))))], (10950 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972537), _972539), _972541)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972537), _972543), _972541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972537), _972539), _972543)))]]], (41080 ^ _777959) ^ [] : [41082 ^ _777959 : [(41085 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), 41081 ^ []))], (41083 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), 41081 ^ []), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))))]], -(c_Com_OWT__bodies)], (28040 ^ _777959) ^ [_1307068] : [c_Nat__Transfer_Onat__set(_1307068), 28043 ^ _777959 : [(28044 ^ _777959) ^ [_1307134] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1307134), _1307068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1307134)))]]], (1840 ^ _777959) ^ [_803683, _803685] : [-(hBOOL(_803683)), _803685 = _803683, hBOOL(_803685)], (51102 ^ _777959) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (43964 ^ _777959) ^ [_1652158, _1652160, _1652162, _1652164, _1652166, _1652168] : [class_Orderings_Olinorder(_1652158), -(hBOOL(hAPP(_1652160, _1652162))), -(hAPP(c_List_Ofilter(_1652164, _1652160), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1652164, _1652158, _1652166), _1652162), _1652168)) = hAPP(c_List_Ofilter(_1652164, _1652160), _1652168))], (48926 ^ _777959) ^ [_1765710, _1765712, _1765714, _1765716] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1765710, _1765710)), hAPP(hAPP(c_Product__Type_OPair(_1765710, _1765710), _1765712), _1765714)), c_Transitive__Closure_Ortrancl(_1765710, hAPP(c_Relation_Oconverse(_1765710, _1765710), _1765716)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765710, _1765710)), hAPP(hAPP(c_Product__Type_OPair(_1765710, _1765710), _1765714), _1765712)), c_Transitive__Closure_Ortrancl(_1765710, _1765716))))], (50380 ^ _777959) ^ [_1799586, _1799588, _1799590] : [-(c_Lazy__Sequence_Ohb__flat(_1799586, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1799586))), _1799588, _1799590)) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(_1799586), hAPP(c_Option_Ooption_Ooption__case(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1799586)), tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1799586)), c_Lazy__Sequence_Ohit__bound(_1799586), c_COMBI(tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1799586)))), _1799588), c_Lazy__Sequence_Ohb__flat(_1799586, _1799590)))], (45256 ^ _777959) ^ [_1680124] : [c_List_Onat__list(_1680124), -(c_List_Oembed__list(c_List_Oreturn__list(_1680124)) = _1680124)], (41928 ^ _777959) ^ [_1603806, _1603808, _1603810] : [41929 ^ _777959 : [(41932 ^ _777959) ^ [] : [_1603810 = c_List_Olist_ONil(_1603806)], (41930 ^ _777959) ^ [] : [_1603808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_List_Otake(_1603806), _1603808), _1603810) = c_List_Olist_ONil(_1603806))], (26864 ^ _777959) ^ [_1286706, _1286708, _1286710, _1286712] : [class_Fields_Ofield__inverse__zero(_1286706), -(_1286708 = c_Groups_Ozero__class_Ozero(_1286706)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1286706), _1286710), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286706), _1286712), _1286708)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286706), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1286706), _1286712), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286706), _1286710), _1286708))), _1286708))], (35475 ^ _777959) ^ [_1450543, _1450545, _1450547] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450543, _1450543), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1450545), _1450547))), -(_1450543 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1450545 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (40742 ^ _777959) ^ [_1569601, _1569603, _1569605, _1569607] : [40744 ^ _777959 : [(40747 ^ _777959) ^ [] : [hBOOL(hAPP(_1569605, hAPP(hAPP(c_List_Onth(_1569601), _1569603), 40743 ^ [_1569601, _1569603, _1569605, _1569607])))], (40745 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40743 ^ [_1569601, _1569603, _1569605, _1569607]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1569601)), _1569603))))]], hBOOL(hAPP(hAPP(c_member(_1569601), _1569607), hAPP(c_List_Oset(_1569601), _1569603))), -(hBOOL(hAPP(_1569605, _1569607)))], (35860 ^ _777959) ^ [_1458484, _1458486] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1458484, _1458486) = 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), _1458484), _1458486)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1458484, _1458486)))], (39045 ^ _777959) ^ [_1529937, _1529939, _1529941, _1529943, _1529945] : [c_Fun_Oinj__on(_1529937, _1529939, _1529941, c_Orderings_Otop__class_Otop(tc_fun(_1529937, tc_HOL_Obool))), c_Fun_Oinj__on(_1529943, _1529937, _1529945, c_Orderings_Otop__class_Otop(tc_fun(_1529943, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1529943, _1529939, hAPP(c_Fun_Ocomp(_1529937, _1529939, _1529943, _1529941), _1529945), c_Orderings_Otop__class_Otop(tc_fun(_1529943, tc_HOL_Obool))))], (19075 ^ _777959) ^ [_1144608, _1144610] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1144608), _1144610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1144608)), _1144610)))], (12125 ^ _777959) ^ [_997968, _997970, _997972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997968), _997970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997968), _997972)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997970), _997972))))], (17649 ^ _777959) ^ [_1115133, _1115135, _1115137] : [class_Orderings_Olinorder(_1115133), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115133), _1115135)), 17656 ^ _777959 : [(17663 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1115133, tc_HOL_Obool)), _1115135), hAPP(hAPP(c_Set_Oinsert(_1115133), _1115137), c_Orderings_Obot__class_Obot(tc_fun(_1115133, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1115133, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1115133, hAPP(hAPP(c_Set_Oinsert(_1115133), _1115137), _1115135)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1115133), _1115137), c_Big__Operators_Olinorder__class_OMin(_1115133, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1115133, tc_HOL_Obool)), _1115135), hAPP(hAPP(c_Set_Oinsert(_1115133), _1115137), c_Orderings_Obot__class_Obot(tc_fun(_1115133, tc_HOL_Obool)))))))], (17657 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1115133, tc_HOL_Obool)), _1115135), hAPP(hAPP(c_Set_Oinsert(_1115133), _1115137), c_Orderings_Obot__class_Obot(tc_fun(_1115133, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1115133, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1115133, hAPP(hAPP(c_Set_Oinsert(_1115133), _1115137), _1115135)) = _1115137)]]], (51270 ^ _777959) ^ [_1812840] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1812840)))], (50294 ^ _777959) ^ [_1797519, _1797521, _1797523] : [-(hAPP(c_New__DSequence_Opos__single(_1797519, _1797521), _1797523) = hAPP(c_Lazy__Sequence_Osingle(_1797519), _1797521))], (26338 ^ _777959) ^ [_1277189, _1277191, _1277193, _1277195, _1277197] : [class_Fields_Ofield(_1277189), -(_1277191 = c_Groups_Ozero__class_Ozero(_1277189)), -(_1277193 = c_Groups_Ozero__class_Ozero(_1277189)), 26349 ^ _777959 : [(26356 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277189), _1277195), _1277193) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277189), _1277197), _1277191), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277189), _1277195), _1277191) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277189), _1277197), _1277193))], (26350 ^ _777959) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277189), _1277195), _1277191) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277189), _1277197), _1277193), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277189), _1277195), _1277193) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277189), _1277197), _1277191))]]], (46660 ^ _777959) ^ [_1710461, _1710463, _1710465, _1710467, _1710469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1710461, _1710463)), hAPP(_1710461, _1710465))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1710467, _1710467)), hAPP(hAPP(c_Product__Type_OPair(_1710467, _1710467), _1710463), _1710465)), c_List_Omeasures(_1710467, _1710469))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1710467, _1710467)), hAPP(hAPP(c_Product__Type_OPair(_1710467, _1710467), _1710463), _1710465)), c_List_Omeasures(_1710467, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1710467, tc_Nat_Onat)), _1710461), _1710469)))))], (22802 ^ _777959) ^ [_1212881, _1212883, _1212885] : [class_Rings_Ocomm__semiring__1(_1212881), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1212881), _1212883), hAPP(c_Nat_OSuc, _1212885)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1212881), _1212883), hAPP(hAPP(c_Power_Opower__class_Opower(_1212881), _1212883), _1212885)))], (40373 ^ _777959) ^ [_1561581, _1561583, _1561585, _1561587, _1561589, _1561591] : [-(_1561581 = _1561583), -(hAPP(hAPP(c_List_Olist__update(_1561585, hAPP(hAPP(c_List_Olist__update(_1561585, _1561587), _1561581), _1561589)), _1561583), _1561591) = hAPP(hAPP(c_List_Olist__update(_1561585, hAPP(hAPP(c_List_Olist__update(_1561585, _1561587), _1561583), _1561591)), _1561581), _1561589))], (33417 ^ _777959) ^ [_1407970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1407970)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1407970), c_Int_OPls)))], (48899 ^ _777959) ^ [_1764957, _1764959, _1764961, _1764963, _1764965] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764957, _1764957)), hAPP(hAPP(c_Product__Type_OPair(_1764957, _1764957), _1764959), _1764961)), c_Transitive__Closure_Ortrancl(_1764957, _1764963))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1764957, _1764957), tc_HOL_Obool)), _1764963), hAPP(hAPP(c_Product__Type_OSigma(_1764957, _1764957), _1764965), hAPP(c_COMBK(tc_fun(_1764957, tc_HOL_Obool), _1764957), _1764965)))), -(_1764959 = _1764961), -(hBOOL(hAPP(hAPP(c_member(_1764957), _1764959), _1764965)))], (15456 ^ _777959) ^ [_1071867, _1071869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071867), hAPP(c_Nat_OSuc, _1071869))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071867), _1071869))), -(_1071867 = hAPP(c_Nat_OSuc, _1071869))], (7836 ^ _777959) ^ [_911202, _911204, _911206, _911208] : [c_Com_Ocom_OWhile(_911202, _911204) = c_Com_Ocom_OWhile(_911206, _911208), 7839 ^ _777959 : [(7842 ^ _777959) ^ [] : [-(_911204 = _911208)], (7840 ^ _777959) ^ [] : [-(_911202 = _911206)]]], (36109 ^ _777959) ^ [_1462643, _1462645] : [-(_1462643 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36112 ^ _777959 : [(36119 ^ _777959) ^ [] : [-(_1462645 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1462643, _1462645) = 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, _1462645))), 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)), _1462645)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1462643))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1462645), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1462643), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1462643, _1462645)), 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), _1462645))))), c_Divides_Opdivmod(_1462643, _1462645)))))], (36113 ^ _777959) ^ [] : [_1462645 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1462643, _1462645) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1462643))]]], (32027 ^ _777959) ^ [_1382773, _1382775, _1382777, _1382779] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382773), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382773), _1382775), _1382777)), hAPP(c_Int_Onumber__class_Onumber__of(_1382773), _1382779)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382773), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382773), _1382775), hAPP(c_Int_Onumber__class_Onumber__of(_1382773), _1382779))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382773), _1382777), hAPP(c_Int_Onumber__class_Onumber__of(_1382773), _1382779)))), class_Int_Onumber(_1382773), class_Rings_Oring(_1382773)], (49494 ^ _777959) ^ [_1780559, _1780561, _1780563, _1780565] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780559, _1780559)), hAPP(hAPP(c_Product__Type_OPair(_1780559, _1780559), _1780561), _1780563)), c_Transitive__Closure_Otrancl(_1780559, _1780565))), 49498 ^ _777959 : [(49501 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780559, _1780559)), hAPP(hAPP(c_Product__Type_OPair(_1780559, _1780559), 49497 ^ [_1780559, _1780561, _1780563, _1780565]), _1780563)), c_Transitive__Closure_Ortrancl(_1780559, _1780565))))], (49499 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780559, _1780559)), hAPP(hAPP(c_Product__Type_OPair(_1780559, _1780559), _1780561), 49497 ^ [_1780559, _1780561, _1780563, _1780565])), _1780565)))]]], (7980 ^ _777959) ^ [_914187, _914189] : [hBOOL(hAPP(c_Com_OWT, _914187)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_914189, _914187))))], (28877 ^ _777959) ^ [_1322309, _1322311, _1322313] : [28879 ^ _777959 : [(28882 ^ _777959) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1322313, 28878 ^ [_1322309, _1322311, _1322313]))], (28880 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1322309), 28878 ^ [_1322309, _1322311, _1322313]), _1322311)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1322309, tc_Int_Oint), _1322313), _1322311) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1322309, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1322309), c_Int_Onat), _1322313)), _1322311)))], (43685 ^ _777959) ^ [_1646381, _1646383, _1646385, _1646387, _1646389] : [c_Finite__Set_Ofun__left__comm__idem(_1646381, _1646383, _1646385), -(hAPP(hAPP(c_Finite__Set_Ofold(_1646381, _1646383, _1646385), _1646387), hAPP(c_List_Oset(_1646381), _1646389)) = hAPP(c_List_Ofoldl(_1646383, _1646381, hAPP(c_COMBC(_1646381, _1646383, _1646383), _1646385), _1646387), _1646389))], (3950 ^ _777959) ^ [_837797, _837799, _837801, _837803] : [-(c_Random_Oinc__shift(_837803, _837799) = c_Random_Oinc__shift(_837801, _837797)), _837803 = _837801, _837799 = _837797], (50758 ^ _777959) ^ [_1807427, _1807429] : [class_Lattices_Obounded__lattice(_1807427), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1807429, _1807427)))], (15364 ^ _777959) ^ [_1070232, _1070234] : [class_Rings_Ocomm__semiring__1(_1070232), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070232), _1070234), c_Groups_Oone__class_Oone(_1070232)) = _1070234)], (8170 ^ _777959) ^ [_918476, _918478, _918480, _918482] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918476, tc_HOL_Obool)), _918478), hAPP(hAPP(c_Set_Oinsert(_918476), _918480), _918482)))), 8173 ^ _777959 : [(8176 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918476, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918476, tc_HOL_Obool)), _918478), hAPP(hAPP(c_Set_Oinsert(_918476), _918480), c_Orderings_Obot__class_Obot(tc_fun(_918476, tc_HOL_Obool))))), _918482))], (8174 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_918476), _918480), _918478)))]], 8177 ^ _777959 : [(8180 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918476, tc_HOL_Obool)), _918478), _918482))], (8178 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_918476), _918480), _918478))]]], (7636 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (12095 ^ _777959) ^ [_997370, _997372] : [12096 ^ _777959 : [(12097 ^ _777959) ^ [_997420] : [_997372 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997370), _997420)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997370), _997372)))], (35699 ^ _777959) ^ [_1454712, _1454714, _1454716, _1454718, _1454720] : [hBOOL(hAPP(hAPP(_1454712, _1454714), _1454716)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1454718, _1454720, tc_HOL_Obool), _1454712), hAPP(hAPP(c_Product__Type_OPair(_1454718, _1454720), _1454714), _1454716))))], (26158 ^ _777959) ^ [_1273913, _1273915, _1273917, _1273919] : [class_Fields_Olinordered__field__inverse__zero(_1273913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273913), _1273915), _1273917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273913), c_Groups_Ozero__class_Ozero(_1273913)), _1273919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273913), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273913), _1273915), _1273919)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273913), _1273917), _1273919))))], (13427 ^ _777959) ^ [_1024208, _1024210] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1024208, _1024210)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1024208, _1024210), tc_HOL_Obool)))), 13430 ^ _777959 : [(13433 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1024210), c_Orderings_Otop__class_Otop(tc_fun(_1024210, tc_HOL_Obool)))))], (13431 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1024208), c_Orderings_Otop__class_Otop(tc_fun(_1024208, tc_HOL_Obool)))))]]], (50422 ^ _777959) ^ [_1800710, _1800712, _1800714] : [-(_1800712 = _1800714), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1800710, _1800710, hAPP(hAPP(c_COMBB(tc_fun(_1800710, tc_HOL_Obool), tc_fun(_1800710, tc_HOL_Obool), _1800710), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1800710), c_fNot)), c_fequal)), _1800712), _1800714)))], (16843 ^ _777959) ^ [_1100431, _1100433, _1100435, _1100437] : [class_Orderings_Olinorder(_1100431), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100431), _1100433), _1100435)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100431), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100431), _1100437), _1100433)), _1100435)))], (30239 ^ _777959) ^ [_1349910, _1349912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1349910), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30242 ^ _777959 : [(30245 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1349910), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1349912, _1349910))))], (30243 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1349912, _1349910)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (22796 ^ _777959) ^ [] : [-(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))], (6945 ^ _777959) ^ [_892031, _892033, _892035] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_892031, _892033, _892035))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _892033))))], (33241 ^ _777959) ^ [_1405282] : [class_Int_Onumber__ring(_1405282), -(hAPP(c_Int_Onumber__class_Onumber__of(_1405282), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1405282))], (47986 ^ _777959) ^ [_1744122, _1744124, _1744126] : [-(c_List_Olist__ex(_1744122, _1744124, _1744126)), 47987 ^ _777959 : [(47988 ^ _777959) ^ [_1744179] : [hBOOL(hAPP(hAPP(c_member(_1744122), _1744179), hAPP(c_List_Oset(_1744122), _1744126))), hBOOL(hAPP(_1744124, _1744179))]]], (7758 ^ _777959) ^ [_909598, _909600, _909602, _909604, _909606] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_909598, _909600, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_909598)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_909598), hAPP(hAPP(c_COMBC(_909598, tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_HOL_Obool)), _909598), c_COMBS(tc_Com_Ostate, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate, tc_HOL_Obool), tc_fun(tc_Com_Ostate, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _909598), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Com_Ostate), c_fconj)), _909602))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate), c_fNot), _909604))), c_Com_Ocom_OWhile(_909604, _909606)), _909602)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_909598), tc_HOL_Obool)))))], (33509 ^ _777959) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (31504 ^ _777959) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (11523 ^ _777959) ^ [_983768, _983770, _983772, _983774, _983776] : [class_Complete__Lattice_Ocomplete__lattice(_983768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983770, tc_HOL_Obool)), _983772), _983774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983768), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_983770, _983768), _983772), _983776)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_983770, _983768), _983774), _983776))))], (23124 ^ _777959) ^ [_1218682, _1218684, _1218686, _1218688] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1218682, _1218684)), c_Sum__Type_OPlus(_1218682, _1218684, _1218686, _1218688))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1218684), _1218688)))], (2846 ^ _777959) ^ [_820447, _820449, _820451, _820453, _820455, _820457] : [-(c_List_Olist_Olist__size(_820457, _820453, _820449) = c_List_Olist_Olist__size(_820455, _820451, _820447)), _820457 = _820455, _820453 = _820451, _820449 = _820447], (38846 ^ _777959) ^ [_1524154, _1524156, _1524158, _1524160] : [-(hAPP(c_Set_Oimage(_1524154, _1524156, _1524158), hAPP(c_Set_Ovimage(_1524154, _1524156, _1524158), _1524160)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1524156, tc_HOL_Obool)), _1524160), hAPP(c_Set_Oimage(_1524154, _1524156, _1524158), c_Orderings_Otop__class_Otop(tc_fun(_1524154, tc_HOL_Obool)))))], (48727 ^ _777959) ^ [_1760572, _1760574] : [-(c_Transitive__Closure_Ortrancl(_1760572, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1760572, _1760572), tc_HOL_Obool)), _1760574), c_Relation_OId(_1760572))) = c_Transitive__Closure_Ortrancl(_1760572, _1760574))], (48212 ^ _777959) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42515 ^ _777959) ^ [_1619241, _1619243] : [-(c_Product__Type_Omap__pair(_1619241, _1619241, _1619243, _1619243, c_COMBI(_1619241), c_COMBI(_1619243)) = c_Fun_Oid(tc_prod(_1619241, _1619243)))], (46910 ^ _777959) ^ [_1718448, _1718450, _1718452] : [c_Wellfounded_Owf(_1718448, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1718448, _1718448), tc_HOL_Obool)), _1718450), _1718452)), -(c_Wellfounded_Owf(_1718448, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1718448, _1718448), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1718448, _1718448), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1718448, _1718448, _1718448), _1718450), _1718450)), hAPP(hAPP(c_Relation_Orel__comp(_1718448, _1718448, _1718448), _1718452), _1718450))), _1718452)))], (12924 ^ _777959) ^ [_1012813, _1012815, _1012817] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1012813, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1012813, tc_HOL_Obool)), _1012815), _1012817)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012813, tc_HOL_Obool)), _1012815), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1012813, tc_HOL_Obool), _1012817)))], (49359 ^ _777959) ^ [_1776606, _1776608, _1776610, _1776612] : [-(hAPP(hAPP(c_Nat_Ocompow(_1776606, _1776606), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1776608), _1776610)), _1776612) = hAPP(c_Fun_Ocomp(_1776606, _1776606, _1776606, hAPP(hAPP(c_Nat_Ocompow(_1776606, _1776606), _1776608), _1776612)), hAPP(hAPP(c_Nat_Ocompow(_1776606, _1776606), _1776610), _1776612)))], (50994 ^ _777959) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (17857 ^ _777959) ^ [_1119269, _1119271] : [class_Orderings_Olinorder(_1119269), -(c_Big__Operators_Olattice_OInf__fin(_1119269, c_Orderings_Oord__class_Omin(_1119269), hAPP(hAPP(c_Set_Oinsert(_1119269), _1119271), c_Orderings_Obot__class_Obot(tc_fun(_1119269, tc_HOL_Obool)))) = _1119271)], (34505 ^ _777959) ^ [] : [-(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)))))], (17753 ^ _777959) ^ [_1117058] : [class_Orderings_Oord(_1117058), -(c_Orderings_Oord__class_Omax(_1117058) = c_Orderings_Oord_Omax(_1117058, c_Orderings_Oord__class_Oless__eq(_1117058)))], (44759 ^ _777959) ^ [_1667966] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1667966)), c_List_Otranspose__rel(_1667966)), c_List_Olist_ONil(tc_List_Olist(_1667966)))), -(c_List_Otranspose(_1667966, c_List_Olist_ONil(tc_List_Olist(_1667966))) = c_List_Olist_ONil(tc_List_Olist(_1667966)))], (40813 ^ _777959) ^ [_1571486, _1571488, _1571490, _1571492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1571486), _1571488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1571490, tc_HOL_Obool)), hAPP(c_List_Oset(_1571490), hAPP(hAPP(c_List_Otake(_1571490), _1571486), _1571492))), hAPP(c_List_Oset(_1571490), hAPP(hAPP(c_List_Otake(_1571490), _1571488), _1571492)))))], (38584 ^ _777959) ^ [_1518292, _1518294, _1518296, _1518298, _1518300] : [c_Typedef_Otype__definition(_1518292, _1518294, _1518296, _1518298, _1518300), -(hAPP(c_Set_Oimage(_1518294, _1518292, _1518298), _1518300) = c_Orderings_Otop__class_Otop(tc_fun(_1518292, tc_HOL_Obool)))], (49372 ^ _777959) ^ [_1776928, _1776930, _1776932] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776928, _1776928)), _1776930), c_Transitive__Closure_Otrancl(_1776928, _1776932)))), 49373 ^ _777959 : [(49374 ^ _777959) ^ [_1777007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1777007)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1776928, _1776928)), _1776930), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1776928, _1776928), tc_HOL_Obool), _1777007), _1776932)))]]], (12020 ^ _777959) ^ [_996124, _996126] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996124), _996126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996126), _996124)), -(_996124 = _996126)], (23186 ^ _777959) ^ [_1219863, _1219865, _1219867, _1219869] : [class_Rings_Olinordered__semidom(_1219863), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219863), _1219865), _1219867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1219863), c_Groups_Ozero__class_Ozero(_1219863)), _1219865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1219869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1219863), hAPP(hAPP(c_Power_Opower__class_Opower(_1219863), _1219865), _1219869)), hAPP(hAPP(c_Power_Opower__class_Opower(_1219863), _1219867), _1219869))))], (5952 ^ _777959) ^ [_872909, _872911] : [class_Orderings_Opreorder(_872909), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_872909), _872911), _872911)))], (3864 ^ _777959) ^ [_836458, _836460, _836462, _836464, _836466, _836468] : [-(c_List_Olinorder__class_Oinsort__key(_836468, _836464, _836460) = c_List_Olinorder__class_Oinsort__key(_836466, _836462, _836458)), _836468 = _836466, _836464 = _836462, _836460 = _836458], (34077 ^ _777959) ^ [_1419820, _1419822] : [_1419820 = _1419822, -(c_Int_OBit0(_1419820) = c_Int_OBit0(_1419822))], (47011 ^ _777959) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (30982 ^ _777959) ^ [_1363244, _1363246, _1363248, _1363250] : [class_Fields_Olinordered__field(_1363244), -(hAPP(c_Groups_Oabs__class_Oabs(_1363244), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1363246, _1363244), _1363248), _1363250)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1363246, _1363244), hAPP(hAPP(c_COMBB(_1363244, _1363244, _1363246), c_Groups_Oabs__class_Oabs(_1363244)), _1363248)), _1363250))], (33379 ^ _777959) ^ [_1407382] : [class_Int_Onumber__ring(_1407382), -(c_Groups_Oone__class_Oone(_1407382) = hAPP(c_Int_Onumber__class_Onumber__of(_1407382), c_Int_OBit1(c_Int_OPls)))], (38983 ^ _777959) ^ [_1528301, _1528303, _1528305, _1528307, _1528309, _1528311] : [-(hAPP(hAPP(c_Option_Omap(_1528301, _1528303), _1528305), hAPP(hAPP(c_Option_Omap(_1528307, _1528301), _1528309), _1528311)) = hAPP(hAPP(c_Option_Omap(_1528307, _1528303), hAPP(c_Fun_Ocomp(_1528301, _1528303, _1528307, _1528305), _1528309)), _1528311))], (34789 ^ _777959) ^ [_1432573, _1432575, _1432577] : [class_Groups_Omonoid__mult(_1432573), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1432573), _1432575), 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)))), _1432577))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432573), _1432575), hAPP(hAPP(c_Power_Opower__class_Opower(_1432573), hAPP(hAPP(c_Power_Opower__class_Opower(_1432573), _1432575), _1432577)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (50992 ^ _777959) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (22760 ^ _777959) ^ [_1211980, _1211982, _1211984] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1211980), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1211982), _1211984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1211980), _1211982)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1211980), _1211984)))], (5482 ^ _777959) ^ [_861745, _861747, _861749, _861751] : [-(tc_sum(_861751, _861747) = tc_sum(_861749, _861745)), _861751 = _861749, _861747 = _861745], (14732 ^ _777959) ^ [_1054871, _1054873, _1054875, _1054877, _1054879] : [hBOOL(hAPP(hAPP(c_member(_1054871), _1054873), c_SetInterval_Oord_OgreaterThanLessThan(_1054871, _1054875, _1054877, _1054879))), 14735 ^ _777959 : [(14738 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1054875, _1054873), _1054879)))], (14736 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1054875, _1054877), _1054873)))]]], (12267 ^ _777959) ^ [_1000679, _1000681, _1000683] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000679), _1000681)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000679), _1000683)), 12274 ^ _777959 : [(12281 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000681), _1000683)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1000681), _1000679)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1000683), _1000679))))], (12275 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1000681), _1000679)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1000683), _1000679))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000681), _1000683)))]]], (40785 ^ _777959) ^ [_1570810, _1570812, _1570814, _1570816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1570810), _1570812)), -(hAPP(hAPP(c_List_Onth(_1570814), hAPP(hAPP(c_List_Otake(_1570814), _1570812), _1570816)), _1570810) = hAPP(hAPP(c_List_Onth(_1570814), _1570816), _1570810))], (48230 ^ _777959) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46115 ^ _777959) ^ [_1698291, _1698293, _1698295] : [46117 ^ _777959 : [(46120 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1698293, 46116 ^ [_1698291, _1698293, _1698295])))], (46118 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1698291), 46116 ^ [_1698291, _1698293, _1698295]), hAPP(c_List_Oset(_1698291), c_List_OdropWhile(_1698291, _1698293, _1698295)))))]], -(c_List_OtakeWhile(_1698291, _1698293, _1698295) = hAPP(c_List_Ofilter(_1698291, _1698293), _1698295))], (35055 ^ _777959) ^ [_1437695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1437695), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1437695)), c_Int_OMin)))], (3050 ^ _777959) ^ [_823655, _823657, _823659, _823661] : [-(c_Fun_Ofun__upd(_823661, _823657) = c_Fun_Ofun__upd(_823659, _823655)), _823661 = _823659, _823657 = _823655], (36972 ^ _777959) ^ [_1480637, _1480639, _1480641, _1480643] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1480637), _1480639)), -(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), _1480637), _1480641)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1480639), _1480643))), c_FunDef_Opair__less)))], (10699 ^ _777959) ^ [_967895, _967897, _967899, _967901] : [class_Groups_Ocancel__semigroup__add(_967895), 10702 ^ _777959 : [(10709 ^ _777959) ^ [] : [_967899 = _967901, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967895), _967897), _967899) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967895), _967897), _967901))], (10703 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967895), _967897), _967899) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967895), _967897), _967901), -(_967899 = _967901)]]], (34497 ^ _777959) ^ [_1427297, _1427299, _1427301] : [class_Groups_Omonoid__mult(_1427297), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427297), _1427299), 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)))), _1427301)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1427297), hAPP(hAPP(c_Power_Opower__class_Opower(_1427297), _1427299), _1427301)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (22042 ^ _777959) ^ [_1197199, _1197201, _1197203, _1197205, _1197207] : [class_Groups_Ocomm__monoid__mult(_1197199), hBOOL(hAPP(c_Finite__Set_Ofinite(_1197201), _1197203)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1197201, _1197199), _1197205), hAPP(hAPP(c_Set_Oinsert(_1197201), _1197207), _1197203)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197199), hAPP(_1197205, _1197207)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1197201, _1197199), _1197205), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1197201, tc_HOL_Obool)), _1197203), hAPP(hAPP(c_Set_Oinsert(_1197201), _1197207), c_Orderings_Obot__class_Obot(tc_fun(_1197201, tc_HOL_Obool)))))))], (51002 ^ _777959) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (15102 ^ _777959) ^ [_1065228, _1065230, _1065232, _1065234] : [class_Rings_Ocomm__semiring__1(_1065228), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065228), _1065230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065228), _1065232), _1065234)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065228), _1065232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065228), _1065230), _1065234)))], (14363 ^ _777959) ^ [_1046174, _1046176, _1046178] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046174), _1046176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1046174), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1046174, tc_HOL_Obool)), _1046176), hAPP(hAPP(c_Set_Oinsert(_1046174), _1046178), c_Orderings_Obot__class_Obot(tc_fun(_1046174, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1046174), _1046176))))], (38658 ^ _777959) ^ [_1519583, _1519585, _1519587, _1519589] : [c_Fun_Oinj__on(_1519583, _1519585, _1519587, c_Orderings_Otop__class_Otop(tc_fun(_1519583, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1519583, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1519583, _1519585, _1519587), hAPP(hAPP(c_Set_Oinsert(_1519585), _1519589), c_Orderings_Obot__class_Obot(tc_fun(_1519585, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1519583), c_HOL_OThe(_1519583, hAPP(hAPP(c_COMBC(_1519583, _1519585, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1519585, tc_fun(_1519585, tc_HOL_Obool), _1519583), c_fequal), _1519587)), _1519589))), c_Orderings_Obot__class_Obot(tc_fun(_1519583, tc_HOL_Obool))))))], (51362 ^ _777959) ^ [_1813698, _1813700, _1813702, _1813704] : [-(hAPP(hAPP(c_COMBK(_1813698, _1813700), _1813702), _1813704) = _1813702)], (39490 ^ _777959) ^ [_1540031, _1540033, _1540035, _1540037, _1540039, _1540041, _1540043] : [c_Hoare__Mirabelle_Ohoare__derivs(_1540031, _1540033, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1540031)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1540031), c_Hoare__Mirabelle_Opeek__and(_1540031, _1540035, _1540037)), _1540039), _1540041)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1540031), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_1540031, _1540033, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1540031)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1540031), c_Hoare__Mirabelle_Opeek__and(_1540031, _1540035, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1540037))), _1540043), _1540041)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1540031), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1540031, _1540033, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1540031)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1540031), _1540035), c_Com_Ocom_OCond(_1540037, _1540039, _1540043)), _1540041)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1540031), tc_HOL_Obool)))))], (17255 ^ _777959) ^ [_1107894] : [class_Complete__Lattice_Ocomplete__lattice(_1107894), -(c_Complete__Lattice_OInf__class_OInf(_1107894, c_Orderings_Otop__class_Otop(tc_fun(_1107894, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1107894))], (39013 ^ _777959) ^ [_1529071, _1529073, _1529075, _1529077, _1529079] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1529071), tc_Option_Ooption(_1529073), tc_Option_Ooption(_1529075), hAPP(c_Option_Omap(_1529071, _1529073), _1529077)), hAPP(c_Option_Omap(_1529075, _1529071), _1529079)) = hAPP(c_Option_Omap(_1529075, _1529073), hAPP(c_Fun_Ocomp(_1529071, _1529073, _1529075, _1529077), _1529079)))], (43562 ^ _777959) ^ [_1643733, _1643735, _1643737] : [-(hAPP(c_List_Orotate(_1643733, hAPP(c_Nat_OSuc, _1643735)), _1643737) = hAPP(c_List_Orotate1(_1643733), hAPP(c_List_Orotate(_1643733, _1643735), _1643737)))], (22364 ^ _777959) ^ [_1203906, _1203908, _1203910] : [-(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), _1203906)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1203908))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1203910))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1203910), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203906), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203906), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1203910), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1203908)))))], (51058 ^ _777959) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (18253 ^ _777959) ^ [_1126614, _1126616, _1126618] : [class_Orderings_Olinorder(_1126614), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126614), _1126616)), hBOOL(hAPP(hAPP(c_member(_1126614), _1126618), _1126616)), 18264 ^ _777959 : [(18271 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1126614, tc_HOL_Obool)), _1126616), hAPP(hAPP(c_Set_Oinsert(_1126614), _1126618), c_Orderings_Obot__class_Obot(tc_fun(_1126614, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1126614, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1126614, c_Orderings_Oord__class_Omax(_1126614), _1126616) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1126614), _1126618), c_Big__Operators_Olattice_OSup__fin(_1126614, c_Orderings_Oord__class_Omax(_1126614), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1126614, tc_HOL_Obool)), _1126616), hAPP(hAPP(c_Set_Oinsert(_1126614), _1126618), c_Orderings_Obot__class_Obot(tc_fun(_1126614, tc_HOL_Obool)))))))], (18265 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1126614, tc_HOL_Obool)), _1126616), hAPP(hAPP(c_Set_Oinsert(_1126614), _1126618), c_Orderings_Obot__class_Obot(tc_fun(_1126614, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1126614, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1126614, c_Orderings_Oord__class_Omax(_1126614), _1126616) = _1126618)]]], (19110 ^ _777959) ^ [_1145256] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1145256))))], (32007 ^ _777959) ^ [_1382287, _1382289, _1382291, _1382293] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382287), hAPP(c_Int_Onumber__class_Onumber__of(_1382287), _1382289)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382287), _1382291), _1382293)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382287), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382287), hAPP(c_Int_Onumber__class_Onumber__of(_1382287), _1382289)), _1382291)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382287), hAPP(c_Int_Onumber__class_Onumber__of(_1382287), _1382289)), _1382293))), class_Int_Onumber(_1382287), class_Rings_Osemiring(_1382287)], (45170 ^ _777959) ^ [_1678455, _1678457, _1678459] : [-(c_List_OtakeWhile(_1678455, _1678457, _1678459) = hAPP(hAPP(c_List_Otake(_1678455), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678455)), c_List_OtakeWhile(_1678455, _1678457, _1678459))), _1678459))], (50712 ^ _777959) ^ [_1806663, _1806665, _1806667] : [hBOOL(hAPP(hAPP(c_List_Omember(_1806663), _1806665), _1806667)), -(hBOOL(hAPP(hAPP(c_member(_1806663), _1806667), hAPP(c_List_Oset(_1806663), _1806665))))], (51276 ^ _777959) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (31845 ^ _777959) ^ [_1379462, _1379464, _1379466] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1379462, _1379464, _1379466))), -(hBOOL(hAPP(c_Com_OWT, _1379466)))], (8394 ^ _777959) ^ [_923532, _923534, _923536] : [class_Lattices_Olattice(_923532), hBOOL(hAPP(c_Finite__Set_Ofinite(_923532), _923534)), hBOOL(hAPP(hAPP(c_member(_923532), _923536), _923534)), 8405 ^ _777959 : [(8412 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923532, tc_HOL_Obool)), _923534), hAPP(hAPP(c_Set_Oinsert(_923532), _923536), c_Orderings_Obot__class_Obot(tc_fun(_923532, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_923532, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_923532, _923534) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_923532), _923536), c_Big__Operators_Olattice__class_OSup__fin(_923532, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923532, tc_HOL_Obool)), _923534), hAPP(hAPP(c_Set_Oinsert(_923532), _923536), c_Orderings_Obot__class_Obot(tc_fun(_923532, tc_HOL_Obool)))))))], (8406 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923532, tc_HOL_Obool)), _923534), hAPP(hAPP(c_Set_Oinsert(_923532), _923536), c_Orderings_Obot__class_Obot(tc_fun(_923532, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_923532, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_923532, _923534) = _923536)]]], (37714 ^ _777959) ^ [_1499474, _1499476, _1499478] : [c_Equiv__Relations_Oequivp(_1499474, _1499476), -(hBOOL(hAPP(hAPP(_1499476, _1499478), _1499478)))], (45262 ^ _777959) ^ [_1680205, _1680207] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680205)), c_List_Oremdups(_1680205, c_List_Oconcat(_1680205, _1680207))) = hAPP(c_Finite__Set_Ocard(_1680205), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1680205), tc_fun(_1680205, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1680205)), _1680207)), c_List_Oset(_1680205))))], (13630 ^ _777959) ^ [_1028643, _1028645, _1028647, _1028649, _1028651] : [-(hAPP(hAPP(c_Set_Oinsert(_1028643), _1028645), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1028647, tc_fun(_1028643, tc_HOL_Obool)), _1028649), _1028651)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1028647, tc_fun(_1028643, tc_HOL_Obool)), _1028649), hAPP(hAPP(c_COMBB(tc_fun(_1028643, tc_HOL_Obool), tc_fun(_1028643, tc_HOL_Obool), _1028647), hAPP(c_Set_Oinsert(_1028643), _1028645)), _1028651)))], (39800 ^ _777959) ^ [_1547267, _1547269, _1547271, _1547273] : [-(hBOOL(hAPP(hAPP(c_member(_1547267), _1547269), hAPP(c_List_Oset(_1547267), _1547271)))), hBOOL(hAPP(hAPP(c_member(_1547267), _1547269), hAPP(c_List_Oset(_1547267), c_List_Oremove1(_1547267, _1547273, _1547271))))], (26382 ^ _777959) ^ [_1277962, _1277964, _1277966, _1277968] : [class_Fields_Ofield__inverse__zero(_1277962), 26385 ^ _777959 : [(26386 ^ _777959) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277962), _1277964), _1277966) = _1277968, 26389 ^ _777959 : [(26396 ^ _777959) ^ [] : [_1277966 = c_Groups_Ozero__class_Ozero(_1277962), -(_1277968 = c_Groups_Ozero__class_Ozero(_1277962))], (26390 ^ _777959) ^ [] : [-(_1277966 = c_Groups_Ozero__class_Ozero(_1277962)), -(_1277964 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277962), _1277968), _1277966))]]], (26402 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277962), _1277964), _1277966) = _1277968), 26405 ^ _777959 : [(26408 ^ _777959) ^ [] : [_1277964 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277962), _1277968), _1277966)], (26406 ^ _777959) ^ [] : [_1277966 = c_Groups_Ozero__class_Ozero(_1277962)]], 26409 ^ _777959 : [(26412 ^ _777959) ^ [] : [_1277968 = c_Groups_Ozero__class_Ozero(_1277962)], (26410 ^ _777959) ^ [] : [-(_1277966 = c_Groups_Ozero__class_Ozero(_1277962))]]]]], (10380 ^ _777959) ^ [_961048, _961050, _961052, _961054, _961056] : [class_Groups_Oab__group__add(_961048), hBOOL(hAPP(c_Finite__Set_Ofinite(_961050), _961052)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_961050, tc_HOL_Obool)), _961054), _961052)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_961050, _961048), _961056), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_961050, tc_HOL_Obool)), _961052), _961054)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_961048), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_961050, _961048), _961056), _961052)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_961050, _961048), _961056), _961054)))], (43642 ^ _777959) ^ [_1645582] : [class_Groups_Omonoid__add(_1645582), -(c_List_Omonoid__add__class_Olistsum(_1645582) = c_List_Ofoldl(_1645582, _1645582, c_Groups_Oplus__class_Oplus(_1645582), c_Groups_Ozero__class_Ozero(_1645582)))], (46439 ^ _777959) ^ [_1705637, _1705639, _1705641, _1705643] : [c_List_Olist__all2(_1705637, _1705639, _1705641, c_List_Olist_ONil(_1705637), _1705643), -(_1705643 = c_List_Olist_ONil(_1705639))], (50300 ^ _777959) ^ [_1797741, _1797743, _1797745, _1797747] : [-(c_Lazy__Sequence_Oproduct(_1797741, _1797743, _1797745, _1797747) = hAPP(c_Lazy__Sequence_Obind(_1797741, tc_prod(_1797741, _1797743), _1797745), hAPP(hAPP(c_COMBB(tc_fun(_1797743, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1797741, _1797743))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1797741, _1797743)), _1797741), c_Lazy__Sequence_Obind(_1797743, tc_prod(_1797741, _1797743), _1797747)), hAPP(hAPP(c_COMBB(tc_fun(_1797743, tc_prod(_1797741, _1797743)), tc_fun(_1797743, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1797741, _1797743))), _1797741), hAPP(c_COMBB(tc_prod(_1797741, _1797743), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1797741, _1797743)), _1797743), c_Lazy__Sequence_Osingle(tc_prod(_1797741, _1797743)))), c_Product__Type_OPair(_1797741, _1797743)))))], (35049 ^ _777959) ^ [_1437600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1437600)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1437600), c_Int_OMin)))], (13739 ^ _777959) ^ [_1031883, _1031885, _1031887, _1031889, _1031891, _1031893] : [hAPP(_1031883, _1031885) = hAPP(c_Option_Ooption_OSome(_1031887), _1031889), -(hAPP(c_Map_Omap__add(_1031891, _1031887, _1031893, _1031883), _1031885) = hAPP(c_Option_Ooption_OSome(_1031887), _1031889))], (10978 ^ _777959) ^ [_973159, _973161] : [-(_973159 = hAPP(c_Option_Ooption_OSome(_973161), 10979 ^ [_973159, _973161])), -(_973159 = c_Option_Ooption_ONone(_973161))], (5628 ^ _777959) ^ [_863956, _863958, _863960, _863962] : [-(tc_fun(_863962, _863958) = tc_fun(_863960, _863956)), _863962 = _863960, _863958 = _863956], (26820 ^ _777959) ^ [_1285925, _1285927, _1285929, _1285931, _1285933] : [class_Fields_Ofield(_1285925), -(_1285927 = c_Groups_Ozero__class_Ozero(_1285925)), -(_1285929 = c_Groups_Ozero__class_Ozero(_1285925)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1285925), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285925), _1285931), _1285927)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285925), _1285933), _1285929)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285925), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1285925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285925), _1285931), _1285929)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285925), _1285933), _1285927))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285925), _1285927), _1285929)))], (28239 ^ _777959) ^ [_1310398] : [c_Nat__Transfer_Onat__set(_1310398), 28242 ^ _777959 : [(28249 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1310398))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1310398)))], (28243 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1310398)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1310398))))]]], (49308 ^ _777959) ^ [_1775167, _1775169, _1775171, _1775173] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775167, _1775167), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1775169), _1775171)), _1775173) = hAPP(hAPP(c_Relation_Orel__comp(_1775167, _1775167, _1775167), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775167, _1775167), tc_HOL_Obool), _1775169), _1775173)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775167, _1775167), tc_HOL_Obool), _1775171), _1775173)))], (29573 ^ _777959) ^ [_1335618, _1335620] : [-(hBOOL(hAPP(_1335618, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1335618, _1335620)), 29581 ^ _777959 : [(29584 ^ _777959) ^ [_1335856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1335856), 29580 ^ [_1335618, _1335620])), hBOOL(hAPP(_1335618, _1335856))], (29590 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1335618, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 29580 ^ [_1335618, _1335620]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (29582 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 29580 ^ [_1335618, _1335620]), _1335620)))]]], (10104 ^ _777959) ^ [_954146, _954148, _954150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_954146, tc_HOL_Obool)), _954148), _954150)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954146, tc_HOL_Obool)), _954150), _954148) = _954148)], (41831 ^ _777959) ^ [_1601060, _1601062, _1601064] : [41833 ^ _777959 : [(41836 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1601060), 41832 ^ [_1601060, _1601062, _1601064]), _1601064))], (41834 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601060), 41832 ^ [_1601060, _1601062, _1601064]), hAPP(c_List_Oset(_1601060), _1601062))))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1601060)), _1601062), c_List_Olists(_1601060, _1601064))))], (20789 ^ _777959) ^ [_1173898, _1173900, _1173902] : [class_Groups_Ocomm__monoid__add(_1173898), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1173900, _1173898), _1173902), c_Orderings_Obot__class_Obot(tc_fun(_1173900, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1173898))], (35997 ^ _777959) ^ [_1460826] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1460826) = 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)))], (14678 ^ _777959) ^ [_1053773, _1053775, _1053777, _1053779] : [hBOOL(hAPP(hAPP(c_member(_1053773), _1053775), c_SetInterval_Oord_OatLeast(_1053773, _1053777, _1053779))), -(hBOOL(hAPP(hAPP(_1053777, _1053779), _1053775)))], (38774 ^ _777959) ^ [_1522338, _1522340, _1522342, _1522344, _1522346, _1522348] : [-(hAPP(c_Set_Ovimage(_1522338, _1522340, _1522342), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1522344, tc_fun(_1522340, tc_HOL_Obool)), _1522346), _1522348)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1522344, tc_fun(_1522338, tc_HOL_Obool)), _1522346), hAPP(hAPP(c_COMBB(tc_fun(_1522340, tc_HOL_Obool), tc_fun(_1522338, tc_HOL_Obool), _1522344), c_Set_Ovimage(_1522338, _1522340, _1522342)), _1522348)))], (6913 ^ _777959) ^ [_891040, _891042, _891044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891040, tc_HOL_Obool)), _891042), hAPP(hAPP(c_Set_Oinsert(_891040), _891044), c_Orderings_Obot__class_Obot(tc_fun(_891040, tc_HOL_Obool))))), -(_891042 = c_Orderings_Obot__class_Obot(tc_fun(_891040, tc_HOL_Obool))), -(_891042 = hAPP(hAPP(c_Set_Oinsert(_891040), _891044), c_Orderings_Obot__class_Obot(tc_fun(_891040, tc_HOL_Obool))))], (13235 ^ _777959) ^ [_1019764, _1019766, _1019768, _1019770] : [class_Lattices_Osemilattice__inf(_1019764), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019764), _1019766)), 13245 ^ _777959 : [(13248 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019764), _1019768), 13244 ^ [_1019764, _1019766, _1019768, _1019770]))], (13246 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1019764), 13244 ^ [_1019764, _1019766, _1019768, _1019770]), _1019766)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1019764), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1019764), _1019768), _1019770)), hAPP(hAPP(c_Finite__Set_Ofold(_1019764, _1019764, c_Lattices_Osemilattice__inf__class_Oinf(_1019764)), _1019770), _1019766))))], (47387 ^ _777959) ^ [_1729845, _1729847, _1729849, _1729851] : [hBOOL(hAPP(c_Predicate_ODomainP(_1729845, _1729847, hAPP(hAPP(c_COMBC(_1729845, tc_fun(tc_prod(_1729845, _1729847), tc_HOL_Obool), tc_fun(_1729847, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1729847, tc_fun(tc_fun(tc_prod(_1729845, _1729847), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1729845, _1729847), tc_HOL_Obool), tc_fun(_1729847, tc_HOL_Obool)), _1729845), c_COMBC(_1729847, tc_fun(tc_prod(_1729845, _1729847), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1729847, tc_prod(_1729845, _1729847)), tc_fun(_1729847, tc_fun(tc_fun(tc_prod(_1729845, _1729847), tc_HOL_Obool), tc_HOL_Obool)), _1729845), hAPP(c_COMBB(tc_prod(_1729845, _1729847), tc_fun(tc_fun(tc_prod(_1729845, _1729847), tc_HOL_Obool), tc_HOL_Obool), _1729847), c_member(tc_prod(_1729845, _1729847)))), c_Product__Type_OPair(_1729845, _1729847)))), _1729849)), _1729851)), -(hBOOL(hAPP(hAPP(c_member(_1729845), _1729851), hAPP(c_Relation_ODomain(_1729845, _1729847), _1729849))))], (49136 ^ _777959) ^ [_1771068, _1771070, _1771072] : [c_Relation_Ototal__on(_1771068, _1771070, _1771072), -(c_Relation_Ototal__on(_1771068, _1771070, hAPP(c_Relation_Oconverse(_1771068, _1771068), _1771072)))], (37128 ^ _777959) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (41593 ^ _777959) ^ [_1593610, _1593612, _1593614, _1593616, _1593618, _1593620, _1593622] : [-(c_Map_Omap__upds(_1593610, _1593612, _1593614, hAPP(hAPP(c_List_Olist_OCons(_1593610), _1593616), _1593618), hAPP(hAPP(c_List_Olist_OCons(_1593612), _1593620), _1593622)) = c_Map_Omap__upds(_1593610, _1593612, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1593610, tc_Option_Ooption(_1593612)), _1593614), _1593616), hAPP(c_Option_Ooption_OSome(_1593612), _1593620)), _1593618, _1593622))], (43258 ^ _777959) ^ [_1636947, _1636949, _1636951] : [-(hAPP(hAPP(c_List_Odrop(_1636947), _1636949), c_List_Obutlast(_1636947, _1636951)) = c_List_Obutlast(_1636947, hAPP(hAPP(c_List_Odrop(_1636947), _1636949), _1636951)))], (41223 ^ _777959) ^ [_1584802, _1584804, _1584806, _1584808, _1584810] : [c_Relation_Orefl__on(_1584802, _1584804, _1584806), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584802, _1584802)), hAPP(hAPP(c_Product__Type_OPair(_1584802, _1584802), _1584808), _1584810)), _1584806)), -(hBOOL(hAPP(hAPP(c_member(_1584802), _1584808), _1584804)))], (48821 ^ _777959) ^ [_1762794, _1762796, _1762798, _1762800] : [c_Wellfounded_Owf(_1762794, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1762794, _1762794)), hAPP(hAPP(c_Product__Type_OPair(_1762794, _1762794), _1762796), _1762798)), _1762800)), 48824 ^ _777959 : [(48827 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1762794, _1762794)), hAPP(hAPP(c_Product__Type_OPair(_1762794, _1762794), _1762798), _1762796)), c_Transitive__Closure_Ortrancl(_1762794, _1762800)))], (48825 ^ _777959) ^ [] : [-(c_Wellfounded_Owf(_1762794, _1762800))]]], (10066 ^ _777959) ^ [_953354, _953356, _953358] : [10068 ^ _777959 : [(10074 ^ _777959) ^ [] : [-(10067 ^ [_953354, _953356, _953358] = 10070 ^ [_953354, _953356, _953358])], (10072 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_953354), 10070 ^ [_953354, _953356, _953358]), _953358)))], (10069 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_953354), 10067 ^ [_953354, _953356, _953358]), _953356)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953354, tc_HOL_Obool)), _953356), _953358) = c_Orderings_Obot__class_Obot(tc_fun(_953354, tc_HOL_Obool)))], (6611 ^ _777959) ^ [_884992, _884994, _884996] : [hBOOL(hAPP(hAPP(c_member(_884992), _884994), c_Option_Oset(_884992, _884996))), -(_884996 = hAPP(c_Option_Ooption_OSome(_884992), _884994))], (2804 ^ _777959) ^ [_819830, _819832, _819834, _819836] : [-(c_Nitpick_Ocard_H(_819836, _819832) = c_Nitpick_Ocard_H(_819834, _819830)), _819836 = _819834, _819832 = _819830], (1420 ^ _777959) ^ [_798433, _798435] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_798433)), _798435 = _798433, class_Groups_Oordered__cancel__ab__semigroup__add(_798435)], (4148 ^ _777959) ^ [_840766, _840768] : [_840768 = _840766, -(c_Fun_Oid(_840768) = c_Fun_Oid(_840766))], (41733 ^ _777959) ^ [_1598467, _1598469, _1598471, _1598473, _1598475, _1598477] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1598467, _1598469), _1598467, tc_prod(_1598471, _1598473), c_Product__Type_Ofst(_1598467, _1598469)), c_Product__Type_Omap__pair(_1598471, _1598467, _1598473, _1598469, _1598475, _1598477)) = hAPP(c_Fun_Ocomp(_1598471, _1598467, tc_prod(_1598471, _1598473), _1598475), c_Product__Type_Ofst(_1598471, _1598473)))], (200 ^ _777959) ^ [_781231, _781233] : [-(class_Rings_Odivision__ring(_781231)), _781233 = _781231, class_Rings_Odivision__ring(_781233)], (24490 ^ _777959) ^ [_1243025, _1243027] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1243025)), hAPP(c_Option_Ooption_OSome(_1243025), _1243027)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50392 ^ _777959) ^ [_1799922, _1799924, _1799926] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799922)), c_List_Osplice(_1799922, _1799924, _1799926)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799922)), _1799924)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799922)), _1799926)))], (23036 ^ _777959) ^ [_1217190, _1217192] : [class_Rings_Osemiring__1(_1217190), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217190), hAPP(c_Nat_OSuc, _1217192)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217190), c_Groups_Oone__class_Oone(_1217190)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217190), _1217192)))], (47456 ^ _777959) ^ [_1731621, _1731623] : [c_Wellfounded_OwfP(_1731621, _1731623), 47459 ^ _777959 : [(47460 ^ _777959) ^ [_1731685] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1731621, _1731623), _1731685)))]]], (29783 ^ _777959) ^ [_1340627, _1340629, _1340631] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1340627, tc_HOL_Obool)), _1340631), hAPP(c_Set_OPow(_1340627), _1340629))), -(hBOOL(hAPP(c_Predicate_OPowp(_1340627, hAPP(hAPP(c_COMBC(_1340627, tc_fun(_1340627, tc_HOL_Obool), tc_HOL_Obool), c_member(_1340627)), _1340629)), _1340631)))], (16274 ^ _777959) ^ [_1089305, _1089307, _1089309, _1089311, _1089313] : [class_Groups_Ocomm__monoid__mult(_1089305), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089307), _1089309)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1089307), _1089311)), 16288 ^ _777959 : [(16291 ^ _777959) ^ [] : [hAPP(_1089313, 16287 ^ [_1089305, _1089307, _1089309, _1089311, _1089313]) = c_Groups_Oone__class_Oone(_1089305)], (16289 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1089307), 16287 ^ [_1089305, _1089307, _1089309, _1089311, _1089313]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1089307, tc_HOL_Obool)), _1089309), _1089311))))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1089305, _1089307, c_Groups_Otimes__class_Otimes(_1089305)), _1089313), c_Groups_Oone__class_Oone(_1089305)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1089307, tc_HOL_Obool)), _1089309), _1089311)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1089305), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1089305, _1089307, c_Groups_Otimes__class_Otimes(_1089305)), _1089313), c_Groups_Oone__class_Oone(_1089305)), _1089309)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1089305, _1089307, c_Groups_Otimes__class_Otimes(_1089305)), _1089313), c_Groups_Oone__class_Oone(_1089305)), _1089311)))], (34645 ^ _777959) ^ [_1429863, _1429865] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1429863), hAPP(c_Int_Onumber__class_Onumber__of(_1429863), _1429865)), 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(_1429863), hAPP(c_Int_Onumber__class_Onumber__of(_1429863), _1429865)), hAPP(c_Int_Onumber__class_Onumber__of(_1429863), _1429865))), class_Groups_Omonoid__mult(_1429863), class_Int_Onumber(_1429863)], (49269 ^ _777959) ^ [_1774266, _1774268, _1774270] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1774266, _1774266)), _1774268), c_Transitive__Closure_Ortrancl(_1774266, _1774270))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774266, _1774266)), _1774268), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1774266, _1774266), 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(_1774266, _1774266), tc_HOL_Obool), tc_fun(tc_prod(_1774266, _1774266), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1774266, _1774266), tc_HOL_Obool)), _1774270)))))], (7508 ^ _777959) ^ [_904097, _904099, _904101, _904103, _904105] : [c_Finite__Set_Ofolding__one(_904097, _904099, _904101), hBOOL(hAPP(c_Finite__Set_Ofinite(_904097), _904103)), -(hBOOL(hAPP(hAPP(c_member(_904097), _904105), _904103))), -(_904103 = c_Orderings_Obot__class_Obot(tc_fun(_904097, tc_HOL_Obool))), -(hAPP(_904101, hAPP(hAPP(c_Set_Oinsert(_904097), _904105), _904103)) = hAPP(hAPP(_904099, _904105), hAPP(_904101, _904103)))], (36215 ^ _777959) ^ [_1464530, _1464532, _1464534, _1464536, _1464538] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1464530, _1464532), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1464534), _1464536))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1464532)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1464538), _1464530), _1464532), 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), _1464538), _1464534)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1464538), _1464536)), _1464532))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1464538), _1464536), _1464532)))))], (33391 ^ _777959) ^ [_1407568] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407568), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1407568), c_Int_OPls)))], (30497 ^ _777959) ^ [_1354646, _1354648] : [-(_1354646 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30500 ^ _777959 : [(30507 ^ _777959) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1354648, _1354646) = 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), _1354648)), _1354646) = 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), _1354648), _1354646))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30501 ^ _777959) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1354648, _1354646) = 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), _1354648)), _1354646) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1354648), _1354646)))]]], (21472 ^ _777959) ^ [_1186012, _1186014, _1186016, _1186018] : [class_Rings_Olinordered__ring__strict(_1186012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186012), c_Groups_Ozero__class_Ozero(_1186012)), _1186014)), 21479 ^ _777959 : [(21486 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186012), _1186016), _1186018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186012), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186012), _1186014), _1186016)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186012), _1186014), _1186018))))], (21480 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186012), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186012), _1186014), _1186016)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186012), _1186014), _1186018))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186012), _1186016), _1186018)))]]], (19434 ^ _777959) ^ [_1150282, _1150284] : [class_Groups_Olinordered__ab__group__add(_1150282), 19437 ^ _777959 : [(19444 ^ _777959) ^ [] : [_1150284 = c_Groups_Ozero__class_Ozero(_1150282), -(_1150284 = hAPP(c_Groups_Ouminus__class_Ouminus(_1150282), _1150284))], (19438 ^ _777959) ^ [] : [_1150284 = hAPP(c_Groups_Ouminus__class_Ouminus(_1150282), _1150284), -(_1150284 = c_Groups_Ozero__class_Ozero(_1150282))]]], (23909 ^ _777959) ^ [_1232535, _1232537, _1232539, _1232541] : [class_Rings_Olinordered__semidom(_1232535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232535), c_Groups_Oone__class_Oone(_1232535)), _1232537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232535), hAPP(hAPP(c_Power_Opower__class_Opower(_1232535), _1232537), _1232539)), hAPP(hAPP(c_Power_Opower__class_Opower(_1232535), _1232537), _1232541))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1232539), _1232541)))], (42407 ^ _777959) ^ [_1615356, _1615358, _1615360] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1615356))), -(c_List_Osublist(_1615358, hAPP(hAPP(c_List_Olist_OCons(_1615358), _1615360), c_List_Olist_ONil(_1615358)), _1615356) = c_List_Olist_ONil(_1615358))], (50908 ^ _777959) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (12556 ^ _777959) ^ [_1006273, _1006275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006273), _1006275)), _1006275 = _1006273], (15757 ^ _777959) ^ [_1077710, _1077712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077710), _1077712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077710), hAPP(c_Nat_OSuc, _1077712))))], (28034 ^ _777959) ^ [_1306931, _1306933, _1306935] : [class_Rings_Oring__1(_1306931), -(hAPP(c_Int_Oring__1__class_Oof__int(_1306931), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1306933), _1306935)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1306931), hAPP(c_Int_Oring__1__class_Oof__int(_1306931), _1306933)), _1306935))], (47431 ^ _777959) ^ [_1731195, _1731197] : [c_Wellfounded_Owf(_1731195, hAPP(c_Set_OCollect(tc_prod(_1731195, _1731195)), hAPP(c_Product__Type_Oprod_Oprod__case(_1731195, _1731195, tc_HOL_Obool), _1731197))), -(c_Wellfounded_OwfP(_1731195, _1731197))], (12141 ^ _777959) ^ [_998282, _998284, _998286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998282), _998284)), _998286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998284), _998286)))], (35311 ^ _777959) ^ [_1441829, _1441831, _1441833, _1441835, _1441837] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1441829, _1441831), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1441833), _1441835))), -(_1441831 = 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)), _1441837)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1441829, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1441831), _1441837)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1441833), _1441837)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1441831), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1441833, _1441837))), _1441835)))))], (50658 ^ _777959) ^ [_1805485, _1805487, _1805489] : [-(hAPP(hAPP(c_List_Oappend(_1805485), c_List_Oreplicate(_1805485, _1805487, _1805489)), hAPP(hAPP(c_List_Olist_OCons(_1805485), _1805489), c_List_Olist_ONil(_1805485))) = hAPP(hAPP(c_List_Olist_OCons(_1805485), _1805489), c_List_Oreplicate(_1805485, _1805487, _1805489)))], (48384 ^ _777959) ^ [_1751486, _1751488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751486), _1751488)), -(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), _1751486), _1751488)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (33189 ^ _777959) ^ [_1404491, _1404493] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404491))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404491)), _1404493)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1404493))], (46503 ^ _777959) ^ [_1706812, _1706814, _1706816, _1706818, _1706820, _1706822] : [c_List_Olist__all2(_1706812, _1706814, _1706816, _1706818, _1706820), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706822), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706812)), _1706818))), -(hBOOL(hAPP(hAPP(_1706816, hAPP(hAPP(c_List_Onth(_1706812), _1706818), _1706822)), hAPP(hAPP(c_List_Onth(_1706814), _1706820), _1706822))))], (12339 ^ _777959) ^ [_1002018, _1002020, _1002022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002018), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002020), _1002022))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1002018), _1002022)), _1002020)))], (13089 ^ _777959) ^ [_1016617, _1016619, _1016621] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1016617, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1016617, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1016617, tc_HOL_Obool), tc_HOL_Obool)), _1016619), _1016621))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1016617, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1016617, tc_HOL_Obool), _1016619)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1016617, tc_HOL_Obool), _1016621)))))], (28028 ^ _777959) ^ [_1306828, _1306830] : [class_Rings_Oring__1(_1306828), -(hBOOL(hAPP(hAPP(c_member(_1306828), hAPP(c_Int_Oring__1__class_Oof__int(_1306828), _1306830)), c_Int_Oring__1__class_OInts(_1306828))))], (19809 ^ _777959) ^ [_1156252, _1156254, _1156256] : [class_Groups_Oordered__comm__monoid__add(_1156252), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156252), c_Groups_Ozero__class_Ozero(_1156252)), _1156254)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156252), c_Groups_Ozero__class_Ozero(_1156252)), _1156256)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156252), c_Groups_Ozero__class_Ozero(_1156252)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156252), _1156254), _1156256))))], (48368 ^ _777959) ^ [_1751239, _1751241] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1751239, _1751241) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1751239), hAPP(c_Code__Numeral_Onat__of, _1751241))))], (10014 ^ _777959) ^ [_952166, _952168, _952170, _952172] : [class_Lattices_Odistrib__lattice(_952166), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_952166), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952166), _952168), _952170)), _952172) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952166), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_952166), _952168), _952172)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_952166), _952170), _952172)))], (40339 ^ _777959) ^ [_1560851, _1560853, _1560855, _1560857, _1560859] : [class_Orderings_Olinorder(_1560851), -(hBOOL(hAPP(hAPP(c_member(_1560851), hAPP(_1560853, _1560855)), hAPP(c_Set_Oimage(_1560857, _1560851, _1560853), hAPP(c_List_Oset(_1560857), _1560859))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1560857, _1560851, _1560853, _1560855, _1560859) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1560857, _1560851, _1560853), _1560855), _1560859))], (31857 ^ _777959) ^ [_1379650, _1379652] : [class_Int_Onumber__ring(_1379650), -(hAPP(c_Int_Onumber__class_Onumber__of(_1379650), _1379652) = hAPP(c_Int_Oring__1__class_Oof__int(_1379650), _1379652))], (31322 ^ _777959) ^ [_1369633, _1369635, _1369637] : [class_Rings_Olinordered__idom(_1369633), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369633), c_Groups_Ozero__class_Ozero(_1369633)), _1369635)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369633), hAPP(c_Groups_Oabs__class_Oabs(_1369633), _1369637)), _1369635) = hAPP(c_Groups_Oabs__class_Oabs(_1369633), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369633), _1369637), _1369635)))], (31420 ^ _777959) ^ [_1371502] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371502), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1371502) = _1371502)], (14055 ^ _777959) ^ [_1039106, _1039108, _1039110, _1039112, _1039114] : [hBOOL(hAPP(hAPP(c_member(_1039106), _1039108), c_Map_Odom(_1039106, _1039110, _1039112))), -(hAPP(c_Map_Omap__add(_1039106, _1039110, _1039114, _1039112), _1039108) = hAPP(_1039112, _1039108))], (44051 ^ _777959) ^ [_1654028, _1654030] : [c_List_Otranspose(_1654028, _1654030) = c_List_Olist_ONil(tc_List_Olist(_1654028)), 44054 ^ _777959 : [(44055 ^ _777959) ^ [_1654123] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1654028)), _1654123), hAPP(c_List_Oset(tc_List_Olist(_1654028)), _1654030))), -(_1654123 = c_List_Olist_ONil(_1654028))]]], (28022 ^ _777959) ^ [_1306717, _1306719] : [class_Rings_Oring__1(_1306717), -(hAPP(c_Int_Oring__1__class_Oof__int(_1306717), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1306719)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1306717), hAPP(c_Int_Oring__1__class_Oof__int(_1306717), _1306719)))], (15827 ^ _777959) ^ [_1078874, _1078876, _1078878, _1078880, _1078882, _1078884] : [hAPP(_1078874, _1078876) = c_Option_Ooption_ONone(_1078878), -(c_Map_Omap__comp(_1078878, _1078880, _1078882, _1078884, _1078874, _1078876) = c_Option_Ooption_ONone(_1078880))], (13167 ^ _777959) ^ [_1018267, _1018269] : [class_Complete__Lattice_Ocomplete__lattice(_1018267), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018267), _1018269)), -(_1018269 = c_Orderings_Obot__class_Obot(tc_fun(_1018267, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1018267, _1018269) = c_Complete__Lattice_OSup__class_OSup(_1018267, _1018269))], (35037 ^ _777959) ^ [_1437392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1437392)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437392), c_Int_OMin)))], (36690 ^ _777959) ^ [_1474032, _1474034, _1474036, _1474038, _1474040, _1474042] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1474032, _1474034), _1474034, _1474036), hAPP(hAPP(c_COMBB(_1474038, tc_fun(_1474034, _1474036), tc_prod(_1474032, _1474034)), _1474040), hAPP(hAPP(c_COMBB(_1474032, _1474038, tc_prod(_1474032, _1474034)), _1474042), c_Product__Type_Ofst(_1474032, _1474034)))), c_Product__Type_Osnd(_1474032, _1474034)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1474032, _1474034, _1474036), hAPP(hAPP(c_COMBB(_1474038, tc_fun(_1474034, _1474036), _1474032), _1474040), _1474042)))], (28632 ^ _777959) ^ [_1317333, _1317335, _1317337] : [-(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)), _1317333)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1317335, _1317337)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1317335), _1317333), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1317337), _1317333)))], (1410 ^ _777959) ^ [_798308, _798310] : [-(class_Enum_Oenum(_798308)), _798310 = _798308, class_Enum_Oenum(_798310)], (50256 ^ _777959) ^ [_1796735, _1796737, _1796739] : [-(hAPP(c_Lazy__Sequence_Oyield(_1796735), c_Lazy__Sequence_Olazy__sequence_OInsert(_1796735, _1796737, _1796739)) = hAPP(c_Option_Ooption_OSome(tc_prod(_1796735, tc_Lazy__Sequence_Olazy__sequence(_1796735))), hAPP(hAPP(c_Product__Type_OPair(_1796735, tc_Lazy__Sequence_Olazy__sequence(_1796735)), _1796737), _1796739)))], (43320 ^ _777959) ^ [_1638510, _1638512, _1638514, _1638516] : [hAPP(hAPP(c_List_Oappend(_1638510), _1638512), _1638514) = _1638516, 43323 ^ _777959 : [(43326 ^ _777959) ^ [] : [-(_1638514 = hAPP(hAPP(c_List_Odrop(_1638510), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638510)), _1638512)), _1638516))], (43324 ^ _777959) ^ [] : [-(_1638512 = hAPP(hAPP(c_List_Otake(_1638510), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638510)), _1638512)), _1638516))]]], (38596 ^ _777959) ^ [_1518518, _1518520, _1518522, _1518524, _1518526, _1518528] : [c_Typedef_Otype__definition(_1518518, _1518520, _1518522, _1518524, _1518526), -(hBOOL(hAPP(hAPP(c_member(_1518520), hAPP(_1518522, _1518528)), _1518526)))], (14958 ^ _777959) ^ [_1062260, _1062262, _1062264, _1062266, _1062268] : [class_Groups_Ocomm__monoid__mult(_1062260), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062262), _1062264)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062262), _1062266)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062262, tc_HOL_Obool)), _1062264), _1062266) = c_Orderings_Obot__class_Obot(tc_fun(_1062262, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1062260, _1062262, c_Groups_Otimes__class_Otimes(_1062260)), _1062268), c_Groups_Oone__class_Oone(_1062260)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1062262, tc_HOL_Obool)), _1062264), _1062266)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1062260), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1062260, _1062262, c_Groups_Otimes__class_Otimes(_1062260)), _1062268), c_Groups_Oone__class_Oone(_1062260)), _1062264)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1062260, _1062262, c_Groups_Otimes__class_Otimes(_1062260)), _1062268), c_Groups_Oone__class_Oone(_1062260)), _1062266)))], (41342 ^ _777959) ^ [_1587786, _1587788, _1587790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1587786), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1587788)), _1587790))), -(hAPP(hAPP(c_List_Otake(_1587788), _1587786), c_List_Obutlast(_1587788, _1587790)) = hAPP(hAPP(c_List_Otake(_1587788), _1587786), _1587790))], (23477 ^ _777959) ^ [_1224887] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1224887)) = _1224887)], (14287 ^ _777959) ^ [_1044314, _1044316, _1044318] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044314), _1044316)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1044314), _1044318)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1044314), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1044314, tc_HOL_Obool)), _1044316), _1044318))), hAPP(c_Finite__Set_Ocard(_1044314), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1044314, tc_HOL_Obool)), _1044316), _1044318))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1044314), _1044316)), hAPP(c_Finite__Set_Ocard(_1044314), _1044318)))], (47360 ^ _777959) ^ [_1729021, _1729023, _1729025] : [-(hAPP(c_Set_Oimage(tc_prod(_1729021, _1729023), _1729021, c_Product__Type_Ofst(_1729021, _1729023)), _1729025) = hAPP(c_Relation_ODomain(_1729021, _1729023), _1729025))], (32017 ^ _777959) ^ [_1382530, _1382532, _1382534, _1382536] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382530), hAPP(c_Int_Onumber__class_Onumber__of(_1382530), _1382532)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382530), _1382534), _1382536)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1382530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382530), hAPP(c_Int_Onumber__class_Onumber__of(_1382530), _1382532)), _1382534)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382530), hAPP(c_Int_Onumber__class_Onumber__of(_1382530), _1382532)), _1382536))), class_Int_Onumber(_1382530), class_Rings_Oring(_1382530)], (5783 ^ _777959) ^ [_869539, _869541, _869543, _869545] : [hAPP(c_Set_Oimage(_869539, _869541, _869543), _869545) = c_Orderings_Obot__class_Obot(tc_fun(_869541, tc_HOL_Obool)), -(_869545 = c_Orderings_Obot__class_Obot(tc_fun(_869539, tc_HOL_Obool)))], (28183 ^ _777959) ^ [_1309481, _1309483] : [class_Rings_Olinordered__idom(_1309481), 28186 ^ _777959 : [(28193 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309483)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309481), c_Groups_Ozero__class_Ozero(_1309481)), hAPP(c_Int_Oring__1__class_Oof__int(_1309481), _1309483))))], (28187 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309481), c_Groups_Ozero__class_Ozero(_1309481)), hAPP(c_Int_Oring__1__class_Oof__int(_1309481), _1309483))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309483)))]]], (6791 ^ _777959) ^ [_888401, _888403, _888405, _888407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888401, tc_HOL_Obool)), _888403), _888405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888401, tc_HOL_Obool)), _888403), hAPP(hAPP(c_Set_Oinsert(_888401), _888407), _888405))))], (5530 ^ _777959) ^ [_862447, _862449, _862451, _862453, _862455, _862457] : [-(c_COMBC(_862457, _862453, _862449) = c_COMBC(_862455, _862451, _862447)), _862457 = _862455, _862453 = _862451, _862449 = _862447], (4170 ^ _777959) ^ [_841085, _841087] : [_841087 = _841085, -(c_Nat_Ofunpow(_841087) = c_Nat_Ofunpow(_841085))], (19510 ^ _777959) ^ [_1151327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151327), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (41729 ^ _777959) ^ [_1598283, _1598285, _1598287, _1598289, _1598291, _1598293, _1598295, _1598297, _1598299, _1598301] : [-(c_Product__Type_Omap__pair(_1598283, _1598285, _1598287, _1598289, hAPP(c_Fun_Ocomp(_1598291, _1598285, _1598283, _1598293), _1598295), hAPP(c_Fun_Ocomp(_1598297, _1598289, _1598287, _1598299), _1598301)) = hAPP(c_Fun_Ocomp(tc_prod(_1598291, _1598297), tc_prod(_1598285, _1598289), tc_prod(_1598283, _1598287), c_Product__Type_Omap__pair(_1598291, _1598285, _1598297, _1598289, _1598293, _1598299)), c_Product__Type_Omap__pair(_1598283, _1598291, _1598287, _1598297, _1598295, _1598301)))], (22426 ^ _777959) ^ [_1205413, _1205415, _1205417] : [-(hAPP(c_Finite__Set_Ocard(_1205413), _1205415) = hAPP(c_Nat_OSuc, _1205417)), 22427 ^ _777959 : [(22428 ^ _777959) ^ [_1205513, _1205515] : [_1205415 = hAPP(hAPP(c_Set_Oinsert(_1205413), _1205515), _1205513), -(hBOOL(hAPP(hAPP(c_member(_1205413), _1205515), _1205513))), hAPP(c_Finite__Set_Ocard(_1205413), _1205513) = _1205417, 22439 ^ _777959 : [(22442 ^ _777959) ^ [] : [_1205513 = c_Orderings_Obot__class_Obot(tc_fun(_1205413, tc_HOL_Obool))], (22440 ^ _777959) ^ [] : [-(_1205417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (23695 ^ _777959) ^ [_1228742, _1228744, _1228746] : [class_Power_Opower(_1228742), class_Rings_Omult__zero(_1228742), class_Rings_Ono__zero__divisors(_1228742), class_Rings_Ozero__neq__one(_1228742), 23710 ^ _777959 : [(23719 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1228742), _1228744), _1228746) = c_Groups_Ozero__class_Ozero(_1228742)), _1228744 = c_Groups_Ozero__class_Ozero(_1228742), -(_1228746 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23711 ^ _777959) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1228742), _1228744), _1228746) = c_Groups_Ozero__class_Ozero(_1228742), 23714 ^ _777959 : [(23717 ^ _777959) ^ [] : [_1228746 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23715 ^ _777959) ^ [] : [-(_1228744 = c_Groups_Ozero__class_Ozero(_1228742))]]]]], (44775 ^ _777959) ^ [_1668420, _1668422] : [-(c_List_Oconcat(_1668420, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1668420), tc_List_Olist(_1668420)), c_List_Olist_Olist__case(tc_List_Olist(_1668420), _1668420, c_List_Olist_ONil(_1668420), hAPP(hAPP(c_COMBB(tc_List_Olist(_1668420), tc_fun(tc_List_Olist(_1668420), tc_List_Olist(_1668420)), _1668420), c_COMBK(tc_List_Olist(_1668420), tc_List_Olist(_1668420))), hAPP(hAPP(c_COMBC(_1668420, tc_List_Olist(_1668420), tc_List_Olist(_1668420)), c_List_Olist_OCons(_1668420)), c_List_Olist_ONil(_1668420))))), _1668422)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1668420), _1668420), c_List_Ohd(_1668420)), hAPP(c_List_Ofilter(tc_List_Olist(_1668420), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1668420)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1668420), tc_List_Olist(_1668420), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1668420)))), _1668422)))], (43358 ^ _777959) ^ [_1639391, _1639393, _1639395, _1639397, _1639399] : [hAPP(hAPP(c_List_Oappend(_1639391), _1639393), _1639395) = hAPP(hAPP(c_List_Oappend(_1639391), _1639397), _1639399), 43361 ^ _777959 : [(43370 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639391)), _1639393)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639391)), _1639397)))), 43373 ^ _777959 : [(43376 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1639391), hAPP(hAPP(c_List_Odrop(_1639391), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639391)), _1639397)), _1639393)), _1639395) = _1639399)], (43374 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1639391), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639391)), _1639397)), _1639393) = _1639397)]]], (43362 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639391)), _1639393)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639391)), _1639397))), 43365 ^ _777959 : [(43368 ^ _777959) ^ [] : [-(_1639395 = hAPP(hAPP(c_List_Oappend(_1639391), hAPP(hAPP(c_List_Odrop(_1639391), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639391)), _1639393)), _1639397)), _1639399))], (43366 ^ _777959) ^ [] : [-(_1639393 = hAPP(hAPP(c_List_Otake(_1639391), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639391)), _1639393)), _1639397))]]]]], (39912 ^ _777959) ^ [_1550678, _1550680, _1550682] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550678)), _1550680) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550678)), _1550682)), _1550680 = _1550682], (23403 ^ _777959) ^ [_1223696, _1223698] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223696), _1223698) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223698), _1223696))], (31280 ^ _777959) ^ [_1368784, _1368786, _1368788] : [class_Rings_Olinordered__idom(_1368784), -(hAPP(c_Groups_Oabs__class_Oabs(_1368784), hAPP(hAPP(c_Power_Opower__class_Opower(_1368784), hAPP(c_Groups_Ouminus__class_Ouminus(_1368784), _1368786)), _1368788)) = hAPP(c_Groups_Oabs__class_Oabs(_1368784), hAPP(hAPP(c_Power_Opower__class_Opower(_1368784), _1368786), _1368788)))], (19658 ^ _777959) ^ [_1153642] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1153642) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51352 ^ _777959) ^ [] : [-(class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral))], (19652 ^ _777959) ^ [_1153527, _1153529, _1153531] : [class_Groups_Ocomm__monoid__mult(_1153527), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1153529, _1153527), hAPP(c_COMBK(_1153527, _1153529), c_Groups_Oone__class_Oone(_1153527))), _1153531) = c_Groups_Oone__class_Oone(_1153527))], (4492 ^ _777959) ^ [_845924, _845926] : [_845926 = _845924, -(c_Enum_Oenum__class_Oenum(_845926) = c_Enum_Oenum__class_Oenum(_845924))], (44589 ^ _777959) ^ [_1664193, _1664195] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1664193, _1664195) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1664193), hAPP(c_Nat_OSuc, _1664195))))], (24061 ^ _777959) ^ [_1235445, _1235447, _1235449] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235445)), _1235445 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1235447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235445), _1235449)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235447), _1235445)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1235449)))], (12908 ^ _777959) ^ [_1012389, _1012391, _1012393] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1012389, tc_HOL_Obool)), _1012391), _1012393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012389, tc_HOL_Obool)), _1012391), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1012389, tc_HOL_Obool), _1012393))))], (50980 ^ _777959) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (51392 ^ _777959) ^ [_1814191] : [-(hBOOL(_1814191)), -(hBOOL(hAPP(c_fNot, _1814191)))], (20925 ^ _777959) ^ [_1175905, _1175907, _1175909] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1175905), c_Map_Odom(_1175905, _1175907, hAPP(c_Map_Omap__of(_1175905, _1175907), _1175909)))))], (39741 ^ _777959) ^ [_1546064, _1546066, _1546068, _1546070, _1546072] : [hBOOL(hAPP(hAPP(c_member(_1546064), _1546066), hAPP(c_List_Oset(_1546064), _1546068))), -(hAPP(hAPP(c_Map_Omap__of(_1546064, _1546070), hAPP(hAPP(c_List_Ozip(_1546064, _1546070), _1546068), hAPP(hAPP(c_List_Omap(_1546064, _1546070), _1546072), _1546068))), _1546066) = hAPP(c_Option_Ooption_OSome(_1546070), hAPP(_1546072, _1546066)))], (39426 ^ _777959) ^ [_1538598, _1538600, _1538602, _1538604, _1538606, _1538608] : [c_Finite__Set_Ofolding(_1538598, _1538600, _1538602, _1538604), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538598), _1538606)), -(hAPP(hAPP(_1538604, _1538606), _1538608) = hAPP(hAPP(c_Finite__Set_Ofold(_1538598, _1538600, _1538602), _1538608), _1538606))], (6991 ^ _777959) ^ [_893646, _893648, _893650] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _893646)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _893648), _893646), _893650)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate), _893648), _893646), _893650)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (26282 ^ _777959) ^ [_1276141, _1276143, _1276145] : [class_Fields_Olinordered__field(_1276141), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276141), _1276143), c_Groups_Ozero__class_Ozero(_1276141))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276141), c_Groups_Ozero__class_Ozero(_1276141)), _1276145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276141), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276141), _1276143), _1276145)), c_Groups_Ozero__class_Ozero(_1276141))))], (48495 ^ _777959) ^ [_1753967, _1753969, _1753971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1753967, _1753967), tc_HOL_Obool)), _1753969), hAPP(hAPP(c_Product__Type_OSigma(_1753967, _1753967), _1753971), hAPP(c_COMBK(tc_fun(_1753967, tc_HOL_Obool), _1753967), _1753971)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1753967, _1753967), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1753967, _1753969)), hAPP(hAPP(c_Product__Type_OSigma(_1753967, _1753967), _1753971), hAPP(c_COMBK(tc_fun(_1753967, tc_HOL_Obool), _1753967), _1753971)))))], (45422 ^ _777959) ^ [_1683255, _1683257, _1683259] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683255)), c_List_OdropWhile(_1683255, _1683257, _1683259))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683255)), _1683259))))], (4124 ^ _777959) ^ [_840396, _840398, _840400, _840402] : [-(c_Relation_OId__on(_840402, _840398) = c_Relation_OId__on(_840400, _840396)), _840402 = _840400, _840398 = _840396], (30301 ^ _777959) ^ [_1350867, _1350869] : [-(_1350867 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1350869), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1350867), _1350869))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350867, _1350869)))], (16455 ^ _777959) ^ [_1092936, _1092938, _1092940] : [class_Orderings_Olinorder(_1092936), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092936), _1092938), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092936), _1092938), _1092940)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092936), _1092938), _1092940))], (33651 ^ _777959) ^ [_1411676, _1411678] : [class_Int_Onumber__ring(_1411676), -(hAPP(c_Int_Onumber__class_Onumber__of(_1411676), c_Int_Opred(_1411678)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411676), hAPP(c_Groups_Ouminus__class_Ouminus(_1411676), c_Groups_Oone__class_Oone(_1411676))), hAPP(c_Int_Onumber__class_Onumber__of(_1411676), _1411678)))], (34955 ^ _777959) ^ [] : [c_Int_OMin = c_Int_OPls], (18556 ^ _777959) ^ [_1134692, _1134694, _1134696] : [-(hAPP(c_Finite__Set_Ofold1(_1134692, _1134694), hAPP(hAPP(c_Set_Oinsert(_1134692), _1134696), c_Orderings_Obot__class_Obot(tc_fun(_1134692, tc_HOL_Obool)))) = _1134696)], (50284 ^ _777959) ^ [_1797274, _1797276, _1797278, _1797280, _1797282] : [-(_1797274 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1797276, _1797278, _1797280, _1797282), _1797274) = c_Lazy__Sequence_Ohb__bind(_1797276, _1797278, hAPP(_1797280, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1797274), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1797276, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1797278))), _1797282), _1797274)))], (50988 ^ _777959) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (12391 ^ _777959) ^ [_1002981, _1002983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1002981), _1002983)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002983), _1002981)), _1002981) = _1002983)], (49503 ^ _777959) ^ [_1780819, _1780821] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780819, _1780819)), _1780821), c_Relation_OId(_1780819))), -(_1780821 = hAPP(hAPP(c_Product__Type_OPair(_1780819, _1780819), 49506 ^ [_1780819, _1780821]), 49506 ^ [_1780819, _1780821]))], (4330 ^ _777959) ^ [_843517, _843519] : [_843519 = _843517, -(c_Groups_Otimes__class_Otimes(_843519) = c_Groups_Otimes__class_Otimes(_843517))], (11739 ^ _777959) ^ [_989319, _989321, _989323, _989325, _989327] : [11741 ^ _777959 : [(11744 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989319, tc_HOL_Obool)), hAPP(_989325, 11740 ^ [_989319, _989321, _989323, _989325, _989327])), _989327))], (11742 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_989321), 11740 ^ [_989319, _989321, _989323, _989325, _989327]), _989323)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989319, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989321, tc_fun(_989319, tc_HOL_Obool)), _989323), _989325)), _989327)))], (43927 ^ _777959) ^ [_1651326, _1651328, _1651330, _1651332] : [-(hAPP(c_List_Ofilter(_1651326, _1651328), hAPP(hAPP(c_List_Oappend(_1651326), _1651330), _1651332)) = hAPP(hAPP(c_List_Oappend(_1651326), hAPP(c_List_Ofilter(_1651326, _1651328), _1651330)), hAPP(c_List_Ofilter(_1651326, _1651328), _1651332)))], (24319 ^ _777959) ^ [_1240147] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1240147)), -(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)), _1240147))))], (49275 ^ _777959) ^ [_1774473, _1774475] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1774473, _1774473)), hAPP(hAPP(c_Product__Type_OPair(_1774473, _1774473), 49276 ^ [_1774473, _1774475]), 49276 ^ [_1774473, _1774475])), c_Transitive__Closure_Otrancl(_1774473, _1774475)))), -(c_Wellfounded_Oacyclic(_1774473, _1774475))], (38944 ^ _777959) ^ [_1527172, _1527174, _1527176, _1527178] : [-(hAPP(c_List_Oset(_1527172), hAPP(hAPP(c_List_Omap(_1527174, _1527172), _1527176), _1527178)) = hAPP(c_Set_Oimage(_1527174, _1527172, _1527176), hAPP(c_List_Oset(_1527174), _1527178)))], (2786 ^ _777959) ^ [_819529, _819531, _819533, _819535, _819537, _819539, _819541, _819543] : [-(c_Nitpick_Osetsum_H(_819543, _819539, _819535, _819531) = c_Nitpick_Osetsum_H(_819541, _819537, _819533, _819529)), _819543 = _819541, _819539 = _819537, _819535 = _819533, _819531 = _819529], (16955 ^ _777959) ^ [_1102346, _1102348, _1102350, _1102352] : [class_Orderings_Olinorder(_1102346), 16958 ^ _777959 : [(16967 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102346), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1102346), _1102348), _1102350)), _1102352))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102346), _1102348), _1102352)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102346), _1102350), _1102352))], (16959 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102346), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1102346), _1102348), _1102350)), _1102352)), 16962 ^ _777959 : [(16965 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102346), _1102350), _1102352)))], (16963 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102346), _1102348), _1102352)))]]]]], (8692 ^ _777959) ^ [_927982, _927984, _927986] : [class_Orderings_Olinorder(_927982), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927982), _927984), _927986))), -(_927984 = _927986), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927982), _927986), _927984)))], (6111 ^ _777959) ^ [_875858, _875860, _875862] : [-(_875858 = _875860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875862, tc_HOL_Obool)), _875858), _875860)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875862, tc_HOL_Obool)), _875860), _875858))], (7632 ^ _777959) ^ [_906661] : [hAPP(c_Com_Ocom_OBODY, _906661) = c_Com_Ocom_OSKIP], (43654 ^ _777959) ^ [_1645810, _1645812] : [class_Groups_Omonoid__add(_1645810), -(hAPP(c_List_Ofoldl(_1645810, _1645810, c_Groups_Oplus__class_Oplus(_1645810), c_Groups_Ozero__class_Ozero(_1645810)), _1645812) = c_List_Ofoldr(_1645810, _1645810, c_Groups_Oplus__class_Oplus(_1645810), _1645812, c_Groups_Ozero__class_Ozero(_1645810)))], (37166 ^ _777959) ^ [_1485761, _1485763, _1485765, _1485767, _1485769] : [-(hAPP(c_Relation_OImage(_1485761, _1485763, _1485765), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1485761, tc_HOL_Obool)), _1485767), _1485769)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1485763, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1485761, _1485763, _1485765), _1485767)), hAPP(c_Relation_OImage(_1485761, _1485763, _1485765), _1485769)))], (17221 ^ _777959) ^ [_1107276, _1107278, _1107280] : [class_Complete__Lattice_Ocomplete__lattice(_1107276), hBOOL(hAPP(hAPP(c_member(_1107276), _1107278), _1107280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1107276), c_Complete__Lattice_OInf__class_OInf(_1107276, _1107280)), _1107278)))], (27345 ^ _777959) ^ [_1295410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295410), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1295410) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44328 ^ _777959) ^ [_1659420, _1659422] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1659420, _1659422)))], (25684 ^ _777959) ^ [_1265038, _1265040] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OWhile(_1265038, _1265040)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1265040)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44813 ^ _777959) ^ [_1669405, _1669407] : [c_List_Olist_ONil(_1669405) = hAPP(c_List_Orev(_1669405), _1669407), -(_1669407 = c_List_Olist_ONil(_1669405))], (34961 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (37834 ^ _777959) ^ [_1502133, _1502135, _1502137, _1502139, _1502141, _1502143, _1502145, _1502147, _1502149, _1502151, _1502153] : [c_Equiv__Relations_Oequiv(_1502133, _1502135, _1502137), c_Equiv__Relations_Oequiv(_1502139, _1502141, _1502143), c_Equiv__Relations_Ocongruent2(_1502133, _1502139, tc_fun(_1502145, tc_HOL_Obool), _1502137, _1502143, _1502147), hBOOL(hAPP(hAPP(c_member(tc_fun(_1502133, tc_HOL_Obool)), _1502149), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1502133), _1502135), _1502137))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1502139, tc_HOL_Obool)), _1502151), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1502139), _1502141), _1502143))), 37856 ^ _777959 : [(37862 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1502145, tc_HOL_Obool)), hAPP(hAPP(_1502147, 37855 ^ [_1502133, _1502135, _1502137, _1502139, _1502141, _1502143, _1502145, _1502147, _1502149, _1502151, _1502153]), 37858 ^ [_1502133, _1502135, _1502137, _1502139, _1502141, _1502143, _1502145, _1502147, _1502149, _1502151, _1502153])), _1502153))], (37860 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502139), 37858 ^ [_1502133, _1502135, _1502137, _1502139, _1502141, _1502143, _1502145, _1502147, _1502149, _1502151, _1502153]), _1502141)))], (37857 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1502133), 37855 ^ [_1502133, _1502135, _1502137, _1502139, _1502141, _1502143, _1502145, _1502147, _1502149, _1502151, _1502153]), _1502135)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1502145, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1502133, tc_fun(_1502145, tc_HOL_Obool)), _1502149), hAPP(hAPP(c_COMBB(tc_fun(_1502139, tc_fun(_1502145, tc_HOL_Obool)), tc_fun(_1502145, tc_HOL_Obool), _1502133), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1502139, tc_fun(_1502145, tc_HOL_Obool)), _1502151)), _1502147))), _1502153)))], (34985 ^ _777959) ^ [_1436621] : [_1436621 = c_Int_OMin, -(c_Int_OBit1(_1436621) = c_Int_OMin)], (14493 ^ _777959) ^ [_1050024, _1050026, _1050028, _1050030] : [14495 ^ _777959 : [(14498 ^ _777959) ^ [] : [hAPP(_1050030, 14494 ^ [_1050024, _1050026, _1050028, _1050030]) = c_Orderings_Otop__class_Otop(tc_fun(_1050026, tc_HOL_Obool))], (14496 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1050024), 14494 ^ [_1050024, _1050026, _1050028, _1050030]), _1050028)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1050024, tc_fun(_1050026, tc_HOL_Obool)), _1050028), _1050030) = c_Orderings_Otop__class_Otop(tc_fun(_1050026, tc_HOL_Obool)))], (32859 ^ _777959) ^ [_1398684, _1398686] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398684)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398684)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398686)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398684)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398686))))], (51340 ^ _777959) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (2 ^ _777959) ^ [_777986] : [-(_777986 = _777986)], (17881 ^ _777959) ^ [_1119752, _1119754, _1119756] : [class_Orderings_Olinorder(_1119752), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119752), _1119754)), -(_1119754 = c_Orderings_Obot__class_Obot(tc_fun(_1119752, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1119752, c_Orderings_Oord__class_Omin(_1119752), hAPP(hAPP(c_Set_Oinsert(_1119752), _1119756), _1119754)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1119752), _1119756), c_Big__Operators_Olattice_OInf__fin(_1119752, c_Orderings_Oord__class_Omin(_1119752), _1119754)))], (50540 ^ _777959) ^ [_1803259, _1803261, _1803263, _1803265] : [-(hAPP(hAPP(c_List_Odrop(_1803259), _1803261), c_List_Oreplicate(_1803259, _1803263, _1803265)) = c_List_Oreplicate(_1803259, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1803263), _1803261), _1803265))], (35485 ^ _777959) ^ [_1450659, _1450661, _1450663, _1450665] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450659, _1450661), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1450663), _1450665))), -(_1450661 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1450659, _1450661) = _1450665)], (42114 ^ _777959) ^ [_1607836, _1607838, _1607840] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1607836, _1607838), c_Orderings_Obot__class_Obot(tc_fun(_1607836, tc_HOL_Obool))), _1607840) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1607836, _1607838), tc_HOL_Obool)))], (34301 ^ _777959) ^ [_1423711, _1423713] : [class_Int_Onumber__ring(_1423711), class_Int_Oring__char__0(_1423711), 34308 ^ _777959 : [(34315 ^ _777959) ^ [] : [c_Int_Oiszero(_1423711, hAPP(c_Int_Onumber__class_Onumber__of(_1423711), _1423713)), -(c_Int_Oiszero(_1423711, hAPP(c_Int_Onumber__class_Onumber__of(_1423711), c_Int_OBit0(_1423713))))], (34309 ^ _777959) ^ [] : [c_Int_Oiszero(_1423711, hAPP(c_Int_Onumber__class_Onumber__of(_1423711), c_Int_OBit0(_1423713))), -(c_Int_Oiszero(_1423711, hAPP(c_Int_Onumber__class_Onumber__of(_1423711), _1423713)))]]], (10976 ^ _777959) ^ [_973118, _973120] : [hAPP(c_Option_Ooption_OSome(_973118), _973120) = c_Option_Ooption_ONone(_973118)], (7798 ^ _777959) ^ [_910509, _910511, _910513, _910515] : [hBOOL(hAPP(hAPP(c_member(_910509), _910511), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910509, tc_HOL_Obool)), _910513), _910515))), 7801 ^ _777959 : [(7804 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_910509), _910511), _910515))], (7802 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910509), _910511), _910513)))]]], (10210 ^ _777959) ^ [_957110, _957112, _957114, _957116] : [hBOOL(hAPP(hAPP(c_member(_957110), _957112), _957114)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957110, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_957110), _957112), _957116)), _957114) = hAPP(hAPP(c_Set_Oinsert(_957110), _957112), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957110, tc_HOL_Obool)), _957116), _957114)))], (8518 ^ _777959) ^ [_925205, _925207, _925209] : [class_Orderings_Oorder(_925205), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925205), _925207), _925209)), _925207 = _925209], (37096 ^ _777959) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (34029 ^ _777959) ^ [_1418864, _1418866] : [class_Int_Onumber__ring(_1418864), 34032 ^ _777959 : [(34039 ^ _777959) ^ [] : [c_Int_Oiszero(_1418864, hAPP(c_Int_Onumber__class_Onumber__of(_1418864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1418866)))), -(c_Groups_Ozero__class_Ozero(_1418864) = hAPP(c_Int_Onumber__class_Onumber__of(_1418864), _1418866))], (34033 ^ _777959) ^ [] : [c_Groups_Ozero__class_Ozero(_1418864) = hAPP(c_Int_Onumber__class_Onumber__of(_1418864), _1418866), -(c_Int_Oiszero(_1418864, hAPP(c_Int_Onumber__class_Onumber__of(_1418864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1418866)))))]]], (31094 ^ _777959) ^ [_1365417, _1365419] : [class_Groups_Oordered__ab__group__add__abs(_1365417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365417), c_Groups_Ozero__class_Ozero(_1365417)), _1365419)), -(hAPP(c_Groups_Oabs__class_Oabs(_1365417), _1365419) = _1365419)], (34951 ^ _777959) ^ [_1436181] : [c_Int_OMin = c_Int_OBit0(_1436181)], (12088 ^ _777959) ^ [_997263, _997265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997263), _997265)), -(_997265 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997263), 12091 ^ [_997263, _997265]))], (44332 ^ _777959) ^ [_1659478, _1659480] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1659478), _1659480)) = c_List_Oupt(_1659478, _1659480))], (1190 ^ _777959) ^ [_795558, _795560] : [-(class_Int_Onumber__ring(_795558)), _795560 = _795558, class_Int_Onumber__ring(_795560)], (48260 ^ _777959) ^ [_1749418] : [-(_1749418 = 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)), _1749418)))], (30309 ^ _777959) ^ [_1351109, _1351111] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1351109), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1351111), _1351109)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1351111), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1351111, _1351109)))], (45400 ^ _777959) ^ [_1682926, _1682928, _1682930] : [class_Orderings_Olinorder(_1682926), c_List_Olinorder__class_Osorted(_1682926, _1682928), -(c_List_Olinorder__class_Osorted(_1682926, c_List_OdropWhile(_1682926, _1682930, _1682928)))], (31238 ^ _777959) ^ [_1368069, _1368071, _1368073] : [class_Groups_Oordered__ab__group__add__abs(_1368069), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368069), hAPP(c_Groups_Oabs__class_Oabs(_1368069), _1368071)), _1368073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1368069), hAPP(c_Groups_Ouminus__class_Ouminus(_1368069), _1368071)), _1368073)))], (19150 ^ _777959) ^ [_1145881, _1145883, _1145885, _1145887] : [class_Rings_Ocomm__semiring__1(_1145881), class_Rings_Ono__zero__divisors(_1145881), hBOOL(hAPP(c_Finite__Set_Ofinite(_1145883), _1145885)), 19161 ^ _777959 : [(19171 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1145883, _1145881), _1145887), _1145885) = c_Groups_Ozero__class_Ozero(_1145881)), 19172 ^ _777959 : [(19173 ^ _777959) ^ [_1146259] : [hBOOL(hAPP(hAPP(c_member(_1145883), _1146259), _1145885)), hAPP(_1145887, _1146259) = c_Groups_Ozero__class_Ozero(_1145881)]]], (19162 ^ _777959) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1145883, _1145881), _1145887), _1145885) = c_Groups_Ozero__class_Ozero(_1145881), 19166 ^ _777959 : [(19169 ^ _777959) ^ [] : [-(hAPP(_1145887, 19165 ^ [_1145881, _1145883, _1145885, _1145887]) = c_Groups_Ozero__class_Ozero(_1145881))], (19167 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1145883), 19165 ^ [_1145881, _1145883, _1145885, _1145887]), _1145885)))]]]]], (7974 ^ _777959) ^ [_914031, _914033, _914035] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_914031, tc_HOL_Obool)), _914033), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_914031, tc_HOL_Obool)), _914035), _914033)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_914031, tc_HOL_Obool)), _914033), _914035))], (6357 ^ _777959) ^ [_880607, _880609, _880611, _880613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880607, tc_HOL_Obool)), _880609), _880611)), hBOOL(hAPP(hAPP(c_member(_880607), _880613), _880609)), -(hBOOL(hAPP(hAPP(c_member(_880607), _880613), _880611)))], (40534 ^ _777959) ^ [_1564827, _1564829, _1564831, _1564833, _1564835, _1564837] : [-(hBOOL(hAPP(hAPP(c_member(_1564827), _1564829), hAPP(c_List_Oset(_1564827), _1564831)))), -(hAPP(c_Map_Omap__upds(_1564827, _1564833, _1564835, _1564831, _1564837), _1564829) = hAPP(_1564835, _1564829))], (51346 ^ _777959) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (17895 ^ _777959) ^ [_1119972, _1119974, _1119976] : [class_Orderings_Olinorder(_1119972), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119972), _1119974)), -(_1119974 = c_Orderings_Obot__class_Obot(tc_fun(_1119972, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1119972, c_Orderings_Oord__class_Omax(_1119972), hAPP(hAPP(c_Set_Oinsert(_1119972), _1119976), _1119974)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1119972), _1119976), c_Big__Operators_Olattice_OSup__fin(_1119972, c_Orderings_Oord__class_Omax(_1119972), _1119974)))], (27205 ^ _777959) ^ [_1293194] : [hBOOL(hAPP(_1293194, 27206 ^ [_1293194])), 27209 ^ _777959 : [(27210 ^ _777959) ^ [_1293288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293288)), -(hBOOL(hAPP(_1293194, hAPP(c_Int_Onat, _1293288))))]]], (10616 ^ _777959) ^ [_966073, _966075, _966077, _966079, _966081] : [hBOOL(hAPP(hAPP(c_member(_966073), _966075), _966077)), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_966073, tc_Option_Ooption(_966079)), c_Map_Orestrict__map(_966073, _966079, _966081, _966077)), _966075), c_Option_Ooption_ONone(_966079)) = c_Map_Orestrict__map(_966073, _966079, _966081, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966073, tc_HOL_Obool)), _966077), hAPP(hAPP(c_Set_Oinsert(_966073), _966075), c_Orderings_Obot__class_Obot(tc_fun(_966073, tc_HOL_Obool))))))], (41235 ^ _777959) ^ [_1585062, _1585064] : [c_Predicate_Oreflp(_1585062, _1585064), -(c_Relation_Orefl__on(_1585062, c_Orderings_Otop__class_Otop(tc_fun(_1585062, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1585062, _1585062)), hAPP(c_Product__Type_Oprod_Oprod__case(_1585062, _1585062, tc_HOL_Obool), _1585064))))], (30154 ^ _777959) ^ [_1348233, _1348235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1348233), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1348233), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1348235, _1348233))))], (13947 ^ _777959) ^ [_1036446, _1036448, _1036450] : [-(hAPP(hAPP(c_Set_Oinsert(_1036446), _1036448), _1036450) = hAPP(c_Set_OCollect(_1036446), hAPP(hAPP(c_COMBS(_1036446, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1036446), c_fdisj), hAPP(hAPP(c_COMBC(_1036446, _1036446, tc_HOL_Obool), c_fequal), _1036448))), hAPP(hAPP(c_COMBC(_1036446, tc_fun(_1036446, tc_HOL_Obool), tc_HOL_Obool), c_member(_1036446)), _1036450))))], (5934 ^ _777959) ^ [_872558, _872560, _872562] : [_872560 = _872562, -(hAPP(c_Option_Ooption_OSome(_872558), _872560) = hAPP(c_Option_Ooption_OSome(_872558), _872562))], (37994 ^ _777959) ^ [_1505926, _1505928, _1505930, _1505932, _1505934, _1505936] : [c_Fun_Oinj__on(_1505926, _1505928, _1505930, _1505932), hBOOL(hAPP(hAPP(c_member(_1505926), _1505934), _1505932)), hBOOL(hAPP(hAPP(c_member(_1505926), _1505936), _1505932)), 38005 ^ _777959 : [(38012 ^ _777959) ^ [] : [_1505934 = _1505936, -(hAPP(_1505930, _1505934) = hAPP(_1505930, _1505936))], (38006 ^ _777959) ^ [] : [hAPP(_1505930, _1505934) = hAPP(_1505930, _1505936), -(_1505934 = _1505936)]]], (41070 ^ _777959) ^ [] : [c_Com_OWT__bodies, 41073 ^ _777959 : [(41074 ^ _777959) ^ [_1581024] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname, tc_Com_Ocom)), _1581024), hAPP(c_List_Oset(tc_prod(tc_Com_Opname, tc_Com_Ocom)), c_Com_Obodies))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname, tc_Com_Ocom, tc_HOL_Obool), hAPP(c_COMBK(tc_fun(tc_Com_Ocom, tc_HOL_Obool), tc_Com_Opname), c_Com_OWT)), _1581024)))]]], (31286 ^ _777959) ^ [_1368923, _1368925] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1368923), _1368925)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1368923) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (2692 ^ _777959) ^ [_818030, _818032, _818034, _818036, _818038, _818040, _818042, _818044] : [-(c_Fun_Othe__inv__into(_818044, _818040, _818036, _818032) = c_Fun_Othe__inv__into(_818042, _818038, _818034, _818030)), _818044 = _818042, _818040 = _818038, _818036 = _818034, _818032 = _818030], (28333 ^ _777959) ^ [_1311958, _1311960] : [c_Nat__Transfer_Ois__nat(_1311958), c_Nat__Transfer_Onat__set(_1311960), 28340 ^ _777959 : [(28347 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1311958)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311960))), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1311958), _1311960)))], (28341 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1311958), _1311960)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1311958)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311960))))]]], (47564 ^ _777959) ^ [_1733668, _1733670] : [-(c_Nitpick_Owf_H(_1733668, _1733670)), c_Wellfounded_Oacyclic(_1733668, _1733670), 47569 ^ _777959 : [(47572 ^ _777959) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)], (47570 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1733668, _1733668)), _1733670))]]], (36742 ^ _777959) ^ [_1475092, _1475094, _1475096, _1475098, _1475100] : [-(c_Product__Type_Oprod_Oprod__size(_1475092, _1475094, _1475096, _1475098, _1475100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1475096, hAPP(c_Product__Type_Ofst(_1475092, _1475094), _1475100))), hAPP(_1475098, hAPP(c_Product__Type_Osnd(_1475092, _1475094), _1475100)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (44620 ^ _777959) ^ [_1664760, _1664762] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1664760, _1664762) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1664760), _1664762)))], (8118 ^ _777959) ^ [_917313, _917315, _917317, _917319, _917321, _917323, _917325, _917327] : [c_Finite__Set_Ofolding__image__simple(_917313, _917315, _917317, _917319, _917321, _917323), hBOOL(hAPP(c_Finite__Set_Ofinite(_917315), _917325)), hBOOL(hAPP(hAPP(c_member(_917315), _917327), _917325)), -(hAPP(_917323, _917325) = hAPP(hAPP(_917317, hAPP(_917321, _917327)), hAPP(_917323, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917315, tc_HOL_Obool)), _917325), hAPP(hAPP(c_Set_Oinsert(_917315), _917327), c_Orderings_Obot__class_Obot(tc_fun(_917315, tc_HOL_Obool)))))))], (44903 ^ _777959) ^ [_1671175] : [-(c_List_Oconcat(_1671175, c_List_Olist_ONil(tc_List_Olist(_1671175))) = c_List_Olist_ONil(_1671175))], (9338 ^ _777959) ^ [_938454, _938456, _938458] : [class_Lattices_Olattice(_938454), hBOOL(hAPP(c_Finite__Set_Ofinite(_938454), _938456)), -(_938456 = c_Orderings_Obot__class_Obot(tc_fun(_938454, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_938454), _938458)), -(_938458 = c_Orderings_Obot__class_Obot(tc_fun(_938454, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_938454, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938454, tc_HOL_Obool)), _938456), _938458)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938454), c_Big__Operators_Olattice__class_OSup__fin(_938454, _938456)), c_Big__Operators_Olattice__class_OSup__fin(_938454, _938458)))], (11934 ^ _777959) ^ [_994653, _994655, _994657] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994653), _994655)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994657), _994655)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994653), _994657))], (49818 ^ _777959) ^ [_1788254, _1788256, _1788258] : [c_List_Olist__all(_1788254, _1788256, _1788258), -(c_List_Olist__all(_1788254, _1788256, hAPP(c_List_Orev(_1788254), _1788258)))], (42531 ^ _777959) ^ [_1619523, _1619525] : [-(c_Product__Type_Oapsnd(_1619523, _1619523, _1619525, c_Fun_Oid(_1619523)) = c_Fun_Oid(tc_prod(_1619525, _1619523)))], (50870 ^ _777959) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (850 ^ _777959) ^ [_790974, _790976] : [-(class_Rings_Oinverse(_790974)), _790976 = _790974, class_Rings_Oinverse(_790976)], (47516 ^ _777959) ^ [_1733010, _1733012, _1733014] : [c_Wellfounded_Oacyclic(_1733010, _1733012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1733010, _1733010), tc_HOL_Obool)), _1733014), _1733012)), -(c_Wellfounded_Oacyclic(_1733010, _1733014))], (45202 ^ _777959) ^ [_1678976, _1678978, _1678980, _1678982, _1678984] : [-(hBOOL(hAPP(_1678976, _1678978))), -(c_List_OtakeWhile(_1678980, _1678976, hAPP(hAPP(c_List_Oappend(_1678980), _1678982), hAPP(hAPP(c_List_Olist_OCons(_1678980), _1678978), _1678984))) = c_List_OtakeWhile(_1678980, _1678976, _1678982))], (14307 ^ _777959) ^ [_1044828, _1044830, _1044832, _1044834, _1044836] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1044828)), hAPP(c_Set_Oimage(_1044830, tc_Option_Ooption(_1044828), _1044832), c_Orderings_Otop__class_Otop(tc_fun(_1044830, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1044828)), hAPP(c_Set_Oimage(_1044830, tc_Option_Ooption(_1044828), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1044830, tc_Option_Ooption(_1044828)), _1044832), _1044834), hAPP(c_Option_Ooption_OSome(_1044828), _1044836))), c_Orderings_Otop__class_Otop(tc_fun(_1044830, tc_HOL_Obool))))))], (26716 ^ _777959) ^ [_1283907, _1283909, _1283911, _1283913] : [class_Fields_Olinordered__field(_1283907), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283907), c_Groups_Ozero__class_Ozero(_1283907)), _1283909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283907), _1283911), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283907), _1283913), _1283909))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283907), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1283907), _1283911), _1283909)), _1283913)))], (40841 ^ _777959) ^ [_1572144, _1572146, _1572148, _1572150] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1572144), tc_List_Olist(_1572144))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1572144), tc_List_Olist(_1572144)), _1572146), _1572148)), c_List_Olexord(_1572144, _1572150))), 40846 ^ _777959 : [(40849 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1572144), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572144)), _1572146)), _1572148) = _1572146)], (40847 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572144)), _1572146)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572144)), _1572148))))]], 40851 ^ _777959 : [(40856 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1572144, _1572144)), hAPP(hAPP(c_Product__Type_OPair(_1572144, _1572144), hAPP(hAPP(c_List_Onth(_1572144), _1572146), 40850 ^ [_1572144, _1572146, _1572148, _1572150])), hAPP(hAPP(c_List_Onth(_1572144), _1572148), 40850 ^ [_1572144, _1572146, _1572148, _1572150]))), _1572150)))], (40854 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1572144), 40850 ^ [_1572144, _1572146, _1572148, _1572150]), _1572146) = hAPP(hAPP(c_List_Otake(_1572144), 40850 ^ [_1572144, _1572146, _1572148, _1572150]), _1572148))], (40852 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40850 ^ [_1572144, _1572146, _1572148, _1572150]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572144)), _1572146)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572144)), _1572148)))))]]], (34525 ^ _777959) ^ [_1427797, _1427799] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1427797)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1427799))) = 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), _1427797), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427799))))], (50946 ^ _777959) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (7486 ^ _777959) ^ [_903601, _903603, _903605, _903607, _903609] : [class_Lattices_Olattice(_903601), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903603, _903601)), _903605), _903607), _903609) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_903601), hAPP(_903605, _903609)), hAPP(_903607, _903609)))], (41918 ^ _777959) ^ [_1603694, _1603696, _1603698] : [hAPP(hAPP(c_List_Otake(_1603694), _1603696), _1603698) = c_List_Olist_ONil(_1603694), -(_1603696 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1603698 = c_List_Olist_ONil(_1603694))], (34695 ^ _777959) ^ [_1430620, _1430622, _1430624] : [class_Rings_Oring__1(_1430620), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1430620), hAPP(c_Groups_Ouminus__class_Ouminus(_1430620), _1430622)), 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)))), _1430624)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1430620), _1430622), 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)))), _1430624)))], (40371 ^ _777959) ^ [_1561493, _1561495, _1561497, _1561499, _1561501, _1561503, _1561505] : [-(hAPP(hAPP(c_List_Ozip(_1561493, _1561495), hAPP(hAPP(c_List_Olist__update(_1561493, _1561497), _1561499), _1561501)), hAPP(hAPP(c_List_Olist__update(_1561495, _1561503), _1561499), _1561505)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1561493, _1561495), hAPP(hAPP(c_List_Ozip(_1561493, _1561495), _1561497), _1561503)), _1561499), hAPP(hAPP(c_Product__Type_OPair(_1561493, _1561495), _1561501), _1561505)))], (16885 ^ _777959) ^ [_1101169, _1101171, _1101173] : [class_Orderings_Olinorder(_1101169), 16888 ^ _777959 : [(16895 ^ _777959) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1101169), _1101171), _1101173) = _1101171, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101169), _1101171), _1101173)))], (16889 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101169), _1101171), _1101173)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1101169), _1101171), _1101173) = _1101171)]]], (6167 ^ _777959) ^ [_876947, _876949, _876951, _876953] : [6168 ^ _777959 : [(6169 ^ _777959) ^ [_877057] : [hBOOL(hAPP(hAPP(c_member(_876947), _877057), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876947, tc_HOL_Obool)), _876949), _876951))), hBOOL(hAPP(_876953, _877057))]], 6177 ^ _777959 : [(6180 ^ _777959) ^ [] : [-(hBOOL(hAPP(_876953, 6176 ^ [_876947, _876949, _876951, _876953])))], (6178 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_876947), 6176 ^ [_876947, _876949, _876951, _876953]), _876949)))]], 6182 ^ _777959 : [(6185 ^ _777959) ^ [] : [-(hBOOL(hAPP(_876953, 6181 ^ [_876947, _876949, _876951, _876953])))], (6183 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_876947), 6181 ^ [_876947, _876949, _876951, _876953]), _876951)))]]], (27381 ^ _777959) ^ [_1296010, _1296012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1296010)), 27384 ^ _777959 : [(27391 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1296012), _1296010)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1296012)), hAPP(c_Int_Onat, _1296010))))], (27385 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1296012)), hAPP(c_Int_Onat, _1296010))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1296012), _1296010)))]]], (8470 ^ _777959) ^ [_924680, _924682, _924684] : [class_Orderings_Olinorder(_924680), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924680), _924682), _924684))), -(_924682 = _924684), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924680), _924684), _924682)))], (10653 ^ _777959) ^ [_966872, _966874, _966876, _966878, _966880] : [class_Groups_Ocomm__monoid__add(_966872), hBOOL(hAPP(c_Finite__Set_Ofinite(_966874), _966876)), hBOOL(hAPP(hAPP(c_member(_966874), _966878), _966876)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966874, _966872), _966880), _966876) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_966872), hAPP(_966880, _966878)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966874, _966872), _966880), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966874, tc_HOL_Obool)), _966876), hAPP(hAPP(c_Set_Oinsert(_966874), _966878), c_Orderings_Obot__class_Obot(tc_fun(_966874, tc_HOL_Obool)))))))], (10228 ^ _777959) ^ [_957423, _957425, _957427, _957429] : [-(hBOOL(hAPP(hAPP(c_member(_957423), _957425), _957427))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957423, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_957423), _957425), _957429)), _957427) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957423, tc_HOL_Obool)), _957429), _957427))], (14483 ^ _777959) ^ [_1049795, _1049797, _1049799, _1049801] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1049795, tc_fun(_1049797, tc_HOL_Obool)), _1049799), _1049801) = c_Orderings_Otop__class_Otop(tc_fun(_1049797, tc_HOL_Obool)), 14486 ^ _777959 : [(14487 ^ _777959) ^ [_1049911] : [hBOOL(hAPP(hAPP(c_member(_1049795), _1049911), _1049799)), -(hAPP(_1049801, _1049911) = c_Orderings_Otop__class_Otop(tc_fun(_1049797, tc_HOL_Obool)))]]], (11729 ^ _777959) ^ [_989061, _989063, _989065, _989067, _989069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989061, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989063, tc_fun(_989061, tc_HOL_Obool)), _989065), _989067)), _989069)), 11732 ^ _777959 : [(11733 ^ _777959) ^ [_989194] : [hBOOL(hAPP(hAPP(c_member(_989063), _989194), _989065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_989061, tc_HOL_Obool)), hAPP(_989067, _989194)), _989069)))]]], (44628 ^ _777959) ^ [_1664961, _1664963] : [class_Orderings_Olinorder(_1664961), hBOOL(hAPP(c_Finite__Set_Ofinite(_1664961), _1664963)), 44635 ^ _777959 : [(44640 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1664961), c_List_Olinorder__class_Osorted__list__of__set(_1664961, _1664963))))], (44638 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1664961, c_List_Olinorder__class_Osorted__list__of__set(_1664961, _1664963)))], (44636 ^ _777959) ^ [] : [-(hAPP(c_List_Oset(_1664961), c_List_Olinorder__class_Osorted__list__of__set(_1664961, _1664963)) = _1664963)]]], (25828 ^ _777959) ^ [_1267703, _1267705] : [class_Rings_Odivision__ring(_1267703), -(_1267705 = c_Groups_Ozero__class_Ozero(_1267703)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267703), _1267705), _1267705) = c_Groups_Oone__class_Oone(_1267703))], (16229 ^ _777959) ^ [_1087922, _1087924, _1087926, _1087928, _1087930] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1087922), _1087924)), 16232 ^ _777959 : [(16239 ^ _777959) ^ [] : [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), _1087924), _1087922)), _1087926)), _1087928) = _1087930, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087924), _1087926)), _1087928) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087922), _1087926)), _1087930))], (16233 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087924), _1087926)), _1087928) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087922), _1087926)), _1087930), -(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), _1087924), _1087922)), _1087926)), _1087928) = _1087930)]]], (38590 ^ _777959) ^ [_1518405, _1518407, _1518409, _1518411, _1518413] : [c_Typedef_Otype__definition(_1518405, _1518407, _1518409, _1518411, _1518413), -(hAPP(c_Set_Oimage(_1518405, _1518407, _1518409), c_Orderings_Otop__class_Otop(tc_fun(_1518405, tc_HOL_Obool))) = _1518413)], (46725 ^ _777959) ^ [_1712566, _1712568, _1712570, _1712572] : [-(c_Wellfounded_Omax__extp(_1712566, _1712568, _1712570, _1712572)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1712566), _1712570)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1712566), _1712572)), -(_1712572 = c_Orderings_Obot__class_Obot(tc_fun(_1712566, tc_HOL_Obool))), 46739 ^ _777959 : [(46742 ^ _777959) ^ [_1712911] : [hBOOL(hAPP(hAPP(c_member(_1712566), _1712911), _1712572)), hBOOL(hAPP(hAPP(_1712568, 46738 ^ [_1712566, _1712568, _1712570, _1712572]), _1712911))], (46740 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1712566), 46738 ^ [_1712566, _1712568, _1712570, _1712572]), _1712570)))]]], (13593 ^ _777959) ^ [_1027739] : [class_Finite__Set_Ofinite(_1027739), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1027739), c_Orderings_Otop__class_Otop(tc_fun(_1027739, tc_HOL_Obool)))))], (33821 ^ _777959) ^ [_1414687, _1414689] : [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(_1414689))), 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)), _1414687))))), -(hAPP(c_Nat_OSuc, _1414687) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414689))], (11501 ^ _777959) ^ [_983270, _983272, _983274, _983276] : [-(hAPP(c_Set_Oimage(_983270, _983272, _983274), _983276) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_983270, tc_fun(_983272, tc_HOL_Obool)), _983276), hAPP(hAPP(c_COMBC(_983270, tc_fun(_983272, tc_HOL_Obool), tc_fun(_983272, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_983272, tc_fun(tc_fun(_983272, tc_HOL_Obool), tc_fun(_983272, tc_HOL_Obool)), _983270), c_Set_Oinsert(_983272)), _983274)), c_Orderings_Obot__class_Obot(tc_fun(_983272, tc_HOL_Obool)))))], (12914 ^ _777959) ^ [_1012520, _1012522, _1012524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1012520, tc_HOL_Obool), tc_HOL_Obool)), _1012522), _1012524)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012520, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1012520, tc_HOL_Obool), _1012522)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1012520, tc_HOL_Obool), _1012524))))], (6367 ^ _777959) ^ [_880792, _880794, _880796] : [class_Orderings_Oorder(_880792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880792), _880794), _880796)), 6374 ^ _777959 : [(6381 ^ _777959) ^ [] : [_880796 = _880794, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880792), _880796), _880794)))], (6375 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880792), _880796), _880794)), -(_880796 = _880794)]]], (16479 ^ _777959) ^ [_1093454, _1093456, _1093458, _1093460] : [class_Orderings_Olinorder(_1093454), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093454), _1093456), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093454), _1093458), _1093460)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093454), _1093458), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093454), _1093456), _1093460)))], (4134 ^ _777959) ^ [_840545, _840547, _840549, _840551, _840553, _840555] : [-(c_Relation_OImage(_840555, _840551, _840547) = c_Relation_OImage(_840553, _840549, _840545)), _840555 = _840553, _840551 = _840549, _840547 = _840545], (39940 ^ _777959) ^ [_1551179, _1551181] : [hAPP(c_Finite__Set_Ocard(_1551179), hAPP(c_List_Oset(_1551179), _1551181)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551179)), _1551181), -(hBOOL(hAPP(c_List_Odistinct(_1551179), _1551181)))], (44781 ^ _777959) ^ [_1668651, _1668653] : [-(c_List_Oconcat(_1668651, _1668653) = hAPP(c_List_Ofoldl(tc_List_Olist(_1668651), tc_List_Olist(_1668651), c_List_Oappend(_1668651), c_List_Olist_ONil(_1668651)), _1668653))], (25328 ^ _777959) ^ [_1257972, _1257974] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257972)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257974)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1257972, _1257974))))], (42590 ^ _777959) ^ [_1620641, _1620643, _1620645, _1620647] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1620643, _1620641), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1620641, tc_prod(_1620643, _1620641), 42586 ^ [_1620641, _1620643, _1620645, _1620647]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1620643, tc_fun(_1620641, tc_HOL_Obool)), _1620645), _1620647))), hAPP(hAPP(c_Product__Type_OSigma(_1620643, _1620641), _1620645), _1620647))))], (36295 ^ _777959) ^ [_1466093, _1466095, _1466097, _1466099] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1466093, _1466095), _1466097)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1466093, _1466095), _1466099)), -(_1466097 = _1466099)], (28465 ^ _777959) ^ [_1314469, _1314471] : [28467 ^ _777959 : [(28470 ^ _777959) ^ [] : [hBOOL(hAPP(_1314471, 28466 ^ [_1314469, _1314471]))], (28468 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 28466 ^ [_1314469, _1314471]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1314469))))]], 28471 ^ _777959 : [(28472 ^ _777959) ^ [_1314624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1314624), _1314469)), -(hBOOL(hAPP(_1314471, _1314624)))]]], (47383 ^ _777959) ^ [_1729693, _1729695, _1729697] : [-(hAPP(c_Relation_ODomain(_1729693, _1729695), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1729693, _1729695), tc_HOL_Obool), _1729697)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1729693, _1729695), tc_HOL_Obool), tc_fun(_1729693, tc_HOL_Obool)), _1729697), c_Relation_ODomain(_1729693, _1729695)))], (37668 ^ _777959) ^ [_1498161, _1498163] : [c_Equiv__Relations_Oequiv(_1498161, c_Orderings_Otop__class_Otop(tc_fun(_1498161, tc_HOL_Obool)), _1498163), -(c_Equiv__Relations_Oequivp(_1498161, hAPP(hAPP(c_COMBC(_1498161, tc_fun(tc_prod(_1498161, _1498161), tc_HOL_Obool), tc_fun(_1498161, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498161, tc_fun(tc_fun(tc_prod(_1498161, _1498161), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1498161, _1498161), tc_HOL_Obool), tc_fun(_1498161, tc_HOL_Obool)), _1498161), c_COMBC(_1498161, tc_fun(tc_prod(_1498161, _1498161), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498161, tc_prod(_1498161, _1498161)), tc_fun(_1498161, tc_fun(tc_fun(tc_prod(_1498161, _1498161), tc_HOL_Obool), tc_HOL_Obool)), _1498161), hAPP(c_COMBB(tc_prod(_1498161, _1498161), tc_fun(tc_fun(tc_prod(_1498161, _1498161), tc_HOL_Obool), tc_HOL_Obool), _1498161), c_member(tc_prod(_1498161, _1498161)))), c_Product__Type_OPair(_1498161, _1498161)))), _1498163)))], (43352 ^ _777959) ^ [_1639190, _1639192, _1639194, _1639196] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1639190), _1639192)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639194)), _1639196))), -(hAPP(hAPP(c_List_Onth(_1639194), hAPP(hAPP(c_List_Odrop(_1639194), _1639190), _1639196)), _1639192) = hAPP(hAPP(c_List_Onth(_1639194), _1639196), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1639190), _1639192)))], (7662 ^ _777959) ^ [_907177, _907179, _907181, _907183] : [c_Finite__Set_Ofolding__one(_907177, _907179, _907181), hBOOL(hAPP(c_Finite__Set_Ofinite(_907177), _907183)), -(_907183 = c_Orderings_Obot__class_Obot(tc_fun(_907177, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_907177), hAPP(hAPP(_907179, 7675 ^ [_907177, _907179, _907181, _907183]), 7676 ^ [_907177, _907179, _907181, _907183])), hAPP(hAPP(c_Set_Oinsert(_907177), 7675 ^ [_907177, _907179, _907181, _907183]), hAPP(hAPP(c_Set_Oinsert(_907177), 7676 ^ [_907177, _907179, _907181, _907183]), c_Orderings_Obot__class_Obot(tc_fun(_907177, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_907177), hAPP(_907181, _907183)), _907183)))], (8138 ^ _777959) ^ [_917791, _917793, _917795] : [-(hBOOL(hAPP(hAPP(c_member(_917791), _917793), _917795))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917791, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_917791), _917793), _917795)), hAPP(hAPP(c_Set_Oinsert(_917791), _917793), c_Orderings_Obot__class_Obot(tc_fun(_917791, tc_HOL_Obool)))) = _917795)], (39850 ^ _777959) ^ [_1548651, _1548653, _1548655, _1548657, _1548659, _1548661] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548651, _1548653)), hAPP(hAPP(c_Product__Type_OPair(_1548651, _1548653), _1548655), _1548657)), hAPP(c_List_Oset(tc_prod(_1548651, _1548653)), hAPP(hAPP(c_List_Ozip(_1548651, _1548653), _1548659), _1548661)))), -(hBOOL(hAPP(hAPP(c_member(_1548651), _1548655), hAPP(c_List_Oset(_1548651), _1548659))))], (48130 ^ _777959) ^ [_1746986, _1746988] : [_1746986 = _1746988, -(c_Random_Oinc__shift(_1746986, _1746988) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (18438 ^ _777959) ^ [_1131959, _1131961, _1131963] : [class_Orderings_Olinorder(_1131959), hAPP(_1131961, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1131959), 18443 ^ [_1131959, _1131961, _1131963]), 18444 ^ [_1131959, _1131961, _1131963])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1131959), hAPP(_1131961, 18443 ^ [_1131959, _1131961, _1131963])), hAPP(_1131961, 18444 ^ [_1131959, _1131961, _1131963])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131959), _1131963)), -(_1131963 = c_Orderings_Obot__class_Obot(tc_fun(_1131959, tc_HOL_Obool))), -(hAPP(_1131961, c_Big__Operators_Olattice_OInf__fin(_1131959, c_Orderings_Oord__class_Omin(_1131959), _1131963)) = c_Big__Operators_Olattice_OInf__fin(_1131959, c_Orderings_Oord__class_Omin(_1131959), hAPP(c_Set_Oimage(_1131959, _1131959, _1131961), _1131963)))], (35844 ^ _777959) ^ [_1458026, _1458028, _1458030] : [-(c_HOL_OThe(tc_prod(_1458026, _1458028), _1458030) = c_HOL_OThe(tc_prod(_1458026, _1458028), hAPP(c_Product__Type_Oprod_Oprod__case(_1458026, _1458028, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1458028, tc_prod(_1458026, _1458028)), tc_fun(_1458028, tc_HOL_Obool), _1458026), hAPP(c_COMBB(tc_prod(_1458026, _1458028), tc_HOL_Obool, _1458028), _1458030)), c_Product__Type_OPair(_1458026, _1458028)))))], (2330 ^ _777959) ^ [_812409, _812411, _812413, _812415] : [-(c_SMT_Oz3mod(_812415, _812411) = c_SMT_Oz3mod(_812413, _812409)), _812415 = _812413, _812411 = _812409], (35898 ^ _777959) ^ [_1459158] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1459158) = 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), _1459158), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (36257 ^ _777959) ^ [_1465350, _1465352, _1465354] : [36259 ^ _777959 : [(36262 ^ _777959) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1465350, _1465352), 36258 ^ [_1465350, _1465352, _1465354]))], (36260 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1465352, 36258 ^ [_1465350, _1465352, _1465354]), _1465354)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1465350, _1465352), _1465354)))], (32957 ^ _777959) ^ [_1400484, _1400486] : [c_Int_OBit1(_1400484) = c_Int_OBit1(_1400486), -(_1400484 = _1400486)], (5697 ^ _777959) ^ [_867888, _867890] : [c_Com_OWT__bodies, hAPP(c_Com_Obody, _867888) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _867890), -(hBOOL(hAPP(c_Com_OWT, _867890)))], (7420 ^ _777959) ^ [_902405, _902407] : [class_Lattices_Obounded__lattice__bot(_902405), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902405), c_Orderings_Obot__class_Obot(_902405)), _902407) = _902407)], (47064 ^ _777959) ^ [_1721499, _1721501, _1721503] : [c_Wellfounded_Owf(_1721499, _1721501), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1721499, tc_HOL_Obool)), _1721503), hAPP(c_Relation_OImage(_1721499, _1721499, _1721501), _1721503))), -(_1721503 = c_Orderings_Obot__class_Obot(tc_fun(_1721499, tc_HOL_Obool)))], (33317 ^ _777959) ^ [_1406443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1406443), 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), _1406443)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (13591 ^ _777959) ^ [_1027706] : [c_Orderings_Otop__class_Otop(tc_fun(_1027706, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_1027706, tc_HOL_Obool))], (35848 ^ _777959) ^ [_1458208, _1458210, _1458212, _1458214, _1458216] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1458208, _1458210, _1458212), _1458214), _1458216)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1458208, _1458210)), hAPP(hAPP(c_Product__Type_OPair(_1458208, _1458210), _1458214), _1458216)), _1458212)))], (9108 ^ _777959) ^ [_934249, _934251, _934253, _934255] : [class_Orderings_Opreorder(_934249), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934249), _934251), _934253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934249), _934253), _934255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934249), _934251), _934255)))], (48154 ^ _777959) ^ [_1747363, _1747365] : [-(_1747363 = c_List_Olist_ONil(_1747365)), -(c_Random_Oselect__weight(_1747365, hAPP(hAPP(c_List_Omap(_1747365, tc_prod(tc_Code__Numeral_Ocode__numeral, _1747365)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1747365), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1747363)) = c_Random_Oselect(_1747365, _1747363))], (47029 ^ _777959) ^ [_1720842, _1720844] : [hBOOL(hAPP(hAPP(c_member(_1720842), 47030 ^ [_1720842, _1720844]), c_Wellfounded_Oacc(_1720842, _1720844))), -(c_Wellfounded_Owf(_1720842, _1720844))], (2544 ^ _777959) ^ [_815674, _815676, _815678, _815680] : [-(c_Nitpick_Onat__gcd(_815680, _815676) = c_Nitpick_Onat__gcd(_815678, _815674)), _815680 = _815678, _815676 = _815674], (11900 ^ _777959) ^ [_993925, _993927, _993929, _993931, _993933] : [-(_993925 = c_Orderings_Obot__class_Obot(tc_fun(_993927, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_993929, tc_HOL_Obool)), _993931), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993927, tc_fun(_993929, tc_HOL_Obool)), _993925), _993933)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993927, tc_fun(_993929, tc_HOL_Obool)), _993925), hAPP(hAPP(c_COMBB(tc_fun(_993929, tc_HOL_Obool), tc_fun(_993929, tc_HOL_Obool), _993927), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_993929, tc_HOL_Obool)), _993931)), _993933)))], (30311 ^ _777959) ^ [_1351156, _1351158] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1351156, _1351158) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1351156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1351156), _1351158)), _1351158)))], (51132 ^ _777959) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (38514 ^ _777959) ^ [_1516786, _1516788, _1516790, _1516792] : [c_Fun_Oinj__on(_1516786, tc_Option_Ooption(_1516788), c_Map_Omap__add(_1516786, _1516788, _1516790, _1516792), c_Map_Odom(_1516786, _1516788, _1516792)), -(c_Fun_Oinj__on(_1516786, tc_Option_Ooption(_1516788), _1516792, c_Map_Odom(_1516786, _1516788, _1516792)))], (24938 ^ _777959) ^ [_1250709, _1250711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250709)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250711), 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), _1250709), _1250711)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (17379 ^ _777959) ^ [_1110237, _1110239, _1110241] : [class_Orderings_Olinorder(_1110237), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110237), _1110239)), -(_1110239 = c_Orderings_Obot__class_Obot(tc_fun(_1110237, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1110237, hAPP(hAPP(c_Set_Oinsert(_1110237), _1110241), _1110239)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1110237), _1110241), c_Big__Operators_Olinorder__class_OMin(_1110237, _1110239)))], (49263 ^ _777959) ^ [_1774083, _1774085, _1774087, _1774089, _1774091] : [c_Relation_Osingle__valued(_1774083, _1774085, hAPP(c_Relation_Oconverse(_1774085, _1774083), _1774087)), -(hAPP(c_Relation_OImage(_1774085, _1774083, _1774087), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1774085, tc_HOL_Obool)), _1774089), _1774091)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1774083, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1774085, _1774083, _1774087), _1774089)), hAPP(c_Relation_OImage(_1774085, _1774083, _1774087), _1774091)))], (40115 ^ _777959) ^ [_1555588, _1555590, _1555592] : [_1555588 = _1555590, 40118 ^ _777959 : [(40121 ^ _777959) ^ [_1555736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1555736), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555592)), _1555588))), -(hAPP(hAPP(c_List_Onth(_1555592), _1555588), _1555736) = hAPP(hAPP(c_List_Onth(_1555592), _1555590), _1555736))], (40119 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555592)), _1555588) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555592)), _1555590))]]], (22607 ^ _777959) ^ [_1209316, _1209318] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(_1209316, _1209318)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1209316)), c_Com_Ocom_Ocom__size(_1209318))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6050 ^ _777959) ^ [_874718, _874720, _874722, _874724] : [class_Orderings_Oord(_874718), 6053 ^ _777959 : [(6060 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874718), hAPP(_874722, 6061 ^ [_874718, _874720, _874722, _874724])), hAPP(_874724, 6061 ^ [_874718, _874720, _874722, _874724]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874720, _874718)), _874722), _874724)))], (6054 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874720, _874718)), _874722), _874724)), 6057 ^ _777959 : [(6058 ^ _777959) ^ [_874875] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874718), hAPP(_874722, _874875)), hAPP(_874724, _874875))))]]]]], (11356 ^ _777959) ^ [_980307, _980309, _980311, _980313, _980315] : [class_Complete__Lattice_Ocomplete__lattice(_980307), hBOOL(hAPP(c_Finite__Set_Ofinite(_980309), _980311)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_980307), _980313), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980309, _980307), _980311), _980315)) = hAPP(hAPP(c_Finite__Set_Ofold(_980309, _980307, hAPP(hAPP(c_COMBB(_980307, tc_fun(_980307, _980307), _980309), c_Lattices_Osemilattice__sup__class_Osup(_980307)), _980315)), _980313), _980311))], (39033 ^ _777959) ^ [_1529633, _1529635, _1529637, _1529639, _1529641] : [hAPP(c_Set_Oimage(_1529633, _1529635, _1529637), c_Orderings_Otop__class_Otop(tc_fun(_1529633, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1529635, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1529635, _1529639, _1529641), c_Orderings_Otop__class_Otop(tc_fun(_1529635, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1529639, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1529633, _1529639, hAPP(c_Fun_Ocomp(_1529635, _1529639, _1529633, _1529641), _1529637)), c_Orderings_Otop__class_Otop(tc_fun(_1529633, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1529639, tc_HOL_Obool)))], (9008 ^ _777959) ^ [_932848, _932850, _932852] : [class_Orderings_Opreorder(_932848), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932848), _932850), _932852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932848), _932850), _932852)))], (29715 ^ _777959) ^ [_1338633, _1338635] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1338633, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1338633, tc_HOL_Obool))), hAPP(c_Set_OPow(_1338633), _1338635))))], (34513 ^ _777959) ^ [_1427581, _1427583] : [class_Rings_Olinordered__idom(_1427581), -(hAPP(c_Groups_Oabs__class_Oabs(_1427581), hAPP(hAPP(c_Power_Opower__class_Opower(_1427581), _1427583), 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(_1427581), _1427583), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (25346 ^ _777959) ^ [_1258282, _1258284] : [25348 ^ _777959 : [(25351 ^ _777959) ^ [] : [hBOOL(hAPP(_1258284, 25347 ^ [_1258282, _1258284]))], (25349 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25347 ^ [_1258282, _1258284]), _1258282)))]], 25352 ^ _777959 : [(25353 ^ _777959) ^ [_1258432] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1258432), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258282))), -(hBOOL(hAPP(_1258284, _1258432)))]]], (35355 ^ _777959) ^ [_1444343, _1444345, _1444347, _1444349, _1444351, _1444353] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1444343, _1444345)), hAPP(hAPP(c_Product__Type_OPair(_1444343, _1444345), _1444351), _1444353)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool)), _1444347), _1444349))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1444343, tc_fun(_1444345, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1444343, tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_fun(_1444345, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1444345, tc_fun(tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_fun(_1444345, tc_HOL_Obool)), _1444343), c_COMBC(_1444345, tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1444345, tc_prod(_1444343, _1444345)), tc_fun(_1444345, tc_fun(tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_HOL_Obool)), _1444343), hAPP(c_COMBB(tc_prod(_1444343, _1444345), tc_fun(tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_HOL_Obool), _1444345), c_member(tc_prod(_1444343, _1444345)))), c_Product__Type_OPair(_1444343, _1444345)))), _1444347)), hAPP(hAPP(c_COMBC(_1444343, tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_fun(_1444345, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1444345, tc_fun(tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_fun(_1444345, tc_HOL_Obool)), _1444343), c_COMBC(_1444345, tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1444345, tc_prod(_1444343, _1444345)), tc_fun(_1444345, tc_fun(tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_HOL_Obool)), _1444343), hAPP(c_COMBB(tc_prod(_1444343, _1444345), tc_fun(tc_fun(tc_prod(_1444343, _1444345), tc_HOL_Obool), tc_HOL_Obool), _1444345), c_member(tc_prod(_1444343, _1444345)))), c_Product__Type_OPair(_1444343, _1444345)))), _1444349)), _1444351), _1444353)))], (43500 ^ _777959) ^ [_1642479, _1642481, _1642483] : [-(hAPP(c_List_Otl(_1642479), hAPP(hAPP(c_List_Odrop(_1642479), _1642481), _1642483)) = hAPP(hAPP(c_List_Odrop(_1642479), _1642481), hAPP(c_List_Otl(_1642479), _1642483)))], (1904 ^ _777959) ^ [_805416, _805418, _805420, _805422, _805424, _805426] : [-(c_Partial__Function_Oflat__lub(_805426, _805422, _805418) = c_Partial__Function_Oflat__lub(_805424, _805420, _805416)), _805426 = _805424, _805422 = _805420, _805418 = _805416], (8798 ^ _777959) ^ [_929756, _929758, _929760, _929762] : [-(c_Nitpick_Ofold__graph_H(_929756, _929758, _929760, _929762, c_Orderings_Obot__class_Obot(tc_fun(_929756, tc_HOL_Obool)), _929762))], (20181 ^ _777959) ^ [_1163090, _1163092] : [class_Groups_Olinordered__ab__group__add(_1163090), 20184 ^ _777959 : [(20191 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163090), _1163092), c_Groups_Ozero__class_Ozero(_1163090))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163090), _1163092), _1163092)), c_Groups_Ozero__class_Ozero(_1163090))))], (20185 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163090), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163090), _1163092), _1163092)), c_Groups_Ozero__class_Ozero(_1163090))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163090), _1163092), c_Groups_Ozero__class_Ozero(_1163090))))]]], (45522 ^ _777959) ^ [_1685644, _1685646, _1685648] : [-(c_List_Opartition(_1685644, _1685646, _1685648) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1685644), tc_List_Olist(_1685644)), hAPP(c_List_Ofilter(_1685644, _1685646), _1685648)), hAPP(c_List_Ofilter(_1685644, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1685644, c_fNot), _1685646)), _1685648)))], (8548 ^ _777959) ^ [_925671, _925673, _925675] : [class_Orderings_Oorder(_925671), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925671), _925673), _925675)), _925673 = _925675], (37090 ^ _777959) ^ [] : [-(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)))))], (45284 ^ _777959) ^ [_1680622, _1680624] : [c_List_Olist_ONil(_1680622) = c_List_Oremdups(_1680622, _1680624), -(_1680624 = c_List_Olist_ONil(_1680622))], (8626 ^ _777959) ^ [_926918, _926920, _926922, _926924] : [class_Orderings_Oord(_926918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926918), _926920), _926922)), _926922 = _926924, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926918), _926920), _926924)))], (43727 ^ _777959) ^ [_1647272, _1647274, _1647276] : [class_Orderings_Olinorder(_1647272), -(c_Big__Operators_Olattice_OInf__fin(_1647272, c_Orderings_Oord__class_Omin(_1647272), hAPP(c_List_Oset(_1647272), hAPP(hAPP(c_List_Olist_OCons(_1647272), _1647274), _1647276))) = hAPP(c_List_Ofoldl(_1647272, _1647272, c_Orderings_Oord__class_Omin(_1647272), _1647274), _1647276))], (28946 ^ _777959) ^ [_1323621, _1323623] : [c_Nat__Transfer_Ois__nat(_1323621), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1323621, _1323623)))], (30193 ^ _777959) ^ [_1348873] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1348873, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1348873)], (44917 ^ _777959) ^ [_1671479, _1671481] : [44919 ^ _777959 : [(44922 ^ _777959) ^ [] : [44918 ^ [_1671479, _1671481] = c_List_Olist_ONil(_1671479)], (44920 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1671479)), 44918 ^ [_1671479, _1671481]), hAPP(c_List_Oset(tc_List_Olist(_1671479)), _1671481))))]], -(c_List_Oconcat(_1671479, _1671481) = c_List_Olist_ONil(_1671479))], (40409 ^ _777959) ^ [_1562314, _1562316, _1562318, _1562320] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1562314, tc_HOL_Obool)), hAPP(c_List_Oset(_1562314), hAPP(hAPP(c_List_Olist__update(_1562314, _1562316), _1562318), _1562320))), hAPP(hAPP(c_Set_Oinsert(_1562314), _1562320), hAPP(c_List_Oset(_1562314), _1562316)))))], (39554 ^ _777959) ^ [_1541872, _1541874, _1541876, _1541878] : [-(hBOOL(hAPP(c_List_Odistinct(_1541872), hAPP(hAPP(c_List_Omap(_1541874, _1541872), _1541876), _1541878)))), hBOOL(hAPP(c_List_Odistinct(_1541874), _1541878)), c_Fun_Oinj__on(_1541874, _1541872, _1541876, hAPP(c_List_Oset(_1541874), _1541878))], (13285 ^ _777959) ^ [_1020822, _1020824] : [-(hBOOL(hAPP(hAPP(c_member(_1020822), _1020824), c_Orderings_Otop__class_Otop(tc_fun(_1020822, tc_HOL_Obool)))))], (13297 ^ _777959) ^ [_1021060, _1021062, _1021064, _1021066, _1021068, _1021070] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1021060, tc_fun(_1021062, tc_HOL_Obool)), _1021064), _1021066), _1021068)), hBOOL(hAPP(hAPP(c_member(_1021060), _1021070), _1021064)), -(hBOOL(hAPP(hAPP(_1021066, _1021070), _1021068)))], (49404 ^ _777959) ^ [_1777719, _1777721] : [-(c_List_Orotate(_1777719, _1777721) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1777719), tc_List_Olist(_1777719)), _1777721), c_List_Orotate1(_1777719)))], (22499 ^ _777959) ^ [_1206789, _1206791, _1206793] : [class_Groups_Ocomm__monoid__add(_1206789), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1206789), _1206791), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206793))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1206789), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1206789), _1206791), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1206793))), hAPP(_1206791, _1206793)))], (35133 ^ _777959) ^ [_1438858, _1438860] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1438858), _1438860), hAPP(c_Int_Onumber__class_Onumber__of(_1438858), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1438858), _1438860)), class_Fields_Ofield__inverse__zero(_1438858), class_Int_Onumber__ring(_1438858)], (28762 ^ _777959) ^ [_1319798, _1319800, _1319802, _1319804] : [class_Orderings_Oorder(_1319798), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319798, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1319798, _1319800, _1319802)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1319798, _1319802, _1319804)) = c_Orderings_Obot__class_Obot(tc_fun(_1319798, tc_HOL_Obool)))], (51004 ^ _777959) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (33001 ^ _777959) ^ [_1401137, _1401139] : [class_Int_Onumber__ring(_1401137), -(hAPP(c_Int_Onumber__class_Onumber__of(_1401137), c_Int_OBit1(_1401139)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1401137), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1401137), c_Groups_Oone__class_Oone(_1401137)), hAPP(c_Int_Onumber__class_Onumber__of(_1401137), _1401139))), hAPP(c_Int_Onumber__class_Onumber__of(_1401137), _1401139)))], (45742 ^ _777959) ^ [_1690636, _1690638] : [-(c_Enum_Oenum__class_Oenum(tc_fun(_1690636, _1690638)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1690638), tc_fun(_1690636, _1690638)), hAPP(hAPP(c_COMBB(tc_fun(_1690636, tc_Option_Ooption(_1690638)), tc_fun(_1690636, _1690638), tc_List_Olist(_1690638)), c_Fun_Ocomp(tc_Option_Ooption(_1690638), _1690638, _1690636, c_Option_Othe(_1690638))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1690636, _1690638)), tc_fun(_1690636, tc_Option_Ooption(_1690638)), tc_List_Olist(_1690638)), c_Map_Omap__of(_1690636, _1690638)), hAPP(c_List_Ozip(_1690636, _1690638), c_Enum_Oenum__class_Oenum(_1690636))))), c_Enum_On__lists(_1690638, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690636)), c_Enum_Oenum__class_Oenum(_1690636)), c_Enum_Oenum__class_Oenum(_1690638)))), class_Enum_Oenum(_1690636), class_HOL_Oequal(_1690636), class_Enum_Oenum(_1690638)], (8384 ^ _777959) ^ [_923293, _923295, _923297, _923299, _923301, _923303, _923305] : [hBOOL(hAPP(hAPP(c_member(_923293), _923295), _923297)), c_Nitpick_Ofold__graph_H(_923293, _923299, _923301, _923303, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_923293, tc_HOL_Obool)), _923297), hAPP(hAPP(c_Set_Oinsert(_923293), _923295), c_Orderings_Obot__class_Obot(tc_fun(_923293, tc_HOL_Obool)))), _923305), -(c_Nitpick_Ofold__graph_H(_923293, _923299, _923301, _923303, _923297, hAPP(hAPP(_923301, _923295), _923305)))], (6275 ^ _777959) ^ [_879152, _879154, _879156] : [_879152 = _879154, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879156, tc_HOL_Obool)), _879154), _879152)))], (45135 ^ _777959) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (46267 ^ _777959) ^ [_1701645, _1701647, _1701649] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1701645)), _1701649), c_List_Olists(_1701645, _1701647))), -(hBOOL(hAPP(c_List_Olistsp(_1701645, hAPP(hAPP(c_COMBC(_1701645, tc_fun(_1701645, tc_HOL_Obool), tc_HOL_Obool), c_member(_1701645)), _1701647)), _1701649)))], (5226 ^ _777959) ^ [_857937, _857939, _857941, _857943, _857945, _857947] : [-(c_List_Osplice(_857947, _857943, _857939) = c_List_Osplice(_857945, _857941, _857937)), _857947 = _857945, _857943 = _857941, _857939 = _857937], (46481 ^ _777959) ^ [_1706427, _1706429, _1706431] : [_1706427 = _1706429, -(c_List_Olist__all2(_1706431, _1706431, c_fequal, _1706427, _1706429))], (47859 ^ _777959) ^ [_1741299, _1741301, _1741303, _1741305] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1741299), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1741301)), _1741303))), 47865 ^ _777959 : [(47868 ^ _777959) ^ [] : [hBOOL(hAPP(_1741305, 47864 ^ [_1741299, _1741301, _1741303, _1741305]))], (47866 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1741301), 47864 ^ [_1741299, _1741301, _1741303, _1741305]), hAPP(c_List_Oset(_1741301), _1741303))))]], -(hBOOL(hAPP(_1741305, hAPP(hAPP(c_List_Onth(_1741301), _1741303), _1741299))))], (19005 ^ _777959) ^ [_1142928, _1142930, _1142932, _1142934] : [hAPP(hAPP(c_Option_Omap(_1142928, _1142930), _1142932), _1142934) = c_Option_Ooption_ONone(_1142930), -(_1142934 = c_Option_Ooption_ONone(_1142928))], (13307 ^ _777959) ^ [_1021257, _1021259, _1021261, _1021263, _1021265, _1021267] : [hBOOL(hAPP(hAPP(c_member(_1021257), _1021259), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1021261, tc_fun(_1021257, tc_HOL_Obool)), _1021263), _1021265))), -(hBOOL(hAPP(hAPP(c_member(_1021257), _1021259), hAPP(_1021265, _1021267)))), hBOOL(hAPP(hAPP(c_member(_1021261), _1021267), _1021263))], (43113 ^ _777959) ^ [_1633178, _1633180, _1633182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1633178), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633180)), _1633182))), -(hAPP(hAPP(c_List_Otake(_1633180), hAPP(c_Nat_OSuc, _1633178)), _1633182) = hAPP(hAPP(c_List_Oappend(_1633180), hAPP(hAPP(c_List_Otake(_1633180), _1633178), _1633182)), hAPP(hAPP(c_List_Olist_OCons(_1633180), hAPP(hAPP(c_List_Onth(_1633180), _1633182), _1633178)), c_List_Olist_ONil(_1633180))))], (27720 ^ _777959) ^ [_1301683, _1301685, _1301687] : [class_Groups_Oordered__ab__group__add(_1301683), -(hAPP(c_Set_Oimage(_1301683, _1301683, c_Groups_Ouminus__class_Ouminus(_1301683)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1301683, _1301685), _1301687)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1301683, hAPP(c_Groups_Ouminus__class_Ouminus(_1301683), _1301687), hAPP(c_Groups_Ouminus__class_Ouminus(_1301683), _1301685)))], (21308 ^ _777959) ^ [_1182863, _1182865, _1182867, _1182869] : [class_Rings_Olinordered__semiring__strict(_1182863), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182863), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182863), _1182865), _1182867)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182863), _1182865), _1182869))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182863), c_Groups_Ozero__class_Ozero(_1182863)), _1182865)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182863), _1182867), _1182869)))], (742 ^ _777959) ^ [_789336, _789338, _789340, _789342, _789344, _789346, _789348, _789350, _789352, _789354] : [-(c_Typedef_Otype__definition(_789352, _789348, _789344, _789340, _789336)), c_Typedef_Otype__definition(_789354, _789350, _789346, _789342, _789338), _789354 = _789352, _789350 = _789348, _789346 = _789344, _789342 = _789340, _789338 = _789336], (23303 ^ _777959) ^ [_1222036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1222036)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (51256 ^ _777959) ^ [] : [-(class_Smallcheck_Osmall(tc_Product__Type_Ounit))], (38904 ^ _777959) ^ [_1525557, _1525559, _1525561, _1525563, _1525565, _1525567] : [-(hBOOL(hAPP(hAPP(c_member(_1525557), _1525559), _1525561))), 38907 ^ _777959 : [(38914 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525557), _1525563), _1525561))), -(hAPP(c_Set_Ovimage(_1525565, _1525557, hAPP(hAPP(c_COMBC(_1525565, _1525557, _1525557), hAPP(hAPP(c_COMBC(_1525565, _1525557, tc_fun(_1525557, _1525557)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525557, tc_fun(_1525557, _1525557)), _1525565), c_If(_1525557)), hAPP(hAPP(c_COMBC(_1525565, tc_fun(_1525565, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525565)), _1525567))), _1525559)), _1525563)), _1525561) = c_Orderings_Obot__class_Obot(tc_fun(_1525565, tc_HOL_Obool)))], (38908 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1525557), _1525563), _1525561)), -(hAPP(c_Set_Ovimage(_1525565, _1525557, hAPP(hAPP(c_COMBC(_1525565, _1525557, _1525557), hAPP(hAPP(c_COMBC(_1525565, _1525557, tc_fun(_1525557, _1525557)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525557, tc_fun(_1525557, _1525557)), _1525565), c_If(_1525557)), hAPP(hAPP(c_COMBC(_1525565, tc_fun(_1525565, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525565)), _1525567))), _1525559)), _1525563)), _1525561) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1525565, tc_HOL_Obool)), _1525567))]]], (28107 ^ _777959) ^ [_1308203, _1308205, _1308207, _1308209] : [class_Rings_Oring__1(_1308203), -(hAPP(c_Int_Oring__1__class_Oof__int(_1308203), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1308205, tc_Int_Oint), _1308207), _1308209)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1308205, _1308203), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1308203, _1308205), c_Int_Oring__1__class_Oof__int(_1308203)), _1308207)), _1308209))], (51016 ^ _777959) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (31120 ^ _777959) ^ [_1365825, _1365827] : [class_Groups_Oordered__ab__group__add__abs(_1365825), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365825), c_Groups_Ozero__class_Ozero(_1365825)), hAPP(c_Groups_Oabs__class_Oabs(_1365825), _1365827))))], (41213 ^ _777959) ^ [_1584607, _1584609, _1584611, _1584613, _1584615] : [c_Relation_Orefl__on(_1584607, _1584609, _1584611), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584607, _1584607)), hAPP(hAPP(c_Product__Type_OPair(_1584607, _1584607), _1584613), _1584615)), _1584611)), -(hBOOL(hAPP(hAPP(c_member(_1584607), _1584615), _1584609)))], (9952 ^ _777959) ^ [_950915, _950917, _950919, _950921] : [class_Lattices_Osemilattice__inf(_950915), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950915), _950917), _950919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_950915), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950915), _950921), _950917)), _950919)))], (46674 ^ _777959) ^ [_1710900, _1710902, _1710904, _1710906, _1710908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1710900, _1710902)), hAPP(_1710900, _1710904))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1710906, _1710906)), hAPP(hAPP(c_Product__Type_OPair(_1710906, _1710906), _1710902), _1710904)), c_List_Omeasures(_1710906, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1710906, tc_Nat_Onat)), _1710900), _1710908)))))], (1030 ^ _777959) ^ [_793558, _793560] : [-(class_Groups_Oordered__ab__group__add__abs(_793558)), _793560 = _793558, class_Groups_Oordered__ab__group__add__abs(_793560)], (32147 ^ _777959) ^ [_1385205, _1385207, _1385209] : [class_Int_Onumber__ring(_1385205), -(hAPP(c_Int_Onumber__class_Onumber__of(_1385205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1385207), _1385209)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385205), hAPP(c_Int_Onumber__class_Onumber__of(_1385205), _1385207)), hAPP(c_Int_Onumber__class_Onumber__of(_1385205), _1385209)))], (45087 ^ _777959) ^ [_1676283, _1676285] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1676283), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1676283))), _1676285))), 45090 ^ _777959 : [(45097 ^ _777959) ^ [] : [-(_1676285 = c_List_Olist_ONil(tc_List_Olist(_1676283))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1676283))), c_List_Otranspose(_1676283, _1676285)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676283)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1676283)), _1676285), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45091 ^ _777959) ^ [] : [_1676285 = c_List_Olist_ONil(tc_List_Olist(_1676283)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1676283))), c_List_Otranspose(_1676283, _1676285)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (23062 ^ _777959) ^ [_1217709, _1217711] : [-(c_Option_Ooption_Ooption__size(_1217709, _1217711, c_Option_Ooption_ONone(_1217709)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12113 ^ _777959) ^ [_997746, _997748, _997750] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997746), _997748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997746), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997748), _997750))))], (18644 ^ _777959) ^ [_1136134, _1136136, _1136138] : [class_Lattices_Osemilattice__inf(_1136134), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136134), _1136136)), -(_1136136 = c_Orderings_Obot__class_Obot(tc_fun(_1136134, tc_HOL_Obool))), 18655 ^ _777959 : [(18656 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136134), _1136138), hAPP(c_Finite__Set_Ofold1(_1136134, c_Lattices_Osemilattice__inf__class_Oinf(_1136134)), _1136136))), 18659 ^ _777959 : [(18660 ^ _777959) ^ [_1136427] : [hBOOL(hAPP(hAPP(c_member(_1136134), _1136427), _1136136)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136134), _1136138), _1136427)))]]], (18666 ^ _777959) ^ [] : [18668 ^ _777959 : [(18671 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136134), _1136138), 18667 ^ [_1136134, _1136136, _1136138]))], (18669 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1136134), 18667 ^ [_1136134, _1136136, _1136138]), _1136136)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136134), _1136138), hAPP(c_Finite__Set_Ofold1(_1136134, c_Lattices_Osemilattice__inf__class_Oinf(_1136134)), _1136136))))]]], (28277 ^ _777959) ^ [_1311027, _1311029] : [class_Groups_Oordered__ab__group__add(_1311027), -(hAPP(c_Set_Oimage(_1311027, _1311027, c_Groups_Ouminus__class_Ouminus(_1311027)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1311027), _1311029)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1311027), hAPP(c_Groups_Ouminus__class_Ouminus(_1311027), _1311029)))], (27976 ^ _777959) ^ [_1305847, _1305849, _1305851] : [class_Rings_Olinordered__idom(_1305847), 27979 ^ _777959 : [(27986 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1305849), _1305851)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305847), hAPP(c_Int_Oring__1__class_Oof__int(_1305847), _1305849)), hAPP(c_Int_Oring__1__class_Oof__int(_1305847), _1305851))))], (27980 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305847), hAPP(c_Int_Oring__1__class_Oof__int(_1305847), _1305849)), hAPP(c_Int_Oring__1__class_Oof__int(_1305847), _1305851))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1305849), _1305851)))]]], (7392 ^ _777959) ^ [_901983, _901985, _901987] : [class_Lattices_Obounded__lattice__bot(_901983), 7395 ^ _777959 : [(7404 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901983), _901985), _901987) = c_Orderings_Obot__class_Obot(_901983)), _901985 = c_Orderings_Obot__class_Obot(_901983), _901987 = c_Orderings_Obot__class_Obot(_901983)], (7396 ^ _777959) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901983), _901985), _901987) = c_Orderings_Obot__class_Obot(_901983), 7399 ^ _777959 : [(7402 ^ _777959) ^ [] : [-(_901987 = c_Orderings_Obot__class_Obot(_901983))], (7400 ^ _777959) ^ [] : [-(_901985 = c_Orderings_Obot__class_Obot(_901983))]]]]], (47094 ^ _777959) ^ [_1722059, _1722061] : [c_FunDef_Oreduction__pair(_1722059, _1722061), 47097 ^ _777959 : [(47100 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1722059, _1722059), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1722059, _1722059, _1722059), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1722059, _1722059), tc_HOL_Obool), tc_fun(tc_prod(_1722059, _1722059), tc_HOL_Obool)), _1722061)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1722059, _1722059), tc_HOL_Obool), tc_fun(tc_prod(_1722059, _1722059), tc_HOL_Obool)), _1722061))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1722059, _1722059), tc_HOL_Obool), tc_fun(tc_prod(_1722059, _1722059), tc_HOL_Obool)), _1722061))))], (47098 ^ _777959) ^ [] : [-(c_Wellfounded_Owf(_1722059, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1722059, _1722059), tc_HOL_Obool), tc_fun(tc_prod(_1722059, _1722059), tc_HOL_Obool)), _1722061)))]]], (10968 ^ _777959) ^ [_972953, _972955, _972957] : [class_Groups_Ogroup__add(_972953), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972953), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_972953), _972955), _972957)), _972957) = _972955)], (30920 ^ _777959) ^ [_1361924, _1361926, _1361928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1361924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1361926), 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), _1361926), _1361928))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1361924))), _1361928)))], (19328 ^ _777959) ^ [_1148691, _1148693] : [class_Rings_Omult__zero(_1148691), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148691), c_Groups_Ozero__class_Ozero(_1148691)), _1148693) = c_Groups_Ozero__class_Ozero(_1148691))], (43504 ^ _777959) ^ [_1642585, _1642587, _1642589] : [-(hAPP(c_List_Orotate1(_1642585), hAPP(c_List_Orotate(_1642585, _1642587), _1642589)) = hAPP(c_List_Orotate(_1642585, _1642587), hAPP(c_List_Orotate1(_1642585), _1642589)))], (41022 ^ _777959) ^ [_1579327, _1579329, _1579331, _1579333] : [41024 ^ _777959 : [(41027 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1579327, _1579327, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1579327, tc_fun(_1579327, _1579329), tc_fun(_1579327, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1579329, tc_HOL_Obool), tc_fun(tc_fun(_1579327, _1579329), tc_fun(_1579327, tc_HOL_Obool)), _1579327), c_COMBB(_1579329, tc_HOL_Obool, _1579327)), hAPP(hAPP(c_COMBB(_1579329, tc_fun(_1579329, tc_HOL_Obool), _1579327), c_fequal), _1579333))), _1579333)), 41023 ^ [_1579327, _1579329, _1579331, _1579333]))], (41025 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1579327, _1579327)), 41023 ^ [_1579327, _1579329, _1579331, _1579333]), _1579331)))]], -(c_Equiv__Relations_Ocongruent(_1579327, _1579329, _1579331, _1579333))], (40989 ^ _777959) ^ [_1578387] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1578387, tc_HOL_Obool) = c_Set_OBall(_1578387))], (19346 ^ _777959) ^ [_1148988, _1148990] : [class_Groups_Ogroup__add(_1148988), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1148988), _1148990), c_Groups_Ozero__class_Ozero(_1148988)) = _1148990)], (34325 ^ _777959) ^ [_1424064] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1424064)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424064)), 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))))], (16069 ^ _777959) ^ [_1084115, _1084117, _1084119] : [class_Orderings_Olinorder(_1084115), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084115, tc_HOL_Obool)), _1084117), _1084119)), -(_1084117 = c_Orderings_Obot__class_Obot(tc_fun(_1084115, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084115), _1084119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084115), c_Big__Operators_Olinorder__class_OMax(_1084115, _1084117)), c_Big__Operators_Olinorder__class_OMax(_1084115, _1084119))))], (17089 ^ _777959) ^ [_1104799, _1104801, _1104803] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1104799), _1104801)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1104803), _1104801)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1104799), _1104803)), _1104801))], (20481 ^ _777959) ^ [_1168585, _1168587, _1168589, _1168591] : [class_Rings_Olinordered__ring__strict(_1168585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168585), _1168587), _1168589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168585), _1168591), c_Groups_Ozero__class_Ozero(_1168585))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168585), _1168589), _1168591)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168585), _1168587), _1168591))))], (43568 ^ _777959) ^ [_1643896, _1643898, _1643900] : [-(c_List_Orotate(_1643896, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1643898), _1643900)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1643896), tc_List_Olist(_1643896), tc_List_Olist(_1643896), c_List_Orotate(_1643896, _1643898)), c_List_Orotate(_1643896, _1643900)))], (39286 ^ _777959) ^ [_1535347, _1535349, _1535351, _1535353] : [hAPP(hAPP(c_Map_Omap__of(_1535347, _1535349), _1535351), _1535353) = c_Option_Ooption_ONone(_1535349), hBOOL(hAPP(hAPP(c_member(_1535347), _1535353), hAPP(c_Set_Oimage(tc_prod(_1535347, _1535349), _1535347, c_Product__Type_Ofst(_1535347, _1535349)), hAPP(c_List_Oset(tc_prod(_1535347, _1535349)), _1535351))))], (29691 ^ _777959) ^ [] : [-(c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname, tc_Com_Ocom), c_Com_Obodies))], (37782 ^ _777959) ^ [_1500736, _1500738, _1500740, _1500742, _1500744, _1500746, _1500748, _1500750, _1500752] : [c_Equiv__Relations_Oequiv(_1500736, _1500738, _1500740), c_Equiv__Relations_Oequiv(_1500742, _1500744, _1500746), c_Equiv__Relations_Ocongruent2(_1500736, _1500742, tc_fun(_1500748, tc_HOL_Obool), _1500740, _1500746, _1500750), hBOOL(hAPP(hAPP(c_member(_1500742), _1500752), _1500744)), -(c_Equiv__Relations_Ocongruent(_1500736, tc_fun(_1500748, tc_HOL_Obool), _1500740, hAPP(hAPP(c_COMBB(tc_fun(_1500742, tc_fun(_1500748, tc_HOL_Obool)), tc_fun(_1500748, tc_HOL_Obool), _1500736), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1500742, tc_fun(_1500748, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1500742, _1500742, _1500746), hAPP(hAPP(c_Set_Oinsert(_1500742), _1500752), c_Orderings_Obot__class_Obot(tc_fun(_1500742, tc_HOL_Obool)))))), _1500750)))], (34403 ^ _777959) ^ [_1425654] : [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), _1425654))), 34406 ^ _777959 : [(34409 ^ _777959) ^ [] : [-(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(_1425654)))))], (34407 ^ _777959) ^ [] : [-(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(_1425654)))))]]], (25660 ^ _777959) ^ [_1264497, _1264499, _1264501, _1264503, _1264505] : [class_Fields_Ofield(_1264497), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264499), _1264501)), -(hAPP(_1264503, _1264505) = c_Groups_Ozero__class_Ozero(_1264497)), 25671 ^ _777959 : [(25678 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1264499), _1264505), _1264501))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1264499, _1264497), _1264503), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1264499, tc_HOL_Obool)), _1264501), hAPP(hAPP(c_Set_Oinsert(_1264499), _1264505), c_Orderings_Obot__class_Obot(tc_fun(_1264499, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1264499, _1264497), _1264503), _1264501))], (25672 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1264499), _1264505), _1264501)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1264499, _1264497), _1264503), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1264499, tc_HOL_Obool)), _1264501), hAPP(hAPP(c_Set_Oinsert(_1264499), _1264505), c_Orderings_Obot__class_Obot(tc_fun(_1264499, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1264497), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1264499, _1264497), _1264503), _1264501)), hAPP(_1264503, _1264505)))]]], (4300 ^ _777959) ^ [_843062, _843064, _843066, _843068] : [-(c_Nitpick_Oint__lcm(_843068, _843064) = c_Nitpick_Oint__lcm(_843066, _843062)), _843068 = _843066, _843064 = _843062], (5176 ^ _777959) ^ [_857176, _857178, _857180, _857182, _857184, _857186] : [-(c_Product__Type_Oprod_Oprod__case(_857186, _857182, _857178) = c_Product__Type_Oprod_Oprod__case(_857184, _857180, _857176)), _857186 = _857184, _857182 = _857180, _857178 = _857176], (20009 ^ _777959) ^ [_1160016, _1160018, _1160020] : [class_Rings_Oordered__ring(_1160016), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160016), _1160018), c_Groups_Ozero__class_Ozero(_1160016))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160016), _1160020), c_Groups_Ozero__class_Ozero(_1160016))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160016), c_Groups_Ozero__class_Ozero(_1160016)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160016), _1160018), _1160020))))], (2890 ^ _777959) ^ [_821123, _821125, _821127, _821129, _821131, _821133] : [-(c_Set_Ovimage(_821133, _821129, _821125) = c_Set_Ovimage(_821131, _821127, _821123)), _821133 = _821131, _821129 = _821127, _821125 = _821123], (2086 ^ _777959) ^ [_808439, _808441, _808443, _808445, _808447, _808449, _808451, _808453, _808455, _808457] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_808457, _808453, _808449, _808445, _808441) = c_SetInterval_Oord_OgreaterThanAtMost(_808455, _808451, _808447, _808443, _808439)), _808457 = _808455, _808453 = _808451, _808449 = _808447, _808445 = _808443, _808441 = _808439], (35105 ^ _777959) ^ [_1438408, _1438410] : [class_Int_Onumber__ring(_1438408), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1438408), hAPP(c_Int_Onumber__class_Onumber__of(_1438408), c_Int_OMin)), _1438410) = hAPP(c_Groups_Ouminus__class_Ouminus(_1438408), _1438410))], (43610 ^ _777959) ^ [_1644797, _1644799, _1644801, _1644803, _1644805, _1644807] : [-(hAPP(c_List_Ofoldl(_1644797, _1644799, _1644801, _1644803), hAPP(hAPP(c_List_Oappend(_1644799), _1644805), _1644807)) = hAPP(c_List_Ofoldl(_1644797, _1644799, _1644801, hAPP(c_List_Ofoldl(_1644797, _1644799, _1644801, _1644803), _1644805)), _1644807))], (13673 ^ _777959) ^ [_1030476, _1030478] : [-(hAPP(c_Set_OCollect(_1030476), hAPP(hAPP(c_COMBC(_1030476, tc_fun(_1030476, tc_HOL_Obool), tc_HOL_Obool), c_member(_1030476)), _1030478)) = _1030478)], (37207 ^ _777959) ^ [_1487060, _1487062, _1487064, _1487066, _1487068] : [-(hBOOL(hAPP(hAPP(c_member(_1487060), _1487062), hAPP(c_Relation_OImage(_1487064, _1487060, _1487066), _1487068)))), 37208 ^ _777959 : [(37209 ^ _777959) ^ [_1487146] : [hBOOL(hAPP(hAPP(c_member(_1487064), _1487146), _1487068)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1487064, _1487060)), hAPP(hAPP(c_Product__Type_OPair(_1487064, _1487060), _1487146), _1487062)), _1487066))]]], (30826 ^ _777959) ^ [_1360390, _1360392, _1360394] : [-(hBOOL(hAPP(_1360390, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1360392, _1360394)))), 30829 ^ _777959 : [(30832 ^ _777959) ^ [] : [hBOOL(hAPP(_1360390, _1360392))], (30830 ^ _777959) ^ [] : [-(_1360394 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 30833 ^ _777959 : [(30838 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 30836 ^ [_1360390, _1360392, _1360394]), _1360394)))], (30840 ^ _777959) ^ [] : [-(_1360392 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1360394), 30835 ^ [_1360390, _1360392, _1360394])), 30836 ^ [_1360390, _1360392, _1360394]))], (30842 ^ _777959) ^ [] : [hBOOL(hAPP(_1360390, 30836 ^ [_1360390, _1360392, _1360394]))], (30834 ^ _777959) ^ [] : [_1360394 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (30790 ^ _777959) ^ [_1359687, _1359689] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1359687, _1359689) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1359687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1359687), _1359689)), _1359689)))], (34463 ^ _777959) ^ [_1426717, _1426719] : [class_Rings_Ocomm__semiring__1(_1426717), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1426717), _1426719), _1426719) = hAPP(hAPP(c_Power_Opower__class_Opower(_1426717), _1426719), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (32823 ^ _777959) ^ [_1397971] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1397971))), -(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), _1397971)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (47850 ^ _777959) ^ [_1741072, _1741074, _1741076] : [-(hBOOL(hAPP(hAPP(c_member(_1741072), _1741074), c_Wellfounded_Oacc(_1741072, _1741076)))), 47854 ^ _777959 : [(47857 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1741072), 47853 ^ [_1741072, _1741074, _1741076]), c_Wellfounded_Oacc(_1741072, _1741076)))], (47855 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1741072, _1741072)), hAPP(hAPP(c_Product__Type_OPair(_1741072, _1741072), 47853 ^ [_1741072, _1741074, _1741076]), _1741074)), _1741076)))]]], (41503 ^ _777959) ^ [_1591589, _1591591, _1591593, _1591595] : [_1591589 = _1591591, -(c_List_Oremove1(_1591593, _1591589, hAPP(hAPP(c_List_Olist_OCons(_1591593), _1591591), _1591595)) = _1591595)], (45682 ^ _777959) ^ [_1689560, _1689562] : [class_Enum_Oenum(_1689560), -(hBOOL(hAPP(hAPP(c_member(_1689560), _1689562), hAPP(c_List_Oset(_1689560), c_Enum_Oenum__class_Oenum(_1689560)))))], (31997 ^ _777959) ^ [_1382044, _1382046, _1382048, _1382050] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382044), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382044), _1382046), _1382048)), hAPP(c_Int_Onumber__class_Onumber__of(_1382044), _1382050)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1382044), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382044), _1382046), hAPP(c_Int_Onumber__class_Onumber__of(_1382044), _1382050))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1382044), _1382048), hAPP(c_Int_Onumber__class_Onumber__of(_1382044), _1382050)))), class_Int_Onumber(_1382044), class_Rings_Osemiring(_1382044)], (6303 ^ _777959) ^ [_879658, _879660, _879662, _879664, _879666] : [class_Orderings_Oord(_879658), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879660, _879658)), _879662), _879664)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879658), hAPP(_879662, _879666)), hAPP(_879664, _879666))))], (20865 ^ _777959) ^ [_1175070, _1175072] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175070), _1175072) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20870 ^ _777959 : [(20873 ^ _777959) ^ [] : [-(_1175072 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20871 ^ _777959) ^ [] : [-(_1175070 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20874 ^ _777959 : [(20877 ^ _777959) ^ [] : [-(_1175072 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20875 ^ _777959) ^ [] : [-(_1175070 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (50964 ^ _777959) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (2232 ^ _777959) ^ [_810884, _810886, _810888, _810890, _810892, _810894, _810896, _810898] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_810898, _810894, _810890, _810886) = c_Nat_Osemiring__1__class_Oof__nat__aux(_810896, _810892, _810888, _810884)), _810898 = _810896, _810894 = _810892, _810890 = _810888, _810886 = _810884], (33883 ^ _777959) ^ [_1416224, _1416226] : [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(_1416224))), 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)), _1416226)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416224)), hAPP(c_Nat_OSuc, _1416226))))], (41868 ^ _777959) ^ [_1602056, _1602058, _1602060] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602056), tc_List_Olist(_1602056))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602056), tc_List_Olist(_1602056)), c_List_Olist_ONil(_1602056)), _1602058)), c_List_Olistrel(_1602056, _1602060))), -(_1602058 = c_List_Olist_ONil(_1602056))], (34057 ^ _777959) ^ [_1419361, _1419363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1419361), 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)))), _1419363)), 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)))), _1419361)) = 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), _1419363), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1419361))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (37950 ^ _777959) ^ [_1505156, _1505158, _1505160, _1505162, _1505164] : [c_Fun_Oinj__on(_1505156, _1505158, _1505160, _1505162), -(c_Fun_Oinj__on(_1505156, _1505158, _1505160, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1505156, tc_HOL_Obool)), _1505162), _1505164)))], (2636 ^ _777959) ^ [_817106, _817108] : [_817108 = _817106, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_817108) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_817106))], (42000 ^ _777959) ^ [_1605635, _1605637, _1605639, _1605641] : [hAPP(hAPP(c_List_Olist__update(_1605635, _1605637), _1605639), _1605641) = c_List_Olist_ONil(_1605635), -(_1605637 = c_List_Olist_ONil(_1605635))], (34569 ^ _777959) ^ [_1428584, _1428586, _1428588] : [class_Rings_Olinordered__semidom(_1428584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428584), hAPP(hAPP(c_Power_Opower__class_Opower(_1428584), _1428586), 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(_1428584), _1428588), 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(_1428584), c_Groups_Ozero__class_Ozero(_1428584)), _1428588)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428584), _1428586), _1428588)))], (44899 ^ _777959) ^ [_1671061, _1671063, _1671065, _1671067, _1671069] : [-(c_List_Ofoldr(_1671061, _1671063, _1671065, _1671067, _1671069) = hAPP(c_List_Ofoldl(_1671063, _1671061, hAPP(c_COMBC(_1671061, _1671063, _1671063), _1671065), _1671069), hAPP(c_List_Orev(_1671061), _1671067)))], (47050 ^ _777959) ^ [_1721195, _1721197] : [c_Wellfounded_Owf(_1721195, _1721197), 47054 ^ _777959 : [(47055 ^ _777959) ^ [_1721331] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1721195, _1721195)), hAPP(hAPP(c_Product__Type_OPair(_1721195, _1721195), hAPP(_1721331, hAPP(c_Nat_OSuc, 47053 ^ [_1721195, _1721197, _1721331]))), hAPP(_1721331, 47053 ^ [_1721195, _1721197, _1721331]))), _1721197))]]], (43400 ^ _777959) ^ [_1640492, _1640494, _1640496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1640492), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640494)), _1640496))), -(hAPP(hAPP(c_List_Olist_OCons(_1640494), hAPP(hAPP(c_List_Onth(_1640494), _1640496), _1640492)), hAPP(hAPP(c_List_Odrop(_1640494), hAPP(c_Nat_OSuc, _1640492)), _1640496)) = hAPP(hAPP(c_List_Odrop(_1640494), _1640492), _1640496))], (3792 ^ _777959) ^ [_835340, _835342, _835344, _835346] : [-(c_Map_Omap__of(_835346, _835342) = c_Map_Omap__of(_835344, _835340)), _835346 = _835344, _835342 = _835340], (43412 ^ _777959) ^ [_1640815, _1640817, _1640819, _1640821] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1640815) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1640817), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1640815)), hAPP(hAPP(c_List_Olist_OCons(_1640817), _1640819), _1640821)) = hAPP(hAPP(c_List_Odrop(_1640817), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1640815)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1640821))], (12944 ^ _777959) ^ [_1013438, _1013440, _1013442, _1013444] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1013438, tc_HOL_Obool), tc_fun(_1013440, tc_HOL_Obool)), _1013442), hAPP(hAPP(c_COMBC(tc_fun(_1013438, tc_HOL_Obool), tc_fun(_1013438, tc_fun(_1013440, tc_HOL_Obool)), tc_fun(_1013440, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1013438, tc_fun(_1013440, tc_HOL_Obool))), _1013444)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1013438, tc_fun(_1013440, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1013438, tc_HOL_Obool), _1013442)), _1013444))], (4216 ^ _777959) ^ [_841790, _841792, _841794, _841796] : [-(c_Nat_Ocompow(_841796, _841792) = c_Nat_Ocompow(_841794, _841790)), _841796 = _841794, _841792 = _841790], (37916 ^ _777959) ^ [_1504350, _1504352, _1504354, _1504356] : [c_Fun_Oinj__on(_1504350, _1504352, _1504354, _1504356), 37919 ^ _777959 : [(37920 ^ _777959) ^ [_1504458] : [hBOOL(hAPP(hAPP(c_member(_1504350), _1504458), _1504356)), 37923 ^ _777959 : [(37924 ^ _777959) ^ [_1504560] : [hBOOL(hAPP(hAPP(c_member(_1504350), _1504560), _1504356)), hAPP(_1504354, _1504458) = hAPP(_1504354, _1504560), -(_1504458 = _1504560)]]]]], (38768 ^ _777959) ^ [_1522225, _1522227, _1522229, _1522231, _1522233] : [hBOOL(hAPP(_1522231, hAPP(_1522229, _1522233))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1522225, _1522227, _1522229), _1522231), _1522233)))], (31969 ^ _777959) ^ [_1381490, _1381492, _1381494, _1381496, _1381498] : [c_Com_Ocom_OLocal(_1381490, _1381492, _1381494) = c_Com_Ocom_OSemi(_1381496, _1381498)], (10204 ^ _777959) ^ [_957016, _957018, _957020, _957022] : [-(hBOOL(hAPP(hAPP(c_member(_957016), _957018), _957020))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957016, tc_HOL_Obool)), _957020), hAPP(hAPP(c_Set_Oinsert(_957016), _957018), _957022)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957016, tc_HOL_Obool)), _957020), _957022))], (51432 ^ _777959) ^ [_1814713, _1814715] : [hBOOL(hAPP(hAPP(c_fdisj, _1814713), _1814715)), -(hBOOL(_1814713)), -(hBOOL(_1814715))], (37298 ^ _777959) ^ [_1489529] : [-(hAPP(c_Relation_OField(_1489529), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489529, _1489529), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1489529, tc_HOL_Obool)))], (20717 ^ _777959) ^ [_1172684, _1172686] : [class_Rings_Olinordered__idom(_1172684), 20720 ^ _777959 : [(20727 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172684), _1172686), c_Groups_Ozero__class_Ozero(_1172684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172684), _1172686), hAPP(c_Groups_Ouminus__class_Ouminus(_1172684), _1172686))))], (20721 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172684), _1172686), hAPP(c_Groups_Ouminus__class_Ouminus(_1172684), _1172686))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172684), _1172686), c_Groups_Ozero__class_Ozero(_1172684))))]]], (49386 ^ _777959) ^ [_1777277, _1777279, _1777281, _1777283, _1777285] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1777277, _1777277)), hAPP(hAPP(c_Product__Type_OPair(_1777277, _1777277), _1777279), _1777281)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777277, _1777277), tc_HOL_Obool), _1777283), _1777285))), 49391 ^ _777959 : [(49394 ^ _777959) ^ [] : [-(_1777279 = _1777281)], (49392 ^ _777959) ^ [] : [-(_1777283 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 49397 ^ _777959 : [(49402 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777277, _1777277)), hAPP(hAPP(c_Product__Type_OPair(_1777277, _1777277), 49395 ^ [_1777277, _1777279, _1777281, _1777283, _1777285]), _1777281)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777277, _1777277), tc_HOL_Obool), 49396 ^ [_1777277, _1777279, _1777281, _1777283, _1777285]), _1777285))))], (49400 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777277, _1777277)), hAPP(hAPP(c_Product__Type_OPair(_1777277, _1777277), _1777279), 49395 ^ [_1777277, _1777279, _1777281, _1777283, _1777285])), _1777285)))], (49398 ^ _777959) ^ [] : [-(_1777283 = hAPP(c_Nat_OSuc, 49396 ^ [_1777277, _1777279, _1777281, _1777283, _1777285]))]]], (4676 ^ _777959) ^ [_848940, _848942, _848944, _848946, _848948, _848950, _848952, _848954] : [-(c_New__Random__Sequence_Opos__map(_848954, _848950, _848946, _848942) = c_New__Random__Sequence_Opos__map(_848952, _848948, _848944, _848940)), _848954 = _848952, _848950 = _848948, _848946 = _848944, _848942 = _848940], (24494 ^ _777959) ^ [_1243106, _1243108, _1243110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1243106), _1243108)), -(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)), _1243106)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1243110), _1243108)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243110), _1243106)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243108), _1243106)))], (45178 ^ _777959) ^ [_1678608, _1678610] : [-(c_List_OtakeWhile(_1678608, _1678610, c_List_Olist_ONil(_1678608)) = c_List_Olist_ONil(_1678608))], (10216 ^ _777959) ^ [_957275, _957277, _957279, _957281] : [-(hBOOL(hAPP(hAPP(c_member(_957275), _957277), _957279))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957275, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_957275), _957277), _957281)), _957279) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957275, tc_HOL_Obool)), _957281), _957279))], (2840 ^ _777959) ^ [_820362, _820364] : [_820364 = _820362, -(c_HOL_OAll(_820364) = c_HOL_OAll(_820362))], (6559 ^ _777959) ^ [_884056, _884058, _884060] : [_884056 = _884058, 6562 ^ _777959 : [(6565 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884060, tc_HOL_Obool)), _884058), _884056)))], (6563 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884060, tc_HOL_Obool)), _884056), _884058)))]]], (38928 ^ _777959) ^ [_1526289, _1526291, _1526293, _1526295, _1526297] : [-(hAPP(c_Map_Omap__of(_1526289, _1526291), hAPP(hAPP(c_List_Omap(tc_prod(_1526289, _1526293), tc_prod(_1526289, _1526291)), hAPP(c_Product__Type_Oprod_Oprod__case(_1526289, _1526293, tc_prod(_1526289, _1526291)), hAPP(hAPP(c_COMBC(_1526289, tc_fun(_1526293, _1526291), tc_fun(_1526293, tc_prod(_1526289, _1526291))), hAPP(hAPP(c_COMBB(tc_fun(_1526291, tc_prod(_1526289, _1526291)), tc_fun(tc_fun(_1526293, _1526291), tc_fun(_1526293, tc_prod(_1526289, _1526291))), _1526289), c_COMBB(_1526291, tc_prod(_1526289, _1526291), _1526293)), c_Product__Type_OPair(_1526289, _1526291))), _1526295))), _1526297)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1526293), tc_Option_Ooption(_1526291), _1526289, hAPP(c_Option_Omap(_1526293, _1526291), _1526295)), hAPP(c_Map_Omap__of(_1526289, _1526293), _1526297)))], (13225 ^ _777959) ^ [_1019381, _1019383, _1019385, _1019387, _1019389, _1019391] : [class_Groups_Ocomm__monoid__add(_1019381), hBOOL(hAPP(c_Finite__Set_Ofinite(_1019383), _1019385)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1019383, _1019381), hAPP(hAPP(c_COMBS(_1019383, _1019381, _1019381), hAPP(hAPP(c_COMBS(_1019383, _1019381, tc_fun(_1019381, _1019381)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1019381, tc_fun(_1019381, _1019381)), _1019383), c_If(_1019381)), _1019387)), _1019389)), _1019391)), _1019385) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1019381), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1019383, _1019381), _1019389), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019383, tc_HOL_Obool)), _1019385), hAPP(c_Set_OCollect(_1019383), _1019387)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1019383, _1019381), _1019391), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019383, tc_HOL_Obool)), _1019385), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1019383, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1019383), _1019387))))))], (43178 ^ _777959) ^ [_1635105, _1635107, _1635109, _1635111, _1635113] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635105), tc_List_Olist(_1635105))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635105), tc_List_Olist(_1635105)), hAPP(hAPP(c_List_Oappend(_1635105), _1635107), _1635109)), hAPP(hAPP(c_List_Oappend(_1635105), _1635107), _1635111))), c_List_Olexord(_1635105, _1635113))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1635105, _1635105)), hAPP(hAPP(c_Product__Type_OPair(_1635105, _1635105), 43183 ^ [_1635105, _1635107, _1635109, _1635111, _1635113]), 43183 ^ [_1635105, _1635107, _1635109, _1635111, _1635113])), _1635113))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635105), tc_List_Olist(_1635105))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635105), tc_List_Olist(_1635105)), _1635109), _1635111)), c_List_Olexord(_1635105, _1635113))))], (32291 ^ _777959) ^ [_1387600, _1387602, _1387604, _1387606] : [class_Fields_Ofield__inverse__zero(_1387600), class_Int_Onumber(_1387600), 32298 ^ _777959 : [(32299 ^ _777959) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387600), _1387602), hAPP(c_Int_Onumber__class_Onumber__of(_1387600), _1387604)) = _1387606, 32302 ^ _777959 : [(32309 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1387600), _1387604) = c_Groups_Ozero__class_Ozero(_1387600), -(_1387606 = c_Groups_Ozero__class_Ozero(_1387600))], (32303 ^ _777959) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1387600), _1387604) = c_Groups_Ozero__class_Ozero(_1387600)), -(_1387602 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387600), _1387606), hAPP(c_Int_Onumber__class_Onumber__of(_1387600), _1387604)))]]], (32315 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387600), _1387602), hAPP(c_Int_Onumber__class_Onumber__of(_1387600), _1387604)) = _1387606), 32318 ^ _777959 : [(32321 ^ _777959) ^ [] : [_1387602 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387600), _1387606), hAPP(c_Int_Onumber__class_Onumber__of(_1387600), _1387604))], (32319 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1387600), _1387604) = c_Groups_Ozero__class_Ozero(_1387600)]], 32322 ^ _777959 : [(32325 ^ _777959) ^ [] : [_1387606 = c_Groups_Ozero__class_Ozero(_1387600)], (32323 ^ _777959) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1387600), _1387604) = c_Groups_Ozero__class_Ozero(_1387600))]]]]], (11754 ^ _777959) ^ [_989820, _989822, _989824, _989826, _989828] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989820, tc_fun(_989822, tc_HOL_Obool)), _989824), hAPP(hAPP(c_COMBS(_989820, tc_fun(_989822, tc_HOL_Obool), tc_fun(_989822, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_989822, tc_HOL_Obool), tc_fun(tc_fun(_989822, tc_HOL_Obool), tc_fun(_989822, tc_HOL_Obool)), _989820), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_989822, tc_HOL_Obool))), _989826)), _989828)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_989822, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989820, tc_fun(_989822, tc_HOL_Obool)), _989824), _989826)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989820, tc_fun(_989822, tc_HOL_Obool)), _989824), _989828)))], (30199 ^ _777959) ^ [_1349020, _1349022, _1349024] : [class_Divides_Osemiring__div(_1349020), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349020), c_Divides_Odiv__class_Omod(_1349020, _1349022, _1349024)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349020), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1349020), _1349022), _1349024)), _1349024)) = _1349022)], (210 ^ _777959) ^ [_781356, _781358] : [-(class_Fields_Ofield(_781356)), _781358 = _781356, class_Fields_Ofield(_781358)], (35541 ^ _777959) ^ [_1451564] : [class_Rings_Osemiring__1(_1451564), -(hBOOL(hAPP(hAPP(c_member(_1451564), c_Groups_Oone__class_Oone(_1451564)), c_Nat_Osemiring__1__class_ONats(_1451564))))], (9728 ^ _777959) ^ [_946681, _946683, _946685] : [class_Lattices_Olattice(_946681), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946681), _946683), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946681), _946683), _946685)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946681), _946683), _946685))], (20051 ^ _777959) ^ [_1160781, _1160783, _1160785] : [class_Rings_Oordered__cancel__semiring(_1160781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160781), c_Groups_Ozero__class_Ozero(_1160781)), _1160783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160781), _1160785), c_Groups_Ozero__class_Ozero(_1160781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160781), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160781), _1160783), _1160785)), c_Groups_Ozero__class_Ozero(_1160781))))], (46814 ^ _777959) ^ [_1715141, _1715143, _1715145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1715141, _1715141), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1715141, _1715141, _1715141), _1715143), _1715145)), _1715143)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1715141, tc_HOL_Obool), tc_fun(_1715141, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1715141, tc_HOL_Obool), tc_fun(_1715141, tc_HOL_Obool), tc_fun(_1715141, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1715141, _1715143)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1715141, tc_HOL_Obool), tc_fun(_1715141, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1715141, _1715145)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1715141, tc_HOL_Obool), tc_fun(_1715141, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1715141, tc_HOL_Obool), tc_fun(_1715141, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1715141, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1715141, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1715141, tc_HOL_Obool), tc_fun(_1715141, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1715141, _1715143))))], (34623 ^ _777959) ^ [_1429488, _1429490, _1429492] : [class_Rings_Olinordered__idom(_1429488), 34626 ^ _777959 : [(34635 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1429488), hAPP(hAPP(c_Power_Opower__class_Opower(_1429488), _1429490), 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(_1429488), _1429492), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1429488)), _1429490 = c_Groups_Ozero__class_Ozero(_1429488), _1429492 = c_Groups_Ozero__class_Ozero(_1429488)], (34627 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1429488), hAPP(hAPP(c_Power_Opower__class_Opower(_1429488), _1429490), 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(_1429488), _1429492), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1429488), 34630 ^ _777959 : [(34633 ^ _777959) ^ [] : [-(_1429492 = c_Groups_Ozero__class_Ozero(_1429488))], (34631 ^ _777959) ^ [] : [-(_1429490 = c_Groups_Ozero__class_Ozero(_1429488))]]]]], (30782 ^ _777959) ^ [_1359457, _1359459, _1359461] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1359457, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1359459), _1359461)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1359459), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1359457), _1359459), _1359461))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1359457, _1359459)))], (42162 ^ _777959) ^ [_1608798] : [class_Orderings_Olinorder(_1608798), -(c_List_Olinorder__class_Osorted__list__of__set(_1608798, c_Orderings_Obot__class_Obot(tc_fun(_1608798, tc_HOL_Obool))) = c_List_Olist_ONil(_1608798))], (32971 ^ _777959) ^ [_1400693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1400693)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400693), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (28452 ^ _777959) ^ [_1314215, _1314217] : [28454 ^ _777959 : [(28457 ^ _777959) ^ [] : [hBOOL(hAPP(_1314217, 28453 ^ [_1314215, _1314217]))], (28455 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 28453 ^ [_1314215, _1314217]), _1314215)))]], 28458 ^ _777959 : [(28459 ^ _777959) ^ [_1314366] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1314366), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1314215))), -(hBOOL(hAPP(_1314217, _1314366)))]]], (37318 ^ _777959) ^ [_1490171, _1490173, _1490175, _1490177, _1490179] : [hBOOL(hAPP(hAPP(c_member(_1490171), _1490173), hAPP(c_Relation_OImage(_1490175, _1490171, _1490177), _1490179))), 37322 ^ _777959 : [(37325 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1490175), 37321 ^ [_1490171, _1490173, _1490175, _1490177, _1490179]), _1490179)))], (37323 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1490175, _1490171)), hAPP(hAPP(c_Product__Type_OPair(_1490175, _1490171), 37321 ^ [_1490171, _1490173, _1490175, _1490177, _1490179]), _1490173)), _1490177)))]]], (21119 ^ _777959) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21452 ^ _777959) ^ [_1185631, _1185633, _1185635, _1185637] : [class_Rings_Olinordered__ring__strict(_1185631), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185631), _1185633), c_Groups_Ozero__class_Ozero(_1185631))), 21459 ^ _777959 : [(21466 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185631), _1185637), _1185635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185631), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185631), _1185633), _1185635)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185631), _1185633), _1185637))))], (21460 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185631), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185631), _1185633), _1185635)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185631), _1185633), _1185637))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185631), _1185637), _1185635)))]]], (46820 ^ _777959) ^ [_1715512, _1715514, _1715516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1715512, _1715512), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1715512, _1715512, _1715512), _1715514), _1715516)), _1715514)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1715512, tc_HOL_Obool), tc_fun(_1715512, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1715512, tc_HOL_Obool), tc_fun(_1715512, tc_HOL_Obool), tc_fun(_1715512, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1715512, _1715514)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1715512, tc_HOL_Obool), tc_fun(_1715512, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1715512, _1715516)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1715512, tc_HOL_Obool), tc_fun(_1715512, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1715512, tc_HOL_Obool), tc_fun(_1715512, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1715512, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1715512, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1715512, tc_HOL_Obool), tc_fun(_1715512, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1715512, _1715514))))], (12431 ^ _777959) ^ [_1003740, _1003742, _1003744] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003740), _1003742)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003740), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003744), _1003742))))], (49330 ^ _777959) ^ [_1775874, _1775876, _1775878] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775874, _1775874)), hAPP(hAPP(c_Product__Type_OPair(_1775874, _1775874), _1775876), _1775876)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775874, _1775874), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1775878))))], (32853 ^ _777959) ^ [_1398567, _1398569] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398567))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398567)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398569)) = 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), _1398569)))], (42473 ^ _777959) ^ [_1616853] : [-(c_List_Olistset(_1616853, c_List_Olist_ONil(tc_fun(_1616853, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1616853)), c_List_Olist_ONil(_1616853)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1616853), tc_HOL_Obool))))], (32897 ^ _777959) ^ [_1399381] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1399381)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399381))))], (23272 ^ _777959) ^ [_1221463, _1221465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221463)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221465))))], (5464 ^ _777959) ^ [_861490, _861492] : [_861492 = _861490, -(c_List_Omember(_861492) = c_List_Omember(_861490))], (29894 ^ _777959) ^ [_1343087, _1343089, _1343091] : [-(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, _1343087, _1343089)), _1343091), _1343089) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1343087), _1343091), _1343089))], (10790 ^ _777959) ^ [_969514, _969516, _969518, _969520] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_969514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969514), _969516), _969518)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969514), _969516), _969520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969514), _969518), _969520)))], (39600 ^ _777959) ^ [_1542880, _1542882, _1542884, _1542886, _1542888] : [hBOOL(hAPP(c_List_Odistinct(_1542880), hAPP(hAPP(c_List_Omap(tc_prod(_1542880, _1542882), _1542880), c_Product__Type_Ofst(_1542880, _1542882)), _1542884))), 39603 ^ _777959 : [(39610 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542880, _1542882)), hAPP(hAPP(c_Product__Type_OPair(_1542880, _1542882), _1542886), _1542888)), hAPP(c_List_Oset(tc_prod(_1542880, _1542882)), _1542884))), -(hAPP(hAPP(c_Map_Omap__of(_1542880, _1542882), _1542884), _1542886) = hAPP(c_Option_Ooption_OSome(_1542882), _1542888))], (39604 ^ _777959) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1542880, _1542882), _1542884), _1542886) = hAPP(c_Option_Ooption_OSome(_1542882), _1542888), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542880, _1542882)), hAPP(hAPP(c_Product__Type_OPair(_1542880, _1542882), _1542886), _1542888)), hAPP(c_List_Oset(tc_prod(_1542880, _1542882)), _1542884))))]]], (8588 ^ _777959) ^ [_926283, _926285, _926287, _926289] : [class_Orderings_Oord(_926283), _926285 = _926287, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926283), _926287), _926289)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926283), _926285), _926289)))], (12648 ^ _777959) ^ [_1007516, _1007518, _1007520] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1007516, tc_HOL_Obool)), _1007518) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1007516, tc_HOL_Obool)), _1007520), -(_1007518 = _1007520)], (50624 ^ _777959) ^ [_1804869, _1804871, _1804873, _1804875] : [hBOOL(hAPP(_1804869, _1804871)), -(hAPP(c_List_Ofilter(_1804873, _1804869), c_List_Oreplicate(_1804873, _1804875, _1804871)) = c_List_Oreplicate(_1804873, _1804875, _1804871))], (4902 ^ _777959) ^ [_852711, _852713, _852715, _852717] : [-(c_Lazy__Sequence_Ohb__single(_852717, _852713) = c_Lazy__Sequence_Ohb__single(_852715, _852711)), _852717 = _852715, _852713 = _852711], (48186 ^ _777959) ^ [_1748125, _1748127, _1748129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748125), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1748127)), _1748129))), -(hAPP(c_Random_Opick(_1748127, hAPP(hAPP(c_List_Omap(_1748127, tc_prod(tc_Code__Numeral_Ocode__numeral, _1748127)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1748127), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1748129)), hAPP(c_Code__Numeral_Oof__nat, _1748125)) = hAPP(hAPP(c_List_Onth(_1748127), _1748129), _1748125))], (45041 ^ _777959) ^ [_1675012, _1675014, _1675016, _1675018] : [-(c_List_Oconcat(_1675012, hAPP(hAPP(c_List_Omap(_1675014, tc_List_Olist(_1675012)), hAPP(hAPP(c_COMBC(_1675014, tc_List_Olist(_1675012), tc_List_Olist(_1675012)), hAPP(hAPP(c_COMBB(_1675012, tc_fun(tc_List_Olist(_1675012), tc_List_Olist(_1675012)), _1675014), c_List_Olist_OCons(_1675012)), _1675016)), c_List_Olist_ONil(_1675012))), _1675018)) = hAPP(hAPP(c_List_Omap(_1675014, _1675012), _1675016), _1675018))], (10578 ^ _777959) ^ [_965336, _965338, _965340, _965342] : [class_Complete__Lattice_Ocomplete__lattice(_965336), hBOOL(hAPP(c_Finite__Set_Ofinite(_965338), _965340)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_965338, _965336), _965340), _965342) = hAPP(hAPP(c_Finite__Set_Ofold(_965338, _965336, hAPP(hAPP(c_COMBB(_965336, tc_fun(_965336, _965336), _965338), c_Lattices_Osemilattice__sup__class_Osup(_965336)), _965342)), c_Orderings_Obot__class_Obot(_965336)), _965340))], (13087 ^ _777959) ^ [_1016560, _1016562, _1016564] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1016560, tc_HOL_Obool)), _1016562), _1016564) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1016560, tc_HOL_Obool)), _1016562), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1016560, tc_HOL_Obool)), _1016564)))], (49180 ^ _777959) ^ [_1771951, _1771953, _1771955] : [49183 ^ _777959 : [(49189 ^ _777959) ^ [] : [49182 ^ [_1771951, _1771953, _1771955] = 49185 ^ [_1771951, _1771953, _1771955]], (49187 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1771951, _1771953)), hAPP(hAPP(c_Product__Type_OPair(_1771951, _1771953), 49181 ^ [_1771951, _1771953, _1771955]), 49185 ^ [_1771951, _1771953, _1771955])), _1771955)))], (49184 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1771951, _1771953)), hAPP(hAPP(c_Product__Type_OPair(_1771951, _1771953), 49181 ^ [_1771951, _1771953, _1771955]), 49182 ^ [_1771951, _1771953, _1771955])), _1771955)))]], -(c_Relation_Osingle__valued(_1771951, _1771953, _1771955))], (19598 ^ _777959) ^ [_1152754, _1152756] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152754), _1152756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1152754 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1152756 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35677 ^ _777959) ^ [_1454209, _1454211, _1454213, _1454215, _1454217, _1454219] : [hBOOL(hAPP(hAPP(_1454209, _1454211), _1454213)), hBOOL(hAPP(hAPP(_1454215, _1454211), _1454213)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454217, tc_fun(_1454219, tc_HOL_Obool))), _1454209), _1454215), _1454211), _1454213)))], (3012 ^ _777959) ^ [_823064, _823066, _823068, _823070] : [-(c_Big__Operators_Olinorder__class_OMax(_823070, _823066) = c_Big__Operators_Olinorder__class_OMax(_823068, _823064)), _823070 = _823068, _823066 = _823064], (13671 ^ _777959) ^ [_1030357, _1030359, _1030361, _1030363, _1030365, _1030367] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030357, tc_fun(_1030359, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1030361, tc_fun(_1030357, tc_HOL_Obool)), _1030363), _1030365)), _1030367) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030361, tc_fun(_1030359, tc_HOL_Obool)), _1030363), hAPP(hAPP(c_COMBC(_1030361, tc_fun(_1030357, tc_fun(_1030359, tc_HOL_Obool)), tc_fun(_1030359, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1030357, tc_HOL_Obool), tc_fun(tc_fun(_1030357, tc_fun(_1030359, tc_HOL_Obool)), tc_fun(_1030359, tc_HOL_Obool)), _1030361), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030357, tc_fun(_1030359, tc_HOL_Obool))), _1030365)), _1030367)))], (1140 ^ _777959) ^ [_794933, _794935] : [-(class_Rings_Oordered__ring(_794933)), _794935 = _794933, class_Rings_Oordered__ring(_794935)], (27245 ^ _777959) ^ [_1293830, _1293832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293830)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293832)), 27252 ^ _777959 : [(27259 ^ _777959) ^ [] : [_1293830 = _1293832, -(hAPP(c_Int_Onat, _1293830) = hAPP(c_Int_Onat, _1293832))], (27253 ^ _777959) ^ [] : [hAPP(c_Int_Onat, _1293830) = hAPP(c_Int_Onat, _1293832), -(_1293830 = _1293832)]]], (4952 ^ _777959) ^ [_853566, _853568] : [_853568 = _853566, -(c_Lazy__Sequence_Oempty(_853568) = c_Lazy__Sequence_Oempty(_853566))], (47493 ^ _777959) ^ [_1732644, _1732646] : [c_Wellfounded_OwfP(_1732644, _1732646), -(c_Wellfounded_Oacyclic(_1732644, hAPP(c_Set_OCollect(tc_prod(_1732644, _1732644)), hAPP(c_Product__Type_Oprod_Oprod__case(_1732644, _1732644, tc_HOL_Obool), _1732646))))], (33941 ^ _777959) ^ [_1417432, _1417434, _1417436, _1417438] : [-(hAPP(c_Nat_Onat_Onat__rec(_1417432, _1417434, _1417436), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1417438)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1417432), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1417438))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1417432, _1417432), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1417432, tc_fun(_1417432, _1417432)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1417432, tc_fun(_1417432, _1417432)), tc_Int_Oint), c_If(_1417432)), c_Nat__Numeral_Oneg)), _1417434)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1417432, _1417432), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1417432, _1417432), tc_Int_Oint), _1417436), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1417432, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1417432, _1417434, _1417436)), c_Int_Onat)))))], (14013 ^ _777959) ^ [_1037998, _1038000, _1038002] : [-(hBOOL(hAPP(_1037998, _1038000))), -(hAPP(c_Set_OCollect(_1038002), hAPP(hAPP(c_COMBS(_1038002, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1038002), c_fconj), hAPP(hAPP(c_COMBC(_1038002, _1038002, tc_HOL_Obool), c_fequal), _1038000))), _1037998)) = c_Orderings_Obot__class_Obot(tc_fun(_1038002, tc_HOL_Obool)))], (42030 ^ _777959) ^ [_1606221, _1606223, _1606225, _1606227] : [hAPP(hAPP(c_List_Omap(_1606221, _1606223), _1606225), _1606227) = c_List_Olist_ONil(_1606223), -(_1606227 = c_List_Olist_ONil(_1606221))], (5767 ^ _777959) ^ [_869161, _869163, _869165, _869167, _869169] : [-(hAPP(c_Set_Oimage(_869161, _869163, _869165), hAPP(hAPP(c_Set_Oinsert(_869161), _869167), _869169)) = hAPP(hAPP(c_Set_Oinsert(_869163), hAPP(_869165, _869167)), hAPP(c_Set_Oimage(_869161, _869163, _869165), _869169)))], (8940 ^ _777959) ^ [_931833, _931835, _931837] : [class_Orderings_Olinorder(_931833), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931833), _931835), _931837))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931833), _931837), _931835)))], (46010 ^ _777959) ^ [_1695950, _1695952, _1695954, _1695956] : [class_Orderings_Oorder(_1695950), class_Enum_Oenum(_1695952), 46017 ^ _777959 : [(46024 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1695952), hAPP(hAPP(c_COMBS(_1695952, _1695950, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1695950, tc_fun(_1695950, tc_HOL_Obool), _1695952), c_Orderings_Oord__class_Oless__eq(_1695950)), _1695954)), _1695956))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1695952, _1695950)), _1695954), _1695956)))], (46018 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1695952, _1695950)), _1695954), _1695956)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1695952), hAPP(hAPP(c_COMBS(_1695952, _1695950, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1695950, tc_fun(_1695950, tc_HOL_Obool), _1695952), c_Orderings_Oord__class_Oless__eq(_1695950)), _1695954)), _1695956))))]]], (39642 ^ _777959) ^ [_1544050, _1544052, _1544054, _1544056, _1544058] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544050, _1544052)), hAPP(hAPP(c_Product__Type_OPair(_1544050, _1544052), _1544054), _1544056)), hAPP(c_List_Oset(tc_prod(_1544050, _1544052)), _1544058))), -(hAPP(hAPP(c_Map_Omap__of(_1544050, _1544052), _1544058), _1544054) = hAPP(c_Option_Ooption_OSome(_1544052), 39645 ^ [_1544050, _1544052, _1544054, _1544056, _1544058]))], (41575 ^ _777959) ^ [_1593144, _1593146, _1593148, _1593150, _1593152, _1593154] : [_1593144 = _1593146, -(hAPP(hAPP(c_Map_Omap__of(_1593148, _1593150), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1593148, _1593150)), hAPP(hAPP(c_Product__Type_OPair(_1593148, _1593150), _1593144), _1593152)), _1593154)), _1593146) = hAPP(c_Option_Ooption_OSome(_1593150), _1593152))], (14574 ^ _777959) ^ [_1051742, _1051744, _1051746, _1051748] : [-(c_Fun_Ooverride__on(_1051742, _1051744, _1051746, _1051748, c_Orderings_Obot__class_Obot(tc_fun(_1051742, tc_HOL_Obool))) = _1051746)], (12060 ^ _777959) ^ [_996750, _996752, _996754] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996750), _996752) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996750), _996754), -(_996752 = _996754)], (1918 ^ _777959) ^ [_805637, _805639, _805641, _805643, _805645, _805647, _805649, _805651, _805653, _805655] : [-(c_Option_Ooption_Ooption__rec(_805655, _805651, _805647, _805643, _805639) = c_Option_Ooption_Ooption__rec(_805653, _805649, _805645, _805641, _805637)), _805655 = _805653, _805651 = _805649, _805647 = _805645, _805643 = _805641, _805639 = _805637], (29930 ^ _777959) ^ [_1343705, _1343707, _1343709, _1343711] : [class_Divides_Oring__div(_1343705), c_Divides_Odiv__class_Omod(_1343705, _1343707, _1343709) = c_Divides_Odiv__class_Omod(_1343705, _1343711, _1343709), -(c_Divides_Odiv__class_Omod(_1343705, hAPP(c_Groups_Ouminus__class_Ouminus(_1343705), _1343707), _1343709) = c_Divides_Odiv__class_Omod(_1343705, hAPP(c_Groups_Ouminus__class_Ouminus(_1343705), _1343711), _1343709))], (38720 ^ _777959) ^ [_1521063, _1521065, _1521067] : [c_Fun_Oinj__on(tc_List_Olist(_1521063), tc_List_Olist(_1521065), hAPP(c_List_Omap(_1521063, _1521065), _1521067), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1521063), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1521063, _1521065, _1521067, c_Orderings_Otop__class_Otop(tc_fun(_1521063, tc_HOL_Obool))))], (12357 ^ _777959) ^ [_1002311, _1002313, _1002315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1002311), _1002313)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1002313), _1002315)), _1002311) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002313), _1002311)), _1002315))], (16391 ^ _777959) ^ [_1091778, _1091780, _1091782, _1091784] : [hBOOL(hAPP(hAPP(c_member(_1091778), _1091780), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1091778, tc_HOL_Obool), _1091782))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1091778, tc_HOL_Obool)), _1091784), _1091782)), -(hBOOL(hAPP(hAPP(c_member(_1091778), _1091780), _1091784)))], (33815 ^ _777959) ^ [_1414564, _1414566] : [hAPP(c_Nat_OSuc, _1414564) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414566), -(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(_1414566))), 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)), _1414564))))))], (48176 ^ _777959) ^ [_1747890, _1747892, _1747894, _1747896] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1747890), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1747892), _1747894)))), -(hAPP(c_Random_Opick(_1747892, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1747892)), _1747894), _1747896)), _1747890) = hAPP(c_Random_Opick(_1747892, _1747896), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1747890), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1747892), _1747894))))], (11004 ^ _777959) ^ [_973473, _973475, _973477, _973479] : [-(hAPP(c_Option_Ooption_Ooption__case(_973473, _973475, _973477, _973479), c_Option_Ooption_ONone(_973475)) = _973477)], (43294 ^ _777959) ^ [_1637859, _1637861, _1637863, _1637865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1637859), _1637861)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1637863, tc_HOL_Obool)), hAPP(c_List_Oset(_1637863), hAPP(hAPP(c_List_Odrop(_1637863), _1637861), _1637865))), hAPP(c_List_Oset(_1637863), hAPP(hAPP(c_List_Odrop(_1637863), _1637859), _1637865)))))], (38552 ^ _777959) ^ [_1517514, _1517516, _1517518, _1517520] : [c_Fun_Oinj__on(_1517514, _1517516, _1517518, _1517520), -(hAPP(c_Set_Oimage(_1517516, _1517514, c_Fun_Othe__inv__into(_1517514, _1517516, _1517520, _1517518)), hAPP(c_Set_Oimage(_1517514, _1517516, _1517518), _1517520)) = _1517520)], (43312 ^ _777959) ^ [_1638282, _1638284, _1638286] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638282)), _1638286)), _1638284)), -(hAPP(hAPP(c_List_Odrop(_1638282), _1638284), _1638286) = c_List_Olist_ONil(_1638282))], (32765 ^ _777959) ^ [_1396810, _1396812, _1396814, _1396816] : [class_Fields_Olinordered__field__inverse__zero(_1396810), class_Int_Onumber(_1396810), 32772 ^ _777959 : [(32773 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396810), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1396810), _1396812), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814))), _1396816)), 32776 ^ _777959 : [(32783 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396810), c_Groups_Ozero__class_Ozero(_1396810)), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814)))), 32786 ^ _777959 : [(32793 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396810), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814)), c_Groups_Ozero__class_Ozero(_1396810)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396810), c_Groups_Ozero__class_Ozero(_1396810)), _1396816)))], (32787 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396810), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814)), c_Groups_Ozero__class_Ozero(_1396810))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396810), _1396816), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814))), _1396812)))]]], (32777 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396810), c_Groups_Ozero__class_Ozero(_1396810)), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396810), _1396812), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396810), _1396816), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814)))))]]], (32799 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396810), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1396810), _1396812), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814))), _1396816))), 32802 ^ _777959 : [(32805 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396810), _1396812), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396810), _1396816), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814))))], (32803 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396810), c_Groups_Ozero__class_Ozero(_1396810)), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814))))]], 32806 ^ _777959 : [(32809 ^ _777959) ^ [] : [32810 ^ _777959 : [(32813 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396810), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1396810), _1396816), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814))), _1396812))], (32811 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396810), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814)), c_Groups_Ozero__class_Ozero(_1396810))))]], 32814 ^ _777959 : [(32817 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1396810), c_Groups_Ozero__class_Ozero(_1396810)), _1396816))], (32815 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396810), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814)), c_Groups_Ozero__class_Ozero(_1396810)))]]], (32807 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1396810), c_Groups_Ozero__class_Ozero(_1396810)), hAPP(c_Int_Onumber__class_Onumber__of(_1396810), _1396814)))]]]]], (47204 ^ _777959) ^ [_1724822, _1724824] : [-(c_Nitpick_Onumber__of__frac(_1724822, _1724824) = c_Nitpick_OAbs__Frac(_1724822, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1724824), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (45970 ^ _777959) ^ [_1695072, _1695074, _1695076] : [class_Enum_Oenum(_1695072), class_Enum_Oenum(_1695074), 45977 ^ _777959 : [(45984 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1695074), hAPP(hAPP(c_COMBB(tc_fun(_1695072, tc_HOL_Obool), tc_HOL_Obool, _1695074), c_Enum_Oenum__class_Oenum__all(_1695072)), hAPP(hAPP(c_COMBB(tc_fun(_1695072, tc_prod(_1695074, _1695072)), tc_fun(_1695072, tc_HOL_Obool), _1695074), hAPP(c_COMBB(tc_prod(_1695074, _1695072), tc_HOL_Obool, _1695072), _1695076)), c_Product__Type_OPair(_1695074, _1695072))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1695074, _1695072)), _1695076)))], (45978 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1695074, _1695072)), _1695076)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1695074), hAPP(hAPP(c_COMBB(tc_fun(_1695072, tc_HOL_Obool), tc_HOL_Obool, _1695074), c_Enum_Oenum__class_Oenum__all(_1695072)), hAPP(hAPP(c_COMBB(tc_fun(_1695072, tc_prod(_1695074, _1695072)), tc_fun(_1695072, tc_HOL_Obool), _1695074), hAPP(c_COMBB(tc_prod(_1695074, _1695072), tc_HOL_Obool, _1695072), _1695076)), c_Product__Type_OPair(_1695074, _1695072))))))]]], (51252 ^ _777959) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (1250 ^ _777959) ^ [_796308, _796310] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_796308)), _796310 = _796308, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_796310)], (48972 ^ _777959) ^ [_1767166, _1767168, _1767170, _1767172, _1767174] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1767168, _1767166)), hAPP(hAPP(c_Product__Type_OPair(_1767168, _1767166), _1767172), _1767170)), _1767174)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1767166, _1767168)), hAPP(hAPP(c_Product__Type_OPair(_1767166, _1767168), _1767170), _1767172)), hAPP(c_Relation_Oconverse(_1767168, _1767166), _1767174))))], (43739 ^ _777959) ^ [_1647542, _1647544, _1647546, _1647548] : [class_Complete__Lattice_Ocomplete__lattice(_1647542), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1647544, _1647542), hAPP(c_List_Oset(_1647544), _1647546)), _1647548) = hAPP(c_List_Ofoldl(_1647542, _1647544, hAPP(c_COMBC(_1647544, _1647542, _1647542), hAPP(hAPP(c_COMBB(_1647542, tc_fun(_1647542, _1647542), _1647544), c_Lattices_Osemilattice__sup__class_Osup(_1647542)), _1647548)), c_Orderings_Obot__class_Obot(_1647542)), _1647546))], (36732 ^ _777959) ^ [_1474901, _1474903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1474901), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1474903), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1474901), _1474903) = 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), _1474901), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1474903)))))], (51140 ^ _777959) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (12153 ^ _777959) ^ [_998504, _998506, _998508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998504), _998506)), _998508)), 12156 ^ _777959 : [(12159 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998506), _998508)))], (12157 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998504), _998508)))]]], (34201 ^ _777959) ^ [_1421916, _1421918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1421916)), c_Int_OBit1(_1421918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1421916), _1421918)))], (43011 ^ _777959) ^ [_1630456, _1630458, _1630460, _1630462] : [43012 ^ _777959 : [(43015 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630456), _1630458), hAPP(c_List_Oset(_1630456), c_List_Obutlast(_1630456, _1630462))))], (43013 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1630456), _1630458), hAPP(c_List_Oset(_1630456), c_List_Obutlast(_1630456, _1630460))))]], -(hBOOL(hAPP(hAPP(c_member(_1630456), _1630458), hAPP(c_List_Oset(_1630456), c_List_Obutlast(_1630456, hAPP(hAPP(c_List_Oappend(_1630456), _1630460), _1630462))))))], (24443 ^ _777959) ^ [_1242226, _1242228, _1242230] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242226), _1242228))), -(c_Smallcheck_Osmall_H(_1242230, _1242226, _1242228) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1242230, _1242226, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1242228), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1242230, _1242228)))], (24013 ^ _777959) ^ [_1234524, _1234526, _1234528, _1234530] : [class_Rings_Olinordered__semidom(_1234524), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1234526), _1234528)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234524), c_Groups_Ozero__class_Ozero(_1234524)), _1234530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234524), _1234530), c_Groups_Oone__class_Oone(_1234524))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234524), hAPP(hAPP(c_Power_Opower__class_Opower(_1234524), _1234530), _1234528)), hAPP(hAPP(c_Power_Opower__class_Opower(_1234524), _1234530), _1234526))))], (21009 ^ _777959) ^ [_1177186, _1177188, _1177190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1177186)), 21012 ^ _777959 : [(21019 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1177188), _1177190)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177186), _1177188)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177186), _1177190))))], (21013 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177186), _1177188)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177186), _1177190))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1177188), _1177190)))]]], (992 ^ _777959) ^ [_793039, _793041, _793043, _793045, _793047, _793049] : [-(c_Relation_Orefl__on(_793047, _793043, _793039)), c_Relation_Orefl__on(_793049, _793045, _793041), _793049 = _793047, _793045 = _793043, _793041 = _793039], (51208 ^ _777959) ^ [_1812102, _1812104] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1812102, _1812104))), class_Lazy__Sequence_Osmall__lazy(_1812102), class_Lazy__Sequence_Osmall__lazy(_1812104)], (46154 ^ _777959) ^ [_1699124, _1699126, _1699128] : [-(c_List_Olistsp(_1699124, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1699124, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1699124, tc_fun(_1699124, tc_HOL_Obool), tc_HOL_Obool), c_member(_1699124)), _1699126)), hAPP(hAPP(c_COMBC(_1699124, tc_fun(_1699124, tc_HOL_Obool), tc_HOL_Obool), c_member(_1699124)), _1699128))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1699124), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699124), tc_fun(tc_List_Olist(_1699124), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1699124))), c_List_Olists(_1699124, _1699126))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1699124), tc_fun(tc_List_Olist(_1699124), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1699124))), c_List_Olists(_1699124, _1699128))))], (33505 ^ _777959) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (5972 ^ _777959) ^ [_873261, _873263, _873265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873261, tc_HOL_Obool)), _873263), _873265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873261, tc_HOL_Obool)), _873265), _873263)), -(_873263 = _873265)], (25456 ^ _777959) ^ [_1260590, _1260592] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260590), _1260592)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1260590)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1260592)))], (19666 ^ _777959) ^ [_1153752, _1153754, _1153756] : [class_Groups_Ocomm__monoid__add(_1153752), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1153754, _1153752), hAPP(c_COMBK(_1153752, _1153754), c_Groups_Ozero__class_Ozero(_1153752))), _1153756) = c_Groups_Ozero__class_Ozero(_1153752))], (23010 ^ _777959) ^ [_1216719] : [class_Rings_Oring__1(_1216719), -(hBOOL(hAPP(hAPP(c_member(_1216719), c_Groups_Oone__class_Oone(_1216719)), c_Int_Oring__1__class_OInts(_1216719))))], (44825 ^ _777959) ^ [_1669608, _1669610] : [hAPP(c_List_Orev(_1669608), _1669610) = c_List_Olist_ONil(_1669608), -(_1669610 = c_List_Olist_ONil(_1669608))], (43019 ^ _777959) ^ [_1630681, _1630683, _1630685] : [-(c_List_Obutlast(_1630681, hAPP(hAPP(c_List_Oappend(_1630681), _1630683), hAPP(hAPP(c_List_Olist_OCons(_1630681), _1630685), c_List_Olist_ONil(_1630681)))) = _1630683)], (47657 ^ _777959) ^ [_1736049, _1736051, _1736053, _1736055, _1736057] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736049)), _1736051) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736053)), _1736055), 47663 ^ _777959 : [(47666 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1736057, hAPP(hAPP(c_List_Onth(_1736049), _1736051), 47662 ^ [_1736049, _1736051, _1736053, _1736055, _1736057])), hAPP(hAPP(c_List_Onth(_1736053), _1736055), 47662 ^ [_1736049, _1736051, _1736053, _1736055, _1736057])))], (47664 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47662 ^ [_1736049, _1736051, _1736053, _1736055, _1736057]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1736049)), _1736051))))]], -(c_List_Olist__all2(_1736049, _1736053, _1736057, _1736051, _1736055))], (39167 ^ _777959) ^ [_1532452, _1532454, _1532456, _1532458, _1532460, _1532462] : [-(hBOOL(hAPP(hAPP(c_member(_1532452), _1532454), hAPP(c_List_Oset(_1532452), _1532456)))), -(hAPP(hAPP(c_List_Omap(_1532452, _1532458), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1532452, _1532458), _1532460), _1532454), _1532462)), _1532456) = hAPP(hAPP(c_List_Omap(_1532452, _1532458), _1532460), _1532456))], (45302 ^ _777959) ^ [_1680904, _1680906] : [_1680906 = c_List_Olist_ONil(_1680904), -(c_List_Oremdups(_1680904, _1680906) = c_List_Olist_ONil(_1680904))], (39856 ^ _777959) ^ [_1548832, _1548834, _1548836, _1548838, _1548840, _1548842] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548832, _1548834)), hAPP(hAPP(c_Product__Type_OPair(_1548832, _1548834), _1548836), _1548838)), hAPP(c_List_Oset(tc_prod(_1548832, _1548834)), hAPP(hAPP(c_List_Ozip(_1548832, _1548834), _1548840), _1548842)))), -(hBOOL(hAPP(hAPP(c_member(_1548834), _1548838), hAPP(c_List_Oset(_1548834), _1548842))))], (1490 ^ _777959) ^ [_799308, _799310] : [-(class_Groups_Ocancel__ab__semigroup__add(_799308)), _799310 = _799308, class_Groups_Ocancel__ab__semigroup__add(_799310)], (3936 ^ _777959) ^ [_837576, _837578, _837580, _837582, _837584, _837586] : [-(c_Random_Ominus__shift(_837586, _837582, _837578) = c_Random_Ominus__shift(_837584, _837580, _837576)), _837586 = _837584, _837582 = _837580, _837578 = _837576], (42210 ^ _777959) ^ [_1609965, _1609967, _1609969] : [-(hAPP(hAPP(c_Map_Omap__of(_1609965, _1609967), c_List_Olist_ONil(tc_prod(_1609965, _1609967))), _1609969) = c_Option_Ooption_ONone(_1609967))], (3496 ^ _777959) ^ [_830690, _830692, _830694, _830696] : [-(c_List_Olistsp(_830696, _830692) = c_List_Olistsp(_830694, _830690)), _830696 = _830694, _830692 = _830690], (27281 ^ _777959) ^ [_1294399, _1294401, _1294403] : [class_Orderings_Oorder(_1294399), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1294399), _1294401), _1294403)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1294399, _1294403, _1294401) = c_Orderings_Obot__class_Obot(tc_fun(_1294399, tc_HOL_Obool)))], (34385 ^ _777959) ^ [_1425203, _1425205] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1425203)), c_Int_OBit1(_1425205)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1425203)), _1425205)))], (49792 ^ _777959) ^ [_1787812, _1787814] : [-(c_List_Olist__all(_1787812, _1787814, c_List_Olist_ONil(_1787812)))], (45115 ^ _777959) ^ [_1677054, _1677056, _1677058, _1677060] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1677054), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1677054))), _1677056))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1677058), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1677054))), c_List_Otranspose(_1677054, _1677056)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1677060), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1677054))), hAPP(c_List_Ofilter(tc_List_Olist(_1677054), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1677054)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1677058)), c_Nat_Osize__class_Osize(tc_List_Olist(_1677054)))), _1677056)))), -(hAPP(hAPP(c_List_Onth(_1677054), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1677054)), c_List_Otranspose(_1677054, _1677056)), _1677058)), _1677060) = hAPP(hAPP(c_List_Onth(_1677054), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1677054)), _1677056), _1677060)), _1677058))], (27998 ^ _777959) ^ [_1306259, _1306261, _1306263] : [class_Rings_Oring__1(_1306259), -(hAPP(c_Int_Oring__1__class_Oof__int(_1306259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1306261), _1306263)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1306259), hAPP(c_Int_Oring__1__class_Oof__int(_1306259), _1306261)), hAPP(c_Int_Oring__1__class_Oof__int(_1306259), _1306263)))], (37866 ^ _777959) ^ [_1503135, _1503137, _1503139, _1503141, _1503143, _1503145, _1503147] : [c_Equiv__Relations_Oequiv(_1503135, _1503137, _1503139), c_Equiv__Relations_Ocongruent(_1503135, tc_fun(_1503141, tc_HOL_Obool), _1503139, _1503143), hBOOL(hAPP(hAPP(c_member(tc_fun(_1503135, tc_HOL_Obool)), _1503145), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1503135), _1503137), _1503139))), 37880 ^ _777959 : [(37883 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1503141, tc_HOL_Obool)), hAPP(_1503143, 37879 ^ [_1503135, _1503137, _1503139, _1503141, _1503143, _1503145, _1503147])), _1503147))], (37881 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503135), 37879 ^ [_1503135, _1503137, _1503139, _1503141, _1503143, _1503145, _1503147]), _1503137)))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1503141, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1503135, tc_fun(_1503141, tc_HOL_Obool)), _1503145), _1503143)), _1503147)))], (49738 ^ _777959) ^ [_1786695] : [-(c_Nitpick_Odenom(_1786695) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1786695, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1786695)))], (35149 ^ _777959) ^ [_1439114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1439114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1439114))))], (15662 ^ _777959) ^ [_1076118, _1076120] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076118), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076120), _1076118)))))], (15292 ^ _777959) ^ [_1069134, _1069136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069134), _1069136)), -(hAPP(c_Nat_OSuc, _1069134) = _1069136), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1069134)), _1069136)))], (32927 ^ _777959) ^ [_1399916, _1399918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1399916), _1399918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1399916)), c_Int_OBit1(_1399918))))], (11156 ^ _777959) ^ [_976587, _976589, _976591] : [class_Lattices_Olattice(_976587), hBOOL(hAPP(c_Finite__Set_Ofinite(_976587), _976589)), hBOOL(hAPP(hAPP(c_member(_976587), _976591), _976589)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_976587), _976591), c_Big__Operators_Olattice__class_OInf__fin(_976587, _976589)) = _976591)], (48051 ^ _777959) ^ [_1745401, _1745403, _1745405, _1745407, _1745409, _1745411, _1745413] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1745401, _1745403, _1745405, _1745407), _1745409), _1745411), _1745413) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1745403, _1745405, _1745407), _1745411), hAPP(_1745409, _1745413)))], (51296 ^ _777959) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (21816 ^ _777959) ^ [_1192282, _1192284, _1192286] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1192282), _1192284)), 21819 ^ _777959 : [(21839 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192282, tc_Nat_Onat), _1192286), _1192284) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 21840 ^ _777959 : [(21841 ^ _777959) ^ [_1192763] : [hBOOL(hAPP(hAPP(c_member(_1192282), _1192763), _1192284)), hAPP(_1192286, _1192763) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21849 ^ _777959 : [(21854 ^ _777959) ^ [] : [hAPP(_1192286, 21848 ^ [_1192282, _1192284, _1192286, _1192763]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21852 ^ _777959) ^ [] : [_1192763 = 21848 ^ [_1192282, _1192284, _1192286, _1192763]], (21850 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1192282), 21848 ^ [_1192282, _1192284, _1192286, _1192763]), _1192284)))]]]]], (21820 ^ _777959) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192282, tc_Nat_Onat), _1192286), _1192284) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21824 ^ _777959 : [(21829 ^ _777959) ^ [_1192602] : [hBOOL(hAPP(hAPP(c_member(_1192282), _1192602), _1192284)), -(21823 ^ [_1192282, _1192284, _1192286] = _1192602), -(hAPP(_1192286, _1192602) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21827 ^ _777959) ^ [] : [-(hAPP(_1192286, 21823 ^ [_1192282, _1192284, _1192286]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21825 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1192282), 21823 ^ [_1192282, _1192284, _1192286]), _1192284)))]]]]], (22717 ^ _777959) ^ [_1211214] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211214) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1211214 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18675 ^ _777959) ^ [_1136712, _1136714, _1136716] : [class_Orderings_Olinorder(_1136712), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136712), _1136714)), hBOOL(hAPP(hAPP(c_member(_1136712), _1136716), _1136714)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136712), hAPP(c_Finite__Set_Ofold1(_1136712, c_Orderings_Oord__class_Omin(_1136712)), _1136714)), _1136716)))], (11882 ^ _777959) ^ [_993514, _993516, _993518, _993520, _993522] : [_993514 = c_Orderings_Obot__class_Obot(tc_fun(_993516, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_993518, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993516, tc_fun(_993518, tc_HOL_Obool)), _993514), _993520)), _993522) = _993522)], (41181 ^ _777959) ^ [_1583894, _1583896, _1583898, _1583900, _1583902] : [c_Relation_Orefl__on(_1583894, _1583896, _1583898), c_Relation_Orefl__on(_1583894, _1583900, _1583902), -(c_Relation_Orefl__on(_1583894, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1583894, tc_HOL_Obool)), _1583896), _1583900), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1583894, _1583894), tc_HOL_Obool)), _1583898), _1583902)))], (26478 ^ _777959) ^ [_1279460, _1279462, _1279464, _1279466, _1279468] : [class_Fields_Olinordered__field(_1279460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279460), c_Groups_Ozero__class_Ozero(_1279460)), _1279462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279460), _1279462), _1279464)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279460), c_Groups_Ozero__class_Ozero(_1279460)), _1279466)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279460), _1279466), _1279468)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279460), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279460), _1279462), _1279468)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279460), _1279464), _1279466))))], (37419 ^ _777959) ^ [_1492624, _1492626, _1492628, _1492630] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1492624, tc_HOL_Obool)), _1492626), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1492624), _1492628), _1492630))), 37423 ^ _777959 : [(37426 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1492624), 37422 ^ [_1492624, _1492626, _1492628, _1492630]), _1492628)))], (37424 ^ _777959) ^ [] : [-(_1492626 = hAPP(c_Relation_OImage(_1492624, _1492624, _1492630), hAPP(hAPP(c_Set_Oinsert(_1492624), 37422 ^ [_1492624, _1492626, _1492628, _1492630]), c_Orderings_Obot__class_Obot(tc_fun(_1492624, tc_HOL_Obool)))))]]], (12237 ^ _777959) ^ [_1000139, _1000141, _1000143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000139), _1000141)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000143), _1000139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1000139), _1000143)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1000141), _1000143))))], (17319 ^ _777959) ^ [_1109138, _1109140, _1109142, _1109144, _1109146] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1109138, _1109140, _1109142), _1109144), _1109146) = c_HOL_OThe(_1109140, c_Finite__Set_Ofold__graph(_1109138, _1109140, _1109142, _1109144, _1109146)))], (4648 ^ _777959) ^ [_848466, _848468, _848470, _848472, _848474, _848476, _848478, _848480, _848482, _848484] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_848484, _848480, _848476, _848472, _848468) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_848482, _848478, _848474, _848470, _848466)), _848484 = _848482, _848480 = _848478, _848476 = _848474, _848472 = _848470, _848468 = _848466], (40497 ^ _777959) ^ [_1564040, _1564042, _1564044, _1564046, _1564048, _1564050] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1564040)), _1564042) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1564044)), _1564046), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1564040, tc_HOL_Obool)), hAPP(c_List_Oset(_1564040), _1564042)), _1564048)), -(c_Map_Orestrict__map(_1564040, _1564044, c_Map_Omap__upds(_1564040, _1564044, _1564050, _1564042, _1564046), _1564048) = c_Map_Omap__upds(_1564040, _1564044, c_Map_Orestrict__map(_1564040, _1564044, _1564050, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1564040, tc_HOL_Obool)), _1564048), hAPP(c_List_Oset(_1564040), _1564042))), _1564042, _1564046))], (37353 ^ _777959) ^ [_1490957, _1490959] : [-(c_Relation_OId__on(_1490957, _1490959) = hAPP(c_Product__Type_Oprod_Oprod__case(_1490957, _1490957, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1490957, tc_HOL_Obool, tc_fun(_1490957, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490957, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1490957, tc_HOL_Obool)), _1490957), c_COMBC(_1490957, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490957, tc_HOL_Obool), tc_fun(_1490957, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1490957), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1490957), c_fconj)), c_fequal))), _1490959)))], (21996 ^ _777959) ^ [_1196227, _1196229] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1196227))), -(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)), _1196227))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1196229)))) = 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)), _1196227))), 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, _1196229))))))], (40158 ^ _777959) ^ [_1556559, _1556561, _1556563, _1556565, _1556567, _1556569] : [class_Orderings_Olinorder(_1556559), -(hAPP(_1556561, _1556563) = hAPP(_1556561, _1556565)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1556567, _1556559, _1556561), _1556565), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1556567, _1556559, _1556561), _1556563), _1556569)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1556567, _1556559, _1556561), _1556563), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1556567, _1556559, _1556561), _1556565), _1556569)))], (42044 ^ _777959) ^ [_1606464, _1606466] : [-(c_List_Olistrelp(_1606464, _1606466, c_List_Olist_ONil(_1606464), c_List_Olist_ONil(_1606464)))], (3412 ^ _777959) ^ [_829378, _829380, _829382, _829384, _829386, _829388, _829390, _829392] : [-(c_Enum_Oproduct(_829392, _829388, _829384, _829380) = c_Enum_Oproduct(_829390, _829386, _829382, _829378)), _829392 = _829390, _829388 = _829386, _829384 = _829382, _829380 = _829378], (24259 ^ _777959) ^ [_1239074, _1239076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1239074), _1239076)), -(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)), _1239074)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1239076))))], (43538 ^ _777959) ^ [_1643269, _1643271, _1643273] : [hBOOL(hAPP(c_List_Odistinct(_1643269), _1643273)), -(hBOOL(hAPP(c_List_Odistinct(_1643269), hAPP(c_List_Orotate(_1643269, _1643271), _1643273))))], (35143 ^ _777959) ^ [_1439031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1439031))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1439031)))], (17549 ^ _777959) ^ [_1113364, _1113366, _1113368] : [class_Orderings_Olinorder(_1113364), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113364), _1113366)), -(hBOOL(hAPP(hAPP(c_member(_1113364), _1113368), _1113366))), -(_1113366 = c_Orderings_Obot__class_Obot(tc_fun(_1113364, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1113364, hAPP(hAPP(c_Set_Oinsert(_1113364), _1113368), _1113366)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1113364), _1113368), c_Big__Operators_Olinorder__class_OMax(_1113364, _1113366)))], (36644 ^ _777959) ^ [_1473114, _1473116, _1473118, _1473120] : [-(_1473114 = _1473116), hAPP(c_Product__Type_Ofst(_1473118, _1473120), _1473114) = hAPP(c_Product__Type_Ofst(_1473118, _1473120), _1473116), hAPP(c_Product__Type_Osnd(_1473118, _1473120), _1473114) = hAPP(c_Product__Type_Osnd(_1473118, _1473120), _1473116)], (16527 ^ _777959) ^ [_1094630, _1094632, _1094634, _1094636] : [class_Orderings_Olinorder(_1094630), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094630), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094630), _1094632), _1094634)), _1094636) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094630), _1094632), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094630), _1094634), _1094636)))], (37249 ^ _777959) ^ [_1488200, _1488202] : [-(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), _1488200), _1488202)), 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), _1488200), _1488202))], (35553 ^ _777959) ^ [_1451758, _1451760] : [-(_1451758 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451760, _1451758), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1451760), _1451758)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1451760, _1451758)))))], (29900 ^ _777959) ^ [_1343222, _1343224] : [-(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, _1343222, _1343224)), _1343224) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1343222), _1343224))], (836 ^ _777959) ^ [_790781, _790783, _790785, _790787] : [-(c_Wellfounded_Owf(_790785, _790781)), c_Wellfounded_Owf(_790787, _790783), _790787 = _790785, _790783 = _790781], (31502 ^ _777959) ^ [_1373070] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1373070)))], (22938 ^ _777959) ^ [_1215353, _1215355, _1215357] : [class_Rings_Osemiring__1(_1215353), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215353), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1215355), _1215357)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215353), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215353), _1215355)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215353), _1215357)))], (45296 ^ _777959) ^ [_1680817, _1680819] : [c_List_Oremdups(_1680817, _1680819) = c_List_Olist_ONil(_1680817), -(_1680819 = c_List_Olist_ONil(_1680817))], (5448 ^ _777959) ^ [_861256, _861258, _861260, _861262] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_861262, _861258) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_861260, _861256)), _861262 = _861260, _861258 = _861256], (35023 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (35934 ^ _777959) ^ [_1459697, _1459699] : [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), _1459697))), 35937 ^ _777959 : [(35944 ^ _777959) ^ [] : [-(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), _1459699)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459697))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459699), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459697)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459697)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459699), 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), _1459697)))))], (35938 ^ _777959) ^ [] : [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), _1459699)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459697)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459699), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459697)) = 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), _1459699)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459697))))]]], (29358 ^ _777959) ^ [_1331412, _1331414, _1331416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331412)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1331414), _1331416)), 29365 ^ _777959 : [(29366 ^ _777959) ^ [_1331608] : [29368 ^ _777959 : [(29374 ^ _777959) ^ [] : [-(_1331608 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 29370 ^ [_1331412, _1331414, _1331416, _1331608]), 29367 ^ [_1331412, _1331414, _1331416, _1331608]))], (29372 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29370 ^ [_1331412, _1331414, _1331416, _1331608]), _1331416)))], (29369 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29367 ^ [_1331412, _1331414, _1331416, _1331608]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1331412))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331608), _1331414)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1331608), _1331412)), _1331414)))]]], (35842 ^ _777959) ^ [_1457920, _1457922, _1457924, _1457926] : [-(c_HOL_OThe(tc_prod(_1457920, _1457922), hAPP(c_Product__Type_Oprod_Oprod__case(_1457920, _1457922, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1457920, tc_fun(_1457922, tc_HOL_Obool), tc_fun(_1457922, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1457922, tc_HOL_Obool), tc_fun(_1457922, tc_HOL_Obool)), _1457920), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1457922)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1457920), c_fconj), hAPP(c_fequal, _1457924)))), hAPP(c_fequal, _1457926)))) = hAPP(hAPP(c_Product__Type_OPair(_1457920, _1457922), _1457924), _1457926))], (29084 ^ _777959) ^ [_1326063, _1326065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1326063), _1326065)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1326065, _1326063) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (19678 ^ _777959) ^ [_1153976, _1153978, _1153980] : [class_Groups_Ocomm__monoid__mult(_1153976), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1153978, _1153976), _1153980), c_Orderings_Obot__class_Obot(tc_fun(_1153978, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1153976))], (21492 ^ _777959) ^ [_1186393, _1186395, _1186397] : [class_Rings_Olinordered__ring__strict(_1186393), 21495 ^ _777959 : [(21504 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186393), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186393), _1186395), _1186395)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186393), _1186397), _1186397))), c_Groups_Ozero__class_Ozero(_1186393)))), _1186395 = c_Groups_Ozero__class_Ozero(_1186393), _1186397 = c_Groups_Ozero__class_Ozero(_1186393)], (21496 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186393), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186393), _1186395), _1186395)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186393), _1186397), _1186397))), c_Groups_Ozero__class_Ozero(_1186393))), 21499 ^ _777959 : [(21502 ^ _777959) ^ [] : [-(_1186397 = c_Groups_Ozero__class_Ozero(_1186393))], (21500 ^ _777959) ^ [] : [-(_1186395 = c_Groups_Ozero__class_Ozero(_1186393))]]]]], (7082 ^ _777959) ^ [_896265, _896267, _896269] : [hBOOL(hAPP(hAPP(c_member(_896265), _896267), hAPP(c_fequal, _896269))), -(_896267 = _896269)], (24638 ^ _777959) ^ [_1245563, _1245565] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1245563), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24641 ^ _777959 : [(24648 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1245565), _1245563)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24642 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1245565), _1245563)), 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)), _1245565)))]]], (11818 ^ _777959) ^ [_992141, _992143] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992141, tc_fun(_992141, tc_HOL_Obool)), _992143), hAPP(hAPP(c_COMBC(_992141, tc_fun(_992141, tc_HOL_Obool), tc_fun(_992141, tc_HOL_Obool)), c_Set_Oinsert(_992141)), c_Orderings_Obot__class_Obot(tc_fun(_992141, tc_HOL_Obool)))) = _992143)], (46493 ^ _777959) ^ [_1706595, _1706597, _1706599, _1706601, _1706603, _1706605] : [c_List_Olist__all2(_1706595, _1706597, _1706599, _1706601, _1706603), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706605), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706597)), _1706603))), -(hBOOL(hAPP(hAPP(_1706599, hAPP(hAPP(c_List_Onth(_1706595), _1706601), _1706605)), hAPP(hAPP(c_List_Onth(_1706597), _1706603), _1706605))))], (7414 ^ _777959) ^ [_902310, _902312] : [class_Lattices_Obounded__lattice__bot(_902310), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_902310), _902312), c_Orderings_Obot__class_Obot(_902310)) = _902312)], (4614 ^ _777959) ^ [_847931, _847933] : [_847933 = _847931, -(c_New__DSequence_Opos__empty(_847933) = c_New__DSequence_Opos__empty(_847931))], (19662 ^ _777959) ^ [_1153697] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1153697) = _1153697)], (33975 ^ _777959) ^ [_1418015] : [class_Int_Onumber__ring(_1418015), -(c_Int_Oiszero(_1418015, hAPP(c_Int_Onumber__class_Onumber__of(_1418015), c_Int_OPls)))], (50250 ^ _777959) ^ [_1796575, _1796577, _1796579] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1796575)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1796575, _1796577, _1796579)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1796575)), _1796579)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (12363 ^ _777959) ^ [_1002448, _1002450, _1002452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1002448), _1002450)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002450), _1002448)), _1002452) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1002450), _1002452)), _1002448))], (5436 ^ _777959) ^ [_861086, _861088] : [_861088 = _861086, -(c_Groups_Oplus__class_Oplus(_861088) = c_Groups_Oplus__class_Oplus(_861086))], (42937 ^ _777959) ^ [_1628935, _1628937, _1628939] : [hAPP(hAPP(c_List_Oappend(_1628935), _1628937), _1628939) = c_List_Olist_ONil(_1628935), 42940 ^ _777959 : [(42943 ^ _777959) ^ [] : [-(_1628939 = c_List_Olist_ONil(_1628935))], (42941 ^ _777959) ^ [] : [-(_1628937 = c_List_Olist_ONil(_1628935))]]], (10080 ^ _777959) ^ [_953561, _953563] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953561, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_953561, tc_HOL_Obool))), _953563) = c_Orderings_Obot__class_Obot(tc_fun(_953561, tc_HOL_Obool)))], (21703 ^ _777959) ^ [_1190199, _1190201, _1190203] : [-(hBOOL(hAPP(_1190199, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1190201), _1190203)))), 21706 ^ _777959 : [(21709 ^ _777959) ^ [] : [hBOOL(hAPP(_1190199, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21707 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1190201), _1190203)))]], 21711 ^ _777959 : [(21714 ^ _777959) ^ [] : [hBOOL(hAPP(_1190199, 21710 ^ [_1190199, _1190201, _1190203]))], (21712 ^ _777959) ^ [] : [-(_1190201 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1190203), 21710 ^ [_1190199, _1190201, _1190203]))]]], (47048 ^ _777959) ^ [_1721152, _1721154] : [-(c_Wellfounded_Owf(_1721152, c_List_Omeasures(_1721152, _1721154)))], (8800 ^ _777959) ^ [_929794, _929796, _929798, _929800] : [class_Orderings_Oord(_929794), 8803 ^ _777959 : [(8812 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929796, _929794)), _929798), _929800))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929796, _929794)), _929798), _929800)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929796, _929794)), _929800), _929798)))], (8804 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_929796, _929794)), _929798), _929800)), 8807 ^ _777959 : [(8810 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929796, _929794)), _929800), _929798))], (8808 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_929796, _929794)), _929798), _929800)))]]]]], (5914 ^ _777959) ^ [_872198, _872200] : [-(hAPP(c_Set_Oimage(_872198, _872198, c_COMBI(_872198)), _872200) = _872200)], (26676 ^ _777959) ^ [_1283145, _1283147, _1283149, _1283151] : [class_Fields_Olinordered__field(_1283145), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283145), c_Groups_Ozero__class_Ozero(_1283145)), _1283147)), 26683 ^ _777959 : [(26690 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283145), _1283149), _1283147)), _1283151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283145), _1283149), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1283145), _1283151), _1283147))))], (26684 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283145), _1283149), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1283145), _1283151), _1283147))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283145), _1283149), _1283147)), _1283151)))]]], (23016 ^ _777959) ^ [_1216814, _1216816] : [class_Rings_Oring__1(_1216814), hBOOL(hAPP(hAPP(c_member(_1216814), _1216816), c_Int_Oring__1__class_OInts(_1216814))), -(hBOOL(hAPP(hAPP(c_member(_1216814), hAPP(c_Groups_Ouminus__class_Ouminus(_1216814), _1216816)), c_Int_Oring__1__class_OInts(_1216814))))], (11696 ^ _777959) ^ [_988294, _988296, _988298, _988300] : [_988294 = c_Orderings_Obot__class_Obot(tc_fun(_988296, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_988296, tc_fun(_988298, tc_HOL_Obool)), _988294), hAPP(c_COMBK(tc_fun(_988298, tc_HOL_Obool), _988296), _988300)) = c_Orderings_Obot__class_Obot(tc_fun(_988298, tc_HOL_Obool)))], (20525 ^ _777959) ^ [_1169406, _1169408, _1169410] : [class_Groups_Oordered__ab__group__add(_1169406), 20528 ^ _777959 : [(20535 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169406), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1169406), _1169408), _1169410)), c_Groups_Ozero__class_Ozero(_1169406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169406), _1169408), _1169410)))], (20529 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169406), _1169408), _1169410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1169406), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1169406), _1169408), _1169410)), c_Groups_Ozero__class_Ozero(_1169406))))]]], (18971 ^ _777959) ^ [_1142223, _1142225, _1142227] : [18973 ^ _777959 : [(18976 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1142223, tc_HOL_Obool)), 18972 ^ [_1142223, _1142225, _1142227]), _1142227))], (18974 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1142223, tc_HOL_Obool)), 18972 ^ [_1142223, _1142225, _1142227]), _1142225)))]], -(_1142225 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1142223, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1142223, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1142223, tc_HOL_Obool), _1142225)), _1142227)))], (39235 ^ _777959) ^ [_1534024, _1534026, _1534028] : [39237 ^ _777959 : [(39240 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1534024), 39236 ^ [_1534024, _1534026, _1534028]), c_Wellfounded_Oacc(_1534024, _1534028)))], (39238 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534024, _1534024)), hAPP(hAPP(c_Product__Type_OPair(_1534024, _1534024), 39236 ^ [_1534024, _1534026, _1534028]), _1534026)), _1534028)))]], -(hBOOL(hAPP(hAPP(c_member(_1534024), _1534026), c_Wellfounded_Oacc(_1534024, _1534028))))], (23337 ^ _777959) ^ [_1222580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222580), 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)), _1222580)), _1222580)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6977 ^ _777959) ^ [_893392, _893394, _893396, _893398] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_893392), _893394)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_893396), hAPP(c_Set_Oimage(_893392, _893396, _893398), _893394))))], (31825 ^ _777959) ^ [_1379016, _1379018, _1379020] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1379016, _1379018, _1379020))), -(hBOOL(hAPP(c_Com_OWT, _1379020)))], (48354 ^ _777959) ^ [_1750995] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1750995), 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, _1750995)) = _1750995)], (11304 ^ _777959) ^ [_979097, _979099, _979101] : [class_Lattices_Olattice(_979097), hBOOL(hAPP(c_Finite__Set_Ofinite(_979097), _979099)), -(c_Big__Operators_Olattice__class_OInf__fin(_979097, hAPP(hAPP(c_Set_Oinsert(_979097), _979101), _979099)) = hAPP(hAPP(c_Finite__Set_Ofold(_979097, _979097, c_Lattices_Osemilattice__inf__class_Oinf(_979097)), _979101), _979099))], (51280 ^ _777959) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (14019 ^ _777959) ^ [_1038080, _1038082, _1038084] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1038080, tc_HOL_Obool)), _1038082), _1038084) = hAPP(c_Set_OCollect(_1038080), hAPP(hAPP(c_COMBS(_1038080, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1038080), c_fconj), hAPP(hAPP(c_COMBC(_1038080, tc_fun(_1038080, tc_HOL_Obool), tc_HOL_Obool), c_member(_1038080)), _1038082))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1038080), c_fNot), hAPP(hAPP(c_COMBC(_1038080, tc_fun(_1038080, tc_HOL_Obool), tc_HOL_Obool), c_member(_1038080)), _1038084)))))], (41241 ^ _777959) ^ [_1585177, _1585179] : [c_Relation_Orefl__on(_1585177, c_Orderings_Otop__class_Otop(tc_fun(_1585177, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1585177, _1585177)), hAPP(c_Product__Type_Oprod_Oprod__case(_1585177, _1585177, tc_HOL_Obool), _1585179))), -(c_Predicate_Oreflp(_1585177, _1585179))], (33335 ^ _777959) ^ [_1406698, _1406700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1406698)), _1406700)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406698), _1406700)))], (5492 ^ _777959) ^ [_861894, _861896] : [_861896 = _861894, -(tc_Option_Ooption(_861896) = tc_Option_Ooption(_861894))], (14819 ^ _777959) ^ [_1056835, _1056837, _1056839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1056835, tc_HOL_Obool)), _1056837), _1056839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1056835, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_1056835, _1056837)), c_Predicate_OPowp(_1056835, _1056839))))], (20079 ^ _777959) ^ [_1161291, _1161293, _1161295] : [class_Rings_Olinordered__ring__strict(_1161291), 20082 ^ _777959 : [(20097 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161291), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161291), _1161293), _1161295)), c_Groups_Ozero__class_Ozero(_1161291)))), 20098 ^ _777959 : [(20105 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161291), _1161293), c_Groups_Ozero__class_Ozero(_1161291))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161291), c_Groups_Ozero__class_Ozero(_1161291)), _1161295))], (20099 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161291), c_Groups_Ozero__class_Ozero(_1161291)), _1161293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161291), _1161295), c_Groups_Ozero__class_Ozero(_1161291)))]]], (20083 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161291), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161291), _1161293), _1161295)), c_Groups_Ozero__class_Ozero(_1161291))), 20088 ^ _777959 : [(20091 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161291), _1161295), c_Groups_Ozero__class_Ozero(_1161291))))], (20089 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161291), c_Groups_Ozero__class_Ozero(_1161291)), _1161293)))]], 20092 ^ _777959 : [(20095 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161291), c_Groups_Ozero__class_Ozero(_1161291)), _1161295)))], (20093 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161291), _1161293), c_Groups_Ozero__class_Ozero(_1161291))))]]]]], (44344 ^ _777959) ^ [_1659662, _1659664] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1659662, _1659664)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1659662), hAPP(c_Nat_OSuc, _1659664)))], (13655 ^ _777959) ^ [_1029426, _1029428, _1029430, _1029432, _1029434, _1029436, _1029438] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029426, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029428, tc_fun(_1029426, tc_HOL_Obool)), _1029430), _1029432)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029434, tc_fun(_1029426, tc_HOL_Obool)), _1029436), _1029438)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029428, tc_fun(_1029426, tc_HOL_Obool)), _1029430), hAPP(hAPP(c_COMBB(tc_fun(_1029434, tc_fun(_1029426, tc_HOL_Obool)), tc_fun(_1029426, tc_HOL_Obool), _1029428), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029434, tc_fun(_1029426, tc_HOL_Obool)), _1029436)), hAPP(hAPP(c_COMBC(_1029428, tc_fun(_1029434, tc_fun(_1029426, tc_HOL_Obool)), tc_fun(_1029434, tc_fun(_1029426, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1029426, tc_HOL_Obool), tc_fun(_1029426, tc_HOL_Obool)), tc_fun(tc_fun(_1029434, tc_fun(_1029426, tc_HOL_Obool)), tc_fun(_1029434, tc_fun(_1029426, tc_HOL_Obool))), _1029428), c_COMBB(tc_fun(_1029426, tc_HOL_Obool), tc_fun(_1029426, tc_HOL_Obool), _1029434)), hAPP(hAPP(c_COMBB(tc_fun(_1029426, tc_HOL_Obool), tc_fun(tc_fun(_1029426, tc_HOL_Obool), tc_fun(_1029426, tc_HOL_Obool)), _1029428), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029426, tc_HOL_Obool))), _1029432))), _1029438))))], (49966 ^ _777959) ^ [_1791216, _1791218, _1791220] : [-(c_List_Olist__ex1(_1791216, _1791218, _1791220)), 49967 ^ _777959 : [(49968 ^ _777959) ^ [_1791310] : [hBOOL(hAPP(hAPP(c_member(_1791216), _1791310), hAPP(c_List_Oset(_1791216), _1791220))), hBOOL(hAPP(_1791218, _1791310)), 49976 ^ _777959 : [(49981 ^ _777959) ^ [] : [49975 ^ [_1791216, _1791218, _1791220, _1791310] = _1791310], (49979 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1791218, 49975 ^ [_1791216, _1791218, _1791220, _1791310])))], (49977 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791216), 49975 ^ [_1791216, _1791218, _1791220, _1791310]), hAPP(c_List_Oset(_1791216), _1791220))))]]]]], (47933 ^ _777959) ^ [_1743061, _1743063, _1743065] : [c_Wellfounded_Owf(_1743061, _1743063), hBOOL(hAPP(hAPP(c_member(tc_prod(_1743061, _1743061)), hAPP(hAPP(c_Product__Type_OPair(_1743061, _1743061), hAPP(_1743065, hAPP(c_Nat_OSuc, 47936 ^ [_1743061, _1743063, _1743065]))), hAPP(_1743065, 47936 ^ [_1743061, _1743063, _1743065]))), _1743063))], (32129 ^ _777959) ^ [_1384766, _1384768, _1384770] : [class_Int_Onumber__ring(_1384766), -(hAPP(c_Int_Onumber__class_Onumber__of(_1384766), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1384768), _1384770)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384766), hAPP(c_Int_Onumber__class_Onumber__of(_1384766), _1384768)), hAPP(c_Int_Onumber__class_Onumber__of(_1384766), _1384770)))], (42242 ^ _777959) ^ [_1610661, _1610663, _1610665, _1610667, _1610669, _1610671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1610661, _1610663), tc_HOL_Obool)), _1610665), hAPP(hAPP(c_Product__Type_OSigma(_1610661, _1610663), _1610667), hAPP(c_COMBK(tc_fun(_1610663, tc_HOL_Obool), _1610661), _1610669)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610663, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1610661, _1610663, _1610665), _1610671)), _1610669)))], (43548 ^ _777959) ^ [_1643474, _1643476, _1643478] : [-(hAPP(c_List_Otl(_1643474), hAPP(hAPP(c_List_Olist_OCons(_1643474), _1643476), _1643478)) = _1643478)], (14179 ^ _777959) ^ [_1041776, _1041778, _1041780] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041776), _1041778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1041776, tc_HOL_Obool)), _1041780), _1041778)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1041776), _1041780)), hAPP(c_Finite__Set_Ocard(_1041776), _1041778))))], (46784 ^ _777959) ^ [_1714102, _1714104, _1714106, _1714108, _1714110, _1714112] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1714102, _1714104, _1714106), _1714108), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1714104, _1714106), tc_HOL_Obool)), _1714110), _1714112)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1714102, _1714106), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1714102, _1714104, _1714106), _1714108), _1714110)), hAPP(hAPP(c_Relation_Orel__comp(_1714102, _1714104, _1714106), _1714108), _1714112)))], (50884 ^ _777959) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (15474 ^ _777959) ^ [_1072143, _1072145] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072143), _1072145))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1072145)), _1072143)))], (43984 ^ _777959) ^ [_1652474, _1652476, _1652478] : [hBOOL(hAPP(c_List_Odistinct(_1652474), _1652476)), -(hBOOL(hAPP(c_List_Odistinct(_1652474), hAPP(c_List_Ofilter(_1652474, _1652478), _1652476))))], (38270 ^ _777959) ^ [_1511175, _1511177, _1511179, _1511181, _1511183] : [c_Fun_Oinj__on(_1511175, _1511177, _1511179, c_Orderings_Otop__class_Otop(tc_fun(_1511175, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1511175, _1511177, _1511179), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511175, tc_HOL_Obool)), _1511181), _1511183)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1511177, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1511175, _1511177, _1511179), _1511181)), hAPP(c_Set_Oimage(_1511175, _1511177, _1511179), _1511183)))], (14782 ^ _777959) ^ [_1055742, _1055744, _1055746, _1055748, _1055750, _1055752] : [hBOOL(hAPP(hAPP(c_member(_1055742), _1055744), c_SetInterval_Oord_OgreaterThanAtMost(_1055742, _1055746, _1055748, _1055750, _1055752))), 14785 ^ _777959 : [(14788 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1055746, _1055744), _1055752)))], (14786 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1055748, _1055750), _1055744)))]]], (25444 ^ _777959) ^ [_1260417, _1260419, _1260421] : [_1260417 = 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), _1260417), _1260419)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1260417), _1260421)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (402 ^ _777959) ^ [_784256, _784258, _784260, _784262, _784264, _784266] : [-(c_Hoare__Mirabelle_Ohoare__valids(_784264, _784260, _784256)), c_Hoare__Mirabelle_Ohoare__valids(_784266, _784262, _784258), _784266 = _784264, _784262 = _784260, _784258 = _784256], (41350 ^ _777959) ^ [_1587975, _1587977] : [-(c_List_Obutlast(_1587975, _1587977) = hAPP(hAPP(c_List_Otake(_1587975), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1587975)), _1587977)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1587977))], (29545 ^ _777959) ^ [_1335094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1335094), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1335094 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 29548 ^ [_1335094]))))], (41269 ^ _777959) ^ [_1585755, _1585757, _1585759, _1585761] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1585755), tc_List_Olist(_1585755))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1585755), tc_List_Olist(_1585755)), _1585757), _1585759)), c_List_Olistrel1(_1585755, _1585761))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1585755)), _1585757) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1585755)), _1585759))], (12562 ^ _777959) ^ [_1006370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006370), _1006370))], (36878 ^ _777959) ^ [_1477724] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1477724)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1477724)], (42547 ^ _777959) ^ [_1619819, _1619821, _1619823] : [-(hAPP(c_Fun_Ocomp(_1619819, _1619819, _1619821, c_Fun_Oid(_1619819)), _1619823) = _1619823)], (21726 ^ _777959) ^ [_1190630, _1190632] : [-(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), _1190630), _1190632)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1190630)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1190632))], (33415 ^ _777959) ^ [] : [-(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))))], (47269 ^ _777959) ^ [_1726689, _1726691, _1726693, _1726695] : [hBOOL(hAPP(hAPP(c_member(_1726691), _1726695), hAPP(c_Relation_ORange(_1726689, _1726691), _1726693))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1726689, _1726691, hAPP(hAPP(c_COMBC(_1726689, tc_fun(tc_prod(_1726689, _1726691), tc_HOL_Obool), tc_fun(_1726691, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1726691, tc_fun(tc_fun(tc_prod(_1726689, _1726691), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1726689, _1726691), tc_HOL_Obool), tc_fun(_1726691, tc_HOL_Obool)), _1726689), c_COMBC(_1726691, tc_fun(tc_prod(_1726689, _1726691), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1726691, tc_prod(_1726689, _1726691)), tc_fun(_1726691, tc_fun(tc_fun(tc_prod(_1726689, _1726691), tc_HOL_Obool), tc_HOL_Obool)), _1726689), hAPP(c_COMBB(tc_prod(_1726689, _1726691), tc_fun(tc_fun(tc_prod(_1726689, _1726691), tc_HOL_Obool), tc_HOL_Obool), _1726691), c_member(tc_prod(_1726689, _1726691)))), c_Product__Type_OPair(_1726689, _1726691)))), _1726693)), _1726695)))], (39446 ^ _777959) ^ [_1538988, _1538990, _1538992, _1538994, _1538996, _1538998] : [c_Finite__Set_Ofolding(_1538988, _1538990, _1538992, _1538994), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538988), _1538996)), -(hBOOL(hAPP(hAPP(c_member(_1538988), _1538998), _1538996))), -(hAPP(_1538994, hAPP(hAPP(c_Set_Oinsert(_1538988), _1538998), _1538996)) = hAPP(c_Fun_Ocomp(_1538990, _1538990, _1538990, hAPP(_1538994, _1538996)), hAPP(_1538992, _1538998)))], (27483 ^ _777959) ^ [_1297629, _1297631] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1297629), _1297631)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1297631), _1297629)))], (31638 ^ _777959) ^ [_1375308, _1375310, _1375312, _1375314, _1375316] : [c_Com_Ocom_OCond(_1375308, _1375310, _1375312) = c_Com_Ocom_OSemi(_1375314, _1375316)], (37355 ^ _777959) ^ [_1491051] : [-(c_Relation_OId__on(_1491051, c_Orderings_Obot__class_Obot(tc_fun(_1491051, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1491051, _1491051), tc_HOL_Obool)))], (9898 ^ _777959) ^ [_949923, _949925, _949927, _949929] : [class_Lattices_Osemilattice__inf(_949923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949923), _949925), _949927)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949923), _949925), _949929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949923), _949925), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949923), _949927), _949929))))], (12530 ^ _777959) ^ [_1005839, _1005841, _1005843] : [12531 ^ _777959 : [(12534 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1005843, _1005841), _1005839))], (12532 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1005839), _1005841)))]], 12537 ^ _777959 : [(12540 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1005843, _1005841), _1005839))], (12538 ^ _777959) ^ [] : [-(_1005839 = _1005841)]], 12543 ^ _777959 : [(12546 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1005843, _1005841), _1005839))], (12544 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1005841), _1005839)))]], -(hBOOL(hAPP(hAPP(_1005843, _1005841), _1005839)))], (41653 ^ _777959) ^ [_1595041, _1595043, _1595045, _1595047, _1595049] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595041, _1595041)), hAPP(hAPP(c_Product__Type_OPair(_1595041, _1595041), _1595043), _1595045)), _1595047)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595041), tc_List_Olist(_1595041))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595041), tc_List_Olist(_1595041)), hAPP(hAPP(c_List_Olist_OCons(_1595041), _1595043), _1595049)), hAPP(hAPP(c_List_Olist_OCons(_1595041), _1595045), _1595049))), c_List_Olistrel1(_1595041, _1595047))))], (11642 ^ _777959) ^ [_986944, _986946, _986948, _986950, _986952, _986954, _986956] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986944, tc_fun(_986946, tc_fun(_986948, tc_HOL_Obool))), _986950), _986952), _986954), _986956))), 11643 ^ _777959 : [(11644 ^ _777959) ^ [_987029] : [hBOOL(hAPP(hAPP(c_member(_986944), _987029), _986950)), hBOOL(hAPP(hAPP(hAPP(_986952, _987029), _986954), _986956))]]], (42479 ^ _777959) ^ [_1617159, _1617161, _1617163, _1617165] : [-(hAPP(c_List_Olist_Olist__case(_1617159, _1617161, _1617163, _1617165), c_List_Olist_ONil(_1617161)) = _1617163)], (31648 ^ _777959) ^ [_1375596, _1375598, _1375600] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCond(_1375596, _1375598, _1375600)], (50962 ^ _777959) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (5018 ^ _777959) ^ [_854569, _854571] : [_854571 = _854569, -(c_Lazy__Sequence_Ohit__bound(_854571) = c_Lazy__Sequence_Ohit__bound(_854569))], (31666 ^ _777959) ^ [_1375862, _1375864, _1375866, _1375868] : [class_Groups_Ocomm__monoid__mult(_1375862), hBOOL(hAPP(c_Finite__Set_Ofinite(_1375864), _1375866)), 31676 ^ _777959 : [(31679 ^ _777959) ^ [] : [hAPP(_1375868, 31675 ^ [_1375862, _1375864, _1375866, _1375868]) = c_Groups_Oone__class_Oone(_1375862)], (31677 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1375864), 31675 ^ [_1375862, _1375864, _1375866, _1375868]), _1375866)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1375862, _1375864, c_Groups_Otimes__class_Otimes(_1375862)), _1375868), c_Groups_Oone__class_Oone(_1375862)), _1375866) = c_Groups_Oone__class_Oone(_1375862))], (50009 ^ _777959) ^ [] : [-(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))))], (15775 ^ _777959) ^ [_1078034, _1078036] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1078034), _1078036)), hAPP(c_Nat_OSuc, _1078034))))], (27738 ^ _777959) ^ [_1302052, _1302054, _1302056] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302052, tc_Nat_Onat), _1302054), _1302056) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302052, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1302052), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1302054)), _1302056)))], (15590 ^ _777959) ^ [_1074270, _1074272, _1074274, _1074276, _1074278, _1074280, _1074282] : [class_Rings_Osemiring__0(_1074270), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074270), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1074272, _1074270), _1074274), _1074276)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1074278, _1074270), _1074280), _1074282)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1074272, _1074270), hAPP(hAPP(c_COMBC(_1074272, tc_fun(_1074278, tc_HOL_Obool), _1074270), hAPP(hAPP(c_COMBB(tc_fun(_1074278, _1074270), tc_fun(tc_fun(_1074278, tc_HOL_Obool), _1074270), _1074272), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1074278, _1074270)), hAPP(hAPP(c_COMBC(_1074272, tc_fun(_1074278, _1074270), tc_fun(_1074278, _1074270)), hAPP(hAPP(c_COMBB(tc_fun(_1074270, _1074270), tc_fun(tc_fun(_1074278, _1074270), tc_fun(_1074278, _1074270)), _1074272), c_COMBB(_1074270, _1074270, _1074278)), hAPP(hAPP(c_COMBB(_1074270, tc_fun(_1074270, _1074270), _1074272), c_Groups_Otimes__class_Otimes(_1074270)), _1074274))), _1074280))), _1074282)), _1074276))], (39699 ^ _777959) ^ [_1545133, _1545135, _1545137, _1545139, _1545141, _1545143, _1545145] : [c_Finite__Set_Ofolding__idem(_1545133, _1545135, _1545137, _1545139), -(hAPP(c_Fun_Ocomp(_1545135, _1545135, _1545141, hAPP(_1545137, _1545143)), hAPP(c_Fun_Ocomp(_1545135, _1545135, _1545141, hAPP(_1545137, _1545143)), _1545145)) = hAPP(c_Fun_Ocomp(_1545135, _1545135, _1545141, hAPP(_1545137, _1545143)), _1545145))], (12107 ^ _777959) ^ [_997621, _997623, _997625] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997623), _997625)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997621), _997623)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997621), _997625))))], (1630 ^ _777959) ^ [_801058, _801060] : [-(class_Divides_Osemiring__div(_801058)), _801060 = _801058, class_Divides_Osemiring__div(_801060)], (51052 ^ _777959) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (42495 ^ _777959) ^ [_1618750, _1618752, _1618754] : [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), _1618750), _1618752))), -(hBOOL(hAPP(hAPP(_1618754, _1618750), _1618752))), 42502 ^ _777959 : [(42505 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 42500 ^ [_1618750, _1618752, _1618754]), 42501 ^ [_1618750, _1618752, _1618754])), -(hBOOL(hAPP(hAPP(_1618754, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 42500 ^ [_1618750, _1618752, _1618754]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 42501 ^ [_1618750, _1618752, _1618754])))], (42511 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1618754, 42500 ^ [_1618750, _1618752, _1618754]), 42501 ^ [_1618750, _1618752, _1618754]))], (42503 ^ _777959) ^ [] : [-(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), 42500 ^ [_1618750, _1618752, _1618754]), 42501 ^ [_1618750, _1618752, _1618754]))))]]], (7316 ^ _777959) ^ [_900637, _900639, _900641] : [class_Lattices_Osemilattice__sup(_900637), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900637), _900639), _900641)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_900637), _900639), _900641) = _900641)], (51036 ^ _777959) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (42919 ^ _777959) ^ [_1628602, _1628604, _1628606] : [_1628606 = c_List_Olist_ONil(_1628604), -(_1628602 = hAPP(hAPP(c_List_Oappend(_1628604), _1628602), _1628606))], (44023 ^ _777959) ^ [_1653161, _1653163, _1653165] : [-(hAPP(c_List_Oset(_1653161), hAPP(c_List_Ofilter(_1653161, _1653163), _1653165)) = hAPP(c_Set_OCollect(_1653161), hAPP(hAPP(c_COMBS(_1653161, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1653161), c_fconj), hAPP(hAPP(c_COMBC(_1653161, tc_fun(_1653161, tc_HOL_Obool), tc_HOL_Obool), c_member(_1653161)), hAPP(c_List_Oset(_1653161), _1653165)))), _1653163)))], (2000 ^ _777959) ^ [_807006, _807008, _807010, _807012, _807014, _807016] : [-(c_SetInterval_Oord_OlessThan(_807016, _807012, _807008) = c_SetInterval_Oord_OlessThan(_807014, _807010, _807006)), _807016 = _807014, _807012 = _807010, _807008 = _807006], (50794 ^ _777959) ^ [_1807901, _1807903] : [-(class_Finite__Set_Ofinite(tc_fun(_1807901, _1807903))), class_Finite__Set_Ofinite(_1807901), class_Finite__Set_Ofinite(_1807903)], (31126 ^ _777959) ^ [_1365928, _1365930] : [class_Groups_Oordered__ab__group__add__abs(_1365928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365928), c_Groups_Ozero__class_Ozero(_1365928)), _1365930)), -(hAPP(c_Groups_Oabs__class_Oabs(_1365928), _1365930) = _1365930)], (24530 ^ _777959) ^ [_1243771, _1243773] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243771), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243773)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243771)), _1243773))], (36796 ^ _777959) ^ [_1476160, _1476162, _1476164] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1476160, _1476162), _1476164))), _1476160 = 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), _1476164)), _1476162)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1476164)), 36803 ^ _777959 : [(36806 ^ _777959) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1476164) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (36804 ^ _777959) ^ [] : [-(_1476162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 36807 ^ _777959 : [(36810 ^ _777959) ^ [] : [36811 ^ _777959 : [(36814 ^ _777959) ^ [] : [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), _1476164))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1476164)), _1476162))], (36812 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1476162)))]], 36819 ^ _777959 : [(36822 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1476162), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1476164))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1476164)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (36820 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1476162))]]], (36808 ^ _777959) ^ [] : [_1476162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (42200 ^ _777959) ^ [_1609729, _1609731, _1609733, _1609735, _1609737, _1609739] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609729, _1609731)), hAPP(hAPP(c_Product__Type_OPair(_1609729, _1609731), _1609733), _1609735)), hAPP(hAPP(c_Product__Type_OSigma(_1609729, _1609731), _1609737), _1609739))), 42203 ^ _777959 : [(42206 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1609731), _1609735), hAPP(_1609739, _1609733))))], (42204 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1609729), _1609733), _1609737)))]]], (48376 ^ _777959) ^ [_1751328, _1751330] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1751328), _1751330) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1751328, 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)))), _1751330))))], (51468 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, v_c)))], (30353 ^ _777959) ^ [_1351843, _1351845, _1351847, _1351849] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1351843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1351845), _1351847)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1351847), 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), _1351845), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1351849, _1351843))), _1351847)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (13361 ^ _777959) ^ [_1022435, _1022437, _1022439] : [hBOOL(hAPP(_1022435, _1022437)), -(hBOOL(hAPP(hAPP(c_member(_1022439), _1022437), hAPP(c_Set_OCollect(_1022439), _1022435))))], (50736 ^ _777959) ^ [_1807145] : [-(c_List_Omember(_1807145) = c_List_Oset(_1807145))], (29406 ^ _777959) ^ [_1332356, _1332358, _1332360] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332356)), 29409 ^ _777959 : [(29410 ^ _777959) ^ [_1332490] : [29412 ^ _777959 : [(29418 ^ _777959) ^ [] : [-(_1332490 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 29414 ^ [_1332356, _1332358, _1332360, _1332490]), 29411 ^ [_1332356, _1332358, _1332360, _1332490]))], (29416 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29414 ^ [_1332356, _1332358, _1332360, _1332490]), _1332358)))], (29413 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29411 ^ [_1332356, _1332358, _1332360, _1332490]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1332356))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1332490), _1332360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1332490), _1332356)), _1332360)))]]], (22880 ^ _777959) ^ [_1214362] : [class_Rings_Osemiring__1(_1214362), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1214362), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1214362))], (30144 ^ _777959) ^ [_1348084, _1348086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1348084)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1348086)), -(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, _1348084, _1348086))))], (25686 ^ _777959) ^ [_1265078, _1265080] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1265078, _1265080))))], (47610 ^ _777959) ^ [_1734986, _1734988] : [47612 ^ _777959 : [(47615 ^ _777959) ^ [] : [hBOOL(hAPP(_1734986, hAPP(c_Int_OAbs__Integ, 47611 ^ [_1734986, _1734988])))], (47613 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 47611 ^ [_1734986, _1734988]), c_Int_OInteg)))]], -(hBOOL(hAPP(_1734986, _1734988)))], (48545 ^ _777959) ^ [_1756046, _1756048] : [-(c_Transitive__Closure_Ortrancl(_1756046, c_Transitive__Closure_Otrancl(_1756046, _1756048)) = c_Transitive__Closure_Ortrancl(_1756046, _1756048))], (45524 ^ _777959) ^ [_1685708, _1685710, _1685712] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1685708), tc_List_Olist(_1685708)), c_List_Opartition(_1685708, _1685710, _1685712)) = hAPP(c_List_Ofilter(_1685708, _1685710), _1685712))], (5651 ^ _777959) ^ [_867128, _867130] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_867128, _867130, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867128), tc_HOL_Obool))))], (18703 ^ _777959) ^ [_1137219, _1137221, _1137223] : [class_Orderings_Olinorder(_1137219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1137219), _1137221)), -(_1137221 = c_Orderings_Obot__class_Obot(tc_fun(_1137219, tc_HOL_Obool))), 18714 ^ _777959 : [(18724 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137219), hAPP(c_Finite__Set_Ofold1(_1137219, c_Orderings_Oord__class_Omin(_1137219)), _1137221)), _1137223))), 18725 ^ _777959 : [(18726 ^ _777959) ^ [_1137608] : [hBOOL(hAPP(hAPP(c_member(_1137219), _1137608), _1137221)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137219), _1137608), _1137223))]]], (18715 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137219), hAPP(c_Finite__Set_Ofold1(_1137219, c_Orderings_Oord__class_Omin(_1137219)), _1137221)), _1137223)), 18719 ^ _777959 : [(18722 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137219), 18718 ^ [_1137219, _1137221, _1137223]), _1137223)))], (18720 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1137219), 18718 ^ [_1137219, _1137221, _1137223]), _1137221)))]]]]], (41962 ^ _777959) ^ [_1604546, _1604548, _1604550, _1604552, _1604554] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1604546, _1604548), _1604550), hAPP(hAPP(c_COMBS(_1604546, tc_fun(_1604548, tc_HOL_Obool), tc_fun(_1604548, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604548, tc_HOL_Obool), tc_fun(tc_fun(_1604548, tc_HOL_Obool), tc_fun(_1604548, tc_HOL_Obool)), _1604546), c_Groups_Ominus__class_Ominus(tc_fun(_1604548, tc_HOL_Obool))), _1604552)), _1604554)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1604546, _1604548), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1604546, _1604548), _1604550), _1604552)), hAPP(hAPP(c_Product__Type_OSigma(_1604546, _1604548), _1604550), _1604554)))], (13383 ^ _777959) ^ [_1022961, _1022963, _1022965, _1022967] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1022961, tc_fun(_1022963, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1022961, tc_HOL_Obool), _1022965)), _1022967) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1022961, tc_HOL_Obool), tc_fun(_1022963, tc_HOL_Obool)), _1022965), hAPP(hAPP(c_COMBC(tc_fun(_1022961, tc_HOL_Obool), tc_fun(_1022961, tc_fun(_1022963, tc_HOL_Obool)), tc_fun(_1022963, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1022961, tc_fun(_1022963, tc_HOL_Obool))), _1022967)))], (31971 ^ _777959) ^ [_1381549, _1381551, _1381553, _1381555, _1381557] : [c_Com_Ocom_OSemi(_1381549, _1381551) = c_Com_Ocom_OLocal(_1381553, _1381555, _1381557)], (10876 ^ _777959) ^ [_971179, _971181, _971183, _971185] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_971179), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971179), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971179), _971181), _971183)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971179), _971181), _971185))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971179), _971183), _971185)))], (1470 ^ _777959) ^ [_799058, _799060] : [-(class_Groups_Oordered__ab__semigroup__add(_799058)), _799060 = _799058, class_Groups_Oordered__ab__semigroup__add(_799060)], (33803 ^ _777959) ^ [_1414295, _1414297] : [class_Int_Onumber__ring(_1414295), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1414295), c_Groups_Oone__class_Oone(_1414295)), hAPP(c_Int_Onumber__class_Onumber__of(_1414295), _1414297)) = hAPP(c_Int_Onumber__class_Onumber__of(_1414295), 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), _1414297))))], (13579 ^ _777959) ^ [_1027405, _1027407, _1027409, _1027411, _1027413] : [_1027405 = c_Orderings_Obot__class_Obot(tc_fun(_1027407, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1027409, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1027407, tc_fun(_1027409, tc_HOL_Obool)), _1027405), _1027411)), _1027413) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1027409, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1027409, tc_HOL_Obool))), _1027413))], (21656 ^ _777959) ^ [_1189320, _1189322, _1189324] : [hBOOL(hAPP(_1189320, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1189322), _1189324))), 21659 ^ _777959 : [(21666 ^ _777959) ^ [_1189505] : [_1189322 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1189324), _1189505), -(hBOOL(hAPP(_1189320, _1189505)))], (21660 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189322), _1189324)), -(hBOOL(hAPP(_1189320, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (15218 ^ _777959) ^ [_1067999, _1068001] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1067999), _1068001))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068001), hAPP(c_Nat_OSuc, _1067999))))], (40095 ^ _777959) ^ [_1555052, _1555054, _1555056] : [class_Orderings_Olinorder(_1555052), hBOOL(hAPP(c_Finite__Set_Ofinite(_1555052), _1555054)), -(c_List_Olinorder__class_Osorted__list__of__set(_1555052, hAPP(hAPP(c_Set_Oinsert(_1555052), _1555056), _1555054)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1555052, _1555052, c_COMBI(_1555052)), _1555056), c_List_Olinorder__class_Osorted__list__of__set(_1555052, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1555052, tc_HOL_Obool)), _1555054), hAPP(hAPP(c_Set_Oinsert(_1555052), _1555056), c_Orderings_Obot__class_Obot(tc_fun(_1555052, tc_HOL_Obool)))))))], (25194 ^ _777959) ^ [_1255429, _1255431] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1255429), _1255431))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1255429), hAPP(c_Nat_OSuc, _1255431)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (8080 ^ _777959) ^ [_916316, _916318, _916320, _916322] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_916316), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916316, tc_HOL_Obool)), _916318), hAPP(hAPP(c_Set_Oinsert(_916316), _916320), _916322)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_916316), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916316, tc_HOL_Obool)), _916318), _916322))))], (35081 ^ _777959) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (2028 ^ _777959) ^ [_807448, _807450, _807452, _807454, _807456, _807458, _807460, _807462] : [-(c_SetInterval_Oord_OatLeastAtMost(_807462, _807458, _807454, _807450) = c_SetInterval_Oord_OatLeastAtMost(_807460, _807456, _807452, _807448)), _807462 = _807460, _807458 = _807456, _807454 = _807452, _807450 = _807448], (31070 ^ _777959) ^ [_1364895] : [class_Groups_Oordered__ab__group__add__abs(_1364895), -(hAPP(c_Groups_Oabs__class_Oabs(_1364895), c_Groups_Ozero__class_Ozero(_1364895)) = c_Groups_Ozero__class_Ozero(_1364895))], (42140 ^ _777959) ^ [_1608428, _1608430, _1608432] : [c_List_Olist_ONil(_1608428) = hAPP(hAPP(c_List_Olist_OCons(_1608428), _1608430), _1608432)], (11702 ^ _777959) ^ [_988431, _988433, _988435, _988437] : [-(_988431 = c_Orderings_Obot__class_Obot(tc_fun(_988433, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_988433, tc_fun(_988435, tc_HOL_Obool)), _988431), hAPP(c_COMBK(tc_fun(_988435, tc_HOL_Obool), _988433), _988437)) = _988437)], (42006 ^ _777959) ^ [_1605738, _1605740, _1605742, _1605744] : [_1605740 = c_List_Olist_ONil(_1605738), -(hAPP(hAPP(c_List_Olist__update(_1605738, _1605740), _1605742), _1605744) = c_List_Olist_ONil(_1605738))], (11429 ^ _777959) ^ [_981906, _981908, _981910] : [class_Lattices_Olattice(_981906), hBOOL(hAPP(c_Finite__Set_Ofinite(_981906), _981908)), hBOOL(hAPP(c_Finite__Set_Ofinite(_981906), _981910)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981906, tc_HOL_Obool)), _981908), _981910) = c_Orderings_Obot__class_Obot(tc_fun(_981906, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981906), c_Big__Operators_Olattice__class_OInf__fin(_981906, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_981906, tc_HOL_Obool)), _981908), _981910))), c_Big__Operators_Olattice__class_OInf__fin(_981906, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_981906, tc_HOL_Obool)), _981908), _981910))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981906), c_Big__Operators_Olattice__class_OInf__fin(_981906, _981908)), c_Big__Operators_Olattice__class_OInf__fin(_981906, _981910)))], (46704 ^ _777959) ^ [_1711697, _1711699, _1711701, _1711703, _1711705] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1711697, _1711699, _1711701), _1711703), _1711705) = hAPP(c_Set_OCollect(tc_prod(_1711697, _1711701)), hAPP(c_Product__Type_Oprod_Oprod__case(_1711697, _1711701, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1711701, tc_fun(_1711699, tc_HOL_Obool)), tc_fun(_1711701, tc_HOL_Obool), _1711697), hAPP(c_COMBB(tc_fun(_1711699, tc_HOL_Obool), tc_HOL_Obool, _1711701), c_HOL_OEx(_1711699))), hAPP(hAPP(c_COMBC(_1711697, tc_fun(_1711701, tc_fun(_1711699, tc_HOL_Obool)), tc_fun(_1711701, tc_fun(_1711699, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1711699, tc_HOL_Obool), tc_fun(_1711699, tc_HOL_Obool)), tc_fun(tc_fun(_1711701, tc_fun(_1711699, tc_HOL_Obool)), tc_fun(_1711701, tc_fun(_1711699, tc_HOL_Obool))), _1711697), c_COMBB(tc_fun(_1711699, tc_HOL_Obool), tc_fun(_1711699, tc_HOL_Obool), _1711701)), hAPP(hAPP(c_COMBB(tc_fun(_1711699, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1711699, tc_HOL_Obool), tc_fun(_1711699, tc_HOL_Obool)), _1711697), c_COMBS(_1711699, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711699, tc_HOL_Obool), tc_fun(_1711699, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1711697), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1711699), c_fconj)), hAPP(hAPP(c_COMBC(_1711697, tc_fun(tc_prod(_1711697, _1711699), tc_HOL_Obool), tc_fun(_1711699, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711699, tc_fun(tc_fun(tc_prod(_1711697, _1711699), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1711697, _1711699), tc_HOL_Obool), tc_fun(_1711699, tc_HOL_Obool)), _1711697), c_COMBC(_1711699, tc_fun(tc_prod(_1711697, _1711699), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711699, tc_prod(_1711697, _1711699)), tc_fun(_1711699, tc_fun(tc_fun(tc_prod(_1711697, _1711699), tc_HOL_Obool), tc_HOL_Obool)), _1711697), hAPP(c_COMBB(tc_prod(_1711697, _1711699), tc_fun(tc_fun(tc_prod(_1711697, _1711699), tc_HOL_Obool), tc_HOL_Obool), _1711699), c_member(tc_prod(_1711697, _1711699)))), c_Product__Type_OPair(_1711697, _1711699)))), _1711703))))), hAPP(hAPP(c_COMBC(_1711701, tc_fun(tc_prod(_1711699, _1711701), tc_HOL_Obool), tc_fun(_1711699, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711699, tc_fun(tc_fun(tc_prod(_1711699, _1711701), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1711699, _1711701), tc_HOL_Obool), tc_fun(_1711699, tc_HOL_Obool)), _1711701), c_COMBC(_1711699, tc_fun(tc_prod(_1711699, _1711701), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1711699, tc_prod(_1711699, _1711701)), tc_fun(_1711699, tc_fun(tc_fun(tc_prod(_1711699, _1711701), tc_HOL_Obool), tc_HOL_Obool)), _1711701), hAPP(c_COMBB(tc_prod(_1711699, _1711701), tc_fun(tc_fun(tc_prod(_1711699, _1711701), tc_HOL_Obool), tc_HOL_Obool), _1711699), c_member(tc_prod(_1711699, _1711701)))), hAPP(c_COMBC(_1711699, _1711701, tc_prod(_1711699, _1711701)), c_Product__Type_OPair(_1711699, _1711701))))), _1711705))))))], (20411 ^ _777959) ^ [_1167268, _1167270, _1167272] : [class_Rings_Olinordered__semiring__strict(_1167268), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167268), _1167270), c_Groups_Ozero__class_Ozero(_1167268))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167268), c_Groups_Ozero__class_Ozero(_1167268)), _1167272)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167268), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167268), _1167270), _1167272)), c_Groups_Ozero__class_Ozero(_1167268))))], (22886 ^ _777959) ^ [_1214449, _1214451, _1214453] : [class_Rings_Olinordered__semidom(_1214449), 22889 ^ _777959 : [(22896 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1214451), _1214453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214449), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1214449), _1214451)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1214449), _1214453))))], (22890 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214449), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1214449), _1214451)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1214449), _1214453))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1214451), _1214453)))]]], (2494 ^ _777959) ^ [_814921, _814923, _814925, _814927] : [-(c_Divides_Odivmod__int__rel(_814927, _814923) = c_Divides_Odivmod__int__rel(_814925, _814921)), _814927 = _814925, _814923 = _814921], (42622 ^ _777959) ^ [_1621551, _1621553, _1621555, _1621557, _1621559, _1621561] : [class_Groups_Ocomm__monoid__add(_1621551), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621553), _1621555)), 42632 ^ _777959 : [(42635 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1621557), hAPP(_1621559, 42631 ^ [_1621551, _1621553, _1621555, _1621557, _1621559, _1621561])))], (42633 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621553), 42631 ^ [_1621551, _1621553, _1621555, _1621557, _1621559, _1621561]), _1621555)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1621553, _1621551), hAPP(hAPP(c_COMBS(_1621553, tc_fun(_1621557, tc_HOL_Obool), _1621551), hAPP(hAPP(c_COMBB(tc_fun(_1621557, _1621551), tc_fun(tc_fun(_1621557, tc_HOL_Obool), _1621551), _1621553), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1621557, _1621551)), _1621561)), _1621559)), _1621555) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1621553, _1621557), _1621551), hAPP(c_Product__Type_Oprod_Oprod__case(_1621553, _1621557, _1621551), _1621561)), hAPP(hAPP(c_Product__Type_OSigma(_1621553, _1621557), _1621555), _1621559)))], (42891 ^ _777959) ^ [_1628109, _1628111] : [-(hAPP(hAPP(c_List_Oappend(_1628109), c_List_Olist_ONil(_1628109)), _1628111) = _1628111)], (40763 ^ _777959) ^ [_1570242, _1570244, _1570246, _1570248, _1570250, _1570252, _1570254] : [hBOOL(hAPP(hAPP(c_member(_1570242), _1570244), hAPP(c_List_Oset(_1570242), hAPP(hAPP(c_List_Otake(_1570242), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1570246)), _1570248)), _1570250)))), -(c_Map_Omap__upds(_1570242, _1570246, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1570242, tc_Option_Ooption(_1570246)), _1570252), _1570244), hAPP(c_Option_Ooption_OSome(_1570246), _1570254)), _1570250, _1570248) = c_Map_Omap__upds(_1570242, _1570246, _1570252, _1570250, _1570248))], (8504 ^ _777959) ^ [_925070, _925072, _925074] : [class_Orderings_Olinorder(_925070), -(_925072 = _925074), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925070), _925072), _925074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925070), _925074), _925072)))], (46633 ^ _777959) ^ [_1709684, _1709686, _1709688, _1709690, _1709692] : [-(c_List_Omaps(_1709684, _1709686, _1709688, hAPP(hAPP(c_List_Olist_OCons(_1709684), _1709690), _1709692)) = hAPP(hAPP(c_List_Oappend(_1709686), hAPP(_1709688, _1709690)), c_List_Omaps(_1709684, _1709686, _1709688, _1709692)))], (39436 ^ _777959) ^ [_1538787, _1538789, _1538791, _1538793, _1538795, _1538797, _1538799] : [c_Finite__Set_Ofolding__image(_1538787, _1538789, _1538791, _1538793, _1538795), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538789), _1538797)), -(hAPP(hAPP(_1538795, _1538799), _1538797) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1538787, _1538789, _1538791), _1538799), _1538793), _1538797))], (46124 ^ _777959) ^ [_1698412, _1698414, _1698416, _1698418] : [46126 ^ _777959 : [(46131 ^ _777959) ^ [] : [hBOOL(hAPP(_1698418, hAPP(hAPP(c_List_Onth(_1698414), _1698416), 46125 ^ [_1698412, _1698414, _1698416, _1698418])))], (46129 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46125 ^ [_1698412, _1698414, _1698416, _1698418]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698414)), _1698416))))], (46127 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46125 ^ [_1698412, _1698414, _1698416, _1698418]), _1698412)))]], 46134 ^ _777959 : [(46137 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1698418, hAPP(hAPP(c_List_Onth(_1698414), _1698416), _1698412))))], (46135 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1698412), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698414)), _1698416))))]], -(c_List_OtakeWhile(_1698414, _1698418, _1698416) = hAPP(hAPP(c_List_Otake(_1698414), _1698412), _1698416))], (43640 ^ _777959) ^ [_1645543, _1645545, _1645547, _1645549] : [-(hAPP(c_List_Ofoldl(_1645543, _1645545, _1645547, _1645549), c_List_Olist_ONil(_1645545)) = _1645549)], (15711 ^ _777959) ^ [_1076930, _1076932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1076930), _1076932)), 15714 ^ _777959 : [(15721 ^ _777959) ^ [] : [_1076932 = _1076930, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076932), hAPP(c_Nat_OSuc, _1076930))))], (15715 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076932), hAPP(c_Nat_OSuc, _1076930))), -(_1076932 = _1076930)]]], (16677 ^ _777959) ^ [_1097560, _1097562, _1097564, _1097566] : [class_Orderings_Olinorder(_1097560), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097560), _1097562), _1097564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097560), _1097562), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1097560), _1097566), _1097564))))], (47377 ^ _777959) ^ [_1729476, _1729478, _1729480, _1729482] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1729476, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1729476, _1729478), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1729476, _1729478), tc_HOL_Obool)), _1729480), _1729482))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1729476, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1729476, _1729478), _1729480)), hAPP(c_Relation_ODomain(_1729476, _1729478), _1729482)))))], (1620 ^ _777959) ^ [_800933, _800935] : [-(class_Groups_Osemigroup__add(_800933)), _800935 = _800933, class_Groups_Osemigroup__add(_800935)], (5066 ^ _777959) ^ [_855325, _855327, _855329, _855331, _855333, _855335] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_855335, _855331, _855327) = c_Lazy__Sequence_Olazy__sequence_OInsert(_855333, _855329, _855325)), _855335 = _855333, _855331 = _855329, _855327 = _855325], (17243 ^ _777959) ^ [_1107694, _1107696] : [class_Complete__Lattice_Ocomplete__lattice(_1107694), -(c_Complete__Lattice_OInf__class_OInf(_1107694, hAPP(hAPP(c_Set_Oinsert(_1107694), _1107696), c_Orderings_Obot__class_Obot(tc_fun(_1107694, tc_HOL_Obool)))) = _1107696)], (23631 ^ _777959) ^ [_1227494, _1227496, _1227498, _1227500] : [class_Groups_Ocomm__monoid__mult(_1227494), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1227494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227494), _1227496), _1227498)), _1227500) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227494), hAPP(hAPP(c_Power_Opower__class_Opower(_1227494), _1227496), _1227500)), hAPP(hAPP(c_Power_Opower__class_Opower(_1227494), _1227498), _1227500)))], (38965 ^ _777959) ^ [_1527752, _1527754, _1527756, _1527758, _1527760] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1527752), tc_List_Olist(_1527754), tc_List_Olist(_1527756), hAPP(c_List_Omap(_1527752, _1527754), _1527758)), hAPP(c_List_Omap(_1527756, _1527752), _1527760)) = hAPP(c_List_Omap(_1527756, _1527754), hAPP(c_Fun_Ocomp(_1527752, _1527754, _1527756, _1527758), _1527760)))], (51326 ^ _777959) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (50330 ^ _777959) ^ [_1798697, _1798699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1798697), _1798699)), -(c_Lazy__Sequence_Osmall__lazy_H(_1798697, _1798699) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (37040 ^ _777959) ^ [_1482514, _1482516, _1482518, _1482520] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1482514), _1482516)), 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)), _1482514), _1482518)), 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)), _1482516), _1482520)), 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)), _1482516), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1482518), _1482520))), c_FunDef_Omin__weak)))], (49042 ^ _777959) ^ [_1768774, _1768776, _1768778] : [-(hAPP(c_Relation_ODomain(_1768774, _1768776), hAPP(c_Relation_Oconverse(_1768776, _1768774), _1768778)) = hAPP(c_Relation_ORange(_1768776, _1768774), _1768778))], (25082 ^ _777959) ^ [_1253086, _1253088, _1253090, _1253092, _1253094] : [class_Groups_Oab__group__add(_1253086), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253088), _1253090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1253090), _1253092)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1253086), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1253086), _1253094), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1253088), _1253092))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1253086), _1253094), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1253088), _1253090))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1253086), _1253094), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1253090), _1253092)))], (12514 ^ _777959) ^ [_1005586, _1005588, _1005590, _1005592] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1005586, tc_HOL_Obool)), _1005588), _1005590)), hBOOL(hAPP(hAPP(c_member(_1005586), _1005592), _1005588)), -(hBOOL(hAPP(hAPP(c_member(_1005586), _1005592), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1005586, tc_HOL_Obool), _1005590))))], (46635 ^ _777959) ^ [_1709744, _1709746] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1709744)), _1709746)), 46641 ^ _777959 : [(46644 ^ _777959) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1709744), 46640 ^ [_1709744, _1709746]))], (46642 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709744)), 46640 ^ [_1709744, _1709746]), hAPP(c_List_Oset(tc_List_Olist(_1709744)), _1709746))))]], 46648 ^ _777959 : [(46652 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709744)), 46650 ^ [_1709744, _1709746]), hAPP(c_List_Oset(tc_List_Olist(_1709744)), _1709746))))], (46654 ^ _777959) ^ [] : [46647 ^ [_1709744, _1709746] = 46650 ^ [_1709744, _1709746]], (46656 ^ _777959) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1709744, tc_HOL_Obool)), hAPP(c_List_Oset(_1709744), 46647 ^ [_1709744, _1709746])), hAPP(c_List_Oset(_1709744), 46650 ^ [_1709744, _1709746])) = c_Orderings_Obot__class_Obot(tc_fun(_1709744, tc_HOL_Obool))], (46649 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1709744)), 46647 ^ [_1709744, _1709746]), hAPP(c_List_Oset(tc_List_Olist(_1709744)), _1709746))))]], -(hBOOL(hAPP(c_List_Odistinct(_1709744), c_List_Oconcat(_1709744, _1709746))))], (32985 ^ _777959) ^ [_1400923] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1400923) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400923)))], (12351 ^ _777959) ^ [_1002258, _1002260] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002258), _1002260))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1002260), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002258), _1002260)) = _1002258)], (40707 ^ _777959) ^ [_1568917, _1568919] : [-(c_Hilbert__Choice_OEps(_1568917, hAPP(c_fequal, _1568919)) = _1568919)], (9320 ^ _777959) ^ [_938140, _938142, _938144] : [class_Lattices_Olattice(_938140), hBOOL(hAPP(c_Finite__Set_Ofinite(_938140), _938142)), -(_938144 = c_Orderings_Obot__class_Obot(tc_fun(_938140, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938140, tc_HOL_Obool)), _938144), _938142)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938140), c_Big__Operators_Olattice__class_OSup__fin(_938140, _938144)), c_Big__Operators_Olattice__class_OSup__fin(_938140, _938142)) = c_Big__Operators_Olattice__class_OSup__fin(_938140, _938142))], (27419 ^ _777959) ^ [_1296602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1296602)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1296602)) = _1296602)], (34801 ^ _777959) ^ [_1432850, _1432852] : [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), _1432850))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1432852))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1432850))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1432852)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1432850)))], (51278 ^ _777959) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (19779 ^ _777959) ^ [_1155781, _1155783, _1155785] : [class_Groups_Oordered__comm__monoid__add(_1155781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155781), c_Groups_Ozero__class_Ozero(_1155781)), _1155783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155781), c_Groups_Ozero__class_Ozero(_1155781)), _1155785)), 19790 ^ _777959 : [(19799 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155781), _1155783), _1155785) = c_Groups_Ozero__class_Ozero(_1155781)), _1155783 = c_Groups_Ozero__class_Ozero(_1155781), _1155785 = c_Groups_Ozero__class_Ozero(_1155781)], (19791 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155781), _1155783), _1155785) = c_Groups_Ozero__class_Ozero(_1155781), 19794 ^ _777959 : [(19797 ^ _777959) ^ [] : [-(_1155785 = c_Groups_Ozero__class_Ozero(_1155781))], (19795 ^ _777959) ^ [] : [-(_1155783 = c_Groups_Ozero__class_Ozero(_1155781))]]]]], (24948 ^ _777959) ^ [_1250874, _1250876, _1250878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250874)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250876)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1250876), _1250878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1250874), _1250878)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1250874), _1250876))))], (6269 ^ _777959) ^ [_879053, _879055, _879057] : [_879053 = _879055, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879057, tc_HOL_Obool)), _879053), _879055)))], (35067 ^ _777959) ^ [_1437891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1437891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1437891))))], (15705 ^ _777959) ^ [_1076827, _1076829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1076827)), _1076829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076827), _1076829)))], (25216 ^ _777959) ^ [_1255811, _1255813, _1255815, _1255817] : [_1255811 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255813), _1255815)), _1255817), -(_1255813 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1255811), _1255813) = _1255815), 25223 ^ _777959 : [(25226 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255817), _1255813))], (25224 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255813)))]], 25231 ^ _777959 : [(25234 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255813), _1255817)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1255817), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (25232 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1255813))]]], (48346 ^ _777959) ^ [_1750849] : [-(hAPP(c_Code__Numeral_Onat__of, _1750849) = c_Code__Numeral_Onat__of__aux(_1750849, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (42588 ^ _777959) ^ [_1620587, _1620589, _1620591, _1620593] : [-(c_Fun_Oinj__on(_1620587, tc_prod(_1620589, _1620587), 42586 ^ [_1620587, _1620589, _1620591, _1620593], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1620589, tc_fun(_1620587, tc_HOL_Obool)), _1620591), _1620593)))], (33429 ^ _777959) ^ [_1408178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1408178))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1408178)))], (38240 ^ _777959) ^ [_1510499, _1510501, _1510503, _1510505, _1510507] : [c_Fun_Oinj__on(_1510499, _1510501, _1510503, c_Orderings_Otop__class_Otop(tc_fun(_1510499, tc_HOL_Obool))), 38243 ^ _777959 : [(38250 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510499, tc_HOL_Obool)), _1510505), _1510507)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510501, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1510499, _1510501, _1510503), _1510505)), hAPP(c_Set_Oimage(_1510499, _1510501, _1510503), _1510507))))], (38244 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510501, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1510499, _1510501, _1510503), _1510505)), hAPP(c_Set_Oimage(_1510499, _1510501, _1510503), _1510507))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510499, tc_HOL_Obool)), _1510505), _1510507)))]]], (1100 ^ _777959) ^ [_794433, _794435] : [-(class_Rings_Oordered__ring__abs(_794433)), _794435 = _794433, class_Rings_Oordered__ring__abs(_794435)], (16425 ^ _777959) ^ [_1092375, _1092377, _1092379] : [class_Orderings_Olinorder(_1092375), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1092375), _1092377), _1092379) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1092375), _1092379), _1092377))], (49044 ^ _777959) ^ [_1768819, _1768821, _1768823] : [-(hAPP(c_Relation_ORange(_1768819, _1768821), _1768823) = hAPP(c_Relation_ODomain(_1768821, _1768819), hAPP(c_Relation_Oconverse(_1768819, _1768821), _1768823)))], (43213 ^ _777959) ^ [_1635927, _1635929] : [_1635929 = c_List_Olist_ONil(_1635927), -(hAPP(c_List_Orotate1(_1635927), _1635929) = c_List_Olist_ONil(_1635927))], (5946 ^ _777959) ^ [_872808, _872810, _872812] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_872808, _872810, _872812))), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _872810))))], (43242 ^ _777959) ^ [_1636517, _1636519, _1636521, _1636523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1636517), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636519)), _1636521))), -(hAPP(hAPP(c_List_Olist__update(_1636519, _1636521), _1636517), _1636523) = hAPP(hAPP(c_List_Oappend(_1636519), hAPP(hAPP(c_List_Otake(_1636519), _1636517), _1636521)), hAPP(hAPP(c_List_Olist_OCons(_1636519), _1636523), hAPP(hAPP(c_List_Odrop(_1636519), hAPP(c_Nat_OSuc, _1636517)), _1636521))))], (41352 ^ _777959) ^ [_1588039, _1588041, _1588043, _1588045] : [_1588039 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588041)), _1588043)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1588041, hAPP(hAPP(c_List_Olist__update(_1588041, _1588043), _1588039), _1588045)) = c_List_Obutlast(_1588041, _1588043))], (14037 ^ _777959) ^ [_1038621, _1038623] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038621, tc_HOL_Obool)), _1038623) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1038621, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1038621, tc_HOL_Obool))), _1038623))], (39822 ^ _777959) ^ [_1547691, _1547693] : [-(hAPP(hAPP(c_List_Ozip(_1547691, _1547691), _1547693), _1547693) = hAPP(hAPP(c_List_Omap(_1547691, tc_prod(_1547691, _1547691)), hAPP(hAPP(c_COMBS(_1547691, _1547691, tc_prod(_1547691, _1547691)), c_Product__Type_OPair(_1547691, _1547691)), c_COMBI(_1547691))), _1547693))], (5390 ^ _777959) ^ [_860397, _860399, _860401, _860403] : [-(c_List_Omap(_860403, _860399) = c_List_Omap(_860401, _860397)), _860403 = _860401, _860399 = _860397], (22106 ^ _777959) ^ [_1198580] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1198580), c_Orderings_Otop__class_Otop(tc_fun(_1198580, 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(_1198580), c_Orderings_Otop__class_Otop(tc_fun(_1198580, tc_HOL_Obool))))))], (50876 ^ _777959) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (13523 ^ _777959) ^ [_1026151, _1026153] : [-(hBOOL(hAPP(_1026153, 13524 ^ [_1026151, _1026153]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1026151, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1026151), _1026153))], (12846 ^ _777959) ^ [_1011063, _1011065, _1011067] : [class_Groups_Oab__group__add(_1011063), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1011063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011063), _1011065), _1011067)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1011063), hAPP(c_Groups_Ouminus__class_Ouminus(_1011063), _1011065)), hAPP(c_Groups_Ouminus__class_Ouminus(_1011063), _1011067)))], (47437 ^ _777959) ^ [_1731304] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1731304), c_Int_OInteg)), -(_1731304 = hAPP(c_Int_ORep__Integ, 47440 ^ [_1731304]))], (21620 ^ _777959) ^ [_1188734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188734)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1188734), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1188734)], (37132 ^ _777959) ^ [_1484174, _1484176] : [-(c_FunDef_Orp__inv__image(_1484174, _1484176) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1484174, _1484174), tc_HOL_Obool), tc_fun(tc_prod(_1484174, _1484174), tc_HOL_Obool), tc_fun(tc_fun(_1484176, _1484174), tc_prod(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1484174, _1484174), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1484174, _1484174), tc_HOL_Obool), tc_fun(tc_fun(_1484176, _1484174), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1484174, _1484174), tc_HOL_Obool), tc_fun(tc_fun(_1484176, _1484174), tc_prod(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1484176, _1484174), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool)), tc_fun(tc_fun(_1484176, _1484174), tc_prod(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1484174, _1484174), tc_HOL_Obool), tc_fun(tc_fun(_1484176, _1484174), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1484174, _1484174), tc_HOL_Obool), tc_fun(tc_fun(_1484176, _1484174), tc_prod(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool))))), tc_fun(tc_prod(_1484174, _1484174), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1484176, _1484174), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool)), tc_fun(tc_fun(_1484176, _1484174), tc_prod(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool))), tc_fun(tc_prod(_1484174, _1484174), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1484176, _1484174), tc_fun(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1484176, _1484174), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool)), tc_fun(tc_fun(_1484176, _1484174), tc_prod(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool)))), tc_fun(tc_prod(_1484174, _1484174), tc_HOL_Obool)), c_COMBS(tc_fun(_1484176, _1484174), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1484176, _1484174), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool)), tc_fun(tc_fun(_1484176, _1484174), tc_fun(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool)))), tc_fun(tc_prod(_1484174, _1484174), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool))), tc_fun(_1484176, _1484174)), c_Product__Type_OPair(tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool), tc_fun(tc_prod(_1484176, _1484176), tc_HOL_Obool)))), c_Relation_Oinv__image(_1484174, _1484176))))), c_Relation_Oinv__image(_1484174, _1484176))))], (8998 ^ _777959) ^ [_932688, _932690, _932692] : [class_Orderings_Olinorder(_932688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932688), _932690), _932692)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932688), _932692), _932690))], (35834 ^ _777959) ^ [_1457723, _1457725, _1457727, _1457729, _1457731] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1457723, _1457725, tc_HOL_Obool), _1457727), hAPP(hAPP(c_Product__Type_OPair(_1457723, _1457725), _1457729), _1457731))), -(hBOOL(hAPP(hAPP(_1457727, _1457729), _1457731)))], (47362 ^ _777959) ^ [_1729088, _1729090, _1729092, _1729094] : [hBOOL(hAPP(hAPP(c_member(_1729088), _1729090), hAPP(c_Relation_ODomain(_1729088, _1729092), _1729094))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1729088, _1729092)), hAPP(hAPP(c_Product__Type_OPair(_1729088, _1729092), _1729090), 47365 ^ [_1729088, _1729090, _1729092, _1729094])), _1729094)))], (29294 ^ _777959) ^ [_1330284, _1330286, _1330288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330284)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1330286), _1330288)), 29301 ^ _777959 : [(29302 ^ _777959) ^ [_1330474] : [29304 ^ _777959 : [(29310 ^ _777959) ^ [] : [-(_1330474 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 29306 ^ [_1330284, _1330286, _1330288, _1330474]), 29303 ^ [_1330284, _1330286, _1330288, _1330474]))], (29308 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29306 ^ [_1330284, _1330286, _1330288, _1330474]), _1330288)))], (29305 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29303 ^ [_1330284, _1330286, _1330288, _1330474]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1330284))))]], -(_1330474 = _1330286), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1330474), _1330284) = _1330286]]], (34171 ^ _777959) ^ [_1421408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421408), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1421408)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8248 ^ _777959) ^ [_920236, _920238, _920240] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_920236, tc_HOL_Obool)), _920238), hAPP(hAPP(c_Set_Oinsert(_920236), _920240), c_Orderings_Obot__class_Obot(tc_fun(_920236, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_920236, _920240, _920238) = c_HOL_OThe(_920236, hAPP(hAPP(c_COMBC(_920236, tc_fun(_920236, tc_HOL_Obool), tc_HOL_Obool), c_member(_920236)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920236, tc_HOL_Obool)), _920238), hAPP(hAPP(c_Set_Oinsert(_920236), _920240), c_Orderings_Obot__class_Obot(tc_fun(_920236, tc_HOL_Obool)))))))], (40212 ^ _777959) ^ [_1557778, _1557780, _1557782, _1557784, _1557786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1557778), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1557780)), _1557782))), -(hAPP(hAPP(c_List_Onth(_1557784), hAPP(hAPP(c_List_Omap(_1557780, _1557784), _1557786), _1557782)), _1557778) = hAPP(_1557786, hAPP(hAPP(c_List_Onth(_1557780), _1557782), _1557778)))], (23793 ^ _777959) ^ [_1230365, _1230367, _1230369, _1230371] : [class_Groups_Omonoid__mult(_1230365), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1230365), _1230367), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1230369), _1230371)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230365), hAPP(hAPP(c_Power_Opower__class_Opower(_1230365), _1230367), _1230369)), hAPP(hAPP(c_Power_Opower__class_Opower(_1230365), _1230367), _1230371)))], (34255 ^ _777959) ^ [_1422855, _1422857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422855), _1422857)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1422855)), c_Int_OBit0(_1422857))))], (21752 ^ _777959) ^ [_1191086, _1191088, _1191090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1191086), _1191088)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1191090), _1191088))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1191088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1191086), _1191090)))], (4236 ^ _777959) ^ [_842088, _842090, _842092, _842094] : [-(c_Transitive__Closure_Ortrancl(_842094, _842090) = c_Transitive__Closure_Ortrancl(_842092, _842088)), _842094 = _842092, _842090 = _842088], (13657 ^ _777959) ^ [_1029629, _1029631, _1029633, _1029635, _1029637] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029629, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029631, tc_fun(_1029629, tc_HOL_Obool)), _1029633), _1029635)), _1029637) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029631, tc_fun(_1029629, tc_HOL_Obool)), _1029633), hAPP(hAPP(c_COMBC(_1029631, tc_fun(_1029629, tc_HOL_Obool), tc_fun(_1029629, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1029629, tc_HOL_Obool), tc_fun(tc_fun(_1029629, tc_HOL_Obool), tc_fun(_1029629, tc_HOL_Obool)), _1029631), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029629, tc_HOL_Obool))), _1029635)), _1029637)))], (44801 ^ _777959) ^ [_1669112, _1669114, _1669116] : [_1669114 = hAPP(hAPP(c_List_Olist_OCons(_1669112), _1669116), c_List_Olist_ONil(_1669112)), -(hAPP(c_List_Orev(_1669112), _1669114) = hAPP(hAPP(c_List_Olist_OCons(_1669112), _1669116), c_List_Olist_ONil(_1669112)))], (4418 ^ _777959) ^ [_844831, _844833] : [_844833 = _844831, -(c_Nitpick_Onum(_844833) = c_Nitpick_Onum(_844831))], (33279 ^ _777959) ^ [_1405831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1405831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1405831))))], (14800 ^ _777959) ^ [_1056088, _1056090, _1056092, _1056094, _1056096, _1056098] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1056088), _1056090)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056092), _1056094)), 14810 ^ _777959 : [(14813 ^ _777959) ^ [] : [hAPP(c_Finite__Set_Ocard(_1056088), hAPP(c_Set_OCollect(_1056088), hAPP(hAPP(c_COMBS(_1056088, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1056088), c_fconj), hAPP(hAPP(c_COMBC(_1056088, tc_fun(_1056088, tc_HOL_Obool), tc_HOL_Obool), c_member(_1056088)), _1056090))), hAPP(hAPP(c_COMBC(_1056088, _1056092, tc_HOL_Obool), _1056096), 14809 ^ [_1056088, _1056090, _1056092, _1056094, _1056096, _1056098])))) = hAPP(_1056098, 14809 ^ [_1056088, _1056090, _1056092, _1056094, _1056096, _1056098])], (14811 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1056092), 14809 ^ [_1056088, _1056090, _1056092, _1056094, _1056096, _1056098]), _1056094)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1056088, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1056092, tc_HOL_Obool), tc_Nat_Onat, _1056088), c_Finite__Set_Ocard(_1056092)), hAPP(hAPP(c_COMBB(tc_fun(_1056092, tc_HOL_Obool), tc_fun(_1056092, tc_HOL_Obool), _1056088), c_Set_OCollect(_1056092)), hAPP(hAPP(c_COMBB(tc_fun(_1056092, tc_HOL_Obool), tc_fun(_1056092, tc_HOL_Obool), _1056088), hAPP(c_COMBS(_1056092, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1056092), c_fconj), hAPP(hAPP(c_COMBC(_1056092, tc_fun(_1056092, tc_HOL_Obool), tc_HOL_Obool), c_member(_1056092)), _1056094)))), _1056096)))), _1056090) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1056092, tc_Nat_Onat), _1056098), _1056094))], (48334 ^ _777959) ^ [_1750633, _1750635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1750633), _1750635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1750633)), hAPP(c_Code__Numeral_Onat__of, _1750635))))], (23435 ^ _777959) ^ [_1224219, _1224221] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224219), _1224221) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224221), _1224219))], (40711 ^ _777959) ^ [_1569001, _1569003] : [hBOOL(hAPP(_1569001, c_Hilbert__Choice_OEps(_1569003, _1569001))), -(hBOOL(hAPP(_1569001, 40714 ^ [_1569001, _1569003])))], (46210 ^ _777959) ^ [_1700465, _1700467, _1700469] : [46212 ^ _777959 : [(46215 ^ _777959) ^ [] : [hBOOL(hAPP(_1700467, 46211 ^ [_1700465, _1700467, _1700469]))], (46213 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1700465), 46211 ^ [_1700465, _1700467, _1700469]), hAPP(c_List_Oset(_1700465), _1700469))))]], -(hBOOL(hAPP(c_List_Olistsp(_1700465, _1700467), _1700469)))], (32893 ^ _777959) ^ [_1399277, _1399279] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399277)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399279)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1399277), _1399279)))], (48749 ^ _777959) ^ [_1761147, _1761149] : [-(hAPP(c_Relation_OImage(_1761147, _1761147, c_Relation_OId(_1761147)), _1761149) = _1761149)], (38698 ^ _777959) ^ [_1520637, _1520639, _1520641] : [c_Fun_Oinj__on(_1520637, _1520639, _1520641, c_Orderings_Otop__class_Otop(tc_fun(_1520637, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1520637), tc_List_Olist(_1520639), hAPP(c_List_Omap(_1520637, _1520639), _1520641), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1520637), tc_HOL_Obool))))], (51092 ^ _777959) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (16545 ^ _777959) ^ [_1095091, _1095093] : [class_Orderings_Olinorder(_1095091), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095091), _1095093), _1095093) = _1095093)], (38870 ^ _777959) ^ [_1524664, _1524666, _1524668, _1524670] : [-(hBOOL(hAPP(hAPP(c_member(_1524664), _1524666), _1524668))), -(hAPP(c_Set_Ovimage(_1524670, _1524664, hAPP(c_COMBK(_1524664, _1524670), _1524666)), _1524668) = c_Orderings_Obot__class_Obot(tc_fun(_1524670, tc_HOL_Obool)))], (40558 ^ _777959) ^ [_1565434, _1565436, _1565438, _1565440, _1565442] : [class_Rings_Osemiring__0(_1565434), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1565434), hAPP(hAPP(c_List_Omap(_1565436, _1565434), hAPP(hAPP(c_COMBC(_1565436, _1565434, _1565434), hAPP(hAPP(c_COMBB(_1565434, tc_fun(_1565434, _1565434), _1565436), c_Groups_Otimes__class_Otimes(_1565434)), _1565438)), _1565440)), _1565442)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1565434), hAPP(c_List_Omonoid__add__class_Olistsum(_1565434), hAPP(hAPP(c_List_Omap(_1565436, _1565434), _1565438), _1565442))), _1565440))], (33215 ^ _777959) ^ [_1404918, _1404920] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1404918)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404920)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1404920))), 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), _1404918)), c_Int_Onat)))))], (34945 ^ _777959) ^ [_1436049, _1436051] : [class_Int_Onumber__ring(_1436049), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1436049), hAPP(c_Int_Onumber__class_Onumber__of(_1436049), 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)))), _1436051))) = hAPP(c_Int_Onumber__class_Onumber__of(_1436049), c_Int_OMin))], (36874 ^ _777959) ^ [_1477665] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1477665)], (3550 ^ _777959) ^ [_831507, _831509, _831511, _831513, _831515, _831517, _831519, _831521] : [-(c_List_Omaps(_831521, _831517, _831513, _831509) = c_List_Omaps(_831519, _831515, _831511, _831507)), _831521 = _831519, _831517 = _831515, _831513 = _831511, _831509 = _831507], (27517 ^ _777959) ^ [_1298175, _1298177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298175)), 27520 ^ _777959 : [(27527 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1298175), _1298177)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1298175)), hAPP(c_Int_Onat, _1298177))))], (27521 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1298175)), hAPP(c_Int_Onat, _1298177))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1298175), _1298177)))]]], (41603 ^ _777959) ^ [_1593869, _1593871, _1593873, _1593875] : [-(_1593869 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1593871), hAPP(hAPP(c_List_Olist_OCons(_1593871), _1593873), _1593875)), _1593869) = hAPP(hAPP(c_List_Onth(_1593871), _1593875), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1593869), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (12335 ^ _777959) ^ [_1001913, _1001915] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001913), _1001915)), _1001913)))], (44577 ^ _777959) ^ [_1663919, _1663921, _1663923, _1663925] : [class_Groups_Ocomm__monoid__add(_1663919), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1663919), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1663919), _1663921), c_List_Oupt(_1663923, _1663925))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1663919), _1663921), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1663923, _1663925))))], (4582 ^ _777959) ^ [_847409, _847411, _847413, _847415, _847417, _847419] : [-(c_Lazy__Sequence_Oanamorph(_847419, _847415, _847411) = c_Lazy__Sequence_Oanamorph(_847417, _847413, _847409)), _847419 = _847417, _847415 = _847413, _847411 = _847409], (33043 ^ _777959) ^ [_1402015, _1402017] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1402015) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402017), 33046 ^ _777959 : [(33049 ^ _777959) ^ [] : [-(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), _1402017))))], (33047 ^ _777959) ^ [] : [-(_1402015 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402017)))]]], (16615 ^ _777959) ^ [_1096469, _1096471, _1096473, _1096475, _1096477] : [class_Orderings_Olinorder(_1096469), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096469), _1096471), _1096473)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096469), _1096475), _1096477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096469), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1096469), _1096471), _1096475)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1096469), _1096473), _1096477))))], (48883 ^ _777959) ^ [_1764556] : [-(c_Relation_OId(_1764556) = hAPP(c_Set_OCollect(tc_prod(_1764556, _1764556)), hAPP(hAPP(c_COMBB(tc_fun(_1764556, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1764556, _1764556)), c_HOL_OEx(_1764556)), hAPP(hAPP(c_COMBC(tc_prod(_1764556, _1764556), tc_fun(_1764556, tc_prod(_1764556, _1764556)), tc_fun(_1764556, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1764556, _1764556), tc_HOL_Obool), tc_fun(tc_fun(_1764556, tc_prod(_1764556, _1764556)), tc_fun(_1764556, tc_HOL_Obool)), tc_prod(_1764556, _1764556)), c_COMBB(tc_prod(_1764556, _1764556), tc_HOL_Obool, _1764556)), c_fequal)), hAPP(hAPP(c_COMBS(_1764556, _1764556, tc_prod(_1764556, _1764556)), c_Product__Type_OPair(_1764556, _1764556)), c_COMBI(_1764556))))))], (11615 ^ _777959) ^ [_986132, _986134, _986136, _986138, _986140] : [11617 ^ _777959 : [(11623 ^ _777959) ^ [] : [hBOOL(hAPP(_986140, 11619 ^ [_986132, _986134, _986136, _986138, _986140]))], (11621 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_986132), 11619 ^ [_986132, _986134, _986136, _986138, _986140]), hAPP(_986138, 11616 ^ [_986132, _986134, _986136, _986138, _986140]))))], (11618 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_986134), 11616 ^ [_986132, _986134, _986136, _986138, _986140]), _986136)))]], 11624 ^ _777959 : [(11625 ^ _777959) ^ [_986442] : [hBOOL(hAPP(hAPP(c_member(_986132), _986442), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986134, tc_fun(_986132, tc_HOL_Obool)), _986136), _986138))), -(hBOOL(hAPP(_986140, _986442)))]]], (42387 ^ _777959) ^ [_1614958, _1614960, _1614962, _1614964] : [-(hAPP(hAPP(c_List_Otake(_1614958), _1614960), hAPP(hAPP(c_List_Olist_OCons(_1614958), _1614962), _1614964)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1614958), c_List_Olist_ONil(_1614958), hAPP(hAPP(c_COMBB(tc_List_Olist(_1614958), tc_List_Olist(_1614958), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1614958), _1614962)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1614958), tc_List_Olist(_1614958)), c_List_Otake(_1614958)), _1614964)), _1614960))], (48998 ^ _777959) ^ [_1767735, _1767737, _1767739, _1767741, _1767743] : [-(hAPP(c_Relation_Oconverse(_1767735, _1767737), hAPP(hAPP(c_Relation_Orel__comp(_1767735, _1767739, _1767737), _1767741), _1767743)) = hAPP(hAPP(c_Relation_Orel__comp(_1767737, _1767739, _1767735), hAPP(c_Relation_Oconverse(_1767739, _1767737), _1767743)), hAPP(c_Relation_Oconverse(_1767735, _1767739), _1767741)))], (38110 ^ _777959) ^ [_1507924, _1507926, _1507928, _1507930] : [c_Fun_Oinj__on(_1507924, _1507926, _1507928, c_Orderings_Otop__class_Otop(tc_fun(_1507924, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1507924, tc_fun(_1507930, _1507926), hAPP(hAPP(c_COMBB(_1507926, tc_fun(_1507930, _1507926), _1507924), c_COMBK(_1507926, _1507930)), _1507928), c_Orderings_Otop__class_Otop(tc_fun(_1507924, tc_HOL_Obool))))], (29074 ^ _777959) ^ [_1325855, _1325857, _1325859] : [class_Orderings_Olinorder(_1325855), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1325855), _1325857), _1325859)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325855, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1325855, _1325857), _1325859)), hAPP(c_SetInterval_Oord__class_OatLeast(_1325855), _1325859)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1325855), _1325857))], (50618 ^ _777959) ^ [_1804761, _1804763, _1804765] : [_1804763 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1804761, _1804763, _1804765) = c_List_Olist_ONil(_1804761))], (29032 ^ _777959) ^ [_1325062, _1325064] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1325062), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1325064), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1325062, _1325064))], (4036 ^ _777959) ^ [_839098, _839100] : [_839100 = _839098, -(c_Lazy__Sequence_Ohb__not__seq(_839100) = c_Lazy__Sequence_Ohb__not__seq(_839098))], (33925 ^ _777959) ^ [_1417173, _1417175] : [class_Int_Onumber__ring(_1417173), 33928 ^ _777959 : [(33935 ^ _777959) ^ [] : [c_Int_Oiszero(_1417173, hAPP(c_Int_Onumber__class_Onumber__of(_1417173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1417175), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1417173), _1417175) = c_Groups_Oone__class_Oone(_1417173))], (33929 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1417173), _1417175) = c_Groups_Oone__class_Oone(_1417173), -(c_Int_Oiszero(_1417173, hAPP(c_Int_Onumber__class_Onumber__of(_1417173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1417175), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))]]], (38416 ^ _777959) ^ [_1514517, _1514519, _1514521, _1514523, _1514525] : [c_Fun_Oinj__on(_1514517, _1514519, _1514521, _1514523), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1514519, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1514517, _1514519, _1514521), _1514523)), _1514525)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514519), _1514525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1514517), _1514523)), hAPP(c_Finite__Set_Ocard(_1514519), _1514525))))], (33115 ^ _777959) ^ [_1403264, _1403266, _1403268] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403264)))), 33118 ^ _777959 : [(33125 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403266)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403264)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403266)), _1403268)) = 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), _1403264), _1403266))), _1403268))], (33119 ^ _777959) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403266))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403264)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403266)), _1403268)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403264)), _1403268))]]], (43520 ^ _777959) ^ [_1642880, _1642882, _1642884, _1642886, _1642888] : [-(hAPP(c_List_Orotate(_1642880, _1642882), hAPP(hAPP(c_List_Omap(_1642884, _1642880), _1642886), _1642888)) = hAPP(hAPP(c_List_Omap(_1642884, _1642880), _1642886), hAPP(c_List_Orotate(_1642884, _1642882), _1642888)))], (23479 ^ _777959) ^ [_1224931, _1224933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1224931), _1224933)), 23482 ^ _777959 : [(23485 ^ _777959) ^ [] : [_1224931 = _1224933], (23483 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224931), _1224933)))]]], (48531 ^ _777959) ^ [_1755688, _1755690, _1755692] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1755688, _1755688)), hAPP(hAPP(c_Product__Type_OPair(_1755688, _1755688), _1755690), _1755690)), c_Transitive__Closure_Ortrancl(_1755688, _1755692))))], (6822 ^ _777959) ^ [_889117, _889119, _889121, _889123, _889125] : [hBOOL(hAPP(hAPP(c_member(_889117), _889119), _889121)), -(hBOOL(hAPP(hAPP(c_member(_889123), hAPP(_889125, _889119)), hAPP(c_Set_Oimage(_889117, _889123, _889125), _889121))))], (46990 ^ _777959) ^ [_1720090] : [-(c_Wellfounded_Owf(tc_fun(_1720090, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1720090)))], (28678 ^ _777959) ^ [_1318222, _1318224, _1318226, _1318228, _1318230] : [class_Orderings_Olinorder(_1318222), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318222, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1318222, _1318224, _1318226)), c_SetInterval_Oord__class_OatLeastAtMost(_1318222, _1318228, _1318230)) = c_SetInterval_Oord__class_OatLeastAtMost(_1318222, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1318222), _1318224), _1318228), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318222), _1318226), _1318230)))], (15374 ^ _777959) ^ [_1070413, _1070415] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1070413)), _1070415) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070413), hAPP(c_Nat_OSuc, _1070415)))], (17713 ^ _777959) ^ [_1116428, _1116430, _1116432] : [class_Orderings_Olinorder(_1116428), hBOOL(hAPP(c_Finite__Set_Ofinite(_1116428), _1116430)), -(hBOOL(hAPP(hAPP(c_member(_1116428), _1116432), _1116430))), -(c_Big__Operators_Olinorder__class_OMax(_1116428, hAPP(hAPP(c_Set_Oinsert(_1116428), _1116432), _1116430)) = hAPP(hAPP(c_Finite__Set_Ofold(_1116428, _1116428, c_Orderings_Oord__class_Omax(_1116428)), _1116432), _1116430))], (39546 ^ _777959) ^ [_1541721, _1541723, _1541725, _1541727] : [hBOOL(hAPP(c_List_Odistinct(_1541721), hAPP(hAPP(c_List_Omap(_1541723, _1541721), _1541725), _1541727))), 39549 ^ _777959 : [(39552 ^ _777959) ^ [] : [-(c_Fun_Oinj__on(_1541723, _1541721, _1541725, hAPP(c_List_Oset(_1541723), _1541727)))], (39550 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1541723), _1541727)))]]], (26624 ^ _777959) ^ [_1282192, _1282194, _1282196, _1282198] : [class_Fields_Olinordered__field__inverse__zero(_1282192), 26627 ^ _777959 : [(26628 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1282192), _1282194), _1282196)), _1282198)), 26631 ^ _777959 : [(26638 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), c_Groups_Ozero__class_Ozero(_1282192)), _1282196))), 26641 ^ _777959 : [(26648 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), _1282196), c_Groups_Ozero__class_Ozero(_1282192)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), c_Groups_Ozero__class_Ozero(_1282192)), _1282198)))], (26642 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), _1282196), c_Groups_Ozero__class_Ozero(_1282192))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282192), _1282198), _1282196)), _1282194)))]]], (26632 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), c_Groups_Ozero__class_Ozero(_1282192)), _1282196)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), _1282194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282192), _1282198), _1282196))))]]], (26654 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1282192), _1282194), _1282196)), _1282198))), 26657 ^ _777959 : [(26660 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), _1282194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282192), _1282198), _1282196)))], (26658 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), c_Groups_Ozero__class_Ozero(_1282192)), _1282196)))]], 26661 ^ _777959 : [(26664 ^ _777959) ^ [] : [26665 ^ _777959 : [(26668 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1282192), _1282198), _1282196)), _1282194))], (26666 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), _1282196), c_Groups_Ozero__class_Ozero(_1282192))))]], 26669 ^ _777959 : [(26672 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), c_Groups_Ozero__class_Ozero(_1282192)), _1282198))], (26670 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), _1282196), c_Groups_Ozero__class_Ozero(_1282192)))]]], (26662 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1282192), c_Groups_Ozero__class_Ozero(_1282192)), _1282196))]]]]], (45574 ^ _777959) ^ [_1687116, _1687118, _1687120] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1687116), tc_List_Olist(_1687116)), c_List_Opartition(_1687116, _1687118, _1687120)) = hAPP(c_List_Ofilter(_1687116, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1687116, c_fNot), _1687118)), _1687120))], (50912 ^ _777959) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (49947 ^ _777959) ^ [_1790783, _1790785, _1790787] : [c_List_Olist__ex1(_1790783, _1790785, _1790787), 49951 ^ _777959 : [(49956 ^ _777959) ^ [_1791029] : [-(_1791029 = 49950 ^ [_1790783, _1790785, _1790787]), hBOOL(hAPP(hAPP(c_member(_1790783), _1791029), hAPP(c_List_Oset(_1790783), _1790787))), hBOOL(hAPP(_1790785, _1791029))], (49954 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1790785, 49950 ^ [_1790783, _1790785, _1790787])))], (49952 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1790783), 49950 ^ [_1790783, _1790785, _1790787]), hAPP(c_List_Oset(_1790783), _1790787))))]]], (31076 ^ _777959) ^ [_1364986, _1364988, _1364990] : [class_Rings_Olinordered__idom(_1364986), -(hAPP(c_Groups_Oabs__class_Oabs(_1364986), hAPP(hAPP(c_Power_Opower__class_Opower(_1364986), _1364988), _1364990)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1364986), hAPP(c_Groups_Oabs__class_Oabs(_1364986), _1364988)), _1364990))], (12297 ^ _777959) ^ [_1001233, _1001235, _1001237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001233), _1001235)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001233), _1001237)), 12304 ^ _777959 : [(12311 ^ _777959) ^ [] : [_1001235 = _1001237, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001235), _1001233) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001237), _1001233))], (12305 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001235), _1001233) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001237), _1001233), -(_1001235 = _1001237)]]], (37130 ^ _777959) ^ [_1484092, _1484094, _1484096] : [-(c_Wellfounded_Omlex__prod(_1484092, _1484094, _1484096) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1484092), _1484092), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1484092, c_Wellfounded_Oless__than, _1484096)), hAPP(hAPP(c_COMBS(_1484092, _1484092, tc_prod(tc_Nat_Onat, _1484092)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1484092, tc_prod(tc_Nat_Onat, _1484092)), _1484092), c_Product__Type_OPair(tc_Nat_Onat, _1484092)), _1484094)), c_COMBI(_1484092))))], (46922 ^ _777959) ^ [_1718852, _1718854, _1718856] : [c_Wellfounded_Owf(_1718852, _1718854), -(c_Wellfounded_Owf(_1718852, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1718852, _1718852), tc_HOL_Obool)), _1718856), _1718854)))], (15763 ^ _777959) ^ [_1077830, _1077832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077830), _1077832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077830)), _1077832)))], (19466 ^ _777959) ^ [_1150740] : [class_Groups_Ogroup__add(_1150740), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1150740), c_Groups_Ozero__class_Ozero(_1150740)) = c_Groups_Ozero__class_Ozero(_1150740))], (44807 ^ _777959) ^ [_1669243, _1669245] : [-(hAPP(c_List_Orev(_1669243), c_List_Oconcat(_1669243, _1669245)) = c_List_Oconcat(_1669243, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1669243), tc_List_Olist(_1669243)), c_List_Orev(_1669243)), hAPP(c_List_Orev(tc_List_Olist(_1669243)), _1669245))))], (3700 ^ _777959) ^ [_833900, _833902, _833904, _833906, _833908, _833910, _833912, _833914] : [-(c_Recdef_Osame__fst(_833914, _833910, _833906, _833902) = c_Recdef_Osame__fst(_833912, _833908, _833904, _833900)), _833914 = _833912, _833910 = _833908, _833906 = _833904, _833902 = _833900], (154 ^ _777959) ^ [_780568, _780570, _780572, _780574, _780576, _780578] : [-(c_Finite__Set_Ofolding__one(_780576, _780572, _780568)), c_Finite__Set_Ofolding__one(_780578, _780574, _780570), _780578 = _780576, _780574 = _780572, _780570 = _780568], (14722 ^ _777959) ^ [_1054660, _1054662, _1054664, _1054666, _1054668] : [-(hBOOL(hAPP(hAPP(c_member(_1054660), _1054662), c_SetInterval_Oord_OatLeastAtMost(_1054660, _1054664, _1054666, _1054668)))), hBOOL(hAPP(hAPP(_1054664, _1054666), _1054662)), hBOOL(hAPP(hAPP(_1054664, _1054662), _1054668))], (5476 ^ _777959) ^ [_861660, _861662] : [_861662 = _861660, -(tc_List_Olist(_861662) = tc_List_Olist(_861660))], (42841 ^ _777959) ^ [_1626851, _1626853, _1626855, _1626857] : [-(hAPP(hAPP(c_List_Oappend(_1626851), hAPP(hAPP(c_List_Oappend(_1626851), _1626853), _1626855)), _1626857) = hAPP(hAPP(c_List_Oappend(_1626851), _1626853), hAPP(hAPP(c_List_Oappend(_1626851), _1626855), _1626857)))], (48771 ^ _777959) ^ [_1761604, _1761606, _1761608, _1761610, _1761612, _1761614] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1761604, _1761604)), hAPP(hAPP(c_Product__Type_OPair(_1761604, _1761604), _1761606), _1761608)), c_Transitive__Closure_Ortrancl(_1761604, _1761610))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1761604), tc_List_Olist(_1761604))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1761604), tc_List_Olist(_1761604)), _1761612), _1761614)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1761604), c_List_Olistrel1(_1761604, _1761610)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1761604), tc_List_Olist(_1761604))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1761604), tc_List_Olist(_1761604)), hAPP(hAPP(c_List_Olist_OCons(_1761604), _1761606), _1761612)), hAPP(hAPP(c_List_Olist_OCons(_1761604), _1761608), _1761614))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1761604), c_List_Olistrel1(_1761604, _1761610)))))], (46603 ^ _777959) ^ [_1709143, _1709145, _1709147] : [-(hBOOL(hAPP(hAPP(c_member(_1709143), _1709145), hAPP(c_List_Oset(_1709143), _1709147)))), -(c_List_Oinsert(_1709143, _1709145, _1709147) = hAPP(hAPP(c_List_Olist_OCons(_1709143), _1709145), _1709147))], (38760 ^ _777959) ^ [_1522060, _1522062] : [-(hAPP(c_Set_Ovimage(_1522060, _1522060, c_COMBI(_1522060)), _1522062) = _1522062)], (36932 ^ _777959) ^ [_1479460, _1479462, _1479464, _1479466, _1479468, _1479470] : [hAPP(_1479466, hAPP(c_Product__Type_Ofst(_1479460, _1479464), _1479468)) = hAPP(_1479470, hAPP(c_Product__Type_Ofst(_1479460, _1479464), _1479468)), -(hAPP(c_Product__Type_Oapfst(_1479460, _1479462, _1479464, _1479466), _1479468) = hAPP(c_Product__Type_Oapfst(_1479460, _1479462, _1479464, _1479470), _1479468))], (15494 ^ _777959) ^ [_1072491, _1072493, _1072495] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1072491), _1072493)), _1072495) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072491), _1072495)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072493), _1072495)))], (23387 ^ _777959) ^ [_1223350, _1223352, _1223354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223350), _1223352)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223354), _1223350)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223354), _1223352))))], (15783 ^ _777959) ^ [_1078196] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078196)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1078196)], (5152 ^ _777959) ^ [_856790, _856792, _856794, _856796, _856798, _856800, _856802, _856804] : [-(c_Lazy__Sequence_Ohb__map(_856804, _856800, _856796, _856792) = c_Lazy__Sequence_Ohb__map(_856802, _856798, _856794, _856790)), _856804 = _856802, _856800 = _856798, _856796 = _856794, _856792 = _856790], (6669 ^ _777959) ^ [_886171, _886173, _886175] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886171, tc_HOL_Obool)), _886173), _886175) = c_Orderings_Obot__class_Obot(tc_fun(_886171, tc_HOL_Obool))), _886173 = c_Orderings_Obot__class_Obot(tc_fun(_886171, tc_HOL_Obool)), _886175 = c_Orderings_Obot__class_Obot(tc_fun(_886171, tc_HOL_Obool))], (5714 ^ _777959) ^ [_868142] : [5715 ^ _777959 : [(5716 ^ _777959) ^ [_868190] : [hAPP(c_Com_Obody, _868142) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), _868190)]], -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _868142))))], (33225 ^ _777959) ^ [_1405096] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1405096) = c_Int_OPls)], (46080 ^ _777959) ^ [_1697461, _1697463, _1697465] : [class_Enum_Oenum(_1697461), class_Enum_Oenum(_1697463), class_HOL_Oequal(_1697463), 46091 ^ _777959 : [(46098 ^ _777959) ^ [] : [c_Enum_Oall__n__lists(_1697461, hAPP(hAPP(c_COMBB(tc_fun(_1697463, _1697461), tc_HOL_Obool, tc_List_Olist(_1697461)), _1697465), hAPP(hAPP(c_COMBB(tc_fun(_1697463, tc_Option_Ooption(_1697461)), tc_fun(_1697463, _1697461), tc_List_Olist(_1697461)), c_Fun_Ocomp(tc_Option_Ooption(_1697461), _1697461, _1697463, c_Option_Othe(_1697461))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1697463, _1697461)), tc_fun(_1697463, tc_Option_Ooption(_1697461)), tc_List_Olist(_1697461)), c_Map_Omap__of(_1697463, _1697461)), hAPP(c_List_Ozip(_1697463, _1697461), c_Enum_Oenum__class_Oenum(_1697463))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697463)), c_Enum_Oenum__class_Oenum(_1697463))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1697463, _1697461)), _1697465)))], (46092 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1697463, _1697461)), _1697465)), -(c_Enum_Oall__n__lists(_1697461, hAPP(hAPP(c_COMBB(tc_fun(_1697463, _1697461), tc_HOL_Obool, tc_List_Olist(_1697461)), _1697465), hAPP(hAPP(c_COMBB(tc_fun(_1697463, tc_Option_Ooption(_1697461)), tc_fun(_1697463, _1697461), tc_List_Olist(_1697461)), c_Fun_Ocomp(tc_Option_Ooption(_1697461), _1697461, _1697463, c_Option_Othe(_1697461))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1697463, _1697461)), tc_fun(_1697463, tc_Option_Ooption(_1697461)), tc_List_Olist(_1697461)), c_Map_Omap__of(_1697463, _1697461)), hAPP(c_List_Ozip(_1697463, _1697461), c_Enum_Oenum__class_Oenum(_1697463))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1697463)), c_Enum_Oenum__class_Oenum(_1697463))))]]], (50664 ^ _777959) ^ [_1805639, _1805641, _1805643] : [-(c_List_Oreplicate(_1805639, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1805639)), hAPP(c_List_Ofilter(_1805639, hAPP(c_fequal, _1805641)), _1805643)), _1805641) = hAPP(c_List_Ofilter(_1805639, hAPP(c_fequal, _1805641)), _1805643))], (38858 ^ _777959) ^ [_1524401, _1524403, _1524405, _1524407] : [c_Fun_Oinj__on(_1524401, _1524403, _1524405, c_Orderings_Otop__class_Otop(tc_fun(_1524401, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1524401, _1524403, _1524405), hAPP(c_Set_Oimage(_1524401, _1524403, _1524405), _1524407)) = _1524407)], (44092 ^ _777959) ^ [_1655088, _1655090, _1655092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655088), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1655090))), c_List_Otranspose(_1655090, _1655092)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1655090)), c_List_Otranspose(_1655090, _1655092)), _1655088) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1655090), _1655090), hAPP(hAPP(c_COMBC(tc_List_Olist(_1655090), tc_Nat_Onat, _1655090), c_List_Onth(_1655090)), _1655088)), hAPP(c_List_Ofilter(tc_List_Olist(_1655090), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1655090)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655088)), c_Nat_Osize__class_Osize(tc_List_Olist(_1655090)))), _1655092)))], (50184 ^ _777959) ^ [_1795074, _1795076] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1795074), _1795076)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1795074)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1795076))))], (45159 ^ _777959) ^ [_1678217, _1678219, _1678221] : [45161 ^ _777959 : [(45164 ^ _777959) ^ [] : [hBOOL(hAPP(_1678219, 45160 ^ [_1678217, _1678219, _1678221]))], (45162 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1678217), 45160 ^ [_1678217, _1678219, _1678221]), hAPP(c_List_Oset(_1678217), _1678221))))]], -(c_List_OtakeWhile(_1678217, _1678219, _1678221) = _1678221)], (22156 ^ _777959) ^ [_1199450, _1199452] : [-(_1199450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1199450), _1199452) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1199450), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1199452)))], (47526 ^ _777959) ^ [_1733169, _1733171] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1733169, _1733169)), _1733171)), 47529 ^ _777959 : [(47536 ^ _777959) ^ [] : [c_Wellfounded_Oacyclic(_1733169, _1733171), -(c_Wellfounded_Owf(_1733169, _1733171))], (47530 ^ _777959) ^ [] : [c_Wellfounded_Owf(_1733169, _1733171), -(c_Wellfounded_Oacyclic(_1733169, _1733171))]]], (24754 ^ _777959) ^ [_1247373, _1247375] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1247373), _1247375)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1247373)), hAPP(c_Nat_OSuc, _1247375)))], (1080 ^ _777959) ^ [_794183, _794185] : [-(class_Rings_Olinordered__semiring__1(_794183)), _794185 = _794183, class_Rings_Olinordered__semiring__1(_794185)], (48483 ^ _777959) ^ [_1753697, _1753699, _1753701, _1753703] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1753697, _1753697)), _1753699), c_Transitive__Closure_Otrancl(_1753697, _1753701))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1753697, _1753697), tc_HOL_Obool)), _1753701), _1753703)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1753697, _1753697)), _1753699), c_Transitive__Closure_Otrancl(_1753697, _1753703))))], (31450 ^ _777959) ^ [_1371983, _1371985, _1371987] : [31452 ^ _777959 : [(31455 ^ _777959) ^ [] : [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(_1371985, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 31451 ^ [_1371983, _1371985, _1371987]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1371985, 31451 ^ [_1371983, _1371985, _1371987])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31453 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31451 ^ [_1371983, _1371985, _1371987]), _1371983)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1371985, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1371987)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371987), hAPP(_1371985, _1371983))), 31465 ^ _777959 : [(31468 ^ _777959) ^ [] : [-(hAPP(_1371985, 31464 ^ [_1371983, _1371985, _1371987]) = _1371987)], (31466 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 31464 ^ [_1371983, _1371985, _1371987]), _1371983)))]]], (19644 ^ _777959) ^ [_1153384, _1153386, _1153388] : [19645 ^ _777959 : [(19648 ^ _777959) ^ [] : [_1153386 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19646 ^ _777959) ^ [] : [_1153384 = _1153388]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1153384), _1153386) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1153388), _1153386))], (50688 ^ _777959) ^ [_1806047, _1806049, _1806051] : [-(hAPP(c_List_Oset(_1806047), c_List_Oreplicate(_1806047, hAPP(c_Nat_OSuc, _1806049), _1806051)) = hAPP(hAPP(c_Set_Oinsert(_1806047), _1806051), c_Orderings_Obot__class_Obot(tc_fun(_1806047, tc_HOL_Obool))))], (7976 ^ _777959) ^ [_914106, _914108, _914110] : [c_Com_Ocom_OWhile(_914106, _914108) = hAPP(c_Com_Ocom_OBODY, _914110)], (43276 ^ _777959) ^ [_1637389, _1637391, _1637393, _1637395] : [-(hAPP(hAPP(c_List_Otake(_1637389), _1637391), hAPP(hAPP(c_List_Odrop(_1637389), _1637393), _1637395)) = hAPP(hAPP(c_List_Odrop(_1637389), _1637393), hAPP(hAPP(c_List_Otake(_1637389), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1637391), _1637393)), _1637395)))], (648 ^ _777959) ^ [_787883, _787885, _787887, _787889] : [-(c_Wellfounded_OwfP(_787887, _787883)), c_Wellfounded_OwfP(_787889, _787885), _787889 = _787887, _787885 = _787883], (33341 ^ _777959) ^ [_1406801] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1406801)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1406801))))], (13821 ^ _777959) ^ [_1033484, _1033486, _1033488] : [-(c_Map_Omap__add(_1033484, _1033486, hAPP(c_COMBK(tc_Option_Ooption(_1033486), _1033484), c_Option_Ooption_ONone(_1033486)), _1033488) = _1033488)], (50534 ^ _777959) ^ [_1803212, _1803214, _1803216] : [-(_1803212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1803214), c_List_Oreplicate(_1803214, _1803212, _1803216)) = _1803216)], (37110 ^ _777959) ^ [_1483675, _1483677, _1483679, _1483681] : [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), _1483675), _1483677)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1483679), _1483681))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1483675), _1483681) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1483679), _1483677))], (35627 ^ _777959) ^ [_1453336, _1453338] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453336), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 35630 ^ _777959 : [(35639 ^ _777959) ^ [] : [-(c_Nitpick_Onorm__frac(_1453338, _1453336) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1453338), _1453336)), 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), _1453338))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1453336)))), -(_1453338 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1453336 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35631 ^ _777959) ^ [] : [35632 ^ _777959 : [(35635 ^ _777959) ^ [] : [_1453336 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (35633 ^ _777959) ^ [] : [_1453338 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1453338, _1453336) = 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)))]]], (22258 ^ _777959) ^ [_1201614, _1201616, _1201618] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1201614), _1201616)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1201614), _1201618)), 22268 ^ _777959 : [(22271 ^ _777959) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22269 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1201614), 22267 ^ [_1201614, _1201616, _1201618]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1201614, tc_HOL_Obool)), _1201616), _1201618))))]], -(hAPP(c_Finite__Set_Ocard(_1201614), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1201614, tc_HOL_Obool)), _1201616), _1201618)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1201614), _1201616)), hAPP(c_Finite__Set_Ocard(_1201614), _1201618)))], (48288 ^ _777959) ^ [_1749866] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1749866)) = _1749866)], (13421 ^ _777959) ^ [_1024068, _1024070] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1024068, _1024070)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1024068, _1024070), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1024070), c_Orderings_Otop__class_Otop(tc_fun(_1024070, tc_HOL_Obool)))))], (51288 ^ _777959) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (38570 ^ _777959) ^ [_1517877, _1517879] : [-(c_Fun_Oinj__on(tc_fun(_1517877, _1517879), tc_fun(tc_prod(_1517877, _1517879), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1517877, _1517879), tc_HOL_Obool), tc_fun(tc_prod(_1517877, _1517879), tc_HOL_Obool), tc_fun(_1517877, _1517879)), c_Set_OCollect(tc_prod(_1517877, _1517879))), hAPP(hAPP(c_COMBB(tc_fun(_1517877, tc_fun(_1517879, tc_HOL_Obool)), tc_fun(tc_prod(_1517877, _1517879), tc_HOL_Obool), tc_fun(_1517877, _1517879)), c_Product__Type_Oprod_Oprod__case(_1517877, _1517879, tc_HOL_Obool)), hAPP(c_COMBB(_1517879, tc_fun(_1517879, tc_HOL_Obool), _1517877), hAPP(c_COMBC(_1517879, _1517879, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1517877, _1517879), tc_HOL_Obool))))], (29749 ^ _777959) ^ [_1339405, _1339407] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1339405), _1339407)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1339405, tc_HOL_Obool)), hAPP(c_Set_OPow(_1339405), _1339407))))], (25450 ^ _777959) ^ [_1260526, _1260528, _1260530] : [-(_1260526 = 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), _1260526), _1260528)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1260526), _1260530)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260528), _1260530))], (38502 ^ _777959) ^ [_1516605, _1516607] : [-(c_Fun_Oinj__on(_1516605, tc_Option_Ooption(_1516605), c_Option_Ooption_OSome(_1516605), _1516607))], (38754 ^ _777959) ^ [_1521909, _1521911, _1521913, _1521915] : [-(hAPP(c_Set_Ovimage(_1521909, _1521911, _1521913), hAPP(c_Set_OCollect(_1521911), _1521915)) = hAPP(c_Set_OCollect(_1521909), hAPP(hAPP(c_COMBB(_1521911, tc_HOL_Obool, _1521909), _1521915), _1521913)))], (15056 ^ _777959) ^ [_1064315, _1064317] : [_1064315 = _1064317, -(hAPP(c_Nat_OSuc, _1064315) = hAPP(c_Nat_OSuc, _1064317))], (13020 ^ _777959) ^ [_1014884, _1014886] : [class_Lattices_Oboolean__algebra(_1014884), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1014884), hAPP(c_Groups_Ouminus__class_Ouminus(_1014884), _1014886)), _1014886) = c_Orderings_Obot__class_Obot(_1014884))], (18620 ^ _777959) ^ [_1135734, _1135736] : [class_Orderings_Olinorder(_1135734), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135734), _1135736)), -(c_Big__Operators_Olattice_OSup__fin(_1135734, c_Orderings_Oord__class_Omax(_1135734), _1135736) = hAPP(c_Finite__Set_Ofold1(_1135734, c_Orderings_Oord__class_Omax(_1135734)), _1135736))], (1450 ^ _777959) ^ [_798808, _798810] : [-(class_Groups_Olinordered__ab__semigroup__add(_798808)), _798810 = _798808, class_Groups_Olinordered__ab__semigroup__add(_798810)], (43079 ^ _777959) ^ [_1632199, _1632201, _1632203, _1632205, _1632207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632199), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632201)), _1632203))), -(hAPP(hAPP(c_List_Olist__update(_1632201, hAPP(hAPP(c_List_Oappend(_1632201), _1632203), _1632205)), _1632199), _1632207) = hAPP(hAPP(c_List_Oappend(_1632201), hAPP(hAPP(c_List_Olist__update(_1632201, _1632203), _1632199), _1632207)), _1632205))], (44264 ^ _777959) ^ [_1658476, _1658478, _1658480] : [class_Orderings_Olinorder(_1658476), c_List_Olinorder__class_Osorted(_1658476, _1658478), hBOOL(hAPP(c_List_Odistinct(_1658476), _1658478)), c_List_Olinorder__class_Osorted(_1658476, _1658480), hBOOL(hAPP(c_List_Odistinct(_1658476), _1658480)), hAPP(c_List_Oset(_1658476), _1658478) = hAPP(c_List_Oset(_1658476), _1658480), -(_1658478 = _1658480)], (49582 ^ _777959) ^ [_1782753, _1782755, _1782757] : [-(hBOOL(hAPP(hAPP(c_member(_1782753), _1782755), hAPP(c_List_Oset(_1782753), _1782757)))), 49583 ^ _777959 : [(49584 ^ _777959) ^ [_1782842, _1782844] : [_1782757 = hAPP(hAPP(c_List_Oappend(_1782753), _1782844), hAPP(hAPP(c_List_Olist_OCons(_1782753), _1782755), _1782842)), -(hBOOL(hAPP(hAPP(c_member(_1782753), _1782755), hAPP(c_List_Oset(_1782753), _1782842))))]]], (51332 ^ _777959) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (14596 ^ _777959) ^ [_1052172] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1052172)), 14600 ^ _777959 : [(14601 ^ _777959) ^ [_1052252] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1052252), _1052172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1052252), 14599 ^ [_1052172])))]]], (14349 ^ _777959) ^ [_1045875, _1045877, _1045879] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045875), _1045877)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1045875), _1045879)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1045875, tc_HOL_Obool)), _1045877), _1045879) = c_Orderings_Obot__class_Obot(tc_fun(_1045875, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1045875), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1045875, tc_HOL_Obool)), _1045877), _1045879)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1045875), _1045877)), hAPP(c_Finite__Set_Ocard(_1045875), _1045879)))], (34121 ^ _777959) ^ [_1420617, _1420619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420617), _1420619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1420617)), c_Int_OBit0(_1420619))))], (37395 ^ _777959) ^ [_1491970, _1491972, _1491974, _1491976, _1491978, _1491980] : [c_Equiv__Relations_Oequiv(_1491970, _1491972, _1491974), hBOOL(hAPP(hAPP(c_member(_1491970), _1491976), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491970, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1491970, _1491970, _1491974), hAPP(hAPP(c_Set_Oinsert(_1491970), _1491978), c_Orderings_Obot__class_Obot(tc_fun(_1491970, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1491970, _1491970, _1491974), hAPP(hAPP(c_Set_Oinsert(_1491970), _1491980), c_Orderings_Obot__class_Obot(tc_fun(_1491970, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1491970, _1491970)), hAPP(hAPP(c_Product__Type_OPair(_1491970, _1491970), _1491978), _1491980)), _1491974)))], (37393 ^ _777959) ^ [_1491883, _1491885, _1491887] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1491883), hAPP(hAPP(c_Set_Oinsert(_1491883), _1491885), c_Orderings_Obot__class_Obot(tc_fun(_1491883, tc_HOL_Obool)))), _1491887) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1491883, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1491883, _1491883, _1491887), hAPP(hAPP(c_Set_Oinsert(_1491883), _1491885), c_Orderings_Obot__class_Obot(tc_fun(_1491883, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1491883, tc_HOL_Obool), tc_HOL_Obool))))], (45282 ^ _777959) ^ [_1680577] : [-(c_List_Oremdups(_1680577, c_List_Olist_ONil(_1680577)) = c_List_Olist_ONil(_1680577))], (43550 ^ _777959) ^ [_1643510, _1643512, _1643514] : [-(_1643510 = c_List_Olist_ONil(_1643512)), -(hAPP(c_List_Otl(_1643512), hAPP(hAPP(c_List_Oappend(_1643512), _1643510), _1643514)) = hAPP(hAPP(c_List_Oappend(_1643512), hAPP(c_List_Otl(_1643512), _1643510)), _1643514))], (50248 ^ _777959) ^ [_1796458, _1796460, _1796462, _1796464, _1796466, _1796468, _1796470] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1796458, _1796460, _1796462, _1796464), _1796466), _1796468), _1796470) = c_New__DSequence_Opos__bind(_1796458, _1796460, hAPP(hAPP(hAPP(_1796462, _1796466), _1796468), _1796470), hAPP(hAPP(c_COMBC(_1796458, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1796460))), hAPP(hAPP(c_COMBC(_1796458, 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(_1796460)))), hAPP(hAPP(c_COMBC(_1796458, 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(_1796460))))), _1796464), _1796466)), _1796468)), _1796470)))], (41952 ^ _777959) ^ [_1604240, _1604242, _1604244] : [-(hAPP(hAPP(c_List_Ozip(_1604240, _1604242), _1604244), c_List_Olist_ONil(_1604242)) = c_List_Olist_ONil(tc_prod(_1604240, _1604242)))], (48443 ^ _777959) ^ [_1752629, _1752631, _1752633, _1752635, _1752637] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1752629, _1752629)), hAPP(hAPP(c_Product__Type_OPair(_1752629, _1752629), _1752631), _1752633)), c_Transitive__Closure_Otrancl(_1752629, _1752635))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1752629, _1752629)), hAPP(hAPP(c_Product__Type_OPair(_1752629, _1752629), _1752633), _1752637)), c_Transitive__Closure_Otrancl(_1752629, _1752635))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1752629, _1752629)), hAPP(hAPP(c_Product__Type_OPair(_1752629, _1752629), _1752631), _1752637)), c_Transitive__Closure_Otrancl(_1752629, _1752635))))], (10824 ^ _777959) ^ [_970175, _970177, _970179, _970181] : [class_Groups_Oordered__ab__semigroup__add(_970175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970175), _970177), _970179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970175), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970175), _970181), _970177)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970175), _970181), _970179))))], (26784 ^ _777959) ^ [_1285207, _1285209, _1285211, _1285213] : [class_Fields_Olinordered__field(_1285207), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285207), _1285209), _1285211)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285207), c_Groups_Ozero__class_Ozero(_1285207)), _1285213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285207), c_Groups_Ozero__class_Ozero(_1285207)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285207), _1285211), _1285209))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285207), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285207), _1285213), _1285211)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285207), _1285213), _1285209))))], (23943 ^ _777959) ^ [_1233175, _1233177, _1233179, _1233181] : [class_Rings_Olinordered__semidom(_1233175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1233177), _1233179)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233175), c_Groups_Oone__class_Oone(_1233175)), _1233181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233175), hAPP(hAPP(c_Power_Opower__class_Opower(_1233175), _1233181), _1233177)), hAPP(hAPP(c_Power_Opower__class_Opower(_1233175), _1233181), _1233179))))], (29664 ^ _777959) ^ [_1337491, _1337493, _1337495, _1337497, _1337499] : [class_Groups_Ocomm__monoid__add(_1337491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337493), _1337495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1337493, tc_HOL_Obool)), _1337497), _1337495)), 29678 ^ _777959 : [(29681 ^ _777959) ^ [] : [hAPP(_1337499, 29677 ^ [_1337491, _1337493, _1337495, _1337497, _1337499]) = c_Groups_Ozero__class_Ozero(_1337491)], (29679 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1337493), 29677 ^ [_1337491, _1337493, _1337495, _1337497, _1337499]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1337493, tc_HOL_Obool)), _1337495), _1337497))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1337493, _1337491), _1337499), _1337495) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1337493, _1337491), _1337499), _1337497))], (14708 ^ _777959) ^ [_1054372, _1054374, _1054376, _1054378] : [hBOOL(hAPP(hAPP(_1054376, _1054378), _1054374)), -(hBOOL(hAPP(hAPP(c_member(_1054372), _1054374), c_SetInterval_Oord_OgreaterThan(_1054372, _1054376, _1054378))))], (24528 ^ _777959) ^ [_1243745] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243745) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31835 ^ _777959) ^ [_1379259, _1379261, _1379263, _1379265] : [c_Com_Ocom_OLocal(_1379259, _1379261, _1379263) = hAPP(c_Com_Ocom_OBODY, _1379265)], (48292 ^ _777959) ^ [_1749939, _1749941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1749939), _1749941)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1749939)), hAPP(c_Code__Numeral_Onat__of, _1749941))))], (50592 ^ _777959) ^ [_1804288, _1804290, _1804292] : [-(hAPP(c_List_Orev(_1804288), c_List_Oreplicate(_1804288, _1804290, _1804292)) = c_List_Oreplicate(_1804288, _1804290, _1804292))], (25526 ^ _777959) ^ [_1261811, _1261813, _1261815] : [hBOOL(hAPP(_1261811, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1261813), _1261815))), 25529 ^ _777959 : [(25536 ^ _777959) ^ [] : [-(_1261815 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25539 ^ _777959 : [(25540 ^ _777959) ^ [_1262063, _1262065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1262063), _1261815)), _1261813 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1261815), _1262065)), _1262063), -(hBOOL(hAPP(_1261811, _1262065)))]]], (25530 ^ _777959) ^ [] : [_1261815 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1261811, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (32135 ^ _777959) ^ [_1384901, _1384903, _1384905, _1384907] : [class_Int_Onumber__ring(_1384901), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384901), hAPP(c_Int_Onumber__class_Onumber__of(_1384901), _1384903)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384901), hAPP(c_Int_Onumber__class_Onumber__of(_1384901), _1384905)), _1384907)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1384901), hAPP(c_Int_Onumber__class_Onumber__of(_1384901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1384903), _1384905))), _1384907))], (19116 ^ _777959) ^ [_1145334, _1145336] : [class_Groups_Ozero(_1145334), 19119 ^ _777959 : [(19126 ^ _777959) ^ [] : [_1145336 = c_Groups_Ozero__class_Ozero(_1145334), -(c_Groups_Ozero__class_Ozero(_1145334) = _1145336)], (19120 ^ _777959) ^ [] : [c_Groups_Ozero__class_Ozero(_1145334) = _1145336, -(_1145336 = c_Groups_Ozero__class_Ozero(_1145334))]]], (9772 ^ _777959) ^ [_947539, _947541] : [class_Lattices_Osemilattice__inf(_947539), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_947539), _947541), _947541) = _947541)], (42865 ^ _777959) ^ [_1627562, _1627564, _1627566, _1627568, _1627570, _1627572] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627562)), _1627564) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627566)), _1627568), -(c_Map_Omap__upds(_1627562, _1627566, _1627570, hAPP(hAPP(c_List_Oappend(_1627562), _1627564), _1627572), _1627568) = c_Map_Omap__upds(_1627562, _1627566, _1627570, _1627564, _1627568))], (15376 ^ _777959) ^ [_1070456, _1070458, _1070460] : [class_Rings_Oidom(_1070456), 15379 ^ _777959 : [(15380 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070456), _1070458), _1070458) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070456), _1070460), _1070460), -(_1070458 = _1070460), -(_1070458 = hAPP(c_Groups_Ouminus__class_Ouminus(_1070456), _1070460))], (15390 ^ _777959) ^ [] : [15391 ^ _777959 : [(15394 ^ _777959) ^ [] : [_1070458 = hAPP(c_Groups_Ouminus__class_Ouminus(_1070456), _1070460)], (15392 ^ _777959) ^ [] : [_1070458 = _1070460]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070456), _1070458), _1070458) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070456), _1070460), _1070460))]]], (50776 ^ _777959) ^ [_1807664, _1807666] : [class_Lattices_Odistrib__lattice(_1807664), -(class_Lattices_Odistrib__lattice(tc_fun(_1807666, _1807664)))], (6313 ^ _777959) ^ [_879843, _879845, _879847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879843, tc_HOL_Obool)), _879845), _879847)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879843, tc_HOL_Obool)), _879845), _879847) = _879847)], (30014 ^ _777959) ^ [_1345489, _1345491, _1345493, _1345495] : [class_Divides_Osemiring__div(_1345489), -(c_Divides_Odiv__class_Omod(_1345489, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345489), _1345491), _1345493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345489), _1345491), _1345495)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345489), _1345491), c_Divides_Odiv__class_Omod(_1345489, _1345493, _1345495)))], (29114 ^ _777959) ^ [_1326632, _1326634, _1326636, _1326638] : [class_Orderings_Olinorder(_1326632), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326632, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1326632), _1326634)), c_SetInterval_Oord__class_OatLeastAtMost(_1326632, _1326636, _1326638)) = c_SetInterval_Oord__class_OatLeastAtMost(_1326632, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1326632), _1326634), _1326636), _1326638))], (35197 ^ _777959) ^ [_1439790, _1439792] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1439790), _1439792) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 35198 ^ _777959 : [(35205 ^ _777959) ^ [] : [_1439790 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1439792 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)], (35199 ^ _777959) ^ [] : [_1439790 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1439792 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (1370 ^ _777959) ^ [_797808, _797810] : [-(class_Groups_Ouminus(_797808)), _797810 = _797808, class_Groups_Ouminus(_797810)], (50192 ^ _777959) ^ [_1795218, _1795220] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1795218), _1795220)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1795218), _1795220) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (27678 ^ _777959) ^ [_1300798, _1300800] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1300798), _1300800) = 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)), _1300798)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1300800))))], (23270 ^ _777959) ^ [_1221412, _1221414] : [-(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), _1221412))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221414))))], (30409 ^ _777959) ^ [_1352903, _1352905, _1352907] : [hBOOL(hAPP(_1352903, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1352905, _1352907))), 30412 ^ _777959 : [(30437 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1352907), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30440 ^ _777959 : [(30441 ^ _777959) ^ [_1353525, _1353527] : [-(hBOOL(hAPP(_1352903, _1353525))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1352907), _1353525)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1353525), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1352905 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1352907), _1353527)), _1353525)]]], (30419 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352907)), 30422 ^ _777959 : [(30423 ^ _777959) ^ [_1353233, _1353235] : [-(hBOOL(hAPP(_1352903, _1353233))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1353233)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1353233), _1352907)), _1352905 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1352907), _1353235)), _1353233)]]], (30413 ^ _777959) ^ [] : [_1352907 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1352903, _1352905)))]]], (36684 ^ _777959) ^ [_1473901, _1473903] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1473901), _1473903) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1473901, _1473903)))], (35956 ^ _777959) ^ [_1460180, _1460182] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1460180, _1460180)), hAPP(hAPP(c_Product__Type_OPair(_1460180, _1460180), 35957 ^ [_1460180, _1460182]), 35957 ^ [_1460180, _1460182])), _1460182)), -(c_Nitpick_Orefl_H(_1460180, _1460182))], (13139 ^ _777959) ^ [_1017733, _1017735, _1017737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017733), _1017735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017733), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017735), _1017737))))], (41693 ^ _777959) ^ [_1596316, _1596318, _1596320, _1596322] : [-(hAPP(c_Map_Omap__of(_1596316, _1596318), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1596316, _1596318)), _1596320), _1596322)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1596316, tc_Option_Ooption(_1596318)), hAPP(c_Map_Omap__of(_1596316, _1596318), _1596322)), hAPP(c_Product__Type_Ofst(_1596316, _1596318), _1596320)), hAPP(c_Option_Ooption_OSome(_1596318), hAPP(c_Product__Type_Osnd(_1596316, _1596318), _1596320))))], (28938 ^ _777959) ^ [_1323442, _1323444] : [class_Orderings_Oorder(_1323442), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1323442, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1323442), _1323444)), hAPP(c_SetInterval_Oord__class_OatLeast(_1323442), _1323444)) = hAPP(hAPP(c_Set_Oinsert(_1323442), _1323444), c_Orderings_Obot__class_Obot(tc_fun(_1323442, tc_HOL_Obool))))], (31578 ^ _777959) ^ [_1374235, _1374237, _1374239, _1374241] : [hAPP(c_Com_Ocom_OBODY, _1374235) = c_Com_Ocom_OCond(_1374237, _1374239, _1374241)], (42885 ^ _777959) ^ [_1628045, _1628047, _1628049] : [-(_1628045 = c_List_Olist_ONil(_1628047)), -(c_List_Obutlast(_1628047, hAPP(hAPP(c_List_Oappend(_1628047), _1628049), _1628045)) = hAPP(hAPP(c_List_Oappend(_1628047), _1628049), c_List_Obutlast(_1628047, _1628045)))], (36315 ^ _777959) ^ [_1466412, _1466414, _1466416] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466412, tc_fun(_1466412, tc_HOL_Obool))), _1466414), _1466416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1466412, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1466412, _1466416)), c_Wellfounded_Oaccp(_1466412, _1466414))))], (34151 ^ _777959) ^ [_1421127] : [c_Int_OPls = c_Int_OBit0(_1421127), -(c_Int_OPls = _1421127)], (33385 ^ _777959) ^ [_1407469] : [class_Int_Onumber__ring(_1407469), -(hAPP(c_Int_Onumber__class_Onumber__of(_1407469), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1407469))], (14001 ^ _777959) ^ [_1037738, _1037740, _1037742] : [-(hBOOL(hAPP(_1037738, _1037740))), -(hAPP(c_Set_OCollect(_1037742), hAPP(hAPP(c_COMBS(_1037742, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1037742), c_fconj), hAPP(c_fequal, _1037740))), _1037738)) = c_Orderings_Obot__class_Obot(tc_fun(_1037742, tc_HOL_Obool)))], (41348 ^ _777959) ^ [_1587927, _1587929] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1587927)), c_List_Obutlast(_1587927, _1587929)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1587927)), _1587929)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (42138 ^ _777959) ^ [_1608376, _1608378, _1608380] : [hAPP(hAPP(c_List_Olist_OCons(_1608376), _1608378), _1608380) = c_List_Olist_ONil(_1608376)], (40363 ^ _777959) ^ [_1561333, _1561335, _1561337, _1561339, _1561341] : [-(_1561333 = _1561335), -(hAPP(hAPP(c_List_Onth(_1561337), hAPP(hAPP(c_List_Olist__update(_1561337, _1561339), _1561333), _1561341)), _1561335) = hAPP(hAPP(c_List_Onth(_1561337), _1561339), _1561335))], (9404 ^ _777959) ^ [_939444, _939446, _939448] : [class_Lattices_Olattice(_939444), hBOOL(hAPP(c_Finite__Set_Ofinite(_939444), _939446)), 9411 ^ _777959 : [(9418 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939444, tc_HOL_Obool)), _939446), hAPP(hAPP(c_Set_Oinsert(_939444), _939448), c_Orderings_Obot__class_Obot(tc_fun(_939444, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_939444, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_939444, hAPP(hAPP(c_Set_Oinsert(_939444), _939448), _939446)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939444), _939448), c_Big__Operators_Olattice__class_OSup__fin(_939444, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939444, tc_HOL_Obool)), _939446), hAPP(hAPP(c_Set_Oinsert(_939444), _939448), c_Orderings_Obot__class_Obot(tc_fun(_939444, tc_HOL_Obool)))))))], (9412 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_939444, tc_HOL_Obool)), _939446), hAPP(hAPP(c_Set_Oinsert(_939444), _939448), c_Orderings_Obot__class_Obot(tc_fun(_939444, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_939444, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_939444, hAPP(hAPP(c_Set_Oinsert(_939444), _939448), _939446)) = _939448)]]], (41904 ^ _777959) ^ [_1603393, _1603395, _1603397] : [-(hAPP(hAPP(c_Map_Omap__of(_1603393, _1603395), c_List_Olist_ONil(tc_prod(_1603393, _1603395))), _1603397) = c_Option_Ooption_ONone(_1603395))], (49710 ^ _777959) ^ [_1786107, _1786109] : [-(c_Nitpick_Oinverse__frac(_1786107, _1786109) = hAPP(hAPP(c_Nitpick_Ofrac(_1786107), hAPP(c_Nitpick_Odenom(_1786107), _1786109)), hAPP(c_Nitpick_Onum(_1786107), _1786109)))], (45526 ^ _777959) ^ [_1685755, _1685757, _1685759] : [hBOOL(hAPP(c_List_Odistinct(_1685755), _1685757)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1685755)), c_Enum_On__lists(_1685755, _1685759, _1685757))))], (6002 ^ _777959) ^ [_873788, _873790, _873792, _873794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873788, tc_HOL_Obool)), _873790), _873792)), hBOOL(hAPP(hAPP(c_member(_873788), _873794), _873790)), -(hBOOL(hAPP(hAPP(c_member(_873788), _873794), _873792)))], (41597 ^ _777959) ^ [_1593762, _1593764, _1593766, _1593768] : [_1593762 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1593764), hAPP(hAPP(c_List_Olist_OCons(_1593764), _1593766), _1593768)), _1593762) = _1593766)], (2324 ^ _777959) ^ [_812324, _812326] : [_812326 = _812324, -(c_SetInterval_Oord__class_OgreaterThan(_812326) = c_SetInterval_Oord__class_OgreaterThan(_812324))], (36922 ^ _777959) ^ [_1479171, _1479173, _1479175, _1479177, _1479179] : [-(hAPP(c_Product__Type_Osnd(_1479171, _1479173), hAPP(c_Product__Type_Oapfst(_1479175, _1479171, _1479173, _1479177), _1479179)) = hAPP(c_Product__Type_Osnd(_1479175, _1479173), _1479179))], (40952 ^ _777959) ^ [_1576409, _1576411, _1576413, _1576415] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1576409), tc_List_Olist(_1576409))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1576409), tc_List_Olist(_1576409)), _1576413), _1576415)), c_List_Olistrel(_1576409, _1576411))), -(c_List_Olistrelp(_1576409, hAPP(hAPP(c_COMBC(_1576409, tc_fun(tc_prod(_1576409, _1576409), tc_HOL_Obool), tc_fun(_1576409, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576409, tc_fun(tc_fun(tc_prod(_1576409, _1576409), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1576409, _1576409), tc_HOL_Obool), tc_fun(_1576409, tc_HOL_Obool)), _1576409), c_COMBC(_1576409, tc_fun(tc_prod(_1576409, _1576409), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576409, tc_prod(_1576409, _1576409)), tc_fun(_1576409, tc_fun(tc_fun(tc_prod(_1576409, _1576409), tc_HOL_Obool), tc_HOL_Obool)), _1576409), hAPP(c_COMBB(tc_prod(_1576409, _1576409), tc_fun(tc_fun(tc_prod(_1576409, _1576409), tc_HOL_Obool), tc_HOL_Obool), _1576409), c_member(tc_prod(_1576409, _1576409)))), c_Product__Type_OPair(_1576409, _1576409)))), _1576411), _1576413, _1576415))], (4336 ^ _777959) ^ [_843602, _843604, _843606, _843608, _843610, _843612] : [-(c_Nitpick_Oof__frac(_843612, _843608, _843604) = c_Nitpick_Oof__frac(_843610, _843606, _843602)), _843612 = _843610, _843608 = _843606, _843604 = _843602], (380 ^ _777959) ^ [_783903, _783905, _783907, _783909, _783911, _783913, _783915, _783917] : [-(c_Equiv__Relations_Ocongruent(_783915, _783911, _783907, _783903)), c_Equiv__Relations_Ocongruent(_783917, _783913, _783909, _783905), _783917 = _783915, _783913 = _783911, _783909 = _783907, _783905 = _783903], (23453 ^ _777959) ^ [_1224528, _1224530, _1224532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224528), _1224530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224530), _1224532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224528), _1224532)))], (11687 ^ _777959) ^ [_988049, _988051, _988053, _988055] : [11689 ^ _777959 : [(11692 ^ _777959) ^ [] : [hAPP(_988055, 11688 ^ [_988049, _988051, _988053, _988055]) = c_Orderings_Obot__class_Obot(tc_fun(_988051, tc_HOL_Obool))], (11690 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_988049), 11688 ^ [_988049, _988051, _988053, _988055]), _988053)))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_988049, tc_fun(_988051, tc_HOL_Obool)), _988053), _988055) = c_Orderings_Obot__class_Obot(tc_fun(_988051, tc_HOL_Obool)))], (10262 ^ _777959) ^ [_958319, _958321, _958323, _958325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958319, tc_HOL_Obool)), _958325), _958321)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958319, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958319, tc_HOL_Obool)), _958321), _958323)), _958325) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958319, tc_HOL_Obool)), _958321), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958319, tc_HOL_Obool)), _958323), _958325)))], (27593 ^ _777959) ^ [_1299296, _1299298] : [27594 ^ _777959 : [(27597 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299298))], (27595 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299296))]], 27598 ^ _777959 : [(27605 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1299296), _1299298)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1299296)), hAPP(c_Int_Onat, _1299298))))], (27599 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1299296)), hAPP(c_Int_Onat, _1299298))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1299296), _1299298)))]]], (23397 ^ _777959) ^ [_1223531, _1223533, _1223535] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1223531), _1223533)), _1223535) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223531), _1223535)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223533), _1223535)))], (50950 ^ _777959) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (33615 ^ _777959) ^ [] : [-(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))))))], (27175 ^ _777959) ^ [_1292711, _1292713] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1292711, _1292713))))], (8718 ^ _777959) ^ [_928365, _928367, _928369, _928371, _928373, _928375] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928365, _928367), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928365, _928367), _928369), _928371), _928373)), _928371), _928375) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928365, _928367), _928369), _928371), _928375))], (39564 ^ _777959) ^ [_1542059, _1542061, _1542063, _1542065] : [hBOOL(hAPP(c_List_Odistinct(_1542059), hAPP(hAPP(c_List_Omap(tc_prod(_1542059, _1542061), _1542059), c_Product__Type_Ofst(_1542059, _1542061)), _1542063))), hBOOL(hAPP(c_List_Odistinct(_1542059), hAPP(hAPP(c_List_Omap(tc_prod(_1542059, _1542061), _1542059), c_Product__Type_Ofst(_1542059, _1542061)), _1542065))), 39571 ^ _777959 : [(39578 ^ _777959) ^ [] : [hAPP(c_List_Oset(tc_prod(_1542059, _1542061)), _1542063) = hAPP(c_List_Oset(tc_prod(_1542059, _1542061)), _1542065), -(hAPP(c_Map_Omap__of(_1542059, _1542061), _1542063) = hAPP(c_Map_Omap__of(_1542059, _1542061), _1542065))], (39572 ^ _777959) ^ [] : [hAPP(c_Map_Omap__of(_1542059, _1542061), _1542063) = hAPP(c_Map_Omap__of(_1542059, _1542061), _1542065), -(hAPP(c_List_Oset(tc_prod(_1542059, _1542061)), _1542063) = hAPP(c_List_Oset(tc_prod(_1542059, _1542061)), _1542065))]]], (24161 ^ _777959) ^ [_1237235, _1237237, _1237239, _1237241, _1237243] : [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), _1237235), _1237237)), _1237239)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237235), _1237241)), _1237243))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237239)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237239), _1237235)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237243), _1237235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237237), _1237241)))], (9704 ^ _777959) ^ [_946127, _946129, _946131, _946133] : [class_Lattices_Osemilattice__inf(_946127), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946127), _946129), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946127), _946131), _946133)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946127), _946131), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946127), _946129), _946133)))], (15938 ^ _777959) ^ [_1081738, _1081740, _1081742] : [class_Orderings_Olinorder(_1081738), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081738), _1081740)), hBOOL(hAPP(hAPP(c_member(_1081738), _1081742), _1081740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081738), c_Big__Operators_Olinorder__class_OMin(_1081738, _1081740)), _1081742)))], (7274 ^ _777959) ^ [_899899, _899901, _899903, _899905] : [class_Lattices_Osemilattice__sup(_899899), 7277 ^ _777959 : [(7286 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899899), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_899899), _899901), _899903)), _899905))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899899), _899901), _899905)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899899), _899903), _899905))], (7278 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899899), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_899899), _899901), _899903)), _899905)), 7281 ^ _777959 : [(7284 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899899), _899903), _899905)))], (7282 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899899), _899901), _899905)))]]]]], (10834 ^ _777959) ^ [_970370, _970372, _970374, _970376] : [class_Groups_Oordered__ab__semigroup__add(_970370), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970370), _970372), _970374)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970370), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970370), _970372), _970376)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970370), _970374), _970376))))], (23042 ^ _777959) ^ [_1217311, _1217313, _1217315] : [class_Rings_Oring__1(_1217311), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1217313), _1217315)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217311), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1217315), _1217313)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1217311), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217311), _1217315)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217311), _1217313)))], (34115 ^ _777959) ^ [_1420516, _1420518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1420516)), c_Int_OBit0(_1420518))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420516), _1420518)))], (49144 ^ _777959) ^ [_1771194, _1771196] : [-(c_Relation_Ototal__on(_1771194, c_Orderings_Obot__class_Obot(tc_fun(_1771194, tc_HOL_Obool)), _1771196))], (37296 ^ _777959) ^ [_1489466, _1489468] : [-(hAPP(c_Relation_OField(_1489466), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1489466, _1489466), tc_HOL_Obool), _1489468)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1489466, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1489466, _1489466), tc_HOL_Obool), tc_fun(_1489466, tc_HOL_Obool), c_Relation_OField(_1489466)), _1489468)))], (5775 ^ _777959) ^ [_869357, _869359, _869361, _869363] : [_869363 = c_Orderings_Obot__class_Obot(tc_fun(_869359, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_869357, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_869359, _869357, _869361), _869363))], (24676 ^ _777959) ^ [_1246235] : [-(_1246235 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1246235), _1246235) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (15410 ^ _777959) ^ [_1071033, _1071035, _1071037] : [class_Rings_Oring(_1071033), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1071033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071033), _1071035), _1071037)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071033), hAPP(c_Groups_Ouminus__class_Ouminus(_1071033), _1071035)), _1071037))], (38486 ^ _777959) ^ [_1516293, _1516295, _1516297, _1516299, _1516301, _1516303] : [c_Fun_Oinj__on(_1516293, _1516295, _1516297, _1516299), hBOOL(hAPP(hAPP(c_member(_1516295), _1516301), hAPP(c_Set_Oimage(_1516293, _1516295, _1516297), _1516299))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1516293, tc_HOL_Obool)), _1516299), _1516303)), -(hBOOL(hAPP(hAPP(c_member(_1516293), hAPP(c_Fun_Othe__inv__into(_1516293, _1516295, _1516299, _1516297), _1516301)), _1516303)))], (14079 ^ _777959) ^ [_1039593, _1039595, _1039597, _1039599] : [hBOOL(hAPP(hAPP(c_member(_1039595), _1039599), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1039593, tc_fun(_1039595, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1039593, tc_HOL_Obool))), _1039597))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1039593, tc_fun(_1039595, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1039593, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1039595, tc_HOL_Obool), tc_fun(_1039595, tc_HOL_Obool), _1039593), hAPP(c_COMBC(_1039595, tc_fun(_1039595, tc_HOL_Obool), tc_HOL_Obool), c_member(_1039595))), _1039597)), _1039599)))], (33943 ^ _777959) ^ [_1417563, _1417565] : [class_Rings_Osemiring__1(_1417563), 33946 ^ _777959 : [(33953 ^ _777959) ^ [] : [_1417565 = c_Groups_Ozero__class_Ozero(_1417563), -(c_Int_Oiszero(_1417563, _1417565))], (33947 ^ _777959) ^ [] : [c_Int_Oiszero(_1417563, _1417565), -(_1417565 = c_Groups_Ozero__class_Ozero(_1417563))]]], (8568 ^ _777959) ^ [_925963, _925965, _925967] : [class_Orderings_Opreorder(_925963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925963), _925965), _925967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925963), _925967), _925965))], (19300 ^ _777959) ^ [_1148294, _1148296, _1148298] : [class_Rings_Oring__no__zero__divisors(_1148294), 19303 ^ _777959 : [(19304 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148294), _1148296), _1148298) = c_Groups_Ozero__class_Ozero(_1148294), -(_1148296 = c_Groups_Ozero__class_Ozero(_1148294)), -(_1148298 = c_Groups_Ozero__class_Ozero(_1148294))], (19314 ^ _777959) ^ [] : [19315 ^ _777959 : [(19318 ^ _777959) ^ [] : [_1148298 = c_Groups_Ozero__class_Ozero(_1148294)], (19316 ^ _777959) ^ [] : [_1148296 = c_Groups_Ozero__class_Ozero(_1148294)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148294), _1148296), _1148298) = c_Groups_Ozero__class_Ozero(_1148294))]]], (24325 ^ _777959) ^ [_1240232] : [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)), _1240232))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1240232)))], (21322 ^ _777959) ^ [_1183132, _1183134, _1183136, _1183138] : [class_Rings_Olinordered__semiring(_1183132), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183132), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183132), _1183134), _1183136)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183132), _1183134), _1183138))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183132), c_Groups_Ozero__class_Ozero(_1183132)), _1183134)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183132), _1183136), _1183138)))], (42810 ^ _777959) ^ [_1626132, _1626134, _1626136, _1626138, _1626140] : [hAPP(hAPP(c_List_Oappend(_1626132), _1626134), _1626136) = hAPP(hAPP(c_List_Oappend(_1626132), _1626138), _1626140), 42816 ^ _777959 : [(42819 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1626132), 42813 ^ [_1626132, _1626134, _1626136, _1626138, _1626140]), _1626136) = _1626140)], (42817 ^ _777959) ^ [] : [-(_1626134 = hAPP(hAPP(c_List_Oappend(_1626132), _1626138), 42813 ^ [_1626132, _1626134, _1626136, _1626138, _1626140]))]], 42820 ^ _777959 : [(42823 ^ _777959) ^ [] : [-(_1626136 = hAPP(hAPP(c_List_Oappend(_1626132), 42813 ^ [_1626132, _1626134, _1626136, _1626138, _1626140]), _1626140))], (42821 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1626132), _1626134), 42813 ^ [_1626132, _1626134, _1626136, _1626138, _1626140]) = _1626138)]]], (12323 ^ _777959) ^ [_1001667, _1001669, _1001671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001667), _1001669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001667), _1001671)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001669), _1001671))))], (45338 ^ _777959) ^ [_1681530, _1681532] : [-(c_List_Oremdups(_1681530, c_List_Oremdups(_1681530, _1681532)) = c_List_Oremdups(_1681530, _1681532))], (36077 ^ _777959) ^ [_1462117, _1462119] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1462117))), 36080 ^ _777959 : [(36087 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1462119))), -(c_Divides_Odivmod__int(_1462117, _1462119) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1462117), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1462119))))], (36081 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1462119)), -(c_Divides_Odivmod__int(_1462117, _1462119) = c_Divides_OnegDivAlg(_1462117, _1462119))]]], (50986 ^ _777959) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (25914 ^ _777959) ^ [_1269172, _1269174] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1269172), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1269174) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1269172, _1269174))], (23595 ^ _777959) ^ [_1226888] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1226888) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (43318 ^ _777959) ^ [_1638407, _1638409, _1638411, _1638413] : [-(hAPP(hAPP(c_List_Odrop(_1638407), _1638409), hAPP(hAPP(c_List_Oappend(_1638407), _1638411), _1638413)) = hAPP(hAPP(c_List_Oappend(_1638407), hAPP(hAPP(c_List_Odrop(_1638407), _1638409), _1638411)), hAPP(hAPP(c_List_Odrop(_1638407), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1638409), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638407)), _1638411))), _1638413)))], (8752 ^ _777959) ^ [_928935, _928937, _928939, _928941, _928943] : [c_Finite__Set_Ofun__left__comm__idem(_928935, _928937, _928939), -(hAPP(hAPP(_928939, _928941), hAPP(hAPP(_928939, _928941), _928943)) = hAPP(hAPP(_928939, _928941), _928943))], (13517 ^ _777959) ^ [_1026043, _1026045] : [c_Orderings_Obot__class_Obot(tc_fun(_1026043, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1026043), _1026045), 13520 ^ _777959 : [(13521 ^ _777959) ^ [_1026128] : [hBOOL(hAPP(_1026045, _1026128))]]], (30277 ^ _777959) ^ [_1350554, _1350556] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350554, _1350556) = 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), _1350554), _1350556) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (13145 ^ _777959) ^ [_1017844, _1017846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017844), _1017846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1017844), _1017846)))], (50322 ^ _777959) ^ [_1798496, _1798498, _1798500, _1798502, _1798504] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1798496), _1798498), _1798500), _1798502), _1798504) = c_New__DSequence_Oneg__single(_1798496, _1798498))], (3232 ^ _777959) ^ [_826554, _826556, _826558, _826560, _826562, _826564, _826566, _826568] : [-(c_List_Olist_Olist__case(_826568, _826564, _826560, _826556) = c_List_Olist_Olist__case(_826566, _826562, _826558, _826554)), _826568 = _826566, _826564 = _826562, _826560 = _826558, _826556 = _826554], (29858 ^ _777959) ^ [_1342372, _1342374, _1342376] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1342372)), 29861 ^ _777959 : [(29862 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1342374, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1342376), _1342372)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1342376, _1342372))), 29865 ^ _777959 : [(29866 ^ _777959) ^ [_1342573, _1342575] : [-(hBOOL(hAPP(hAPP(_1342374, _1342575), _1342573))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1342573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1342573), _1342372)), _1342376 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1342372), _1342575)), _1342573)]]], (29880 ^ _777959) ^ [] : [29883 ^ _777959 : [(29886 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 29882 ^ [_1342372, _1342374, _1342376]), _1342372)))], (29888 ^ _777959) ^ [] : [-(_1342376 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1342372), 29881 ^ [_1342372, _1342374, _1342376])), 29882 ^ [_1342372, _1342374, _1342376]))], (29890 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1342374, 29881 ^ [_1342372, _1342374, _1342376]), 29882 ^ [_1342372, _1342374, _1342376]))], (29884 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29882 ^ [_1342372, _1342374, _1342376])))]], -(hBOOL(hAPP(hAPP(_1342374, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1342376), _1342372)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1342376, _1342372))))]]], (46186 ^ _777959) ^ [_1699968, _1699970, _1699972] : [-(c_List_Olistsp(_1699968, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1699968, tc_HOL_Obool)), _1699970), _1699972)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1699968), tc_HOL_Obool)), c_List_Olistsp(_1699968, _1699970)), c_List_Olistsp(_1699968, _1699972)))], (48703 ^ _777959) ^ [_1759974, _1759976] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1759974, _1759974, _1759974), _1759976), c_Transitive__Closure_Ortrancl(_1759974, _1759976)) = hAPP(hAPP(c_Relation_Orel__comp(_1759974, _1759974, _1759974), c_Transitive__Closure_Ortrancl(_1759974, _1759976)), _1759976))], (38316 ^ _777959) ^ [_1512160, _1512162, _1512164, _1512166, _1512168] : [c_Fun_Oinj__on(_1512160, _1512162, _1512164, c_Orderings_Otop__class_Otop(tc_fun(_1512160, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1512160, _1512162, _1512164), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1512160, tc_HOL_Obool)), _1512166), _1512168)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1512162, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1512160, _1512162, _1512164), _1512166)), hAPP(c_Set_Oimage(_1512160, _1512162, _1512164), _1512168)))], (41844 ^ _777959) ^ [_1601570, _1601572, _1601574, _1601576] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1601570) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1601572), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1601570)), hAPP(hAPP(c_List_Olist_OCons(_1601572), _1601574), _1601576)) = c_List_Olist_ONil(_1601572))], (46782 ^ _777959) ^ [_1714047, _1714049, _1714051, _1714053] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1714047, _1714049, _1714051), _1714053), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1714049, _1714051), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1714047, _1714051), tc_HOL_Obool)))], (50292 ^ _777959) ^ [_1797471, _1797473, _1797475, _1797477, _1797479] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1797471), _1797473), _1797475), _1797477), _1797479) = c_New__DSequence_Opos__single(_1797471, _1797473))], (25758 ^ _777959) ^ [_1266595, _1266597, _1266599, _1266601] : [class_Rings_Odivision__ring(_1266595), -(_1266597 = c_Groups_Ozero__class_Ozero(_1266595)), _1266599 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266595), _1266601), _1266597), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266595), _1266599), _1266597) = _1266601)], (43494 ^ _777959) ^ [_1642409, _1642411, _1642413] : [-(_1642409 = c_List_Olist_ONil(_1642411)), -(hAPP(c_List_Ohd(_1642411), hAPP(c_List_Orotate(_1642411, _1642413), _1642409)) = hAPP(hAPP(c_List_Onth(_1642411), _1642409), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1642413, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642411)), _1642409))))], (15254 ^ _777959) ^ [_1068540, _1068542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068540), _1068542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068540)), hAPP(c_Nat_OSuc, _1068542))))], (40519 ^ _777959) ^ [_1564554] : [40521 ^ _777959 : [(40524 ^ _777959) ^ [] : [40520 ^ [_1564554] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (40522 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 40520 ^ [_1564554]), hAPP(c_List_Oset(tc_Nat_Onat), _1564554))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1564554) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49426 ^ _777959) ^ [_1778249, _1778251, _1778253, _1778255, _1778257] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1778249, _1778249)), hAPP(hAPP(c_Product__Type_OPair(_1778249, _1778249), _1778251), _1778253)), c_Transitive__Closure_Ortrancl(_1778249, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1778249, _1778249), tc_HOL_Obool)), _1778255), _1778257)))), 49432 ^ _777959 : [(49438 ^ _777959) ^ [] : [49431 ^ [_1778249, _1778251, _1778253, _1778255, _1778257] = 49434 ^ [_1778249, _1778251, _1778253, _1778255, _1778257]], (49436 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778249, _1778249)), hAPP(hAPP(c_Product__Type_OPair(_1778249, _1778249), 49431 ^ [_1778249, _1778251, _1778253, _1778255, _1778257]), 49434 ^ [_1778249, _1778251, _1778253, _1778255, _1778257])), _1778257)))], (49433 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778249, _1778249)), hAPP(hAPP(c_Product__Type_OPair(_1778249, _1778249), _1778251), 49431 ^ [_1778249, _1778251, _1778253, _1778255, _1778257])), c_Transitive__Closure_Ortrancl(_1778249, _1778255))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778249, _1778249)), hAPP(hAPP(c_Product__Type_OPair(_1778249, _1778249), _1778251), _1778253)), c_Transitive__Closure_Ortrancl(_1778249, _1778255))))], (20749 ^ _777959) ^ [_1173218, _1173220] : [class_Groups_Ogroup__add(_1173218), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173218), hAPP(c_Groups_Ouminus__class_Ouminus(_1173218), _1173220)), _1173220) = c_Groups_Ozero__class_Ozero(_1173218))], (20895 ^ _777959) ^ [_1175495, _1175497] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175495), _1175497), 20900 ^ _777959 : [(20903 ^ _777959) ^ [] : [-(_1175497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20901 ^ _777959) ^ [] : [-(_1175495 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20904 ^ _777959 : [(20907 ^ _777959) ^ [] : [-(_1175497 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20905 ^ _777959) ^ [] : [-(_1175495 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (37646 ^ _777959) ^ [_1497563, _1497565, _1497567, _1497569, _1497571, _1497573, _1497575, _1497577, _1497579, _1497581] : [c_Equiv__Relations_Oequiv(_1497563, _1497565, _1497567), c_Equiv__Relations_Oequiv(_1497569, _1497571, _1497573), c_Equiv__Relations_Ocongruent2(_1497563, _1497569, tc_fun(_1497575, tc_HOL_Obool), _1497567, _1497573, _1497577), hBOOL(hAPP(hAPP(c_member(_1497563), _1497579), _1497565)), hBOOL(hAPP(hAPP(c_member(_1497569), _1497581), _1497571)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1497563, tc_fun(_1497575, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1497563, _1497563, _1497567), hAPP(hAPP(c_Set_Oinsert(_1497563), _1497579), c_Orderings_Obot__class_Obot(tc_fun(_1497563, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1497569, tc_fun(_1497575, tc_HOL_Obool)), tc_fun(_1497575, tc_HOL_Obool), _1497563), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1497569, tc_fun(_1497575, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1497569, _1497569, _1497573), hAPP(hAPP(c_Set_Oinsert(_1497569), _1497581), c_Orderings_Obot__class_Obot(tc_fun(_1497569, tc_HOL_Obool)))))), _1497577)) = hAPP(hAPP(_1497577, _1497579), _1497581))], (11447 ^ _777959) ^ [_982254, _982256, _982258] : [class_Lattices_Olattice(_982254), hBOOL(hAPP(c_Finite__Set_Ofinite(_982254), _982256)), -(_982256 = c_Orderings_Obot__class_Obot(tc_fun(_982254, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_982254), _982258)), -(_982258 = c_Orderings_Obot__class_Obot(tc_fun(_982254, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982254, tc_HOL_Obool)), _982256), _982258) = c_Orderings_Obot__class_Obot(tc_fun(_982254, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_982254, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982254, tc_HOL_Obool)), _982256), _982258)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_982254), c_Big__Operators_Olattice__class_OInf__fin(_982254, _982256)), c_Big__Operators_Olattice__class_OInf__fin(_982254, _982258)))], (23625 ^ _777959) ^ [_1227353, _1227355, _1227357] : [class_Groups_Omonoid__mult(_1227353), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227353), hAPP(hAPP(c_Power_Opower__class_Opower(_1227353), _1227355), _1227357)), _1227355) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1227353), _1227355), hAPP(hAPP(c_Power_Opower__class_Opower(_1227353), _1227355), _1227357)))], (32177 ^ _777959) ^ [_1385800, _1385802, _1385804, _1385806] : [class_Fields_Ofield__inverse__zero(_1385800), class_Int_Onumber(_1385800), 32184 ^ _777959 : [(32185 ^ _777959) ^ [] : [_1385802 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385800), _1385804), hAPP(c_Int_Onumber__class_Onumber__of(_1385800), _1385806)), 32188 ^ _777959 : [(32195 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1385800), _1385806) = c_Groups_Ozero__class_Ozero(_1385800), -(_1385802 = c_Groups_Ozero__class_Ozero(_1385800))], (32189 ^ _777959) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1385800), _1385806) = c_Groups_Ozero__class_Ozero(_1385800)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385800), _1385802), hAPP(c_Int_Onumber__class_Onumber__of(_1385800), _1385806)) = _1385804)]]], (32201 ^ _777959) ^ [] : [-(_1385802 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1385800), _1385804), hAPP(c_Int_Onumber__class_Onumber__of(_1385800), _1385806))), 32204 ^ _777959 : [(32207 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385800), _1385802), hAPP(c_Int_Onumber__class_Onumber__of(_1385800), _1385806)) = _1385804], (32205 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1385800), _1385806) = c_Groups_Ozero__class_Ozero(_1385800)]], 32208 ^ _777959 : [(32211 ^ _777959) ^ [] : [_1385802 = c_Groups_Ozero__class_Ozero(_1385800)], (32209 ^ _777959) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1385800), _1385806) = c_Groups_Ozero__class_Ozero(_1385800))]]]]], (43522 ^ _777959) ^ [_1642941, _1642943, _1642945, _1642947] : [-(hAPP(hAPP(c_List_Omap(_1642941, _1642943), _1642945), hAPP(c_List_Otl(_1642941), _1642947)) = hAPP(c_List_Otl(_1642943), hAPP(hAPP(c_List_Omap(_1642941, _1642943), _1642945), _1642947)))], (3734 ^ _777959) ^ [_834435, _834437] : [_834437 = _834435, -(c_Nitpick_Oone__frac(_834437) = c_Nitpick_Oone__frac(_834435))], (46629 ^ _777959) ^ [_1709600, _1709602, _1709604, _1709606] : [-(c_List_Omaps(_1709600, _1709602, _1709604, _1709606) = c_List_Oconcat(_1709602, hAPP(hAPP(c_List_Omap(_1709600, tc_List_Olist(_1709602)), _1709604), _1709606)))], (42322 ^ _777959) ^ [_1612818, _1612820, _1612822] : [c_Relation_Orefl__on(_1612818, _1612820, _1612822), 42325 ^ _777959 : [(42328 ^ _777959) ^ [_1613000] : [hBOOL(hAPP(hAPP(c_member(_1612818), _1613000), _1612820)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1612818, _1612818)), hAPP(hAPP(c_Product__Type_OPair(_1612818, _1612818), _1613000), _1613000)), _1612822)))], (42326 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1612818, _1612818), tc_HOL_Obool)), _1612822), hAPP(hAPP(c_Product__Type_OSigma(_1612818, _1612818), _1612820), hAPP(c_COMBK(tc_fun(_1612818, tc_HOL_Obool), _1612818), _1612820)))))]]], (32865 ^ _777959) ^ [_1398754] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398754) = _1398754)], (13032 ^ _777959) ^ [_1015108, _1015110, _1015112] : [class_Lattices_Oboolean__algebra(_1015108), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1015108), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1015108), _1015110), _1015112)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1015108), hAPP(c_Groups_Ouminus__class_Ouminus(_1015108), _1015110)), hAPP(c_Groups_Ouminus__class_Ouminus(_1015108), _1015112)))], (42639 ^ _777959) ^ [_1622028, _1622030, _1622032, _1622034, _1622036, _1622038] : [class_Groups_Ocomm__monoid__mult(_1622028), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622030), _1622032)), 42649 ^ _777959 : [(42652 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1622034), hAPP(_1622036, 42648 ^ [_1622028, _1622030, _1622032, _1622034, _1622036, _1622038])))], (42650 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622030), 42648 ^ [_1622028, _1622030, _1622032, _1622034, _1622036, _1622038]), _1622032)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1622028, _1622030, c_Groups_Otimes__class_Otimes(_1622028)), hAPP(hAPP(c_COMBS(_1622030, tc_fun(_1622034, tc_HOL_Obool), _1622028), hAPP(hAPP(c_COMBC(_1622030, _1622028, tc_fun(tc_fun(_1622034, tc_HOL_Obool), _1622028)), hAPP(hAPP(c_COMBB(tc_fun(_1622034, _1622028), tc_fun(_1622028, tc_fun(tc_fun(_1622034, tc_HOL_Obool), _1622028)), _1622030), c_Finite__Set_Ofold__image(_1622028, _1622034, c_Groups_Otimes__class_Otimes(_1622028))), _1622038)), c_Groups_Oone__class_Oone(_1622028))), _1622036)), c_Groups_Oone__class_Oone(_1622028)), _1622032) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1622028, tc_prod(_1622030, _1622034), c_Groups_Otimes__class_Otimes(_1622028)), hAPP(c_Product__Type_Oprod_Oprod__case(_1622030, _1622034, _1622028), _1622038)), c_Groups_Oone__class_Oone(_1622028)), hAPP(hAPP(c_Product__Type_OSigma(_1622030, _1622034), _1622032), _1622036)))], (6165 ^ _777959) ^ [_876853, _876855, _876857, _876859] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876853, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876853, tc_HOL_Obool)), _876855), _876857)), _876859) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876853, tc_HOL_Obool)), _876855), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876853, tc_HOL_Obool)), _876857), _876859)))], (28604 ^ _777959) ^ [_1316745, _1316747] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1316745, _1316747)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1316745), hAPP(c_Nat_OSuc, _1316747)))], (51284 ^ _777959) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (6081 ^ _777959) ^ [_875323, _875325, _875327] : [class_Orderings_Olinorder(_875323), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875323), _875325), _875327))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875323), _875327), _875325)))], (33271 ^ _777959) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (48118 ^ _777959) ^ [_1746807, _1746809, _1746811] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1746807), _1746809)), -(c_Random_Ominus__shift(_1746811, _1746807, _1746809) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1746811), _1746807)), _1746809))], (7504 ^ _777959) ^ [_903981, _903983, _903985, _903987, _903989, _903991] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_903981, _903983, _903985, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_903981), _903987), _903989), _903991)) = hAPP(hAPP(hAPP(_903985, _903987), _903989), _903991))], (7874 ^ _777959) ^ [_911833, _911835, _911837, _911839] : [c_Com_Ocom_OWhile(_911833, _911835) = c_Com_Ocom_OSemi(_911837, _911839)], (31612 ^ _777959) ^ [_1374852, _1374854, _1374856, _1374858, _1374860] : [c_Com_Ocom_OCond(_1374852, _1374854, _1374856) = c_Com_Ocom_OWhile(_1374858, _1374860)], (662 ^ _777959) ^ [_788076, _788078, _788080, _788082, _788084, _788086, _788088, _788090, _788092, _788094] : [-(c_List_Olist__all2(_788092, _788088, _788084, _788080, _788076)), c_List_Olist__all2(_788094, _788090, _788086, _788082, _788078), _788094 = _788092, _788090 = _788088, _788086 = _788084, _788082 = _788080, _788078 = _788076], (31796 ^ _777959) ^ [_1378486, _1378488, _1378490] : [class_Orderings_Olinorder(_1378486), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378486), _1378488)), 31806 ^ _777959 : [(31809 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1378486), 31805 ^ [_1378486, _1378488, _1378490]), _1378490))], (31807 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1378486), 31805 ^ [_1378486, _1378488, _1378490]), _1378488)))]], hBOOL(hAPP(hAPP(c_member(_1378486), _1378490), _1378488)), -(c_Big__Operators_Olinorder__class_OMax(_1378486, _1378488) = _1378490)], (38686 ^ _777959) ^ [_1520361, _1520363, _1520365] : [c_Fun_Oinj__on(_1520361, _1520363, _1520365, c_Orderings_Otop__class_Otop(tc_fun(_1520361, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1520361), tc_List_Olist(_1520363), hAPP(c_List_Omap(_1520361, _1520363), _1520365), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1520361), tc_HOL_Obool))))], (48411 ^ _777959) ^ [_1751915, _1751917, _1751919, _1751921] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1751915, _1751915)), hAPP(hAPP(c_Product__Type_OPair(_1751915, _1751915), _1751917), _1751919)), _1751921)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1751915, _1751915)), hAPP(hAPP(c_Product__Type_OPair(_1751915, _1751915), _1751917), _1751919)), c_Transitive__Closure_Otrancl(_1751915, _1751921))))], (51046 ^ _777959) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (19498 ^ _777959) ^ [_1151204] : [-(_1151204 = 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)), _1151204)))], (34831 ^ _777959) ^ [_1433359, _1433361, _1433363] : [class_Int_Onumber__ring(_1433359), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1433359), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1433359), _1433361), _1433363)), 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(_1433359), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1433359), hAPP(hAPP(c_Power_Opower__class_Opower(_1433359), _1433361), 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(_1433359), _1433363), 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(_1433359), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433359), hAPP(c_Int_Onumber__class_Onumber__of(_1433359), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1433361)), _1433363)))], (22874 ^ _777959) ^ [_1214258, _1214260] : [class_Rings_Olinordered__semidom(_1214258), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214258), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1214258), _1214260)), c_Groups_Ozero__class_Ozero(_1214258)))], (13038 ^ _777959) ^ [_1015247, _1015249, _1015251] : [class_Lattices_Oboolean__algebra(_1015247), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1015247), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1015247), _1015249), _1015251)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1015247), hAPP(c_Groups_Ouminus__class_Ouminus(_1015247), _1015249)), hAPP(c_Groups_Ouminus__class_Ouminus(_1015247), _1015251)))], (18877 ^ _777959) ^ [_1140348, _1140350, _1140352] : [class_Orderings_Olinorder(_1140348), -(_1140350 = c_Orderings_Obot__class_Obot(tc_fun(_1140348, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1140348, tc_HOL_Obool)), _1140350), _1140352)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1140348), _1140352)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1140348), hAPP(c_Finite__Set_Ofold1(_1140348, c_Orderings_Oord__class_Omin(_1140348)), _1140352)), hAPP(c_Finite__Set_Ofold1(_1140348, c_Orderings_Oord__class_Omin(_1140348)), _1140350))))], (9542 ^ _777959) ^ [_942783, _942785, _942787] : [class_Lattices_Olattice(_942783), hBOOL(hAPP(c_Finite__Set_Ofinite(_942783), _942785)), -(_942785 = c_Orderings_Obot__class_Obot(tc_fun(_942783, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_942783), _942787)), -(_942787 = c_Orderings_Obot__class_Obot(tc_fun(_942783, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942783, tc_HOL_Obool)), _942785), _942787) = c_Orderings_Obot__class_Obot(tc_fun(_942783, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_942783, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_942783, tc_HOL_Obool)), _942785), _942787)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_942783), c_Big__Operators_Olattice__class_OSup__fin(_942783, _942785)), c_Big__Operators_Olattice__class_OSup__fin(_942783, _942787)))], (25812 ^ _777959) ^ [_1267481, _1267483] : [class_Rings_Odivision__ring__inverse__zero(_1267481), 25815 ^ _777959 : [(25822 ^ _777959) ^ [] : [-(_1267483 = c_Groups_Ozero__class_Ozero(_1267481)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267481), _1267483), _1267483) = c_Groups_Oone__class_Oone(_1267481))], (25816 ^ _777959) ^ [] : [_1267483 = c_Groups_Ozero__class_Ozero(_1267481), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267481), _1267483), _1267483) = c_Groups_Ozero__class_Ozero(_1267481))]]], (27433 ^ _777959) ^ [_1296823, _1296825] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1296823) = _1296825), _1296823 = hAPP(c_Int_Onat, _1296825), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1296825))], (17515 ^ _777959) ^ [_1112752, _1112754, _1112756] : [class_Complete__Lattice_Ocomplete__lattice(_1112752), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112752), _1112754)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1112752), _1112756), c_Complete__Lattice_OInf__class_OInf(_1112752, _1112754)) = hAPP(hAPP(c_Finite__Set_Ofold(_1112752, _1112752, c_Lattices_Osemilattice__inf__class_Oinf(_1112752)), _1112756), _1112754))], (19266 ^ _777959) ^ [_1147807, _1147809] : [class_Rings_Ocomm__semiring__1(_1147807), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1147807), c_Groups_Ozero__class_Ozero(_1147807)), _1147809) = _1147809)], (50918 ^ _777959) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (1650 ^ _777959) ^ [_801308, _801310] : [-(class_Nat_Osemiring__char__0(_801308)), _801310 = _801308, class_Nat_Osemiring__char__0(_801310)], (40983 ^ _777959) ^ [_1578280, _1578282, _1578284] : [hBOOL(hAPP(hAPP(c_member(_1578282), _1578280), c_Orderings_Obot__class_Obot(tc_fun(_1578282, tc_HOL_Obool)))), -(hBOOL(hAPP(_1578284, _1578280)))], (40761 ^ _777959) ^ [_1570162, _1570164, _1570166] : [-(c_List_Olist_Olist__size(_1570162, _1570164, _1570166) = 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(_1570162, tc_Nat_Onat), _1570164), _1570166))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1570162)), _1570166)))], (220 ^ _777959) ^ [_781481, _781483] : [-(c_Nat__Transfer_Ois__nat(_781481)), _781483 = _781481, c_Nat__Transfer_Ois__nat(_781483)], (34381 ^ _777959) ^ [] : [-(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))))], (12932 ^ _777959) ^ [_1013023, _1013025, _1013027, _1013029] : [-(hAPP(c_Set_Oimage(_1013023, _1013025, _1013027), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1013023, tc_HOL_Obool), _1013029)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1013023, tc_HOL_Obool), tc_fun(_1013025, tc_HOL_Obool)), _1013029), c_Set_Oimage(_1013023, _1013025, _1013027)))], (13955 ^ _777959) ^ [_1036706, _1036708, _1036710] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1036706, tc_HOL_Obool)), _1036708), _1036710) = hAPP(c_Set_OCollect(_1036706), hAPP(hAPP(c_COMBS(_1036706, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1036706), c_fconj), hAPP(hAPP(c_COMBC(_1036706, tc_fun(_1036706, tc_HOL_Obool), tc_HOL_Obool), c_member(_1036706)), _1036708))), hAPP(hAPP(c_COMBC(_1036706, tc_fun(_1036706, tc_HOL_Obool), tc_HOL_Obool), c_member(_1036706)), _1036710))))], (45558 ^ _777959) ^ [_1686489, _1686491] : [_1686489 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1686491, _1686489, c_List_Olist_ONil(_1686491)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1686491)), c_List_Olist_ONil(_1686491)), c_List_Olist_ONil(tc_List_Olist(_1686491))))], (43502 ^ _777959) ^ [_1642532, _1642534, _1642536] : [-(hAPP(hAPP(c_List_Odrop(_1642532), _1642534), hAPP(c_List_Otl(_1642532), _1642536)) = hAPP(c_List_Otl(_1642532), hAPP(hAPP(c_List_Odrop(_1642532), _1642534), _1642536)))], (23661 ^ _777959) ^ [_1228107, _1228109, _1228111] : [class_Rings_Olinordered__semidom(_1228107), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228107), c_Groups_Ozero__class_Ozero(_1228107)), _1228109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228107), c_Groups_Ozero__class_Ozero(_1228107)), hAPP(hAPP(c_Power_Opower__class_Opower(_1228107), _1228109), _1228111))))], (6046 ^ _777959) ^ [_874634, _874636, _874638] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874634, tc_HOL_Obool)), _874636), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_874634, tc_HOL_Obool)), _874638), _874636))))], (9796 ^ _777959) ^ [_948179, _948181, _948183] : [class_Lattices_Olattice(_948179), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948179), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_948179), _948181), _948183)), _948181)))], (13729 ^ _777959) ^ [_1031700, _1031702, _1031704, _1031706, _1031708] : [-(hAPP(c_Map_Omap__add(_1031700, _1031702, _1031704, _1031706), _1031708) = c_Option_Ooption_ONone(_1031702)), hAPP(_1031706, _1031708) = c_Option_Ooption_ONone(_1031702), hAPP(_1031704, _1031708) = c_Option_Ooption_ONone(_1031702)], (17169 ^ _777959) ^ [_1106210, _1106212, _1106214, _1106216, _1106218, _1106220, _1106222] : [c_Finite__Set_Ofun__left__comm(_1106210, _1106212, _1106214), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1106210, _1106212, _1106214, _1106216, _1106218), _1106220)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1106210, _1106212, _1106214, _1106216, _1106218), _1106222)), -(_1106222 = _1106220)], (37292 ^ _777959) ^ [_1489324] : [-(_1489324 = 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), 37289 ^ [_1489324]), 37290 ^ [_1489324])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (37948 ^ _777959) ^ [_1505127, _1505129] : [-(c_Fun_Oinj__on(_1505127, _1505127, c_COMBI(_1505127), _1505129))], (29170 ^ _777959) ^ [_1327800, _1327802] : [class_Orderings_Olinorder(_1327800), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327800, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1327800), _1327802)), hAPP(hAPP(c_Set_Oinsert(_1327800), _1327802), c_Orderings_Obot__class_Obot(tc_fun(_1327800, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_1327800), _1327802))], (9292 ^ _777959) ^ [_937697, _937699, _937701] : [class_Lattices_Olattice(_937697), hBOOL(hAPP(c_Finite__Set_Ofinite(_937697), _937699)), hBOOL(hAPP(hAPP(c_member(_937697), _937701), _937699)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_937697), _937701), c_Big__Operators_Olattice__class_OSup__fin(_937697, _937699)) = c_Big__Operators_Olattice__class_OSup__fin(_937697, _937699))], (18590 ^ _777959) ^ [_1135257, _1135259] : [class_Orderings_Olinorder(_1135257), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135257), _1135259)), -(c_Big__Operators_Olinorder__class_OMin(_1135257, _1135259) = hAPP(c_Finite__Set_Ofold1(_1135257, c_Orderings_Oord__class_Omin(_1135257)), _1135259))], (51078 ^ _777959) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (30160 ^ _777959) ^ [_1348338, _1348340] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1348338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1348340, _1348338)), _1348338)))], (12712 ^ _777959) ^ [_1008630, _1008632, _1008634] : [class_Lattices_Oboolean__algebra(_1008630), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008630), _1008632), _1008634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008630), hAPP(c_Groups_Ouminus__class_Ouminus(_1008630), _1008634)), hAPP(c_Groups_Ouminus__class_Ouminus(_1008630), _1008632))))], (33871 ^ _777959) ^ [_1415931, _1415933] : [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(_1415933))), 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), _1415931)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415931)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415933))))], (47622 ^ _777959) ^ [_1735181] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 47618 ^ [_1735181]), c_Int_OInteg)))], (46760 ^ _777959) ^ [_1713366, _1713368, _1713370, _1713372, _1713374, _1713376, _1713378, _1713380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1713366, _1713368), tc_HOL_Obool)), _1713370), hAPP(hAPP(c_Product__Type_OSigma(_1713366, _1713368), _1713372), hAPP(c_COMBK(tc_fun(_1713368, tc_HOL_Obool), _1713366), _1713374)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1713368, _1713376), tc_HOL_Obool)), _1713378), hAPP(hAPP(c_Product__Type_OSigma(_1713368, _1713376), _1713374), hAPP(c_COMBK(tc_fun(_1713376, tc_HOL_Obool), _1713368), _1713380)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1713366, _1713376), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1713366, _1713368, _1713376), _1713370), _1713378)), hAPP(hAPP(c_Product__Type_OSigma(_1713366, _1713376), _1713372), hAPP(c_COMBK(tc_fun(_1713376, tc_HOL_Obool), _1713366), _1713380)))))], (31178 ^ _777959) ^ [_1366866, _1366868, _1366870] : [class_Groups_Oordered__ab__group__add__abs(_1366866), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366866), hAPP(c_Groups_Oabs__class_Oabs(_1366866), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1366866), hAPP(c_Groups_Oabs__class_Oabs(_1366866), _1366868)), hAPP(c_Groups_Oabs__class_Oabs(_1366866), _1366870)))), hAPP(c_Groups_Oabs__class_Oabs(_1366866), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1366866), _1366868), _1366870)))))], (49072 ^ _777959) ^ [_1769615, _1769617, _1769619, _1769621, _1769623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1769617, tc_HOL_Obool)), _1769621), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1769617, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1769615, _1769617, hAPP(c_Relation_Oconverse(_1769617, _1769615), _1769619)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1769615, tc_HOL_Obool)), _1769623))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1769615, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1769617, _1769615, _1769619), _1769621)), _1769623)))], (40695 ^ _777959) ^ [_1568720, _1568722, _1568724] : [hBOOL(hAPP(_1568720, _1568722)), -(hBOOL(hAPP(_1568720, c_Hilbert__Choice_OEps(_1568724, _1568720))))], (44736 ^ _777959) ^ [_1667092, _1667094, _1667096, _1667098] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1667092, tc_Nat_Onat), _1667092), c_Product__Type_Ofst(_1667092, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1667092, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1667092, 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(_1667092, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1667092, tc_Nat_Onat))), _1667094)), hAPP(hAPP(c_List_Ozip(_1667092, tc_Nat_Onat), _1667096), c_List_Oupt(_1667098, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1667098), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667092)), _1667096)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1667092, tc_Nat_Onat), _1667092), c_Product__Type_Ofst(_1667092, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1667092, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1667092, 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(_1667092, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1667092, 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(_1667092, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1667092, tc_Nat_Onat))), _1667098))), _1667094)), hAPP(hAPP(c_List_Ozip(_1667092, tc_Nat_Onat), _1667096), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667092)), _1667096))))))], (8886 ^ _777959) ^ [_931058, _931060, _931062] : [class_Orderings_Opreorder(_931058), 8889 ^ _777959 : [(8898 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931058), _931060), _931062))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931058), _931060), _931062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931058), _931062), _931060)))], (8890 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931058), _931060), _931062)), 8893 ^ _777959 : [(8896 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931058), _931062), _931060))], (8894 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931058), _931060), _931062)))]]]]], (12052 ^ _777959) ^ [_996565] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996565), _996565)))], (37887 ^ _777959) ^ [] : [-(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))], (22814 ^ _777959) ^ [_1213143, _1213145, _1213147] : [class_Rings_Ocomm__semiring__1(_1213143), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213143), hAPP(hAPP(c_Power_Opower__class_Opower(_1213143), _1213145), _1213147)), _1213145) = hAPP(hAPP(c_Power_Opower__class_Opower(_1213143), _1213145), hAPP(c_Nat_OSuc, _1213147)))], (22168 ^ _777959) ^ [_1199601, _1199603] : [-(_1199601 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1199601), _1199603) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1199603), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1199601), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1199603)))], (9940 ^ _777959) ^ [_950692, _950694, _950696, _950698] : [class_Lattices_Osemilattice__inf(_950692), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950692), _950694), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950692), _950696), _950698))), 9947 ^ _777959 : [(9950 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950692), _950694), _950698)))], (9948 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950692), _950694), _950696)))]]], (34953 ^ _777959) ^ [_1436215] : [c_Int_OBit0(_1436215) = c_Int_OMin], (45532 ^ _777959) ^ [_1685862, _1685864, _1685866] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1685862))), c_Enum_On__lists(_1685862, _1685864, _1685866)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685862)), _1685866)), _1685864))], (42997 ^ _777959) ^ [_1630137, _1630139, _1630141, _1630143, _1630145] : [-(hAPP(hAPP(c_List_Olist__update(_1630137, hAPP(hAPP(c_List_Oappend(_1630137), _1630139), hAPP(hAPP(c_List_Olist_OCons(_1630137), _1630141), _1630143))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630137)), _1630139)), _1630145) = hAPP(hAPP(c_List_Oappend(_1630137), _1630139), hAPP(hAPP(c_List_Olist_OCons(_1630137), _1630145), _1630143)))], (35385 ^ _777959) ^ [_1447381, _1447383, _1447385, _1447387] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1447381, tc_fun(_1447383, tc_HOL_Obool))), _1447385), _1447387)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1447381, _1447383)), hAPP(hAPP(c_Product__Type_OPair(_1447381, _1447383), _1447385), _1447387)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1447381, _1447383), tc_HOL_Obool)))))], (23463 ^ _777959) ^ [_1224687, _1224689] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224687), _1224689))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224689), _1224687)))], (19053 ^ _777959) ^ [_1144147, _1144149] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1144147, _1144149)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1144147, _1144149), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1144149), c_Orderings_Otop__class_Otop(tc_fun(_1144149, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1144147), c_Orderings_Otop__class_Otop(tc_fun(_1144147, tc_HOL_Obool)))))], (42979 ^ _777959) ^ [_1629655, _1629657, _1629659] : [_1629655 = _1629657, -(_1629655 = hAPP(hAPP(c_List_Oappend(_1629659), c_List_Olist_ONil(_1629659)), _1629657))], (230 ^ _777959) ^ [_781606, _781608] : [-(class_Fields_Olinordered__field__inverse__zero(_781606)), _781608 = _781606, class_Fields_Olinordered__field__inverse__zero(_781608)], (44122 ^ _777959) ^ [_1656000] : [class_Orderings_Olinorder(_1656000), -(c_List_Olinorder__class_Osorted(_1656000, c_List_Olist_ONil(_1656000)))], (12896 ^ _777959) ^ [_1012089, _1012091, _1012093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012089, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1012089, tc_HOL_Obool)), _1012091)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1012089, tc_HOL_Obool)), _1012093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012089, tc_HOL_Obool)), _1012093), _1012091)))], (50324 ^ _777959) ^ [_1798544, _1798546, _1798548, _1798550] : [-(hAPP(c_New__DSequence_Opos__union(_1798544, _1798546, _1798548), _1798550) = c_Lazy__Sequence_Oappend(_1798544, hAPP(_1798546, _1798550), hAPP(_1798548, _1798550)))], (13567 ^ _777959) ^ [_1027053, _1027055, _1027057, _1027059, _1027061] : [_1027053 = c_Orderings_Obot__class_Obot(tc_fun(_1027055, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1027055, tc_fun(_1027057, tc_HOL_Obool)), _1027053), hAPP(hAPP(c_COMBC(_1027055, tc_fun(_1027057, tc_HOL_Obool), tc_fun(_1027057, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1027057, tc_HOL_Obool), tc_fun(tc_fun(_1027057, tc_HOL_Obool), tc_fun(_1027057, tc_HOL_Obool)), _1027055), c_Groups_Ominus__class_Ominus(tc_fun(_1027057, tc_HOL_Obool))), _1027059)), _1027061)) = c_Orderings_Otop__class_Otop(tc_fun(_1027057, tc_HOL_Obool)))], (46104 ^ _777959) ^ [_1698062, _1698064, _1698066, _1698068] : [class_Enum_Oenum(_1698062), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698064)), _1698066) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698062)), c_Enum_Oenum__class_Oenum(_1698062)), -(hAPP(hAPP(c_Map_Omap__of(_1698062, _1698064), hAPP(hAPP(c_List_Ozip(_1698062, _1698064), c_Enum_Oenum__class_Oenum(_1698062)), _1698066)), _1698068) = hAPP(c_Option_Ooption_OSome(_1698064), 46111 ^ [_1698062, _1698064, _1698066, _1698068]))], (23643 ^ _777959) ^ [_1227752, _1227754, _1227756] : [class_Rings_Osemiring__1(_1227752), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1227752), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1227754), _1227756)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1227752), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1227752), _1227754)), _1227756))], (6341 ^ _777959) ^ [_880346, _880348, _880350, _880352] : [_880346 = _880348, 6344 ^ _777959 : [(6351 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_880350), _880348), _880352)), -(hBOOL(hAPP(hAPP(c_member(_880350), _880346), _880352)))], (6345 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_880350), _880346), _880352)), -(hBOOL(hAPP(hAPP(c_member(_880350), _880348), _880352)))]]], (50804 ^ _777959) ^ [_1808030, _1808032] : [class_Lattices_Olattice(_1808030), -(class_Lattices_Olattice(tc_fun(_1808032, _1808030)))], (21968 ^ _777959) ^ [_1195720, _1195722, _1195724, _1195726] : [class_Groups_Ocomm__monoid__mult(_1195720), hBOOL(hAPP(c_Finite__Set_Ofinite(_1195722), _1195724)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1195722, _1195720), _1195726), _1195724) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1195720, _1195722, c_Groups_Otimes__class_Otimes(_1195720)), _1195726), c_Groups_Oone__class_Oone(_1195720)), _1195724))], (43974 ^ _777959) ^ [_1652304, _1652306, _1652308, _1652310] : [-(hAPP(c_List_Ofilter(_1652304, _1652306), c_List_Oremove1(_1652304, _1652308, _1652310)) = c_List_Oremove1(_1652304, _1652308, hAPP(c_List_Ofilter(_1652304, _1652306), _1652310)))], (43340 ^ _777959) ^ [_1638995, _1638997, _1638999, _1639001] : [_1638995 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1638997), _1638995), hAPP(hAPP(c_List_Olist_OCons(_1638997), _1638999), _1639001)) = hAPP(hAPP(c_List_Olist_OCons(_1638997), _1638999), _1639001))], (28592 ^ _777959) ^ [_1316505, _1316507] : [class_Orderings_Oorder(_1316505), -(c_SetInterval_Oord__class_OatLeastAtMost(_1316505, _1316507, _1316507) = hAPP(hAPP(c_Set_Oinsert(_1316505), _1316507), c_Orderings_Obot__class_Obot(tc_fun(_1316505, tc_HOL_Obool))))], (45320 ^ _777959) ^ [_1681190, _1681192] : [hBOOL(hAPP(c_List_Odistinct(_1681190), _1681192)), -(c_List_Oremdups(_1681190, _1681192) = _1681192)], (8654 ^ _777959) ^ [_927356, _927358, _927360, _927362] : [class_Orderings_Opreorder(_927356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927356), _927358), _927360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927356), _927360), _927362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927356), _927358), _927362)))], (38484 ^ _777959) ^ [] : [-(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))], (35505 ^ _777959) ^ [_1450915] : [class_Rings_Osemiring__1(_1450915), -(hBOOL(hAPP(hAPP(c_member(_1450915), c_Groups_Ozero__class_Ozero(_1450915)), c_Nat_Osemiring__1__class_ONats(_1450915))))], (12147 ^ _777959) ^ [_998393, _998395, _998397] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998393), _998395)), _998397)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998393), _998397)))], (24387 ^ _777959) ^ [_1241231, _1241233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241231)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1241233)), -(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), _1241231), _1241233))))], (51014 ^ _777959) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (28560 ^ _777959) ^ [_1315996, _1315998, _1316000] : [class_Orderings_Oorder(_1315996), _1315998 = _1316000, -(c_SetInterval_Oord__class_OatLeastAtMost(_1315996, _1315998, _1316000) = hAPP(hAPP(c_Set_Oinsert(_1315996), _1315998), c_Orderings_Obot__class_Obot(tc_fun(_1315996, tc_HOL_Obool))))], (41431 ^ _777959) ^ [_1590010, _1590012, _1590014, _1590016, _1590018, _1590020] : [c_List_Olistrelp(_1590010, _1590012, hAPP(hAPP(c_List_Olist_OCons(_1590010), _1590014), _1590016), hAPP(hAPP(c_List_Olist_OCons(_1590010), _1590018), _1590020)), 41434 ^ _777959 : [(41437 ^ _777959) ^ [] : [-(c_List_Olistrelp(_1590010, _1590012, _1590016, _1590020))], (41435 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1590012, _1590014), _1590018)))]]], (46298 ^ _777959) ^ [_1702480, _1702482] : [class_Orderings_Olinorder(_1702480), 46301 ^ _777959 : [(46322 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1702480, _1702482)), 46323 ^ _777959 : [(46326 ^ _777959) ^ [_1703040, _1703042] : [_1702482 = hAPP(hAPP(c_List_Olist_OCons(_1702480), _1703040), _1703042), 46332 ^ _777959 : [(46335 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1702480), _1703040), 46331 ^ [_1702480, _1702482, _1703040, _1703042]))], (46333 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1702480), 46331 ^ [_1702480, _1702482, _1703040, _1703042]), hAPP(c_List_Oset(_1702480), _1703042))))]], c_List_Olinorder__class_Osorted(_1702480, _1703042)], (46324 ^ _777959) ^ [] : [_1702482 = c_List_Olist_ONil(_1702480)]]], (46302 ^ _777959) ^ [] : [c_List_Olinorder__class_Osorted(_1702480, _1702482), -(_1702482 = c_List_Olist_ONil(_1702480)), 46311 ^ _777959 : [(46314 ^ _777959) ^ [_1702814] : [hBOOL(hAPP(hAPP(c_member(_1702480), _1702814), hAPP(c_List_Oset(_1702480), 46309 ^ [_1702480, _1702482]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1702480), 46310 ^ [_1702480, _1702482]), _1702814)))], (46320 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1702480, 46309 ^ [_1702480, _1702482]))], (46312 ^ _777959) ^ [] : [-(_1702482 = hAPP(hAPP(c_List_Olist_OCons(_1702480), 46310 ^ [_1702480, _1702482]), 46309 ^ [_1702480, _1702482]))]]]]], (43560 ^ _777959) ^ [_1643682, _1643684, _1643686] : [-(hAPP(hAPP(c_List_Odrop(_1643682), hAPP(c_Nat_OSuc, _1643684)), _1643686) = hAPP(hAPP(c_List_Odrop(_1643682), _1643684), hAPP(c_List_Otl(_1643682), _1643686)))], (10174 ^ _777959) ^ [_956086, _956088, _956090, _956092] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956086, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_956086, tc_fun(_956086, tc_HOL_Obool), tc_HOL_Obool), c_member(_956086)), _956088)), hAPP(hAPP(c_COMBC(_956086, tc_fun(_956086, tc_HOL_Obool), tc_HOL_Obool), c_member(_956086)), _956090)), _956092)), -(hBOOL(hAPP(hAPP(c_member(_956086), _956092), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956086, tc_HOL_Obool)), _956088), _956090))))], (13753 ^ _777959) ^ [_1032299, _1032301, _1032303, _1032305, _1032307] : [_1032299 = c_Orderings_Obot__class_Obot(tc_fun(_1032301, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1032301, tc_fun(_1032303, tc_HOL_Obool)), _1032299), hAPP(hAPP(c_COMBB(tc_fun(_1032303, tc_HOL_Obool), tc_fun(_1032303, tc_HOL_Obool), _1032301), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1032303, tc_HOL_Obool)), _1032305)), _1032307)) = c_Orderings_Otop__class_Otop(tc_fun(_1032303, tc_HOL_Obool)))], (26696 ^ _777959) ^ [_1283526, _1283528, _1283530, _1283532] : [class_Fields_Olinordered__field(_1283526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283526), c_Groups_Ozero__class_Ozero(_1283526)), _1283528)), 26703 ^ _777959 : [(26710 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283526), _1283530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283526), _1283532), _1283528))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283526), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1283526), _1283530), _1283528)), _1283532)))], (26704 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283526), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1283526), _1283530), _1283528)), _1283532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1283526), _1283530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1283526), _1283532), _1283528))))]]], (8218 ^ _777959) ^ [_919599, _919601, _919603, _919605, _919607, _919609, _919611, _919613] : [c_Finite__Set_Ofolding__image__simple__idem(_919599, _919601, _919603, _919605, _919607, _919609), hBOOL(hAPP(c_Finite__Set_Ofinite(_919601), _919611)), -(hAPP(_919609, hAPP(hAPP(c_Set_Oinsert(_919601), _919613), _919611)) = hAPP(hAPP(_919603, hAPP(_919607, _919613)), hAPP(_919609, _919611)))], (49066 ^ _777959) ^ [_1769424, _1769426, _1769428, _1769430, _1769432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1769424, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1769426, _1769424, _1769428), _1769430)), _1769432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1769426, tc_HOL_Obool)), _1769430), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1769426, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1769424, _1769426, hAPP(c_Relation_Oconverse(_1769426, _1769424), _1769428)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1769424, tc_HOL_Obool)), _1769432))))))], (9766 ^ _777959) ^ [_947448, _947450] : [class_Lattices_Osemilattice__inf(_947448), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_947448), _947450), _947450) = _947450)], (50011 ^ _777959) ^ [_1792155, _1792157, _1792159] : [c_FunDef_Ois__measure(_1792155, _1792157), -(c_FunDef_Ois__measure(tc_prod(_1792159, _1792155), hAPP(hAPP(c_COMBB(_1792155, tc_Nat_Onat, tc_prod(_1792159, _1792155)), _1792157), c_Product__Type_Osnd(_1792159, _1792155))))], (48306 ^ _777959) ^ [_1750173] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1750173)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (6455 ^ _777959) ^ [_882262, _882264, _882266, _882268] : [class_Orderings_Oord(_882262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882262), _882264), _882266)), _882266 = _882268, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882262), _882264), _882268)))], (23855 ^ _777959) ^ [_1231608, _1231610, _1231612] : [class_Rings_Olinordered__semidom(_1231608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231608), c_Groups_Oone__class_Oone(_1231608)), _1231610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231608), c_Groups_Oone__class_Oone(_1231608)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231608), _1231610), hAPP(hAPP(c_Power_Opower__class_Opower(_1231608), _1231610), _1231612)))))], (34323 ^ _777959) ^ [_1424035] : [-(c_Int_Osucc(c_Int_OBit0(_1424035)) = c_Int_OBit1(_1424035))], (50934 ^ _777959) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (47189 ^ _777959) ^ [_1724533, _1724535, _1724537, _1724539] : [-(_1724533 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1724535, tc_HOL_Obool), tc_HOL_Obool))), 47195 ^ _777959 : [(47198 ^ _777959) ^ [] : [c_Fun_Oinj__on(_1724535, _1724537, _1724539, 47194 ^ [_1724533, _1724535, _1724537, _1724539])], (47196 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1724535, tc_HOL_Obool)), 47194 ^ [_1724533, _1724535, _1724537, _1724539]), _1724533)))]], -(c_Fun_Oinj__on(_1724535, _1724537, _1724539, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1724535, tc_HOL_Obool), _1724533)))], (14702 ^ _777959) ^ [_1054263, _1054265, _1054267, _1054269] : [hBOOL(hAPP(hAPP(c_member(_1054263), _1054265), c_SetInterval_Oord_OgreaterThan(_1054263, _1054267, _1054269))), -(hBOOL(hAPP(hAPP(_1054267, _1054269), _1054265)))], (41727 ^ _777959) ^ [_1598188, _1598190, _1598192, _1598194, _1598196, _1598198, _1598200, _1598202, _1598204, _1598206] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1598188, _1598190), tc_prod(_1598192, _1598194), tc_prod(_1598196, _1598198), c_Product__Type_Omap__pair(_1598188, _1598192, _1598190, _1598194, _1598200, _1598202)), c_Product__Type_Omap__pair(_1598196, _1598188, _1598198, _1598190, _1598204, _1598206)) = c_Product__Type_Omap__pair(_1598196, _1598192, _1598198, _1598194, hAPP(c_Fun_Ocomp(_1598188, _1598192, _1598196, _1598200), _1598204), hAPP(c_Fun_Ocomp(_1598190, _1598194, _1598198, _1598202), _1598206)))], (32037 ^ _777959) ^ [_1383016, _1383018, _1383020] : [class_Int_Onumber__ring(_1383016), class_Rings_Olinordered__idom(_1383016), 32044 ^ _777959 : [(32051 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383018), _1383020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383016), hAPP(c_Int_Onumber__class_Onumber__of(_1383016), _1383018)), hAPP(c_Int_Onumber__class_Onumber__of(_1383016), _1383020))))], (32045 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383016), hAPP(c_Int_Onumber__class_Onumber__of(_1383016), _1383018)), hAPP(c_Int_Onumber__class_Onumber__of(_1383016), _1383020))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1383018), _1383020)))]]], (2484 ^ _777959) ^ [_814772, _814774, _814776, _814778] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_814778, _814774) = c_Code__Numeral_Odiv__mod__code__numeral(_814776, _814772)), _814778 = _814776, _814774 = _814772], (42046 ^ _777959) ^ [_1606495, _1606497, _1606499, _1606501] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1606495, _1606497), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1606495, tc_HOL_Obool), _1606499)), _1606501) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1606495, tc_HOL_Obool), tc_fun(tc_prod(_1606495, _1606497), tc_HOL_Obool)), _1606499), hAPP(hAPP(c_COMBC(tc_fun(_1606495, tc_HOL_Obool), tc_fun(_1606495, tc_fun(_1606497, tc_HOL_Obool)), tc_fun(tc_prod(_1606495, _1606497), tc_HOL_Obool)), c_Product__Type_OSigma(_1606495, _1606497)), _1606501)))], (41842 ^ _777959) ^ [_1601358, _1601360, _1601362, _1601364, _1601366, _1601368] : [-(hAPP(c_Set_Oimage(_1601358, tc_prod(_1601360, _1601362), hAPP(hAPP(c_COMBS(_1601358, _1601362, tc_prod(_1601360, _1601362)), hAPP(hAPP(c_COMBB(_1601360, tc_fun(_1601362, tc_prod(_1601360, _1601362)), _1601358), c_Product__Type_OPair(_1601360, _1601362)), _1601364)), _1601366)), _1601368) = hAPP(hAPP(c_Product__Type_OSigma(_1601360, _1601362), hAPP(c_Set_Oimage(_1601358, _1601360, _1601364), _1601368)), hAPP(hAPP(c_COMBB(tc_fun(_1601358, tc_HOL_Obool), tc_fun(_1601362, tc_HOL_Obool), _1601360), c_Set_Oimage(_1601358, _1601362, _1601366)), hAPP(hAPP(c_COMBC(_1601360, tc_fun(_1601358, tc_HOL_Obool), tc_fun(_1601358, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1601358, tc_HOL_Obool), tc_fun(tc_fun(_1601358, tc_HOL_Obool), tc_fun(_1601358, tc_HOL_Obool)), _1601360), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1601358, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1601360, tc_HOL_Obool), tc_fun(_1601358, tc_HOL_Obool), _1601360), c_Set_Ovimage(_1601358, _1601360, _1601364)), hAPP(hAPP(c_COMBC(_1601360, tc_fun(_1601360, tc_HOL_Obool), tc_fun(_1601360, tc_HOL_Obool)), c_Set_Oinsert(_1601360)), c_Orderings_Obot__class_Obot(tc_fun(_1601360, tc_HOL_Obool)))))), _1601368))))], (5875 ^ _777959) ^ [_871314, _871316, _871318] : [hAPP(hAPP(c_Set_Oinsert(_871314), _871316), _871318) = c_Orderings_Obot__class_Obot(tc_fun(_871314, tc_HOL_Obool))], (15438 ^ _777959) ^ [_1071518, _1071520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071518), _1071520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071518), hAPP(c_Nat_OSuc, _1071520))))], (23425 ^ _777959) ^ [_1223994, _1223996, _1223998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223994), _1223996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1223994), _1223998)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1223996), _1223998))))], (37698 ^ _777959) ^ [_1499145, _1499147] : [-(c_Equiv__Relations_Oequivp(_1499145, _1499147)), 37703 ^ _777959 : [(37706 ^ _777959) ^ [] : [hAPP(_1499147, 37699 ^ [_1499145, _1499147]) = hAPP(_1499147, 37700 ^ [_1499145, _1499147])], (37704 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1499147, 37699 ^ [_1499145, _1499147]), 37700 ^ [_1499145, _1499147])))]], 37707 ^ _777959 : [(37710 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1499147, 37699 ^ [_1499145, _1499147]), 37700 ^ [_1499145, _1499147]))], (37708 ^ _777959) ^ [] : [-(hAPP(_1499147, 37699 ^ [_1499145, _1499147]) = hAPP(_1499147, 37700 ^ [_1499145, _1499147]))]]], (43512 ^ _777959) ^ [_1642747, _1642749, _1642751] : [_1642751 = c_List_Olist_ONil(_1642747), -(hAPP(c_List_Orotate(_1642747, _1642749), _1642751) = c_List_Olist_ONil(_1642747))], (4974 ^ _777959) ^ [_853885, _853887, _853889, _853891] : [-(c_Lazy__Sequence_Osmall__lazy_H(_853891, _853887) = c_Lazy__Sequence_Osmall__lazy_H(_853889, _853885)), _853891 = _853889, _853887 = _853885], (26058 ^ _777959) ^ [_1272029, _1272031, _1272033, _1272035] : [class_Fields_Olinordered__field(_1272029), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1272029), c_Groups_Ozero__class_Ozero(_1272029)), _1272031)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1272029), _1272033), _1272031)), _1272035)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272029), _1272033), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272029), _1272035), _1272031))))], (9760 ^ _777959) ^ [_947311, _947313, _947315, _947317, _947319] : [class_Lattices_Olattice(_947311), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947313, _947311)), _947315), _947317), _947319) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_947311), hAPP(_947315, _947319)), hAPP(_947317, _947319)))], (35469 ^ _777959) ^ [_1450054, _1450056, _1450058, _1450060, _1450062, _1450064] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1450056, _1450058)), hAPP(hAPP(c_Product__Type_OPair(_1450056, _1450058), _1450062), _1450064)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1450054, tc_fun(tc_prod(_1450056, _1450058), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1450054, tc_HOL_Obool))), _1450060))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1450054, tc_fun(_1450056, tc_fun(_1450058, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1450054, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1450056, _1450058), tc_HOL_Obool), tc_fun(_1450056, tc_fun(_1450058, tc_HOL_Obool)), _1450054), hAPP(c_COMBC(_1450056, tc_fun(tc_prod(_1450056, _1450058), tc_HOL_Obool), tc_fun(_1450058, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450058, tc_fun(tc_fun(tc_prod(_1450056, _1450058), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1450056, _1450058), tc_HOL_Obool), tc_fun(_1450058, tc_HOL_Obool)), _1450056), c_COMBC(_1450058, tc_fun(tc_prod(_1450056, _1450058), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1450058, tc_prod(_1450056, _1450058)), tc_fun(_1450058, tc_fun(tc_fun(tc_prod(_1450056, _1450058), tc_HOL_Obool), tc_HOL_Obool)), _1450056), hAPP(c_COMBB(tc_prod(_1450056, _1450058), tc_fun(tc_fun(tc_prod(_1450056, _1450058), tc_HOL_Obool), tc_HOL_Obool), _1450058), c_member(tc_prod(_1450056, _1450058)))), c_Product__Type_OPair(_1450056, _1450058))))), _1450060)), _1450062), _1450064)))], (16473 ^ _777959) ^ [_1093311, _1093313, _1093315, _1093317] : [class_Orderings_Olinorder(_1093311), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093311), _1093313), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093311), _1093315), _1093317)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093311), _1093315), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093311), _1093313), _1093317)))], (42116 ^ _777959) ^ [_1607885, _1607887, _1607889, _1607891, _1607893, _1607895] : [hBOOL(hAPP(hAPP(c_member(_1607885), _1607887), _1607889)), 42119 ^ _777959 : [(42126 ^ _777959) ^ [] : [_1607893 = _1607895, -(hAPP(hAPP(c_Product__Type_OSigma(_1607891, _1607885), _1607893), hAPP(c_COMBK(tc_fun(_1607885, tc_HOL_Obool), _1607891), _1607889)) = hAPP(hAPP(c_Product__Type_OSigma(_1607891, _1607885), _1607895), hAPP(c_COMBK(tc_fun(_1607885, tc_HOL_Obool), _1607891), _1607889)))], (42120 ^ _777959) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1607891, _1607885), _1607893), hAPP(c_COMBK(tc_fun(_1607885, tc_HOL_Obool), _1607891), _1607889)) = hAPP(hAPP(c_Product__Type_OSigma(_1607891, _1607885), _1607895), hAPP(c_COMBK(tc_fun(_1607885, tc_HOL_Obool), _1607891), _1607889)), -(_1607893 = _1607895)]]], (13669 ^ _777959) ^ [_1030238, _1030240, _1030242, _1030244, _1030246, _1030248] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030238, tc_fun(_1030240, tc_HOL_Obool)), _1030242), hAPP(hAPP(c_COMBC(_1030238, tc_fun(_1030244, tc_fun(_1030240, tc_HOL_Obool)), tc_fun(_1030240, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1030244, tc_HOL_Obool), tc_fun(tc_fun(_1030244, tc_fun(_1030240, tc_HOL_Obool)), tc_fun(_1030240, tc_HOL_Obool)), _1030238), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030244, tc_fun(_1030240, tc_HOL_Obool))), _1030246)), _1030248)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030244, tc_fun(_1030240, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1030238, tc_fun(_1030244, tc_HOL_Obool)), _1030242), _1030246)), _1030248))], (34583 ^ _777959) ^ [_1428847, _1428849, _1428851] : [class_Rings_Olinordered__semidom(_1428847), hAPP(hAPP(c_Power_Opower__class_Opower(_1428847), _1428849), 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(_1428847), _1428851), 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(_1428847), c_Groups_Ozero__class_Ozero(_1428847)), _1428849)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428847), c_Groups_Ozero__class_Ozero(_1428847)), _1428851)), -(_1428849 = _1428851)], (38624 ^ _777959) ^ [_1518993, _1518995, _1518997, _1518999, _1519001, _1519003, _1519005] : [c_Typedef_Otype__definition(_1518993, _1518995, _1518997, _1518999, _1519001), hBOOL(hAPP(hAPP(c_member(_1518995), _1519003), _1519001)), hBOOL(hAPP(hAPP(c_member(_1518995), _1519005), _1519001)), 38635 ^ _777959 : [(38642 ^ _777959) ^ [] : [_1519003 = _1519005, -(hAPP(_1518999, _1519003) = hAPP(_1518999, _1519005))], (38636 ^ _777959) ^ [] : [hAPP(_1518999, _1519003) = hAPP(_1518999, _1519005), -(_1519003 = _1519005)]]], (28396 ^ _777959) ^ [_1313317] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1313317)))], (27351 ^ _777959) ^ [_1295513] : [hAPP(c_Int_Onat, _1295513) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295513), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34503 ^ _777959) ^ [] : [-(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)))))], (23781 ^ _777959) ^ [_1230173, _1230175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1230173)), -(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), _1230173), _1230175))))], (13751 ^ _777959) ^ [_1032209, _1032211, _1032213, _1032215, _1032217] : [-(hAPP(c_Set_Oimage(_1032209, _1032211, hAPP(hAPP(c_COMBB(_1032213, _1032211, _1032209), _1032215), _1032217)), c_Orderings_Otop__class_Otop(tc_fun(_1032209, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_1032213, _1032211, _1032215), hAPP(c_Set_Oimage(_1032209, _1032213, _1032217), c_Orderings_Otop__class_Otop(tc_fun(_1032209, tc_HOL_Obool)))))], (14067 ^ _777959) ^ [_1039289, _1039291, _1039293, _1039295, _1039297] : [-(hBOOL(hAPP(hAPP(c_member(_1039289), _1039291), c_Map_Odom(_1039289, _1039293, _1039295)))), -(hAPP(c_Map_Omap__add(_1039289, _1039293, _1039295, _1039297), _1039291) = hAPP(_1039297, _1039291))], (8008 ^ _777959) ^ [_914734, _914736, _914738] : [hAPP(c_Com_Ocom_OBODY, _914734) = c_Com_Ocom_OSemi(_914736, _914738)], (45348 ^ _777959) ^ [_1681724] : [-(c_List_Oembed__list(_1681724) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1681724))], (49424 ^ _777959) ^ [_1778204, _1778206, _1778208, _1778210] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1778204, _1778206, _1778208, _1778210) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1778204, _1778206), _1778208), _1778210)))], (44202 ^ _777959) ^ [_1657347, _1657349, _1657351, _1657353] : [class_Orderings_Olinorder(_1657347), 44205 ^ _777959 : [(44214 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1657347, hAPP(hAPP(c_List_Olist_OCons(_1657347), _1657349), hAPP(hAPP(c_List_Olist_OCons(_1657347), _1657351), _1657353)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1657347), _1657349), _1657351)), c_List_Olinorder__class_Osorted(_1657347, hAPP(hAPP(c_List_Olist_OCons(_1657347), _1657351), _1657353))], (44206 ^ _777959) ^ [] : [c_List_Olinorder__class_Osorted(_1657347, hAPP(hAPP(c_List_Olist_OCons(_1657347), _1657349), hAPP(hAPP(c_List_Olist_OCons(_1657347), _1657351), _1657353))), 44209 ^ _777959 : [(44212 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1657347, hAPP(hAPP(c_List_Olist_OCons(_1657347), _1657351), _1657353)))], (44210 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1657347), _1657349), _1657351)))]]]]], (24374 ^ _777959) ^ [_1241036] : [24375 ^ _777959 : [(24376 ^ _777959) ^ [_1241093] : [hBOOL(hAPP(_1241036, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241093)))]], 24378 ^ _777959 : [(24381 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1241036, 24377 ^ [_1241036])))], (24379 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24377 ^ [_1241036])))]]], (23407 ^ _777959) ^ [_1223790, _1223792, _1223794] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1223790), _1223792)), _1223794) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223790), _1223794)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223792), _1223794)))], (19019 ^ _777959) ^ [_1143215, _1143217, _1143219, _1143221, _1143223] : [hAPP(hAPP(c_Option_Omap(_1143215, _1143217), _1143219), _1143221) = hAPP(c_Option_Ooption_OSome(_1143217), _1143223), 19023 ^ _777959 : [(19026 ^ _777959) ^ [] : [-(hAPP(_1143219, 19022 ^ [_1143215, _1143217, _1143219, _1143221, _1143223]) = _1143223)], (19024 ^ _777959) ^ [] : [-(_1143221 = hAPP(c_Option_Ooption_OSome(_1143215), 19022 ^ [_1143215, _1143217, _1143219, _1143221, _1143223]))]]], (4776 ^ _777959) ^ [_850666, _850668, _850670, _850672, _850674, _850676, _850678, _850680] : [-(c_New__DSequence_Oneg__bind(_850680, _850676, _850672, _850668) = c_New__DSequence_Oneg__bind(_850678, _850674, _850670, _850666)), _850680 = _850678, _850676 = _850674, _850672 = _850670, _850668 = _850666], (6291 ^ _777959) ^ [_879396, _879398, _879400, _879402] : [hBOOL(hAPP(hAPP(c_member(_879396), _879398), _879400)), -(hBOOL(hAPP(hAPP(c_member(_879396), _879398), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879396, tc_HOL_Obool)), _879400), _879402))))], (44851 ^ _777959) ^ [_1670073, _1670075, _1670077] : [-(c_List_Oconcat(_1670073, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1670073)), _1670075), _1670077)) = hAPP(hAPP(c_List_Oappend(_1670073), c_List_Oconcat(_1670073, _1670075)), c_List_Oconcat(_1670073, _1670077)))], (9204 ^ _777959) ^ [_935960, _935962, _935964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_935960, tc_HOL_Obool)), _935962), _935964)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935960, tc_HOL_Obool)), _935962), _935964)))], (31831 ^ _777959) ^ [_1379135, _1379137, _1379139, _1379141, _1379143, _1379145] : [c_Com_Ocom_OLocal(_1379135, _1379137, _1379139) = c_Com_Ocom_OCond(_1379141, _1379143, _1379145)], (35015 ^ _777959) ^ [_1437065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1437065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1437065))))], (420 ^ _777959) ^ [_784525, _784527, _784529, _784531, _784533, _784535] : [-(c_Hoare__Mirabelle_Otriple__valid(_784533, _784529, _784525)), c_Hoare__Mirabelle_Otriple__valid(_784535, _784531, _784527), _784535 = _784533, _784531 = _784529, _784527 = _784525], (50606 ^ _777959) ^ [_1804563, _1804565, _1804567] : [_1804565 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1804563) = c_List_Oreplicate(_1804563, _1804565, _1804567))], (11226 ^ _777959) ^ [_977912, _977914, _977916] : [class_Lattices_Olattice(_977912), hBOOL(hAPP(c_Finite__Set_Ofinite(_977912), _977914)), -(_977914 = c_Orderings_Obot__class_Obot(tc_fun(_977912, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_977912, hAPP(hAPP(c_Set_Oinsert(_977912), _977916), _977914)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_977912), _977916), c_Big__Operators_Olattice__class_OInf__fin(_977912, _977914)))], (30635 ^ _777959) ^ [_1356993, _1356995] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1356993, _1356995)), _1356993)))], (27185 ^ _777959) ^ [_1292860] : [27186 ^ _777959 : [(27187 ^ _777959) ^ [_1292917] : [hBOOL(hAPP(_1292860, _1292917))]], 27189 ^ _777959 : [(27192 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1292860, hAPP(c_Int_Onat, 27188 ^ [_1292860]))))], (27190 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27188 ^ [_1292860])))]]], (43418 ^ _777959) ^ [_1640896, _1640898, _1640900, _1640902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1640896), _1640898)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1640900)), _1640902))), -(hAPP(hAPP(c_List_Otake(_1640900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1640896), _1640898)), _1640902) = hAPP(hAPP(c_List_Oappend(_1640900), hAPP(hAPP(c_List_Otake(_1640900), _1640896), _1640902)), hAPP(hAPP(c_List_Otake(_1640900), _1640898), hAPP(hAPP(c_List_Odrop(_1640900), _1640896), _1640902))))], (982 ^ _777959) ^ [_792914, _792916] : [-(class_Fields_Olinordered__field(_792914)), _792916 = _792914, class_Fields_Olinordered__field(_792916)], (51344 ^ _777959) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (15890 ^ _777959) ^ [_1080462, _1080464, _1080466, _1080468, _1080470, _1080472] : [class_Rings_Oordered__ring(_1080462), 15893 ^ _777959 : [(15900 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080462), _1080468), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080462), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080462), _1080470), _1080464)), _1080466)), _1080472))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080462), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080462), _1080464), _1080466)), _1080468)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080462), _1080470), _1080466)), _1080472))))], (15894 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080462), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080462), _1080464), _1080466)), _1080468)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080462), _1080470), _1080466)), _1080472))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080462), _1080468), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080462), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080462), _1080470), _1080464)), _1080466)), _1080472))))]]], (27271 ^ _777959) ^ [_1294208, _1294210, _1294212] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1294208), _1294210), _1294212) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1294208), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1294208, tc_Int_Oint), _1294210), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1294212))), class_Groups_Ocomm__monoid__add(_1294208), class_Groups_Ocomm__monoid__mult(_1294208)], (44072 ^ _777959) ^ [_1654467, _1654469, _1654471, _1654473] : [-(c_List_Otranspose(_1654467, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1654469), tc_List_Olist(_1654467)), hAPP(c_List_Omap(_1654469, _1654467), _1654471)), _1654473)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1654469), tc_List_Olist(_1654467)), hAPP(c_List_Omap(_1654469, _1654467), _1654471)), c_List_Otranspose(_1654469, _1654473)))], (31646 ^ _777959) ^ [_1375550, _1375552, _1375554] : [c_Com_Ocom_OCond(_1375550, _1375552, _1375554) = c_Com_Ocom_OSKIP], (16901 ^ _777959) ^ [_1101425, _1101427, _1101429] : [class_Orderings_Olinorder(_1101425), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101425), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1101425), _1101427), _1101429)), _1101429)))], (4062 ^ _777959) ^ [_839481, _839483] : [_839483 = _839481, -(c_HOL_OEx(_839483) = c_HOL_OEx(_839481))], (42656 ^ _777959) ^ [_1622585, _1622587, _1622589, _1622591, _1622593, _1622595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622585)), _1622587)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622589)), _1622591))), -(c_Map_Omap__upds(_1622585, _1622589, _1622593, hAPP(hAPP(c_List_Oappend(_1622585), _1622587), hAPP(hAPP(c_List_Olist_OCons(_1622585), _1622595), c_List_Olist_ONil(_1622585))), _1622591) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1622585, tc_Option_Ooption(_1622589)), c_Map_Omap__upds(_1622585, _1622589, _1622593, _1622587, _1622591)), _1622595), hAPP(c_Option_Ooption_OSome(_1622589), hAPP(hAPP(c_List_Onth(_1622589), _1622591), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1622585)), _1622587)))))], (45483 ^ _777959) ^ [_1684571, _1684573, _1684575, _1684577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1684571), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684573)), c_List_OdropWhile(_1684573, _1684575, _1684577)))), -(hAPP(hAPP(c_List_Onth(_1684573), c_List_OdropWhile(_1684573, _1684575, _1684577)), _1684571) = hAPP(hAPP(c_List_Onth(_1684573), _1684577), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1684571), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684573)), c_List_OtakeWhile(_1684573, _1684575, _1684577)))))], (47242 ^ _777959) ^ [_1725698, _1725700, _1725702] : [-(hAPP(c_Set_Oimage(tc_prod(_1725698, _1725700), _1725700, c_Product__Type_Osnd(_1725698, _1725700)), _1725702) = hAPP(c_Relation_ORange(_1725698, _1725700), _1725702))], (19562 ^ _777959) ^ [_1152200] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152200), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1152200)], (23729 ^ _777959) ^ [_1229234, _1229236, _1229238] : [class_Rings_Olinordered__semidom(_1229234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229234), c_Groups_Oone__class_Oone(_1229234)), _1229236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1229234), c_Groups_Oone__class_Oone(_1229234)), hAPP(hAPP(c_Power_Opower__class_Opower(_1229234), _1229236), _1229238))))], (15626 ^ _777959) ^ [_1075261, _1075263, _1075265, _1075267, _1075269, _1075271] : [class_Rings_Oring(_1075261), 15629 ^ _777959 : [(15636 ^ _777959) ^ [] : [_1075267 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075261), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1075261), _1075269), _1075263)), _1075265)), _1075271), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075261), _1075263), _1075265)), _1075267) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075261), _1075269), _1075265)), _1075271))], (15630 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075261), _1075263), _1075265)), _1075267) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075261), _1075269), _1075265)), _1075271), -(_1075267 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075261), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1075261), _1075269), _1075263)), _1075265)), _1075271))]]], (39584 ^ _777959) ^ [_1542494, _1542496, _1542498, _1542500, _1542502] : [hBOOL(hAPP(c_List_Odistinct(_1542494), hAPP(hAPP(c_List_Omap(tc_prod(_1542494, _1542496), _1542494), c_Product__Type_Ofst(_1542494, _1542496)), _1542498))), 39587 ^ _777959 : [(39594 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1542494, _1542496)), hAPP(hAPP(c_Product__Type_OPair(_1542494, _1542496), _1542502), _1542500)), hAPP(c_List_Oset(tc_prod(_1542494, _1542496)), _1542498))), -(hAPP(c_Option_Ooption_OSome(_1542496), _1542500) = hAPP(hAPP(c_Map_Omap__of(_1542494, _1542496), _1542498), _1542502))], (39588 ^ _777959) ^ [] : [hAPP(c_Option_Ooption_OSome(_1542496), _1542500) = hAPP(hAPP(c_Map_Omap__of(_1542494, _1542496), _1542498), _1542502), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1542494, _1542496)), hAPP(hAPP(c_Product__Type_OPair(_1542494, _1542496), _1542502), _1542500)), hAPP(c_List_Oset(tc_prod(_1542494, _1542496)), _1542498))))]]], (41958 ^ _777959) ^ [_1604353, _1604355, _1604357, _1604359, _1604361] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1604353, _1604355), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1604353, tc_HOL_Obool)), _1604357), _1604359)), _1604361) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1604353, _1604355), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1604353, _1604355), _1604357), _1604361)), hAPP(hAPP(c_Product__Type_OSigma(_1604353, _1604355), _1604359), _1604361)))], (49008 ^ _777959) ^ [_1767988, _1767990, _1767992] : [c_Relation_Orefl__on(_1767988, _1767990, _1767992), -(c_Relation_Orefl__on(_1767988, _1767990, hAPP(c_Relation_Oconverse(_1767988, _1767988), _1767992)))], (49945 ^ _777959) ^ [_1790707, _1790709, _1790711, _1790713, _1790715, _1790717] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1790707, _1790709, _1790711), _1790713), hAPP(hAPP(c_Product__Type_OPair(_1790707, _1790709), _1790715), _1790717)) = hAPP(hAPP(_1790713, _1790715), _1790717))], (24277 ^ _777959) ^ [_1239390, _1239392] : [_1239390 = _1239392, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239390) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239392))], (1310 ^ _777959) ^ [_797058, _797060] : [-(class_Lattices_Osemilattice__inf(_797058)), _797060 = _797058, class_Lattices_Osemilattice__inf(_797060)], (51054 ^ _777959) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (17585 ^ _777959) ^ [_1113838, _1113840, _1113842] : [class_Orderings_Olinorder(_1113838), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113838), _1113840)), 17592 ^ _777959 : [(17599 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1113838, tc_HOL_Obool)), _1113840), hAPP(hAPP(c_Set_Oinsert(_1113838), _1113842), c_Orderings_Obot__class_Obot(tc_fun(_1113838, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1113838, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1113838, hAPP(hAPP(c_Set_Oinsert(_1113838), _1113842), _1113840)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1113838), _1113842), c_Big__Operators_Olinorder__class_OMax(_1113838, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1113838, tc_HOL_Obool)), _1113840), hAPP(hAPP(c_Set_Oinsert(_1113838), _1113842), c_Orderings_Obot__class_Obot(tc_fun(_1113838, tc_HOL_Obool)))))))], (17593 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1113838, tc_HOL_Obool)), _1113840), hAPP(hAPP(c_Set_Oinsert(_1113838), _1113842), c_Orderings_Obot__class_Obot(tc_fun(_1113838, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1113838, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1113838, hAPP(hAPP(c_Set_Oinsert(_1113838), _1113842), _1113840)) = _1113842)]]], (1750 ^ _777959) ^ [_802558, _802560] : [-(class_Rings_Osemiring(_802558)), _802560 = _802558, class_Rings_Osemiring(_802560)], (35367 ^ _777959) ^ [_1445628, _1445630, _1445632, _1445634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool)), _1445632), _1445634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1445628, tc_fun(_1445630, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1445628, tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_fun(_1445630, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445630, tc_fun(tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_fun(_1445630, tc_HOL_Obool)), _1445628), c_COMBC(_1445630, tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445630, tc_prod(_1445628, _1445630)), tc_fun(_1445630, tc_fun(tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_HOL_Obool)), _1445628), hAPP(c_COMBB(tc_prod(_1445628, _1445630), tc_fun(tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_HOL_Obool), _1445630), c_member(tc_prod(_1445628, _1445630)))), c_Product__Type_OPair(_1445628, _1445630)))), _1445632)), hAPP(hAPP(c_COMBC(_1445628, tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_fun(_1445630, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445630, tc_fun(tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_fun(_1445630, tc_HOL_Obool)), _1445628), c_COMBC(_1445630, tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445630, tc_prod(_1445628, _1445630)), tc_fun(_1445630, tc_fun(tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_HOL_Obool)), _1445628), hAPP(c_COMBB(tc_prod(_1445628, _1445630), tc_fun(tc_fun(tc_prod(_1445628, _1445630), tc_HOL_Obool), tc_HOL_Obool), _1445630), c_member(tc_prod(_1445628, _1445630)))), c_Product__Type_OPair(_1445628, _1445630)))), _1445634))))], (38220 ^ _777959) ^ [_1510109, _1510111] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1510109), c_Orderings_Otop__class_Otop(tc_fun(_1510109, tc_HOL_Obool)))), c_Fun_Oinj__on(_1510109, _1510109, _1510111, c_Orderings_Otop__class_Otop(tc_fun(_1510109, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1510109, _1510109, _1510111), c_Orderings_Otop__class_Otop(tc_fun(_1510109, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1510109, tc_HOL_Obool)))], (34807 ^ _777959) ^ [_1432987, _1432989] : [-(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), _1432987)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1432989))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1432987))) = 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), _1432989)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1432987)))], (22553 ^ _777959) ^ [_1207794, _1207796] : [class_Orderings_Oorder(_1207794), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1207794, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1207794), _1207796), c_Orderings_Obot__class_Obot(tc_fun(_1207794, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_1207794), _1207796)) = hAPP(hAPP(c_Set_Oinsert(_1207794), _1207796), c_Orderings_Obot__class_Obot(tc_fun(_1207794, tc_HOL_Obool))))], (15842 ^ _777959) ^ [_1079221, _1079223, _1079225, _1079227, _1079229, _1079231, _1079233] : [-(c_Map_Omap__comp(_1079221, _1079223, _1079225, _1079227, _1079229, _1079231) = hAPP(c_Option_Ooption_OSome(_1079223), _1079233)), 15843 ^ _777959 : [(15844 ^ _777959) ^ [_1079299] : [hAPP(_1079229, _1079231) = hAPP(c_Option_Ooption_OSome(_1079221), _1079299), hAPP(_1079227, _1079299) = hAPP(c_Option_Ooption_OSome(_1079223), _1079233)]]], (20777 ^ _777959) ^ [_1173684, _1173686] : [class_Groups_Ogroup__add(_1173684), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1173684), c_Groups_Ozero__class_Ozero(_1173684)), _1173686) = hAPP(c_Groups_Ouminus__class_Ouminus(_1173684), _1173686))], (19967 ^ _777959) ^ [_1159209, _1159211, _1159213, _1159215] : [class_Rings_Oordered__comm__semiring(_1159209), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159209), _1159211), _1159213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159209), c_Groups_Ozero__class_Ozero(_1159209)), _1159215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159209), _1159215), _1159211)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159209), _1159215), _1159213))))], (47690 ^ _777959) ^ [_1737001, _1737003] : [class_Orderings_Olinorder(_1737001), hBOOL(hAPP(c_Finite__Set_Ofinite(_1737001), _1737003)), 47698 ^ _777959 : [(47701 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1737001, 47697 ^ [_1737001, _1737003]))], (47703 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1737001), 47697 ^ [_1737001, _1737003])))], (47705 ^ _777959) ^ [_1737327] : [-(_1737327 = 47697 ^ [_1737001, _1737003]), hAPP(c_List_Oset(_1737001), _1737327) = _1737003, c_List_Olinorder__class_Osorted(_1737001, _1737327), hBOOL(hAPP(c_List_Odistinct(_1737001), _1737327))], (47699 ^ _777959) ^ [] : [-(hAPP(c_List_Oset(_1737001), 47697 ^ [_1737001, _1737003]) = _1737003)]]], (38467 ^ _777959) ^ [_1515786, _1515788, _1515790, _1515792, _1515794, _1515796, _1515798, _1515800] : [c_Fun_Oinj__on(_1515786, _1515788, _1515790, _1515792), 38473 ^ _777959 : [(38476 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1515786, tc_HOL_Obool)), hAPP(_1515798, 38472 ^ [_1515786, _1515788, _1515790, _1515792, _1515794, _1515796, _1515798, _1515800])), _1515792))], (38474 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515794), 38472 ^ [_1515786, _1515788, _1515790, _1515792, _1515794, _1515796, _1515798, _1515800]), _1515796)))]], hBOOL(hAPP(hAPP(c_member(_1515794), _1515800), _1515796)), -(hAPP(c_Set_Oimage(_1515786, _1515788, _1515790), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1515794, tc_fun(_1515786, tc_HOL_Obool)), _1515796), _1515798)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1515794, tc_fun(_1515788, tc_HOL_Obool)), _1515796), hAPP(hAPP(c_COMBB(tc_fun(_1515786, tc_HOL_Obool), tc_fun(_1515788, tc_HOL_Obool), _1515794), c_Set_Oimage(_1515786, _1515788, _1515790)), _1515798)))], (16157 ^ _777959) ^ [_1086111, _1086113] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1086111), hAPP(c_Nat_OSuc, _1086113)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1086111), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1086113))], (4402 ^ _777959) ^ [_844597, _844599, _844601, _844603] : [-(c_Nitpick_Ouminus__frac(_844603, _844599) = c_Nitpick_Ouminus__frac(_844601, _844597)), _844603 = _844601, _844599 = _844597], (11800 ^ _777959) ^ [_991695, _991697, _991699, _991701, _991703] : [hBOOL(hAPP(hAPP(c_member(_991695), _991697), _991699)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_991701, tc_HOL_Obool)), hAPP(_991703, _991697)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991695, tc_fun(_991701, tc_HOL_Obool)), _991699), _991703)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991695, tc_fun(_991701, tc_HOL_Obool)), _991699), _991703))], (7001 ^ _777959) ^ [_893863, _893865, _893867, _893869, _893871] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_893863), _893865)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_893867, tc_HOL_Obool)), _893869), hAPP(c_Set_Oimage(_893863, _893867, _893871), _893865))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_893867), _893869)))], (39649 ^ _777959) ^ [_1544233, _1544235] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1544233, _1544235))))], (40942 ^ _777959) ^ [_1575347, _1575349] : [-(c_List_Olenlex(_1575347, _1575349) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1575347), tc_List_Olist(_1575347))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1575347), tc_List_Olist(_1575347), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1575347), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1575347), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool)), tc_List_Olist(_1575347)), c_COMBS(tc_List_Olist(_1575347), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool), tc_fun(tc_List_Olist(_1575347), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1575347)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1575347)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1575347), tc_fun(tc_List_Olist(_1575347), tc_Nat_Onat), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1575347), tc_Nat_Onat), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool)), tc_List_Olist(_1575347)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1575347))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1575347)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1575347))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1575347)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1575347), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1575347), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool)), tc_List_Olist(_1575347)), c_COMBS(tc_List_Olist(_1575347), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool), tc_fun(tc_List_Olist(_1575347), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1575347)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1575347)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1575347), tc_fun(tc_List_Olist(_1575347), tc_Nat_Onat), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1575347), tc_Nat_Onat), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool)), tc_List_Olist(_1575347)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1575347))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1575347)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1575347))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1575347)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1575347), tc_fun(tc_prod(tc_List_Olist(_1575347), tc_List_Olist(_1575347)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1575347), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1575347), tc_List_Olist(_1575347)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1575347), tc_List_Olist(_1575347)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1575347), tc_HOL_Obool)), tc_List_Olist(_1575347)), c_COMBC(tc_List_Olist(_1575347), tc_fun(tc_prod(tc_List_Olist(_1575347), tc_List_Olist(_1575347)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1575347), tc_prod(tc_List_Olist(_1575347), tc_List_Olist(_1575347))), tc_fun(tc_List_Olist(_1575347), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1575347), tc_List_Olist(_1575347)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1575347)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1575347), tc_List_Olist(_1575347)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1575347), tc_List_Olist(_1575347)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1575347)), c_member(tc_prod(tc_List_Olist(_1575347), tc_List_Olist(_1575347))))), c_Product__Type_OPair(tc_List_Olist(_1575347), tc_List_Olist(_1575347))))), c_List_Olex(_1575347, _1575349)))))))], (26884 ^ _777959) ^ [_1287062, _1287064, _1287066, _1287068] : [class_Fields_Ofield(_1287062), -(_1287064 = c_Groups_Ozero__class_Ozero(_1287062)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1287062), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287062), _1287066), _1287064)), _1287068) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287062), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1287062), _1287066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287062), _1287064), _1287068))), _1287064))], (50948 ^ _777959) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (36093 ^ _777959) ^ [_1462345, _1462347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1462345)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1462345), _1462347)), -(c_Divides_Odivmod__nat(_1462347, _1462345) = 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), _1462347), _1462345)), _1462345))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1462347), _1462345), _1462345)))], (38126 ^ _777959) ^ [_1508284, _1508286, _1508288, _1508290] : [c_Fun_Oinj__on(_1508284, _1508286, _1508288, c_Orderings_Otop__class_Otop(tc_fun(_1508284, tc_HOL_Obool))), 38129 ^ _777959 : [(38143 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508286), _1508290), hAPP(c_Set_Oimage(_1508284, _1508286, _1508288), c_Orderings_Otop__class_Otop(tc_fun(_1508284, tc_HOL_Obool)))))), 38144 ^ _777959 : [(38145 ^ _777959) ^ [_1508687] : [_1508290 = hAPP(_1508288, _1508687), 38149 ^ _777959 : [(38152 ^ _777959) ^ [] : [38148 ^ [_1508284, _1508286, _1508288, _1508290, _1508687] = _1508687], (38150 ^ _777959) ^ [] : [-(_1508290 = hAPP(_1508288, 38148 ^ [_1508284, _1508286, _1508288, _1508290, _1508687]))]]]]], (38130 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1508286), _1508290), hAPP(c_Set_Oimage(_1508284, _1508286, _1508288), c_Orderings_Otop__class_Otop(tc_fun(_1508284, tc_HOL_Obool))))), 38134 ^ _777959 : [(38137 ^ _777959) ^ [_1508549] : [_1508290 = hAPP(_1508288, _1508549), -(_1508549 = 38133 ^ [_1508284, _1508286, _1508288, _1508290])], (38135 ^ _777959) ^ [] : [-(_1508290 = hAPP(_1508288, 38133 ^ [_1508284, _1508286, _1508288, _1508290]))]]]]], (19340 ^ _777959) ^ [_1148889, _1148891] : [class_Rings_Ocomm__semiring__1(_1148889), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148889), c_Groups_Ozero__class_Ozero(_1148889)), _1148891) = c_Groups_Ozero__class_Ozero(_1148889))], (50468 ^ _777959) ^ [_1801554, _1801556, _1801558, _1801560, _1801562] : [-(c_Predicate_Oconversep(_1801554, _1801556, c_Predicate_Opred__comp(_1801554, _1801558, _1801556, _1801560, _1801562)) = c_Predicate_Opred__comp(_1801556, _1801558, _1801554, c_Predicate_Oconversep(_1801558, _1801556, _1801562), c_Predicate_Oconversep(_1801554, _1801558, _1801560)))], (26558 ^ _777959) ^ [_1280984, _1280986, _1280988] : [class_Fields_Olinordered__field(_1280984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280984), _1280986), c_Groups_Ozero__class_Ozero(_1280984))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280984), _1280988), c_Groups_Ozero__class_Ozero(_1280984))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280984), c_Groups_Ozero__class_Ozero(_1280984)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280984), _1280986), _1280988))))], (8838 ^ _777959) ^ [_930395, _930397, _930399] : [class_Orderings_Olinorder(_930395), 8841 ^ _777959 : [(8848 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930395), _930399), _930397)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930395), _930397), _930399))], (8842 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930395), _930397), _930399))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930395), _930399), _930397)))]]], (34973 ^ _777959) ^ [_1436453] : [c_Int_OMin = _1436453, -(c_Int_OMin = c_Int_OBit1(_1436453))], (12078 ^ _777959) ^ [_997071, _997073, _997075] : [_997071 = _997075, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997071), _997073) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997075), _997073))], (48755 ^ _777959) ^ [_1761251, _1761253, _1761255] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1761251, _1761251, _1761253), c_Relation_OId(_1761251)), _1761255) = _1761255)], (17945 ^ _777959) ^ [_1120856, _1120858, _1120860] : [class_Orderings_Olinorder(_1120856), hBOOL(hAPP(c_Finite__Set_Ofinite(_1120856), _1120858)), hBOOL(hAPP(hAPP(c_member(_1120856), _1120860), _1120858)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1120856), _1120860), c_Big__Operators_Olattice_OInf__fin(_1120856, c_Orderings_Oord__class_Omin(_1120856), _1120858)) = _1120860)], (48942 ^ _777959) ^ [_1766169, _1766171, _1766173, _1766175] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1766169), tc_List_Olist(_1766169))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1766169), tc_List_Olist(_1766169)), _1766171), _1766173)), c_List_Olistrel1(_1766169, hAPP(c_Relation_Oconverse(_1766169, _1766169), _1766175)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1766169), tc_List_Olist(_1766169))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1766169), tc_List_Olist(_1766169)), _1766171), _1766173)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1766169), tc_List_Olist(_1766169)), c_List_Olistrel1(_1766169, _1766175)))))], (33981 ^ _777959) ^ [_1418098, _1418100] : [c_Int_Oiszero(_1418098, hAPP(c_Int_Onumber__class_Onumber__of(_1418098), c_Int_OBit1(_1418100))), class_Int_Onumber__ring(_1418098), class_Int_Oring__char__0(_1418098)], (40180 ^ _777959) ^ [_1556995, _1556997, _1556999, _1557001, _1557003] : [class_Orderings_Olinorder(_1556995), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1556997)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1556997, _1556995, _1556999), _1557001), _1557003)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1556997)), _1557003)))], (22150 ^ _777959) ^ [_1199367, _1199369] : [_1199367 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1199367), _1199369) = _1199369)], (12722 ^ _777959) ^ [_1008809, _1008811, _1008813] : [class_Groups_Oordered__ab__group__add(_1008809), 12725 ^ _777959 : [(12732 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008809), _1008813), hAPP(c_Groups_Ouminus__class_Ouminus(_1008809), _1008811))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008809), _1008811), hAPP(c_Groups_Ouminus__class_Ouminus(_1008809), _1008813))))], (12726 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008809), _1008811), hAPP(c_Groups_Ouminus__class_Ouminus(_1008809), _1008813))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008809), _1008813), hAPP(c_Groups_Ouminus__class_Ouminus(_1008809), _1008811))))]]], (36371 ^ _777959) ^ [_1467505, _1467507] : [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), _1467505), _1467507))), 36374 ^ _777959 : [(36381 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467507), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36384 ^ _777959 : [(36393 ^ _777959) ^ [] : [-(c_Nitpick_Onorm__frac(_1467505, _1467507) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1467505), _1467507)), 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), _1467505))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1467507)))), -(_1467505 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1467507 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36385 ^ _777959) ^ [] : [36386 ^ _777959 : [(36389 ^ _777959) ^ [] : [_1467507 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36387 ^ _777959) ^ [] : [_1467505 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1467505, _1467507) = 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)))]]], (36375 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467507), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1467505, _1467507) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1467505), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1467507)))]]], (46916 ^ _777959) ^ [_1718647, _1718649, _1718651] : [c_Wellfounded_Owf(_1718647, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1718647, _1718647), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1718647, _1718647), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1718647, _1718647, _1718647), _1718649), _1718649)), hAPP(hAPP(c_Relation_Orel__comp(_1718647, _1718647, _1718647), _1718651), _1718649))), _1718651)), -(c_Wellfounded_Owf(_1718647, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1718647, _1718647), tc_HOL_Obool)), _1718649), _1718651)))], (50966 ^ _777959) ^ [] : [-(class_Smallcheck_Osmall(tc_Int_Oint))], (39398 ^ _777959) ^ [_1537992, _1537994, _1537996, _1537998, _1538000, _1538002] : [c_Finite__Set_Ofolding(_1537992, _1537994, _1537996, _1537998), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537992), _1538000)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537992), _1538002)), -(hAPP(c_Fun_Ocomp(_1537994, _1537994, _1537994, hAPP(_1537998, _1538002)), hAPP(_1537998, _1538000)) = hAPP(c_Fun_Ocomp(_1537994, _1537994, _1537994, hAPP(_1537998, _1538000)), hAPP(_1537998, _1538002)))], (39832 ^ _777959) ^ [_1548217, _1548219, _1548221, _1548223] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548217, _1548217)), hAPP(hAPP(c_Product__Type_OPair(_1548217, _1548217), _1548219), _1548221)), hAPP(c_List_Oset(tc_prod(_1548217, _1548217)), hAPP(hAPP(c_List_Ozip(_1548217, _1548217), _1548223), _1548223)))), 39835 ^ _777959 : [(39838 ^ _777959) ^ [] : [-(_1548219 = _1548221)], (39836 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1548217), _1548219), hAPP(c_List_Oset(_1548217), _1548223))))]]], (13949 ^ _777959) ^ [_1036531] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1036531, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1036531, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1036531, tc_HOL_Obool)))], (6957 ^ _777959) ^ [_892231, _892233, _892235] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _892231))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_892233, _892231, _892235))))], (23963 ^ _777959) ^ [_1233605, _1233607, _1233609] : [class_Rings_Olinordered__semidom(_1233605), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1233605), c_Groups_Ozero__class_Ozero(_1233605)), _1233607)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1233605), _1233607), c_Groups_Oone__class_Oone(_1233605))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1233605), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1233605), _1233607), hAPP(hAPP(c_Power_Opower__class_Opower(_1233605), _1233607), _1233609))), hAPP(hAPP(c_Power_Opower__class_Opower(_1233605), _1233607), _1233609))))], (31202 ^ _777959) ^ [_1367444, _1367446, _1367448] : [class_Groups_Oordered__ab__group__add__abs(_1367444), 31205 ^ _777959 : [(31214 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367444), hAPP(c_Groups_Oabs__class_Oabs(_1367444), _1367446)), _1367448))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367444), _1367446), _1367448)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367444), hAPP(c_Groups_Ouminus__class_Ouminus(_1367444), _1367446)), _1367448))], (31206 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367444), hAPP(c_Groups_Oabs__class_Oabs(_1367444), _1367446)), _1367448)), 31209 ^ _777959 : [(31212 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367444), hAPP(c_Groups_Ouminus__class_Ouminus(_1367444), _1367446)), _1367448)))], (31210 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367444), _1367446), _1367448)))]]]]], (50428 ^ _777959) ^ [_1800782, _1800784, _1800786, _1800788, _1800790] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1800782, _1800784, _1800786), _1800788), _1800790)), -(hBOOL(hAPP(hAPP(_1800786, _1800790), _1800788)))], (29024 ^ _777959) ^ [] : [-(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)))], (48984 ^ _777959) ^ [_1767439, _1767441] : [c_Wellfounded_Oacyclic(_1767439, _1767441), -(c_Wellfounded_Oacyclic(_1767439, hAPP(c_Relation_Oconverse(_1767439, _1767439), _1767441)))], (6319 ^ _777959) ^ [_879964, _879966, _879968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879964, tc_HOL_Obool)), _879966), _879968)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879964, tc_HOL_Obool)), _879968), _879966) = _879968)], (40379 ^ _777959) ^ [_1561661, _1561663, _1561665, _1561667, _1561669] : [-(hAPP(hAPP(c_List_Olist__update(_1561661, hAPP(hAPP(c_List_Olist__update(_1561661, _1561663), _1561665), _1561667)), _1561665), _1561669) = hAPP(hAPP(c_List_Olist__update(_1561661, _1561663), _1561665), _1561669))], (7822 ^ _777959) ^ [_910965, _910967] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_910965, _910967))), -(hBOOL(hAPP(c_Com_OWT, _910967)))], (13795 ^ _777959) ^ [_1033057, _1033059, _1033061] : [class_Lattices_Obounded__lattice__top(_1033057), 13798 ^ _777959 : [(13807 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1033057), _1033059), _1033061) = c_Orderings_Otop__class_Otop(_1033057)), _1033059 = c_Orderings_Otop__class_Otop(_1033057), _1033061 = c_Orderings_Otop__class_Otop(_1033057)], (13799 ^ _777959) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1033057), _1033059), _1033061) = c_Orderings_Otop__class_Otop(_1033057), 13802 ^ _777959 : [(13805 ^ _777959) ^ [] : [-(_1033061 = c_Orderings_Otop__class_Otop(_1033057))], (13803 ^ _777959) ^ [] : [-(_1033059 = c_Orderings_Otop__class_Otop(_1033057))]]]]], (47375 ^ _777959) ^ [_1729405, _1729407, _1729409, _1729411, _1729413] : [-(hAPP(c_Relation_ODomain(_1729405, _1729407), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1729405, _1729407)), hAPP(hAPP(c_Product__Type_OPair(_1729405, _1729407), _1729409), _1729411)), _1729413)) = hAPP(hAPP(c_Set_Oinsert(_1729405), _1729409), hAPP(c_Relation_ODomain(_1729405, _1729407), _1729413)))], (35077 ^ _777959) ^ [_1438022] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1438022) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1438022))], (24962 ^ _777959) ^ [_1251113, _1251115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251113)), 24965 ^ _777959 : [(24974 ^ _777959) ^ [] : [-(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), _1251113), _1251115)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1251115), _1251113)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251115))], (24966 ^ _777959) ^ [] : [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), _1251113), _1251115))), 24969 ^ _777959 : [(24972 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251115)))], (24970 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1251115), _1251113)))]]]]], (20834 ^ _777959) ^ [_1174551] : [_1174551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174551), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (33171 ^ _777959) ^ [_1404234, _1404236] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404234)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404234)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404236)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404234)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404236))))], (24684 ^ _777959) ^ [_1246304] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1246304) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1246304))], (25062 ^ _777959) ^ [_1252632, _1252634, _1252636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252632)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1252634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1252636), _1252632)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1252634), _1252636)), _1252632))], (7106 ^ _777959) ^ [_896627, _896629] : [class_Lattices_Osemilattice__sup(_896627), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896627), _896629), _896629) = _896629)], (9962 ^ _777959) ^ [_951094, _951096, _951098, _951100] : [class_Lattices_Osemilattice__inf(_951094), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951094), _951096), _951098)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_951094), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951094), _951096), _951100)), _951098)))], (11503 ^ _777959) ^ [_983360, _983362, _983364, _983366, _983368, _983370] : [hBOOL(hAPP(hAPP(c_member(_983360), _983362), _983364)), hBOOL(hAPP(hAPP(c_member(_983366), _983368), hAPP(_983370, _983362))), -(hBOOL(hAPP(hAPP(c_member(_983366), _983368), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_983360, tc_fun(_983366, tc_HOL_Obool)), _983364), _983370))))], (35987 ^ _777959) ^ [_1460757, _1460759] : [-(c_Divides_OposDivAlg(_1460757, _1460759) = hAPP(c_Divides_Oadjust(_1460759), c_Divides_OposDivAlg(_1460757, 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)))), _1460759)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1460757), _1460759))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1460759), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15138 ^ _777959) ^ [_1066154, _1066156, _1066158, _1066160, _1066162] : [class_Rings_Ocomm__semiring__1(_1066154), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066154), _1066156), _1066158)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066154), _1066160), _1066162)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066154), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066154), _1066156), _1066160)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066154), _1066158), _1066162)))], (38796 ^ _777959) ^ [_1522909, _1522911, _1522913, _1522915, _1522917] : [hBOOL(hAPP(hAPP(c_member(_1522913), hAPP(_1522915, _1522911)), _1522917)), -(hBOOL(hAPP(hAPP(c_member(_1522909), _1522911), hAPP(c_Set_Ovimage(_1522909, _1522913, _1522915), _1522917))))], (36706 ^ _777959) ^ [_1474440, _1474442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474440)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474442)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1474440), _1474442) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1474440, _1474442)))], (50956 ^ _777959) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (40449 ^ _777959) ^ [_1563109, _1563111, _1563113, _1563115] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1563109), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1563111)), _1563113))), -(hBOOL(hAPP(hAPP(c_member(_1563111), _1563115), hAPP(c_List_Oset(_1563111), hAPP(hAPP(c_List_Olist__update(_1563111, _1563113), _1563109), _1563115)))))], (35117 ^ _777959) ^ [_1438616] : [class_Int_Onumber__ring(_1438616), -(hAPP(c_Int_Onumber__class_Onumber__of(_1438616), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1438616), c_Groups_Oone__class_Oone(_1438616)))], (43584 ^ _777959) ^ [_1644230, _1644232, _1644234] : [-(hAPP(c_List_Otl(_1644230), hAPP(hAPP(c_List_Otake(_1644230), _1644232), _1644234)) = hAPP(hAPP(c_List_Otake(_1644230), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1644232), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1644230), _1644234)))], (4552 ^ _777959) ^ [_846938, _846940, _846942, _846944, _846946, _846948, _846950, _846952] : [-(c_New__DSequence_Opos__decr__bind(_846952, _846948, _846944, _846940) = c_New__DSequence_Opos__decr__bind(_846950, _846946, _846942, _846938)), _846952 = _846950, _846948 = _846946, _846944 = _846942, _846940 = _846938], (50896 ^ _777959) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (1950 ^ _777959) ^ [_806175, _806177, _806179, _806181, _806183, _806185, _806187, _806189, _806191, _806193] : [-(c_Fun_Ooverride__on(_806193, _806189, _806185, _806181, _806177) = c_Fun_Ooverride__on(_806191, _806187, _806183, _806179, _806175)), _806193 = _806191, _806189 = _806187, _806185 = _806183, _806181 = _806179, _806177 = _806175], (13279 ^ _777959) ^ [_1020719, _1020721, _1020723, _1020725, _1020727, _1020729] : [-(hBOOL(hAPP(hAPP(c_member(_1020719), _1020721), c_Map_Odom(_1020719, _1020723, _1020725)))), -(c_Map_Omap__add(_1020719, _1020723, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1020719, tc_Option_Ooption(_1020723)), _1020727), _1020721), hAPP(c_Option_Ooption_OSome(_1020723), _1020729)), _1020725) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1020719, tc_Option_Ooption(_1020723)), c_Map_Omap__add(_1020719, _1020723, _1020727, _1020725)), _1020721), hAPP(c_Option_Ooption_OSome(_1020723), _1020729)))], (7816 ^ _777959) ^ [_910848, _910850, _910852] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_910848), _910850)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_910848), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910848, tc_HOL_Obool)), _910850), _910852))))], (31945 ^ _777959) ^ [_1381040, _1381042, _1381044, _1381046, _1381048] : [c_Com_Ocom_OLocal(_1381040, _1381042, _1381044) = c_Com_Ocom_OWhile(_1381046, _1381048)], (25500 ^ _777959) ^ [_1261391, _1261393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1261391)), 25503 ^ _777959 : [(25510 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1261393), _1261391))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1261393), _1261391) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1261393), _1261391)), _1261391)))], (25504 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1261393), _1261391)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1261393), _1261391) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8040 ^ _777959) ^ [_915275, _915277, _915279, _915281, _915283] : [c_Com_Ocom_OSemi(_915275, _915277) = c_Com_Ocom_OCall(_915279, _915281, _915283)], (31879 ^ _777959) ^ [_1380020, _1380022, _1380024, _1380026, _1380028, _1380030] : [-(c_Com_Ocom_OLocal(_1380020, _1380022, _1380024) = c_Com_Ocom_OLocal(_1380026, _1380028, _1380030)), _1380020 = _1380026, _1380022 = _1380028, _1380024 = _1380030], (6067 ^ _777959) ^ [_875082, _875084, _875086] : [hBOOL(hAPP(hAPP(c_member(_875082), _875084), _875086)), -(hBOOL(hAPP(_875086, _875084)))], (40399 ^ _777959) ^ [_1562081, _1562083, _1562085, _1562087, _1562089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1562081, tc_HOL_Obool)), hAPP(c_List_Oset(_1562081), _1562083)), _1562085)), hBOOL(hAPP(hAPP(c_member(_1562081), _1562087), _1562085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1562081, tc_HOL_Obool)), hAPP(c_List_Oset(_1562081), hAPP(hAPP(c_List_Olist__update(_1562081, _1562083), _1562089), _1562087))), _1562085)))], (40471 ^ _777959) ^ [_1563556, _1563558, _1563560, _1563562, _1563564] : [class_Orderings_Olinorder(_1563556), hBOOL(hAPP(hAPP(c_member(_1563556), hAPP(_1563558, _1563560)), hAPP(c_Set_Oimage(_1563562, _1563556, _1563558), hAPP(c_List_Oset(_1563562), _1563564)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1563562, _1563556, _1563558, _1563560, _1563564) = _1563564)], (11342 ^ _777959) ^ [_979946, _979948, _979950, _979952, _979954] : [class_Groups_Oab__group__add(_979946), hBOOL(hAPP(c_Finite__Set_Ofinite(_979948), _979950)), hBOOL(hAPP(c_Finite__Set_Ofinite(_979948), _979952)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_979948, _979946), _979954), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979948, tc_HOL_Obool)), _979950), _979952)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_979946), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979946), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_979948, _979946), _979954), _979950)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_979948, _979946), _979954), _979952))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_979948, _979946), _979954), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979948, tc_HOL_Obool)), _979950), _979952))))], (21099 ^ _777959) ^ [_1178824, _1178826] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1178824), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1178824), _1178826)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31817 ^ _777959) ^ [_1378858] : [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), _1378858))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1378858) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1378858)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (31426 ^ _777959) ^ [_1371546, _1371548] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1371546), _1371548))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1371546))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1371548))))], (3506 ^ _777959) ^ [_830839, _830841, _830843, _830845] : [-(c_List_Olists(_830845, _830841) = c_List_Olists(_830843, _830839)), _830845 = _830843, _830841 = _830839], (43278 ^ _777959) ^ [_1637456, _1637458, _1637460, _1637462] : [-(hAPP(hAPP(c_List_Odrop(_1637456), _1637458), hAPP(hAPP(c_List_Otake(_1637456), _1637460), _1637462)) = hAPP(hAPP(c_List_Otake(_1637456), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1637460), _1637458)), hAPP(hAPP(c_List_Odrop(_1637456), _1637458), _1637462)))], (29552 ^ _777959) ^ [_1335207, _1335209, _1335211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335207)), 29558 ^ _777959 : [(29561 ^ _777959) ^ [] : [hBOOL(hAPP(_1335209, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 29557 ^ [_1335207, _1335209, _1335211]), _1335207)))], (29559 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1335209, 29557 ^ [_1335207, _1335209, _1335211])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1335211)), 29566 ^ _777959 : [(29567 ^ _777959) ^ [_1335496] : [hBOOL(hAPP(_1335209, _1335496)), -(hBOOL(hAPP(_1335209, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1335496), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1335211), _1335207)))))]]], (31568 ^ _777959) ^ [_1374039, _1374041, _1374043] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(_1374039, _1374041, _1374043)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1374041)), c_Com_Ocom_Ocom__size(_1374043))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (24429 ^ _777959) ^ [_1241992] : [class_Power_Opower(_1241992), -(c_Power_Opower__class_Opower(_1241992) = c_Power_Opower_Opower(_1241992, c_Groups_Oone__class_Oone(_1241992), c_Groups_Otimes__class_Otimes(_1241992)))], (24570 ^ _777959) ^ [_1244457, _1244459, _1244461, _1244463, _1244465] : [class_Orderings_Olinorder(_1244457), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244457, _1244459), _1244461) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244457, _1244463), _1244465), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244457), _1244459), _1244461)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244457), _1244463), _1244465)), -(_1244459 = _1244463)], (6725 ^ _777959) ^ [_887184, _887186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887184, tc_HOL_Obool)), _887186), c_Orderings_Obot__class_Obot(tc_fun(_887184, tc_HOL_Obool)))), -(_887186 = c_Orderings_Obot__class_Obot(tc_fun(_887184, tc_HOL_Obool)))], (28261 ^ _777959) ^ [_1310709, _1310711, _1310713] : [class_Orderings_Olinorder(_1310709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1310709), _1310711), _1310713)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310709, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1310709, _1310711, _1310713)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1310709), _1310713)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1310709), _1310711))], (2754 ^ _777959) ^ [_819007, _819009, _819011, _819013, _819015, _819017] : [-(c_Map_Oran(_819017, _819013, _819009) = c_Map_Oran(_819015, _819011, _819007)), _819017 = _819015, _819013 = _819011, _819009 = _819007], (39258 ^ _777959) ^ [_1534627, _1534629, _1534631, _1534633, _1534635] : [hAPP(hAPP(c_Map_Omap__of(_1534627, _1534629), _1534631), _1534633) = hAPP(c_Option_Ooption_OSome(_1534629), _1534635), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534627, _1534629)), hAPP(hAPP(c_Product__Type_OPair(_1534627, _1534629), _1534633), _1534635)), hAPP(c_List_Oset(tc_prod(_1534627, _1534629)), _1534631))))], (34523 ^ _777959) ^ [_1427753] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1427753))), 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), _1427753), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (51192 ^ _777959) ^ [_1811904] : [class_Finite__Set_Ofinite(_1811904), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1811904)))], (12940 ^ _777959) ^ [_1013291, _1013293, _1013295, _1013297] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1013291, tc_fun(_1013293, tc_HOL_Obool)), _1013295), _1013297) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1013293, tc_HOL_Obool), hAPP(c_Set_Oimage(_1013291, tc_fun(_1013293, tc_HOL_Obool), _1013297), _1013295)))], (34213 ^ _777959) ^ [_1422139, _1422141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1422139)), c_Int_OBit1(_1422141))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1422139), _1422141)))], (49346 ^ _777959) ^ [_1776283, _1776285, _1776287] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776283, _1776283)), _1776285), c_Transitive__Closure_Ortrancl(_1776283, _1776287))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776283, _1776283)), _1776285), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1776283, _1776283), tc_HOL_Obool), 49349 ^ [_1776283, _1776285, _1776287]), _1776287))))], (31851 ^ _777959) ^ [_1379553, _1379555, _1379557] : [hBOOL(hAPP(c_Com_OWT, _1379557)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1379553, _1379555, _1379557))))], (11378 ^ _777959) ^ [_980826, _980828, _980830, _980832] : [c_Map_Odom(_980826, _980828, _980830) = hAPP(hAPP(c_Set_Oinsert(_980826), _980832), c_Orderings_Obot__class_Obot(tc_fun(_980826, tc_HOL_Obool))), -(_980830 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_980826, tc_Option_Ooption(_980828)), hAPP(c_COMBK(tc_Option_Ooption(_980828), _980826), c_Option_Ooption_ONone(_980828))), _980832), hAPP(c_Option_Ooption_OSome(_980828), 11381 ^ [_980826, _980828, _980830, _980832])))], (27397 ^ _777959) ^ [_1296269, _1296271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1296269)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1296271)), 27404 ^ _777959 : [(27411 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296269), _1296271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1296269)), hAPP(c_Int_Onat, _1296271))))], (27405 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1296269)), hAPP(c_Int_Onat, _1296271))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1296269), _1296271)))]]], (50490 ^ _777959) ^ [_1802507, _1802509] : [-(c_Predicate_Opred__comp(_1802507, _1802507, _1802507, c_fequal, c_Predicate_Opred__comp(_1802507, _1802507, _1802507, _1802509, c_fequal)) = _1802509)], (1530 ^ _777959) ^ [_799808, _799810] : [-(class_Rings_Olinordered__semiring(_799808)), _799810 = _799808, class_Rings_Olinordered__semiring(_799810)], (36830 ^ _777959) ^ [_1476769, _1476771, _1476773] : [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), _1476769), _1476771))), -(hBOOL(hAPP(hAPP(_1476773, _1476769), _1476771))), 36837 ^ _777959 : [(36840 ^ _777959) ^ [] : [-(36836 ^ [_1476769, _1476771, _1476773] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1476773, 36836 ^ [_1476769, _1476771, _1476773]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 36835 ^ [_1476769, _1476771, _1476773], 36836 ^ [_1476769, _1476771, _1476773]))))], (36846 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1476773, 36835 ^ [_1476769, _1476771, _1476773]), 36836 ^ [_1476769, _1476771, _1476773]))], (36838 ^ _777959) ^ [] : [-(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), 36835 ^ [_1476769, _1476771, _1476773]), 36836 ^ [_1476769, _1476771, _1476773]))))]]], (36860 ^ _777959) ^ [_1477438] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1477438)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1477438)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29916 ^ _777959) ^ [_1343470, _1343472] : [class_Divides_Osemiring__div(_1343470), -(c_Divides_Odiv__class_Omod(_1343470, _1343472, _1343472) = c_Groups_Ozero__class_Ozero(_1343470))], (15610 ^ _777959) ^ [_1074864, _1074866, _1074868, _1074870, _1074872, _1074874] : [class_Rings_Oring(_1074864), 15613 ^ _777959 : [(15620 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074864), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074864), _1074866), _1074872)), _1074868)), _1074870) = _1074874, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074864), _1074866), _1074868)), _1074870) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074864), _1074872), _1074868)), _1074874))], (15614 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074864), _1074866), _1074868)), _1074870) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074864), _1074872), _1074868)), _1074874), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1074864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074864), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1074864), _1074866), _1074872)), _1074868)), _1074870) = _1074874)]]], (35979 ^ _777959) ^ [_1460616, _1460618] : [35980 ^ _777959 : [(35983 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1460618), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35981 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1460616), _1460618))]], -(c_Divides_OposDivAlg(_1460616, _1460618) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1460616))], (30307 ^ _777959) ^ [_1351048, _1351050, _1351052] : [-(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), _1351048), _1351050)), _1351050)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1351048, _1351050))), _1351052) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1351048), _1351052))], (37720 ^ _777959) ^ [_1499563, _1499565, _1499567, _1499569] : [c_Equiv__Relations_Oequivp(_1499563, _1499565), hBOOL(hAPP(hAPP(_1499565, _1499567), _1499569)), -(hBOOL(hAPP(hAPP(_1499565, _1499569), _1499567)))], (38574 ^ _777959) ^ [_1518097, _1518099, _1518101, _1518103, _1518105] : [c_Fun_Oinj__on(_1518097, _1518099, _1518101, _1518103), hBOOL(hAPP(hAPP(c_member(_1518099), _1518105), hAPP(c_Set_Oimage(_1518097, _1518099, _1518101), _1518103))), -(hAPP(_1518101, hAPP(c_Fun_Othe__inv__into(_1518097, _1518099, _1518103, _1518101), _1518105)) = _1518105)], (34333 ^ _777959) ^ [_1424261, _1424263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1424261)), c_Int_OBit0(_1424263))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1424261), _1424263)))], (49058 ^ _777959) ^ [_1769250, _1769252] : [-(c_Transitive__Closure_Otrancl(_1769250, hAPP(c_Relation_Oconverse(_1769250, _1769250), _1769252)) = hAPP(c_Relation_Oconverse(_1769250, _1769250), c_Transitive__Closure_Otrancl(_1769250, _1769252)))], (13252 ^ _777959) ^ [_1020128, _1020130, _1020132, _1020134] : [class_Lattices_Osemilattice__sup(_1020128), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020128), _1020130)), 13262 ^ _777959 : [(13265 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020128), 13261 ^ [_1020128, _1020130, _1020132, _1020134]), _1020132))], (13263 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1020128), 13261 ^ [_1020128, _1020130, _1020132, _1020134]), _1020130)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020128), hAPP(hAPP(c_Finite__Set_Ofold(_1020128, _1020128, c_Lattices_Osemilattice__sup__class_Osup(_1020128)), _1020134), _1020130)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1020128), _1020132), _1020134))))], (34273 ^ _777959) ^ [_1423185, _1423187] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1423185)), c_Int_OBit0(_1423187)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1423185), _1423187)))], (7740 ^ _777959) ^ [_909285, _909287, _909289, _909291, _909293, _909295, _909297, _909299] : [c_Finite__Set_Ofolding__image__simple(_909285, _909287, _909289, _909291, _909293, _909295), hBOOL(hAPP(c_Finite__Set_Ofinite(_909287), _909297)), -(hBOOL(hAPP(hAPP(c_member(_909287), _909299), _909297))), -(hAPP(_909295, hAPP(hAPP(c_Set_Oinsert(_909287), _909299), _909297)) = hAPP(hAPP(_909289, hAPP(_909293, _909299)), hAPP(_909295, _909297)))], (38956 ^ _777959) ^ [_1527495, _1527497, _1527499, _1527501, _1527503] : [38958 ^ _777959 : [(38961 ^ _777959) ^ [] : [hAPP(_1527499, 38957 ^ [_1527495, _1527497, _1527499, _1527501, _1527503]) = hAPP(_1527503, 38957 ^ [_1527495, _1527497, _1527499, _1527501, _1527503])], (38959 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527495), 38957 ^ [_1527495, _1527497, _1527499, _1527501, _1527503]), hAPP(c_List_Oset(_1527495), _1527501))))]], -(hAPP(hAPP(c_List_Omap(_1527495, _1527497), _1527499), _1527501) = hAPP(hAPP(c_List_Omap(_1527495, _1527497), _1527503), _1527501))], (48611 ^ _777959) ^ [_1757597, _1757599, _1757601, _1757603, _1757605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1757597, _1757597)), hAPP(hAPP(c_Product__Type_OPair(_1757597, _1757597), _1757599), _1757601)), c_Transitive__Closure_Otrancl(_1757597, _1757603))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1757597, _1757597)), hAPP(hAPP(c_Product__Type_OPair(_1757597, _1757597), _1757601), _1757605)), c_Transitive__Closure_Ortrancl(_1757597, _1757603))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1757597, _1757597)), hAPP(hAPP(c_Product__Type_OPair(_1757597, _1757597), _1757599), _1757605)), c_Transitive__Closure_Otrancl(_1757597, _1757603))))], (32097 ^ _777959) ^ [_1384070, _1384072, _1384074] : [class_Int_Onumber(_1384070), class_Orderings_Oord(_1384070), 32104 ^ _777959 : [(32111 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384070), hAPP(c_Int_Onumber__class_Onumber__of(_1384070), _1384072)), hAPP(c_Int_Onumber__class_Onumber__of(_1384070), _1384074)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1384070), hAPP(c_Int_Onumber__class_Onumber__of(_1384070), _1384072)), hAPP(c_Int_Onumber__class_Onumber__of(_1384070), _1384074)) = hAPP(c_Int_Onumber__class_Onumber__of(_1384070), _1384072))], (32105 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1384070), hAPP(c_Int_Onumber__class_Onumber__of(_1384070), _1384072)), hAPP(c_Int_Onumber__class_Onumber__of(_1384070), _1384074))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1384070), hAPP(c_Int_Onumber__class_Onumber__of(_1384070), _1384072)), hAPP(c_Int_Onumber__class_Onumber__of(_1384070), _1384074)) = hAPP(c_Int_Onumber__class_Onumber__of(_1384070), _1384074))]]], (21101 ^ _777959) ^ [_1178876, _1178878] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1178876), _1178878) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1178876), _1178878)))], (51328 ^ _777959) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (18498 ^ _777959) ^ [_1133204, _1133206, _1133208, _1133210, _1133212] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1133204, _1133206, hAPP(hAPP(c_Set_Oinsert(_1133204), _1133208), _1133210)), _1133212)), 18503 ^ _777959 : [(18508 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1133204), 18501 ^ [_1133204, _1133206, _1133208, _1133210, _1133212]), 18502 ^ [_1133204, _1133206, _1133208, _1133210, _1133212]))], (18506 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1133204, _1133204, _1133206, 18501 ^ [_1133204, _1133206, _1133208, _1133210, _1133212], 18502 ^ [_1133204, _1133206, _1133208, _1133210, _1133212]), _1133212)))], (18504 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1133204), _1133208), _1133210) = hAPP(hAPP(c_Set_Oinsert(_1133204), 18501 ^ [_1133204, _1133206, _1133208, _1133210, _1133212]), 18502 ^ [_1133204, _1133206, _1133208, _1133210, _1133212]))]]], (27417 ^ _777959) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4246 ^ _777959) ^ [_842237, _842239] : [_842239 = _842237, -(c_Relation_OId(_842239) = c_Relation_OId(_842237))], (37170 ^ _777959) ^ [_1485919, _1485921, _1485923, _1485925, _1485927] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1485919, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1485921, _1485919, _1485923), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485921, tc_HOL_Obool)), _1485925), _1485927))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1485919, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1485921, _1485919, _1485923), _1485925)), hAPP(c_Relation_OImage(_1485921, _1485919, _1485923), _1485927)))))], (292 ^ _777959) ^ [_782435, _782437, _782439, _782441, _782443, _782445, _782447, _782449, _782451, _782453, _782455, _782457] : [-(c_Equiv__Relations_Ocongruent2(_782455, _782451, _782447, _782443, _782439, _782435)), c_Equiv__Relations_Ocongruent2(_782457, _782453, _782449, _782445, _782441, _782437), _782457 = _782455, _782453 = _782451, _782449 = _782447, _782445 = _782443, _782441 = _782439, _782437 = _782435], (33767 ^ _777959) ^ [_1413632, _1413634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413632), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413632)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413634)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50452 ^ _777959) ^ [_1801272, _1801274, _1801276, _1801278, _1801280] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1801272, _1801274, _1801276), _1801278), _1801280)), -(hBOOL(hAPP(hAPP(_1801276, _1801280), _1801278)))], (19017 ^ _777959) ^ [_1143140, _1143142, _1143144, _1143146] : [-(hAPP(hAPP(c_Option_Omap(_1143140, _1143142), _1143144), hAPP(c_Option_Ooption_OSome(_1143140), _1143146)) = hAPP(c_Option_Ooption_OSome(_1143142), hAPP(_1143144, _1143146)))], (35779 ^ _777959) ^ [_1456408, _1456410, _1456412, _1456414, _1456416, _1456418] : [-(hAPP(hAPP(c_Product__Type_OPair(_1456408, _1456410), _1456412), _1456414) = hAPP(hAPP(c_Product__Type_OPair(_1456408, _1456410), _1456416), _1456418)), _1456412 = _1456416, _1456414 = _1456418], (37251 ^ _777959) ^ [_1488252] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1488252) = 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, _1488252)), 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))))))))], (1710 ^ _777959) ^ [_802058, _802060] : [-(class_Rings_Osemiring__1(_802058)), _802060 = _802058, class_Rings_Osemiring__1(_802060)], (32515 ^ _777959) ^ [_1391917, _1391919, _1391921, _1391923] : [class_Fields_Olinordered__field__inverse__zero(_1391917), class_Int_Onumber(_1391917), 32522 ^ _777959 : [(32523 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391917), _1391919), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921))), _1391923)), 32526 ^ _777959 : [(32533 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), c_Groups_Ozero__class_Ozero(_1391917)), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921)))), 32536 ^ _777959 : [(32543 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921)), c_Groups_Ozero__class_Ozero(_1391917)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), c_Groups_Ozero__class_Ozero(_1391917)), _1391923)))], (32537 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921)), c_Groups_Ozero__class_Ozero(_1391917))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391917), _1391923), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921))), _1391919)))]]], (32527 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), c_Groups_Ozero__class_Ozero(_1391917)), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), _1391919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391917), _1391923), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921)))))]]], (32549 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1391917), _1391919), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921))), _1391923))), 32552 ^ _777959 : [(32555 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), _1391919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391917), _1391923), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921))))], (32553 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), c_Groups_Ozero__class_Ozero(_1391917)), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921))))]], 32556 ^ _777959 : [(32559 ^ _777959) ^ [] : [32560 ^ _777959 : [(32563 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391917), _1391923), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921))), _1391919))], (32561 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921)), c_Groups_Ozero__class_Ozero(_1391917))))]], 32564 ^ _777959 : [(32567 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), c_Groups_Ozero__class_Ozero(_1391917)), _1391923))], (32565 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921)), c_Groups_Ozero__class_Ozero(_1391917)))]]], (32557 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1391917), c_Groups_Ozero__class_Ozero(_1391917)), hAPP(c_Int_Onumber__class_Onumber__of(_1391917), _1391921)))]]]]], (34387 ^ _777959) ^ [_1425248, _1425250] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1425248)), c_Int_OBit1(_1425250)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1425248), c_Int_Osucc(_1425250))))], (49288 ^ _777959) ^ [_1774652, _1774654, _1774656] : [-(hAPP(hAPP(c_Nat_Ocompow(_1774652, _1774652), hAPP(c_Nat_OSuc, _1774654)), _1774656) = hAPP(c_Fun_Ocomp(_1774652, _1774652, _1774652, _1774656), hAPP(hAPP(c_Nat_Ocompow(_1774652, _1774652), _1774654), _1774656)))], (80 ^ _777959) ^ [_779309, _779311, _779313, _779315, _779317, _779319] : [-(c_Finite__Set_Ofolding__one__idem(_779317, _779313, _779309)), c_Finite__Set_Ofolding__one__idem(_779319, _779315, _779311), _779319 = _779317, _779315 = _779313, _779311 = _779309], (37283 ^ _777959) ^ [_1489253, _1489255] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1489253, _1489253)), hAPP(hAPP(c_Product__Type_OPair(_1489253, _1489253), 37284 ^ [_1489253, _1489255]), 37284 ^ [_1489253, _1489255])), _1489255))), -(c_Relation_Oirrefl(_1489253, _1489255))], (27216 ^ _777959) ^ [_1293379] : [27218 ^ _777959 : [(27221 ^ _777959) ^ [] : [hBOOL(hAPP(_1293379, hAPP(c_Int_Onat, 27217 ^ [_1293379])))], (27219 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 27217 ^ [_1293379])))]], 27222 ^ _777959 : [(27223 ^ _777959) ^ [_1293512] : [-(hBOOL(hAPP(_1293379, _1293512)))]]], (10256 ^ _777959) ^ [_958134, _958136, _958138, _958140] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958134, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958134, tc_HOL_Obool)), _958136), _958138)), _958140) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958134, tc_HOL_Obool)), _958136), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958134, tc_HOL_Obool)), _958138), _958140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958134, tc_HOL_Obool)), _958140), _958136)))], (36588 ^ _777959) ^ [_1471926, _1471928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1471926), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1471928), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1471926, _1471928) = 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), _1471926), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1471928)))))], (47228 ^ _777959) ^ [_1725372, _1725374] : [-(hAPP(c_Relation_ORange(_1725372, _1725374), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1725372, _1725374), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1725374, tc_HOL_Obool)))], (37134 ^ _777959) ^ [_1484702, _1484704] : [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)), _1484702), 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)), _1484704), 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)), _1484702), _1484704)), c_Int_Ointrel)))], (49142 ^ _777959) ^ [_1771165, _1771167] : [-(c_Relation_Osingle__valued(_1771165, _1771165, c_Relation_OId__on(_1771165, _1771167)))], (50976 ^ _777959) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (28890 ^ _777959) ^ [_1322655, _1322657] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1322655, _1322657))))], (36750 ^ _777959) ^ [_1475322, _1475324, _1475326, _1475328, _1475330, _1475332] : [hBOOL(hAPP(_1475322, _1475324)), hBOOL(hAPP(_1475326, _1475328)), 36757 ^ _777959 : [(36760 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1475326, hAPP(c_Product__Type_Osnd(_1475330, _1475332), hAPP(hAPP(c_Product__Type_OPair(_1475330, _1475332), _1475324), _1475328)))))], (36758 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1475322, hAPP(c_Product__Type_Ofst(_1475330, _1475332), hAPP(hAPP(c_Product__Type_OPair(_1475330, _1475332), _1475324), _1475328)))))]]], (39514 ^ _777959) ^ [_1540772, _1540774, _1540776, _1540778, _1540780] : [-(hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1540772, _1540774, _1540776), _1540778), _1540780))), hBOOL(hAPP(hAPP(_1540774, _1540778), _1540780)), hBOOL(hAPP(_1540776, _1540780))], (2992 ^ _777959) ^ [_822766, _822768, _822770, _822772] : [-(c_Big__Operators_Olattice__class_OInf__fin(_822772, _822768) = c_Big__Operators_Olattice__class_OInf__fin(_822770, _822766)), _822772 = _822770, _822768 = _822766], (24834 ^ _777959) ^ [_1248765, _1248767, _1248769, _1248771, _1248773] : [class_Groups_Ocomm__monoid__add(_1248765), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1248765), _1248767), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1248769), _1248771)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1248773), _1248771))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1248765), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1248765, tc_Nat_Onat), _1248767), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1248771))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1248769), _1248773)))], (7216 ^ _777959) ^ [_898810, _898812, _898814, _898816] : [hBOOL(hAPP(_898810, _898812)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898814, tc_HOL_Obool)), _898816), _898810), _898812)))], (50446 ^ _777959) ^ [_1801135, _1801137, _1801139, _1801141, _1801143] : [hBOOL(hAPP(hAPP(_1801139, _1801143), _1801141)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1801135, _1801137, _1801139), _1801141), _1801143)))], (41968 ^ _777959) ^ [_1604761, _1604763] : [-(hAPP(c_List_OremoveAll(_1604761, _1604763), c_List_Olist_ONil(_1604761)) = c_List_Olist_ONil(_1604761))], (50630 ^ _777959) ^ [_1804976, _1804978, _1804980, _1804982] : [-(hBOOL(hAPP(_1804976, _1804978))), -(hAPP(c_List_Ofilter(_1804980, _1804976), c_List_Oreplicate(_1804980, _1804982, _1804978)) = c_List_Olist_ONil(_1804980))], (48551 ^ _777959) ^ [_1756174, _1756176] : [-(c_Transitive__Closure_Otrancl(_1756174, _1756176) = hAPP(hAPP(c_Relation_Orel__comp(_1756174, _1756174, _1756174), _1756176), c_Transitive__Closure_Ortrancl(_1756174, _1756176)))], (12938 ^ _777959) ^ [_1013234, _1013236, _1013238, _1013240] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1013234, tc_HOL_Obool), hAPP(c_Set_Oimage(_1013236, tc_fun(_1013234, tc_HOL_Obool), _1013238), _1013240)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1013236, tc_fun(_1013234, tc_HOL_Obool)), _1013240), _1013238))], (2880 ^ _777959) ^ [_820974, _820976, _820978, _820980] : [-(c_List_Olistset(_820980, _820976) = c_List_Olistset(_820978, _820974)), _820980 = _820978, _820976 = _820974], (39107 ^ _777959) ^ [_1531209, _1531211, _1531213, _1531215, _1531217, _1531219, _1531221, _1531223] : [class_Groups_Ocomm__monoid__mult(_1531209), c_Fun_Oinj__on(_1531211, _1531213, _1531215, _1531217), _1531219 = hAPP(c_Set_Oimage(_1531211, _1531213, _1531215), _1531217), _1531221 = hAPP(c_Fun_Ocomp(_1531213, _1531209, _1531211, _1531223), _1531215), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1531213, _1531209), _1531223), _1531219) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1531211, _1531209), _1531221), _1531217))], (45190 ^ _777959) ^ [_1678795, _1678797, _1678799, _1678801] : [hBOOL(hAPP(_1678795, _1678797)), -(c_List_OtakeWhile(_1678799, _1678795, hAPP(hAPP(c_List_Olist_OCons(_1678799), _1678797), _1678801)) = hAPP(hAPP(c_List_Olist_OCons(_1678799), _1678797), c_List_OtakeWhile(_1678799, _1678795, _1678801)))], (51120 ^ _777959) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (17727 ^ _777959) ^ [_1116642, _1116644, _1116646] : [class_Orderings_Olinorder(_1116642), hBOOL(hAPP(c_Finite__Set_Ofinite(_1116642), _1116644)), -(hBOOL(hAPP(hAPP(c_member(_1116642), _1116646), _1116644))), -(c_Big__Operators_Olinorder__class_OMin(_1116642, hAPP(hAPP(c_Set_Oinsert(_1116642), _1116646), _1116644)) = hAPP(hAPP(c_Finite__Set_Ofold(_1116642, _1116642, c_Orderings_Oord__class_Omin(_1116642)), _1116646), _1116644))], (31713 ^ _777959) ^ [_1376767, _1376769, _1376771, _1376773] : [class_Orderings_Olinorder(_1376767), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376767), _1376769)), 31723 ^ _777959 : [(31726 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376767), _1376771), 31722 ^ [_1376767, _1376769, _1376771, _1376773]))], (31724 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1376767), 31722 ^ [_1376767, _1376769, _1376771, _1376773]), _1376769)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376767), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376767), _1376771), _1376773)), hAPP(hAPP(c_Finite__Set_Ofold(_1376767, _1376767, c_Orderings_Oord__class_Omin(_1376767)), _1376773), _1376769))))], (24928 ^ _777959) ^ [_1250554, _1250556] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1250554)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250554), _1250556)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1250554), _1250556) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (43564 ^ _777959) ^ [_1643780, _1643782, _1643784] : [-(hAPP(c_List_Otl(_1643780), hAPP(hAPP(c_List_Oappend(_1643780), _1643782), _1643784)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1643780), _1643780, hAPP(c_List_Otl(_1643780), _1643784), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1643780), tc_List_Olist(_1643780)), _1643780), hAPP(hAPP(c_COMBC(tc_List_Olist(_1643780), tc_List_Olist(_1643780), tc_List_Olist(_1643780)), c_List_Oappend(_1643780)), _1643784))), _1643782))], (29176 ^ _777959) ^ [_1327943, _1327945, _1327947] : [class_Orderings_Olinorder(_1327943), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1327943), _1327945), _1327947)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1327943, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1327943), _1327945)), c_SetInterval_Oord__class_OatLeastAtMost(_1327943, _1327945, _1327947)) = hAPP(c_SetInterval_Oord__class_OatMost(_1327943), _1327947))], (6891 ^ _777959) ^ [_890572, _890574, _890576, _890578] : [c_Com_Ocom_OCall(_890572, _890574, _890576) = hAPP(c_Com_Ocom_OBODY, _890578)], (49442 ^ _777959) ^ [_1778808, _1778810, _1778812, _1778814, _1778816] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1778808, _1778808)), hAPP(hAPP(c_Product__Type_OPair(_1778808, _1778808), _1778810), _1778812)), c_Transitive__Closure_Ortrancl(_1778808, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1778808, _1778808), tc_HOL_Obool)), _1778814), _1778816)))), 49448 ^ _777959 : [(49454 ^ _777959) ^ [] : [49450 ^ [_1778808, _1778810, _1778812, _1778814, _1778816] = 49447 ^ [_1778808, _1778810, _1778812, _1778814, _1778816]], (49452 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778808, _1778808)), hAPP(hAPP(c_Product__Type_OPair(_1778808, _1778808), 49450 ^ [_1778808, _1778810, _1778812, _1778814, _1778816]), 49447 ^ [_1778808, _1778810, _1778812, _1778814, _1778816])), _1778816)))], (49449 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778808, _1778808)), hAPP(hAPP(c_Product__Type_OPair(_1778808, _1778808), 49447 ^ [_1778808, _1778810, _1778812, _1778814, _1778816]), _1778812)), c_Transitive__Closure_Ortrancl(_1778808, _1778814))))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1778808, _1778808)), hAPP(hAPP(c_Product__Type_OPair(_1778808, _1778808), _1778810), _1778812)), c_Transitive__Closure_Ortrancl(_1778808, _1778814))))], (49615 ^ _777959) ^ [_1783692, _1783694] : [-(c_Wellfounded_Owf(_1783692, _1783694)), 49618 ^ _777959 : [(49621 ^ _777959) ^ [_1783912] : [hBOOL(hAPP(hAPP(c_member(_1783692), _1783912), 49616 ^ [_1783692, _1783694])), 49625 ^ _777959 : [(49628 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1783692), 49624 ^ [_1783692, _1783694, _1783912]), 49616 ^ [_1783692, _1783694])))], (49626 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1783692, _1783692)), hAPP(hAPP(c_Product__Type_OPair(_1783692, _1783692), 49624 ^ [_1783692, _1783694, _1783912]), _1783912)), _1783694)))]]], (49619 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1783692), 49617 ^ [_1783692, _1783694]), 49616 ^ [_1783692, _1783694])))]]], (10052 ^ _777959) ^ [_953040, _953042, _953044] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953040, tc_HOL_Obool)), _953042), _953044) = c_Orderings_Obot__class_Obot(tc_fun(_953040, tc_HOL_Obool)), 10055 ^ _777959 : [(10056 ^ _777959) ^ [_953164] : [hBOOL(hAPP(hAPP(c_member(_953040), _953164), _953042)), 10059 ^ _777959 : [(10060 ^ _777959) ^ [_953254] : [hBOOL(hAPP(hAPP(c_member(_953040), _953254), _953044)), _953164 = _953254]]]]], (48753 ^ _777959) ^ [_1761212, _1761214, _1761216] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1761212, _1761214, _1761214), _1761216), c_Relation_OId(_1761214)) = _1761216)], (11984 ^ _777959) ^ [_995585, _995587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995585), _995587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995585), _995587))), -(_995585 = _995587)], (37078 ^ _777959) ^ [_1483223] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1483223)), -(_1483223 = 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))), _1483223)), c_FunDef_Omax__strict)))], (31152 ^ _777959) ^ [_1366298, _1366300] : [class_Groups_Oordered__ab__group__add__abs(_1366298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366298), hAPP(c_Groups_Oabs__class_Oabs(_1366298), _1366300)), c_Groups_Ozero__class_Ozero(_1366298)))], (4964 ^ _777959) ^ [_853736, _853738, _853740, _853742] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_853742, _853738) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_853740, _853736)), _853742 = _853740, _853738 = _853736], (17813 ^ _777959) ^ [_1118539, _1118541, _1118543] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1118539, _1118541, c_Orderings_Obot__class_Obot(tc_fun(_1118539, tc_HOL_Obool))), _1118543))], (47261 ^ _777959) ^ [_1726235, _1726237, _1726239, _1726241] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1726235, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1726235, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1726237, _1726235), _1726239)), hAPP(c_Relation_ORange(_1726237, _1726235), _1726241))), hAPP(c_Relation_ORange(_1726237, _1726235), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1726237, _1726235), tc_HOL_Obool)), _1726239), _1726241)))))], (48932 ^ _777959) ^ [_1765891, _1765893, _1765895, _1765897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1765891, _1765891)), hAPP(hAPP(c_Product__Type_OPair(_1765891, _1765891), _1765893), _1765895)), c_Transitive__Closure_Ortrancl(_1765891, _1765897))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765891, _1765891)), hAPP(hAPP(c_Product__Type_OPair(_1765891, _1765891), _1765895), _1765893)), c_Transitive__Closure_Ortrancl(_1765891, hAPP(c_Relation_Oconverse(_1765891, _1765891), _1765897)))))], (45672 ^ _777959) ^ [_1689407, _1689409] : [-(c_Enum_Oenum__class_Oenum(tc_prod(_1689407, _1689409)) = c_Enum_Oproduct(_1689407, _1689409, c_Enum_Oenum__class_Oenum(_1689407), c_Enum_Oenum__class_Oenum(_1689409))), class_Enum_Oenum(_1689407), class_Enum_Oenum(_1689409)], (22846 ^ _777959) ^ [_1213730, _1213732, _1213734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1213730), _1213732)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1213734)), -(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), _1213734)), _1213730)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1213734)), _1213732))))], (20037 ^ _777959) ^ [_1160526, _1160528, _1160530] : [class_Rings_Oordered__cancel__semiring(_1160526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160526), c_Groups_Ozero__class_Ozero(_1160526)), _1160528)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160526), _1160530), c_Groups_Ozero__class_Ozero(_1160526))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160526), _1160530), _1160528)), c_Groups_Ozero__class_Ozero(_1160526))))], (3878 ^ _777959) ^ [_836679, _836681, _836683, _836685] : [-(c_Wellfounded_Omax__ext(_836685, _836681) = c_Wellfounded_Omax__ext(_836683, _836679)), _836685 = _836683, _836681 = _836679], (38528 ^ _777959) ^ [_1517088, _1517090, _1517092, _1517094, _1517096, _1517098] : [c_Fun_Oinj__on(_1517088, _1517090, _1517092, _1517094), hAPP(_1517092, _1517096) = _1517098, hBOOL(hAPP(hAPP(c_member(_1517088), _1517096), _1517094)), -(hAPP(c_Fun_Othe__inv__into(_1517088, _1517090, _1517094, _1517092), _1517098) = _1517096)], (15572 ^ _777959) ^ [_1073845] : [class_Lattices_Oab__semigroup__idem__mult(_1073845), -(c_Finite__Set_Ofun__left__comm__idem(_1073845, _1073845, c_Groups_Otimes__class_Otimes(_1073845)))], (27497 ^ _777959) ^ [_1297860, _1297862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1297860)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1297862)), 27504 ^ _777959 : [(27511 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1297860), _1297862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1297860)), hAPP(c_Int_Onat, _1297862))))], (27505 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1297860)), hAPP(c_Int_Onat, _1297862))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1297860), _1297862)))]]], (1680 ^ _777959) ^ [_801683, _801685] : [-(class_Orderings_Olinorder(_801683)), _801685 = _801683, class_Orderings_Olinorder(_801685)], (49340 ^ _777959) ^ [_1776114, _1776116, _1776118, _1776120] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776114, _1776114)), _1776116), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1776114, _1776114), tc_HOL_Obool), _1776118), _1776120))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776114, _1776114)), _1776116), c_Transitive__Closure_Ortrancl(_1776114, _1776120))))], (240 ^ _777959) ^ [_781731, _781733, _781735, _781737] : [-(c_Int_Oiszero(_781735, _781731)), c_Int_Oiszero(_781737, _781733), _781737 = _781735, _781733 = _781731], (7130 ^ _777959) ^ [_897027, _897029, _897031] : [class_Lattices_Osemilattice__sup(_897027), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897027), _897029), _897031) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897027), _897031), _897029))], (11633 ^ _777959) ^ [_986726, _986728, _986730, _986732, _986734, _986736, _986738] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986726, tc_fun(_986728, tc_fun(_986730, tc_HOL_Obool))), _986732), _986734), _986736), _986738)), 11637 ^ _777959 : [(11640 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_986734, 11636 ^ [_986726, _986728, _986730, _986732, _986734, _986736, _986738]), _986736), _986738)))], (11638 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_986726), 11636 ^ [_986726, _986728, _986730, _986732, _986734, _986736, _986738]), _986732)))]]], (32215 ^ _777959) ^ [_1386410, _1386412, _1386414, _1386416] : [class_Fields_Ofield__inverse__zero(_1386410), class_Int_Onumber(_1386410), 32222 ^ _777959 : [(32223 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1386410), _1386412) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386410), _1386414), _1386416), 32226 ^ _777959 : [(32233 ^ _777959) ^ [] : [_1386416 = c_Groups_Ozero__class_Ozero(_1386410), -(hAPP(c_Int_Onumber__class_Onumber__of(_1386410), _1386412) = c_Groups_Ozero__class_Ozero(_1386410))], (32227 ^ _777959) ^ [] : [-(_1386416 = c_Groups_Ozero__class_Ozero(_1386410)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386410), hAPP(c_Int_Onumber__class_Onumber__of(_1386410), _1386412)), _1386416) = _1386414)]]], (32239 ^ _777959) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1386410), _1386412) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1386410), _1386414), _1386416)), 32242 ^ _777959 : [(32245 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386410), hAPP(c_Int_Onumber__class_Onumber__of(_1386410), _1386412)), _1386416) = _1386414], (32243 ^ _777959) ^ [] : [_1386416 = c_Groups_Ozero__class_Ozero(_1386410)]], 32246 ^ _777959 : [(32249 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1386410), _1386412) = c_Groups_Ozero__class_Ozero(_1386410)], (32247 ^ _777959) ^ [] : [-(_1386416 = c_Groups_Ozero__class_Ozero(_1386410))]]]]], (34109 ^ _777959) ^ [_1420394, _1420396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420394), _1420396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1420394)), c_Int_OBit0(_1420396))))], (22840 ^ _777959) ^ [_1213639] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1213639)), -(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), _1213639))))], (7019 ^ _777959) ^ [_894209, _894211, _894213, _894215] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894209, tc_HOL_Obool)), _894211), _894213), _894215)), -(hBOOL(hAPP(_894211, _894215))), -(hBOOL(hAPP(_894213, _894215)))], (9586 ^ _777959) ^ [_943608, _943610, _943612] : [class_Lattices_Olattice(_943608), hBOOL(hAPP(c_Finite__Set_Ofinite(_943608), _943610)), -(hBOOL(hAPP(hAPP(c_member(_943608), _943612), _943610))), -(c_Big__Operators_Olattice__class_OSup__fin(_943608, hAPP(hAPP(c_Set_Oinsert(_943608), _943612), _943610)) = hAPP(hAPP(c_Finite__Set_Ofold(_943608, _943608, c_Lattices_Osemilattice__sup__class_Osup(_943608)), _943612), _943610))], (48427 ^ _777959) ^ [_1752314, _1752316] : [-(hAPP(c_Relation_ODomain(_1752314, _1752314), c_Transitive__Closure_Otrancl(_1752314, _1752316)) = hAPP(c_Relation_ODomain(_1752314, _1752314), _1752316))], (8046 ^ _777959) ^ [_915393, _915395, _915397, _915399, _915401, _915403, _915405, _915407] : [c_Finite__Set_Ofolding__image__simple(_915393, _915395, _915397, _915399, _915401, _915403), hBOOL(hAPP(c_Finite__Set_Ofinite(_915395), _915405)), -(hAPP(_915403, hAPP(hAPP(c_Set_Oinsert(_915395), _915407), _915405)) = hAPP(hAPP(_915397, hAPP(_915401, _915407)), hAPP(_915403, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915395, tc_HOL_Obool)), _915405), hAPP(hAPP(c_Set_Oinsert(_915395), _915407), c_Orderings_Obot__class_Obot(tc_fun(_915395, tc_HOL_Obool)))))))], (13747 ^ _777959) ^ [_1032083, _1032085, _1032087] : [-(hAPP(c_Set_OCollect(_1032083), hAPP(hAPP(c_COMBS(_1032083, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1032083), c_fconj), _1032085)), _1032087)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1032083, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1032083), _1032085)), hAPP(c_Set_OCollect(_1032083), _1032087)))], (49476 ^ _777959) ^ [_1779987, _1779989, _1779991, _1779993, _1779995] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779987, _1779987)), hAPP(hAPP(c_Product__Type_OPair(_1779987, _1779987), _1779989), _1779991)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1779987, _1779987), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1779993)), _1779995))), 49480 ^ _777959 : [(49483 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779987, _1779987)), hAPP(hAPP(c_Product__Type_OPair(_1779987, _1779987), 49479 ^ [_1779987, _1779989, _1779991, _1779993, _1779995]), _1779991)), _1779995)))], (49481 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779987, _1779987)), hAPP(hAPP(c_Product__Type_OPair(_1779987, _1779987), _1779989), 49479 ^ [_1779987, _1779989, _1779991, _1779993, _1779995])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1779987, _1779987), tc_HOL_Obool), _1779993), _1779995))))]]], (24317 ^ _777959) ^ [_1240103] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1240103) = 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)), _1240103)))], (39021 ^ _777959) ^ [_1529320, _1529322, _1529324, _1529326] : [c_Finite__Set_Ofun__left__comm__idem(_1529320, _1529322, _1529324), -(hAPP(c_Fun_Ocomp(_1529322, _1529322, _1529322, hAPP(_1529324, _1529326)), hAPP(_1529324, _1529326)) = hAPP(_1529324, _1529326))], (2218 ^ _777959) ^ [_810663, _810665, _810667, _810669, _810671, _810673] : [-(c_Option_Ooption_Ooption__size(_810673, _810669, _810665) = c_Option_Ooption_Ooption__size(_810671, _810667, _810663)), _810673 = _810671, _810669 = _810667, _810665 = _810663], (48747 ^ _777959) ^ [_1761108, _1761110] : [-(c_List_Olistrel(_1761108, c_Transitive__Closure_Ortrancl(_1761108, _1761110)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1761108), c_List_Olistrel1(_1761108, _1761110)))], (31758 ^ _777959) ^ [_1377709, _1377711, _1377713, _1377715, _1377717, _1377719] : [class_Groups_Oab__semigroup__mult(_1377709), hBOOL(hAPP(c_Finite__Set_Ofinite(_1377711), _1377713)), 31768 ^ _777959 : [(31771 ^ _777959) ^ [] : [hAPP(_1377715, 31767 ^ [_1377709, _1377711, _1377713, _1377715, _1377717, _1377719]) = hAPP(_1377717, 31767 ^ [_1377709, _1377711, _1377713, _1377715, _1377717, _1377719])], (31769 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1377711), 31767 ^ [_1377709, _1377711, _1377713, _1377715, _1377717, _1377719]), _1377713)))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1377709, _1377711, c_Groups_Otimes__class_Otimes(_1377709)), _1377715), _1377719), _1377713) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1377709, _1377711, c_Groups_Otimes__class_Otimes(_1377709)), _1377717), _1377719), _1377713))], (15022 ^ _777959) ^ [_1063695, _1063697] : [class_Lattices_Oab__semigroup__idem__mult(_1063695), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063695), _1063697), _1063697) = _1063697)], (7908 ^ _777959) ^ [_912586, _912588, _912590, _912592] : [hBOOL(hAPP(hAPP(c_member(_912586), _912588), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912586, tc_HOL_Obool)), _912590), _912592))), 7911 ^ _777959 : [(7914 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_912586), _912588), _912592))], (7912 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912586), _912588), _912590)))]]], (9038 ^ _777959) ^ [_933263, _933265, _933267] : [class_Orderings_Oorder(_933263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933263), _933265), _933267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933263), _933265), _933267))), -(_933265 = _933267)], (3970 ^ _777959) ^ [_838095, _838097] : [_838097 = _838095, -(c_List_Omonoid__add__class_Olistsum(_838097) = c_List_Omonoid__add__class_Olistsum(_838095))], (20587 ^ _777959) ^ [_1170498] : [class_Rings_Olinordered__semidom(_1170498), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170498), c_Groups_Ozero__class_Ozero(_1170498)), c_Groups_Oone__class_Oone(_1170498))))], (11122 ^ _777959) ^ [_975808, _975810, _975812, _975814, _975816] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_975808, tc_Option_Ooption(_975810)), _975812), _975814), hAPP(c_Option_Ooption_OSome(_975810), _975816)) = hAPP(c_COMBK(tc_Option_Ooption(_975810), _975808), c_Option_Ooption_ONone(_975810))], (41287 ^ _777959) ^ [_1586293, _1586295, _1586297, _1586299] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1586293), tc_List_Olist(_1586293))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1586293), tc_List_Olist(_1586293)), _1586295), _1586297)), c_List_Olistrel1(_1586293, _1586299)))), 41288 ^ _777959 : [(41289 ^ _777959) ^ [_1586426, _1586428] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586293, _1586293)), hAPP(hAPP(c_Product__Type_OPair(_1586293, _1586293), hAPP(hAPP(c_List_Onth(_1586293), _1586295), _1586426)), _1586428)), _1586299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1586426), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1586293)), _1586295))), _1586297 = hAPP(hAPP(c_List_Olist__update(_1586293, _1586295), _1586426), _1586428)]]], (41334 ^ _777959) ^ [_1587600, _1587602, _1587604, _1587606] : [-(hAPP(hAPP(c_List_Omap(_1587600, _1587602), _1587604), c_List_Obutlast(_1587600, _1587606)) = c_List_Obutlast(_1587602, hAPP(hAPP(c_List_Omap(_1587600, _1587602), _1587604), _1587606)))], (43292 ^ _777959) ^ [_1637808, _1637810, _1637812] : [-(hAPP(hAPP(c_List_Oappend(_1637808), hAPP(hAPP(c_List_Otake(_1637808), _1637810), _1637812)), hAPP(hAPP(c_List_Odrop(_1637808), _1637810), _1637812)) = _1637812)], (6325 ^ _777959) ^ [_880085, _880087, _880089, _880091] : [_880085 = _880087, 6328 ^ _777959 : [(6335 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_880089), _880091), _880087)), -(hBOOL(hAPP(hAPP(c_member(_880089), _880091), _880085)))], (6329 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_880089), _880091), _880085)), -(hBOOL(hAPP(hAPP(c_member(_880089), _880091), _880087)))]]], (46365 ^ _777959) ^ [_1703916, _1703918, _1703920, _1703922, _1703924, _1703926, _1703928] : [c_List_Olist__all2(_1703922, _1703918, hAPP(hAPP(c_COMBB(_1703916, tc_fun(_1703918, tc_HOL_Obool), _1703922), _1703920), _1703924), _1703926, _1703928), -(c_List_Olist__all2(_1703916, _1703918, _1703920, hAPP(hAPP(c_List_Omap(_1703922, _1703916), _1703924), _1703926), _1703928))], (20227 ^ _777959) ^ [_1163909, _1163911] : [class_Rings_Olinordered__ring(_1163909), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1163909), _1163911), _1163911)), c_Groups_Ozero__class_Ozero(_1163909)))], (42999 ^ _777959) ^ [_1630231, _1630233, _1630235, _1630237] : [hBOOL(hAPP(hAPP(c_member(_1630231), _1630233), hAPP(c_List_Oset(_1630231), _1630235))), -(c_List_Oremove1(_1630231, _1630233, hAPP(hAPP(c_List_Oappend(_1630231), _1630235), _1630237)) = hAPP(hAPP(c_List_Oappend(_1630231), c_List_Oremove1(_1630231, _1630233, _1630235)), _1630237))], (39725 ^ _777959) ^ [_1545676, _1545678, _1545680, _1545682, _1545684, _1545686] : [c_Finite__Set_Ofolding__idem(_1545676, _1545678, _1545680, _1545682), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545676), _1545684)), -(hAPP(_1545682, hAPP(hAPP(c_Set_Oinsert(_1545676), _1545686), _1545684)) = hAPP(c_Fun_Ocomp(_1545678, _1545678, _1545678, hAPP(_1545682, _1545684)), hAPP(_1545680, _1545686)))], (41695 ^ _777959) ^ [_1596399, _1596401, _1596403, _1596405] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1596399), tc_List_Olist(_1596399), c_List_Olistrel(_1596399, _1596401)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1596399)), hAPP(hAPP(c_List_Olist_OCons(_1596399), _1596403), _1596405)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1596399), tc_HOL_Obool)))) = c_List_Oset__Cons(_1596399, hAPP(c_Relation_OImage(_1596399, _1596399, _1596401), hAPP(hAPP(c_Set_Oinsert(_1596399), _1596403), c_Orderings_Obot__class_Obot(tc_fun(_1596399, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1596399), tc_List_Olist(_1596399), c_List_Olistrel(_1596399, _1596401)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1596399)), _1596405), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1596399), tc_HOL_Obool))))))], (5348 ^ _777959) ^ [_859780, _859782] : [_859782 = _859780, -(c_Nat_Osize__class_Osize(_859782) = c_Nat_Osize__class_Osize(_859780))], (50240 ^ _777959) ^ [_1796296] : [-(c_Lazy__Sequence_Oyieldn(_1796296) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1796296), _1796296, c_Lazy__Sequence_Oyield(_1796296)))], (51094 ^ _777959) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (44102 ^ _777959) ^ [_1655518, _1655520, _1655522, _1655524, _1655526] : [class_Orderings_Olinorder(_1655518), hBOOL(hAPP(hAPP(c_member(_1655520), _1655522), hAPP(c_List_Oset(_1655520), _1655524))), c_List_Olinorder__class_Osorted(_1655518, hAPP(hAPP(c_List_Omap(_1655520, _1655518), _1655526), _1655524)), hAPP(c_List_Ohd(_1655520), hAPP(c_List_Ofilter(_1655520, hAPP(hAPP(c_COMBB(_1655518, tc_HOL_Obool, _1655520), hAPP(c_fequal, hAPP(_1655526, _1655522))), _1655526)), _1655524)) = _1655522, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1655520, _1655518, _1655526), _1655522), c_List_Oremove1(_1655520, _1655522, _1655524)) = _1655524)], (10008 ^ _777959) ^ [_952007, _952009, _952011, _952013] : [class_Lattices_Odistrib__lattice(_952007), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952007), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_952007), _952009), _952011)), _952013) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_952007), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952007), _952009), _952013)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_952007), _952011), _952013)))], (51030 ^ _777959) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (33247 ^ _777959) ^ [_1405369] : [class_Int_Onumber__ring(_1405369), -(c_Groups_Ozero__class_Ozero(_1405369) = hAPP(c_Int_Onumber__class_Onumber__of(_1405369), c_Int_OPls))], (46198 ^ _777959) ^ [_1700217, _1700219] : [-(hBOOL(hAPP(c_List_Olistsp(_1700217, _1700219), c_List_Olist_ONil(_1700217))))], (33865 ^ _777959) ^ [_1415786, _1415788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415786)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415788))), -(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(_1415788))), 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), _1415786)), c_Int_Onat))))))], (30704 ^ _777959) ^ [_1358122, _1358124] : [30705 ^ _777959 : [(30706 ^ _777959) ^ [_1358171] : [_1358122 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1358124), _1358171)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1358122, _1358124) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49598 ^ _777959) ^ [_1783173, _1783175] : [c_Wellfounded_Owf(_1783173, _1783175), 49601 ^ _777959 : [(49602 ^ _777959) ^ [_1783305] : [49603 ^ _777959 : [(49604 ^ _777959) ^ [_1783410] : [hBOOL(hAPP(hAPP(c_member(_1783173), _1783410), _1783305))]], 49606 ^ _777959 : [(49609 ^ _777959) ^ [_1783532] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1783173, _1783173)), hAPP(hAPP(c_Product__Type_OPair(_1783173, _1783173), _1783532), 49605 ^ [_1783173, _1783175, _1783305])), _1783175)), hBOOL(hAPP(hAPP(c_member(_1783173), _1783532), _1783305))], (49607 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1783173), 49605 ^ [_1783173, _1783175, _1783305]), _1783305)))]]]]], (1240 ^ _777959) ^ [_796183, _796185] : [-(class_Rings_Oidom(_796183)), _796185 = _796183, class_Rings_Oidom(_796185)], (43759 ^ _777959) ^ [_1648318, _1648320, _1648322] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648318), tc_List_Olist(_1648318))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648318), tc_List_Olist(_1648318)), c_List_Olist_ONil(_1648318)), _1648320)), c_List_Olexord(_1648318, _1648322))), -(_1648320 = hAPP(hAPP(c_List_Olist_OCons(_1648318), 43762 ^ [_1648318, _1648320, _1648322]), 43763 ^ [_1648318, _1648320, _1648322]))], (14039 ^ _777959) ^ [_1038670, _1038672] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038670, tc_HOL_Obool)), _1038672) = hAPP(c_Set_OCollect(_1038670), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1038670), c_fNot), hAPP(hAPP(c_COMBC(_1038670, tc_fun(_1038670, tc_HOL_Obool), tc_HOL_Obool), c_member(_1038670)), _1038672))))], (51302 ^ _777959) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (33305 ^ _777959) ^ [_1406285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1406285), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406285)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (51024 ^ _777959) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (9146 ^ _777959) ^ [_934912, _934914] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934912, tc_HOL_Obool)), _934914), c_Orderings_Obot__class_Obot(tc_fun(_934912, tc_HOL_Obool))))], (15536 ^ _777959) ^ [_1073325, _1073327] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073325), _1073327)), _1073325 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1073327 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (29066 ^ _777959) ^ [_1325678, _1325680, _1325682] : [class_Groups_Ocomm__monoid__add(_1325678), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1325678), _1325680), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1325682))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1325678), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1325678), _1325680), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1325682))), hAPP(_1325680, hAPP(c_Nat_OSuc, _1325682))))], (49130 ^ _777959) ^ [_1770977, _1770979, _1770981] : [c_Relation_Ototal__on(_1770977, _1770979, hAPP(c_Relation_Oconverse(_1770977, _1770977), _1770981)), -(c_Relation_Ototal__on(_1770977, _1770979, _1770981))], (47680 ^ _777959) ^ [_1736676, _1736678, _1736680, _1736682, _1736684, _1736686] : [47683 ^ _777959 : [(47686 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1736682), _1736684), hAPP(hAPP(_1736686, 47681 ^ [_1736676, _1736678, _1736680, _1736682, _1736684, _1736686]), 47682 ^ [_1736676, _1736678, _1736680, _1736682, _1736684, _1736686])))], (47684 ^ _777959) ^ [] : [-(_1736676 = hAPP(hAPP(c_Product__Type_OPair(_1736678, _1736680), 47681 ^ [_1736676, _1736678, _1736680, _1736682, _1736684, _1736686]), 47682 ^ [_1736676, _1736678, _1736680, _1736682, _1736684, _1736686]))]], -(hBOOL(hAPP(hAPP(c_member(_1736682), _1736684), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1736678, _1736680, tc_fun(_1736682, tc_HOL_Obool)), _1736686), _1736676))))], (10896 ^ _777959) ^ [_971569, _971571, _971573, _971575, _971577] : [class_Groups_Oordered__cancel__ab__semigroup__add(_971569), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971569), _971571), _971573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971569), _971575), _971577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971569), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971569), _971571), _971575)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971569), _971573), _971577))))], (42168 ^ _777959) ^ [_1608891, _1608893] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1608891, _1608893), c_Orderings_Otop__class_Otop(tc_fun(_1608891, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1608893, tc_HOL_Obool), _1608891), c_Orderings_Otop__class_Otop(tc_fun(_1608893, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1608891, _1608893), tc_HOL_Obool)))], (23401 ^ _777959) ^ [_1223645, _1223647, _1223649] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223645), _1223647)), _1223649) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223645), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223647), _1223649)))], (48661 ^ _777959) ^ [_1758950, _1758952, _1758954] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1758950, _1758950), tc_HOL_Obool)), _1758952), _1758954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1758950, _1758950), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1758950, _1758952)), c_Transitive__Closure_Ortrancl(_1758950, _1758954))))], (21736 ^ _777959) ^ [_1190785, _1190787, _1190789] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1190785)), 21739 ^ _777959 : [(21746 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1190787), _1190789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1190785), _1190787)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1190785), _1190789))))], (21740 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1190785), _1190787)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1190785), _1190789))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1190787), _1190789)))]]], (44989 ^ _777959) ^ [_1673268, _1673270, _1673272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1673268), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673270)), _1673272))), -(hAPP(hAPP(c_List_Onth(_1673270), hAPP(c_List_Orev(_1673270), _1673272)), _1673268) = hAPP(hAPP(c_List_Onth(_1673270), _1673272), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1673270)), _1673272)), hAPP(c_Nat_OSuc, _1673268))))], (39187 ^ _777959) ^ [_1532988, _1532990, _1532992, _1532994, _1532996] : [class_Groups_Ocomm__monoid__add(_1532988), hBOOL(hAPP(c_Finite__Set_Ofinite(_1532990), _1532992)), c_Fun_Oinj__on(_1532990, _1532990, _1532994, _1532992), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1532990, _1532988), _1532996), hAPP(c_Set_Oimage(_1532990, _1532990, _1532994), _1532992)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1532990, _1532988), hAPP(c_Fun_Ocomp(_1532990, _1532988, _1532990, _1532996), _1532994)), _1532992))], (9136 ^ _777959) ^ [_934715, _934717, _934719, _934721] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_934715, tc_HOL_Obool)), _934717), _934719)), hBOOL(hAPP(hAPP(c_member(_934715), _934721), _934717)), -(hBOOL(hAPP(hAPP(c_member(_934715), _934721), _934719)))], (15492 ^ _777959) ^ [_1072434, _1072436, _1072438] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072434), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1072436), _1072438)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072434), _1072436)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072434), _1072438)))], (24207 ^ _777959) ^ [_1238124, _1238126] : [-(c_Sum__Type_OPlus(_1238124, _1238126, c_Orderings_Otop__class_Otop(tc_fun(_1238124, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1238126, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1238124, _1238126), tc_HOL_Obool)))], (22587 ^ _777959) ^ [_1208933, _1208935] : [class_Rings_Olinordered__idom(_1208933), hBOOL(hAPP(hAPP(c_member(_1208933), _1208935), c_Int_Oring__1__class_OInts(_1208933))), 22594 ^ _777959 : [(22601 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208933), _1208935), c_Groups_Ozero__class_Ozero(_1208933))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208933), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208933), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208933), c_Groups_Oone__class_Oone(_1208933)), _1208935)), _1208935)), c_Groups_Ozero__class_Ozero(_1208933))))], (22595 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208933), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208933), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1208933), c_Groups_Oone__class_Oone(_1208933)), _1208935)), _1208935)), c_Groups_Ozero__class_Ozero(_1208933))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1208933), _1208935), c_Groups_Ozero__class_Ozero(_1208933))))]]], (40242 ^ _777959) ^ [_1558391, _1558393] : [hBOOL(hAPP(c_List_Odistinct(_1558391), _1558393)), 40245 ^ _777959 : [(40246 ^ _777959) ^ [_1558523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1558523), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1558391)), _1558393))), 40249 ^ _777959 : [(40250 ^ _777959) ^ [_1558650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1558650), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1558391)), _1558393))), -(_1558523 = _1558650), hAPP(hAPP(c_List_Onth(_1558391), _1558393), _1558523) = hAPP(hAPP(c_List_Onth(_1558391), _1558393), _1558650)]]]]], (10240 ^ _777959) ^ [_957671, _957673, _957675, _957677] : [hBOOL(hAPP(hAPP(c_member(_957671), _957673), _957675)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957671, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_957671), _957673), _957677)), _957675) = hAPP(hAPP(c_Set_Oinsert(_957671), _957673), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957671, tc_HOL_Obool)), _957677), _957675)))], (44777 ^ _777959) ^ [_1668563, _1668565] : [-(c_Fun_Oinj__on(tc_List_Olist(_1668563), tc_List_Olist(_1668563), c_List_Orev(_1668563), _1668565))], (22319 ^ _777959) ^ [_1202987, _1202989] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1202987)), _1202989) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1202987), 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), _1202987)), _1202989))], (44070 ^ _777959) ^ [_1654433] : [-(c_List_Otranspose(_1654433, c_List_Olist_ONil(tc_List_Olist(_1654433))) = c_List_Olist_ONil(tc_List_Olist(_1654433)))], (33643 ^ _777959) ^ [] : [-(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)))))], (19626 ^ _777959) ^ [_1153111, _1153113, _1153115] : [19627 ^ _777959 : [(19630 ^ _777959) ^ [] : [_1153111 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19628 ^ _777959) ^ [] : [_1153113 = _1153115]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1153111), _1153113) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1153111), _1153115))], (47275 ^ _777959) ^ [_1727046, _1727048, _1727050, _1727052] : [hBOOL(hAPP(hAPP(c_member(_1727046), _1727048), hAPP(c_Relation_ORange(_1727050, _1727046), _1727052))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1727050, _1727046)), hAPP(hAPP(c_Product__Type_OPair(_1727050, _1727046), 47278 ^ [_1727046, _1727048, _1727050, _1727052]), _1727048)), _1727052)))], (48067 ^ _777959) ^ [_1745872, _1745874, _1745876, _1745878, _1745880] : [-(_1745872 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1745874, _1745876, _1745872, _1745878), _1745880) = hAPP(hAPP(c_Product__Type_Oscomp(_1745876, _1745874, _1745876, tc_prod(_1745874, _1745876)), hAPP(_1745878, _1745880)), c_Random_Oiterate(_1745874, _1745876, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1745872), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1745878)))], (9280 ^ _777959) ^ [_937534] : [class_Lattices_Osemilattice__sup(_937534), -(c_Finite__Set_Ofun__left__comm__idem(_937534, _937534, c_Lattices_Osemilattice__sup__class_Osup(_937534)))], (40899 ^ _777959) ^ [_1574024, _1574026, _1574028, _1574030] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1574024), tc_List_Olist(_1574024))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1574024), tc_List_Olist(_1574024)), _1574026), _1574028)), c_List_Olistrel(_1574024, _1574030)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1574024)), _1574026) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1574024)), _1574028), 40905 ^ _777959 : [(40908 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1574024, _1574024)), hAPP(hAPP(c_Product__Type_OPair(_1574024, _1574024), hAPP(hAPP(c_List_Onth(_1574024), _1574026), 40904 ^ [_1574024, _1574026, _1574028, _1574030])), hAPP(hAPP(c_List_Onth(_1574024), _1574028), 40904 ^ [_1574024, _1574026, _1574028, _1574030]))), _1574030))], (40906 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40904 ^ [_1574024, _1574026, _1574028, _1574030]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1574024)), _1574026))))]]], (39653 ^ _777959) ^ [_1544298, _1544300] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1544298, _1544300)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1544298, _1544300))], (42278 ^ _777959) ^ [_1611588, _1611590, _1611592, _1611594] : [-(_1611588 = c_Orderings_Obot__class_Obot(tc_fun(_1611590, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1611592, _1611590), _1611592, c_Product__Type_Ofst(_1611592, _1611590)), hAPP(hAPP(c_Product__Type_OSigma(_1611592, _1611590), _1611594), hAPP(c_COMBK(tc_fun(_1611590, tc_HOL_Obool), _1611592), _1611588))) = _1611594)], (36668 ^ _777959) ^ [_1473538, _1473540, _1473542, _1473544, _1473546] : [-(hAPP(c_Product__Type_Ofst(_1473538, _1473540), hAPP(c_Product__Type_Oapsnd(_1473542, _1473540, _1473538, _1473544), _1473546)) = hAPP(c_Product__Type_Ofst(_1473538, _1473542), _1473546))], (7828 ^ _777959) ^ [_911056, _911058] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_911056, _911058))), 7831 ^ _777959 : [(7834 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _911058)))], (7832 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _911056)))]]], (33909 ^ _777959) ^ [_1416914, _1416916] : [class_Int_Onumber__ring(_1416914), 33912 ^ _777959 : [(33919 ^ _777959) ^ [] : [c_Int_Oiszero(_1416914, hAPP(c_Int_Onumber__class_Onumber__of(_1416914), 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), _1416916)))), -(c_Groups_Oone__class_Oone(_1416914) = hAPP(c_Int_Onumber__class_Onumber__of(_1416914), _1416916))], (33913 ^ _777959) ^ [] : [c_Groups_Oone__class_Oone(_1416914) = hAPP(c_Int_Onumber__class_Onumber__of(_1416914), _1416916), -(c_Int_Oiszero(_1416914, hAPP(c_Int_Onumber__class_Onumber__of(_1416914), 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), _1416916)))))]]], (25096 ^ _777959) ^ [_1253409, _1253411, _1253413, _1253415] : [class_Divides_Osemiring__div(_1253409), -(_1253411 = c_Groups_Ozero__class_Ozero(_1253409)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1253409), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253409), _1253413), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253409), _1253411), _1253415))), _1253411) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253409), _1253415), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1253409), _1253413), _1253411)))], (43005 ^ _777959) ^ [_1630378, _1630380, _1630382, _1630384] : [-(hBOOL(hAPP(hAPP(c_member(_1630378), _1630380), hAPP(c_List_Oset(_1630378), _1630382)))), -(c_List_Oremove1(_1630378, _1630380, hAPP(hAPP(c_List_Oappend(_1630378), _1630382), _1630384)) = hAPP(hAPP(c_List_Oappend(_1630378), _1630382), c_List_Oremove1(_1630378, _1630380, _1630384)))], (41146 ^ _777959) ^ [_1583048] : [-(c_Relation_Orefl__on(_1583048, c_Orderings_Obot__class_Obot(tc_fun(_1583048, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1583048, _1583048), tc_HOL_Obool))))], (23437 ^ _777959) ^ [_1224256, _1224258, _1224260] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224256), _1224258)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224260), _1224256)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224260), _1224258))))], (50924 ^ _777959) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (40944 ^ _777959) ^ [_1575903, _1575905] : [-(c_List_Olenlex(_1575903, _1575905) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1575903)), tc_List_Olist(_1575903)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1575903), c_Wellfounded_Oless__than, c_List_Olex(_1575903, _1575905))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1575903), tc_List_Olist(_1575903), tc_prod(tc_Nat_Onat, tc_List_Olist(_1575903))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1575903), tc_prod(tc_Nat_Onat, tc_List_Olist(_1575903))), tc_List_Olist(_1575903)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1575903))), c_Nat_Osize__class_Osize(tc_List_Olist(_1575903)))), c_COMBI(tc_List_Olist(_1575903)))))], (45141 ^ _777959) ^ [_1677836, _1677838, _1677840, _1677842] : [hBOOL(hAPP(hAPP(c_member(_1677836), _1677838), hAPP(c_List_Oset(_1677836), c_List_OtakeWhile(_1677836, _1677840, _1677842)))), 45144 ^ _777959 : [(45147 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1677840, _1677838)))], (45145 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1677836), _1677838), hAPP(c_List_Oset(_1677836), _1677842))))]]], (48501 ^ _777959) ^ [_1754176, _1754178, _1754180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1754176, _1754176), tc_HOL_Obool)), _1754178), _1754180)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1754176, _1754176), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1754176, _1754176, _1754176), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1754176, _1754176), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1754176, _1754178)), _1754180)), _1754178)), _1754180)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1754176, _1754176), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1754176, _1754178)), _1754180)))], (33847 ^ _777959) ^ [_1415327, _1415329] : [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(_1415327))), 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)), _1415329)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415327)), hAPP(c_Nat_OSuc, _1415329))))], (21266 ^ _777959) ^ [_1182070, _1182072, _1182074] : [class_Groups_Oordered__comm__monoid__add(_1182070), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182070), _1182072), c_Groups_Ozero__class_Ozero(_1182070))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182070), _1182074), c_Groups_Ozero__class_Ozero(_1182070))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182070), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1182070), _1182072), _1182074)), c_Groups_Ozero__class_Ozero(_1182070))))], (34279 ^ _777959) ^ [_1423304, _1423306] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1423304)), c_Int_OBit1(_1423306)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1423304), _1423306)))], (37054 ^ _777959) ^ [_1482795, _1482797, _1482799, _1482801] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1482795), _1482797)), 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)), _1482799), _1482795)), 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)), _1482801), _1482797)), 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)), _1482799), _1482801)), _1482797)), c_FunDef_Omax__strict)))], (51442 ^ _777959) ^ [_1814807, _1814809] : [-(hBOOL(_1814807)), -(hBOOL(hAPP(hAPP(c_fimplies, _1814807), _1814809)))], (11752 ^ _777959) ^ [_989743, _989745, _989747, _989749, _989751, _989753] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989743, tc_fun(_989745, tc_HOL_Obool)), _989747), hAPP(hAPP(c_COMBB(_989749, tc_fun(_989745, tc_HOL_Obool), _989743), _989751), _989753)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989749, tc_fun(_989745, tc_HOL_Obool)), hAPP(c_Set_Oimage(_989743, _989749, _989753), _989747)), _989751))], (20947 ^ _777959) ^ [_1176241, _1176243] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1176241), _1176243))), -(hAPP(c_Finite__Set_Ocard(_1176241), _1176243) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36764 ^ _777959) ^ [_1475624, _1475626, _1475628] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1475624, _1475626), _1475628)), 36767 ^ _777959 : [(36776 ^ _777959) ^ [] : [-(_1475626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 36779 ^ _777959 : [(36788 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1475626))), 36791 ^ _777959 : [(36794 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1475628)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (36792 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1475626), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1475628))))]]], (36780 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1475626)), 36783 ^ _777959 : [(36786 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1475628)), _1475626)))], (36784 ^ _777959) ^ [] : [-(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), _1475628))))]]]]], (36770 ^ _777959) ^ [] : [_1475626 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1475628) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (36768 ^ _777959) ^ [] : [-(_1475624 = 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), _1475628)), _1475626)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1475628)))]]], (13628 ^ _777959) ^ [_1028559, _1028561, _1028563, _1028565, _1028567] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1028559, tc_fun(_1028561, tc_HOL_Obool)), _1028563), hAPP(hAPP(c_COMBB(tc_fun(_1028561, tc_HOL_Obool), tc_fun(_1028561, tc_HOL_Obool), _1028559), hAPP(c_Set_Oinsert(_1028561), _1028565)), _1028567)) = hAPP(hAPP(c_Set_Oinsert(_1028561), _1028565), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1028559, tc_fun(_1028561, tc_HOL_Obool)), _1028563), _1028567)))], (43558 ^ _777959) ^ [_1643632, _1643634, _1643636] : [-(hAPP(c_List_Orotate(_1643632, _1643634), _1643636) = hAPP(c_List_Orotate(_1643632, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1643634, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643632)), _1643636))), _1643636))], (40630 ^ _777959) ^ [_1567236, _1567238, _1567240, _1567242] : [class_Rings_Osemiring__1(_1567236), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1567236), hAPP(hAPP(c_List_Omap(_1567238, _1567236), hAPP(c_COMBK(_1567236, _1567238), _1567240)), _1567242)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1567236), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1567236), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1567238)), _1567242))), _1567240))], (21886 ^ _777959) ^ [_1193838, _1193840, _1193842] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1193838), _1193840)), 21889 ^ _777959 : [(21909 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193838, tc_Nat_Onat), _1193842), _1193840) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 21910 ^ _777959 : [(21911 ^ _777959) ^ [_1194319] : [hBOOL(hAPP(hAPP(c_member(_1193838), _1194319), _1193840)), hAPP(_1193842, _1194319) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 21919 ^ _777959 : [(21924 ^ _777959) ^ [] : [hAPP(_1193842, 21918 ^ [_1193838, _1193840, _1193842, _1194319]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21922 ^ _777959) ^ [] : [_1194319 = 21918 ^ [_1193838, _1193840, _1193842, _1194319]], (21920 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1193838), 21918 ^ [_1193838, _1193840, _1193842, _1194319]), _1193840)))]]]]], (21890 ^ _777959) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193838, tc_Nat_Onat), _1193842), _1193840) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 21894 ^ _777959 : [(21899 ^ _777959) ^ [_1194158] : [hBOOL(hAPP(hAPP(c_member(_1193838), _1194158), _1193840)), -(21893 ^ [_1193838, _1193840, _1193842] = _1194158), -(hAPP(_1193842, _1194158) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21897 ^ _777959) ^ [] : [-(hAPP(_1193842, 21893 ^ [_1193838, _1193840, _1193842]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (21895 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1193838), 21893 ^ [_1193838, _1193840, _1193842]), _1193840)))]]]]], (20971 ^ _777959) ^ [_1176555, _1176557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176555)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176557)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1176557), _1176555)), _1176557)))], (33435 ^ _777959) ^ [_1408261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1408261)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1408261))))], (11584 ^ _777959) ^ [_985210, _985212, _985214, _985216, _985218] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985210, tc_fun(_985212, tc_HOL_Obool)), _985214), _985216), _985218))), 11585 ^ _777959 : [(11586 ^ _777959) ^ [_985282] : [hBOOL(hAPP(hAPP(c_member(_985210), _985282), _985214)), hBOOL(hAPP(hAPP(_985216, _985282), _985218))]]], (15328 ^ _777959) ^ [_1069648, _1069650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1069648)), hAPP(c_Nat_OSuc, _1069650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069648), _1069650)))], (51098 ^ _777959) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (17475 ^ _777959) ^ [_1111845, _1111847, _1111849, _1111851, _1111853] : [c_Finite__Set_Ofun__left__comm(_1111845, _1111847, _1111849), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111845), _1111851)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1111845, _1111847, _1111849, _1111853, _1111851), hAPP(hAPP(c_Finite__Set_Ofold(_1111845, _1111847, _1111849), _1111853), _1111851))))], (35810 ^ _777959) ^ [_1457077, _1457079, _1457081] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1457077, tc_HOL_Obool), tc_fun(_1457077, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1457077, tc_HOL_Obool), tc_fun(_1457077, tc_HOL_Obool)), _1457079), _1457081)), c_Wellfounded_Ofinite__psubset(_1457077))), 35813 ^ _777959 : [(35816 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1457077), _1457081)))], (35814 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1457077, tc_HOL_Obool)), _1457079), _1457081)))]]], (50878 ^ _777959) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (27740 ^ _777959) ^ [_1302110, _1302112, _1302114, _1302116] : [class_Orderings_Oorder(_1302110), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302110, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1302110, _1302112, _1302114)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1302110, _1302114, _1302116)) = c_Orderings_Obot__class_Obot(tc_fun(_1302110, tc_HOL_Obool)))], (36680 ^ _777959) ^ [_1473794, _1473796, _1473798] : [-(hAPP(hAPP(c_Product__Type_OPair(_1473794, _1473796), hAPP(c_Product__Type_Ofst(_1473794, _1473796), _1473798)), hAPP(c_Product__Type_Osnd(_1473794, _1473796), _1473798)) = _1473798)], (42415 ^ _777959) ^ [_1615528] : [-(c_List_Olists(_1615528, c_Orderings_Obot__class_Obot(tc_fun(_1615528, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1615528)), c_List_Olist_ONil(_1615528)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1615528), tc_HOL_Obool))))], (348 ^ _777959) ^ [_783425, _783427] : [-(c_Nat__Transfer_Onat__set(_783425)), _783427 = _783425, c_Nat__Transfer_Onat__set(_783427)], (43506 ^ _777959) ^ [_1642652, _1642654, _1642656] : [hAPP(c_List_Orotate(_1642652, _1642654), _1642656) = c_List_Olist_ONil(_1642652), -(_1642656 = c_List_Olist_ONil(_1642652))], (46579 ^ _777959) ^ [_1708666, _1708668, _1708670, _1708672, _1708674] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1708666, _1708668)), _1708670), hAPP(hAPP(c_Product__Type_OSigma(_1708666, _1708668), _1708672), _1708674))), 46583 ^ _777959 : [(46589 ^ _777959) ^ [] : [-(_1708670 = hAPP(hAPP(c_Product__Type_OPair(_1708666, _1708668), 46582 ^ [_1708666, _1708668, _1708670, _1708672, _1708674]), 46585 ^ [_1708666, _1708668, _1708670, _1708672, _1708674]))], (46587 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1708668), 46585 ^ [_1708666, _1708668, _1708670, _1708672, _1708674]), hAPP(_1708674, 46582 ^ [_1708666, _1708668, _1708670, _1708672, _1708674]))))], (46584 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1708666), 46582 ^ [_1708666, _1708668, _1708670, _1708672, _1708674]), _1708672)))]]], (33625 ^ _777959) ^ [_1411248, _1411250] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411248), c_Int_OPls))), 33628 ^ _777959 : [(33635 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411250), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411248)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411250)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411248), _1411250)))], (33629 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411250), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411248)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411250)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411248))]]], (8420 ^ _777959) ^ [_924082, _924084] : [class_Orderings_Opreorder(_924082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924082), _924084), _924084))], (42445 ^ _777959) ^ [_1616162, _1616164] : [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), _1616162), _1616164))), 42448 ^ _777959 : [(42455 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1616162), _1616164))), -(c_List_Oupto(_1616162, _1616164) = c_List_Olist_ONil(tc_Int_Oint))], (42449 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1616162), _1616164)), -(c_List_Oupto(_1616162, _1616164) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1616162), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1616162), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1616164)))]]], (40701 ^ _777959) ^ [_1568813, _1568815] : [40702 ^ _777959 : [(40703 ^ _777959) ^ [_1568859] : [hBOOL(hAPP(_1568813, _1568859))]], -(hBOOL(hAPP(_1568813, c_Hilbert__Choice_OEps(_1568815, _1568813))))], (34157 ^ _777959) ^ [_1421202] : [c_Int_OPls = _1421202, -(c_Int_OPls = c_Int_OBit0(_1421202))], (49732 ^ _777959) ^ [_1786578, _1786580, _1786582] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1786578), c_Nitpick_Oplus__frac(_1786578, _1786580, c_Nitpick_Ouminus__frac(_1786578, _1786582)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1786578, _1786580, _1786582))], (3198 ^ _777959) ^ [_825995, _825997, _825999, _826001, _826003, _826005, _826007, _826009, _826011, _826013] : [-(c_List_Ofoldr(_826013, _826009, _826005, _826001, _825997) = c_List_Ofoldr(_826011, _826007, _826003, _825999, _825995)), _826013 = _826011, _826009 = _826007, _826005 = _826003, _826001 = _825999, _825997 = _825995], (40724 ^ _777959) ^ [_1569206, _1569208] : [40725 ^ _777959 : [(40726 ^ _777959) ^ [_1569252] : [hBOOL(hAPP(_1569206, _1569252))]], -(hBOOL(hAPP(_1569206, c_Hilbert__Choice_OEps(_1569208, _1569206))))], (4350 ^ _777959) ^ [_843823, _843825] : [_843825 = _843823, -(c_Rings_Oinverse__class_Odivide(_843825) = c_Rings_Oinverse__class_Odivide(_843823))], (43620 ^ _777959) ^ [_1645038, _1645040, _1645042] : [class_Groups_Omonoid__add(_1645038), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1645038), _1645040), hAPP(c_List_Ofoldl(_1645038, _1645038, c_Groups_Oplus__class_Oplus(_1645038), c_Groups_Ozero__class_Ozero(_1645038)), _1645042)) = hAPP(c_List_Ofoldl(_1645038, _1645038, c_Groups_Oplus__class_Oplus(_1645038), _1645040), _1645042))], (9808 ^ _777959) ^ [_948393, _948395, _948397] : [class_Lattices_Olattice(_948393), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948393), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_948393), _948395), _948397)), _948397)))], (8558 ^ _777959) ^ [_925817, _925819, _925821] : [class_Orderings_Oorder(_925817), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925817), _925819), _925821)), _925821 = _925819], (12329 ^ _777959) ^ [_1001790, _1001792, _1001794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001790), _1001792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001794), _1001792)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001794), _1001790))))], (44515 ^ _777959) ^ [_1662764, _1662766] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662764)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662766)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662764), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662766)) = c_List_Olist_ONil(tc_Nat_Onat))], (2420 ^ _777959) ^ [_813774, _813776] : [_813776 = _813774, -(c_Int_Osucc(_813776) = c_Int_Osucc(_813774))], (36942 ^ _777959) ^ [_1479736, _1479738, _1479740, _1479742, _1479744, _1479746, _1479748] : [hBOOL(hAPP(_1479736, _1479738)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1479740, _1479740)), hAPP(hAPP(c_Product__Type_OPair(_1479740, _1479740), _1479742), _1479744)), hAPP(_1479746, _1479738))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1479748, _1479740), tc_prod(_1479748, _1479740))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1479748, _1479740), tc_prod(_1479748, _1479740)), hAPP(hAPP(c_Product__Type_OPair(_1479748, _1479740), _1479738), _1479742)), hAPP(hAPP(c_Product__Type_OPair(_1479748, _1479740), _1479738), _1479744))), c_Recdef_Osame__fst(_1479748, _1479740, _1479736, _1479746))))], (48026 ^ _777959) ^ [_1744808, _1744810] : [c_List_Olist__ex(_1744808, _1744810, c_List_Olist_ONil(_1744808))], (35073 ^ _777959) ^ [] : [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)], (36185 ^ _777959) ^ [_1463911, _1463913] : [-(_1463911 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 36188 ^ _777959 : [(36195 ^ _777959) ^ [] : [-(_1463913 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1463911, _1463913) = 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, _1463913))), 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, _1463911)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1463913))), c_Divides_Opdivmod(_1463911, _1463913)), 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), _1463913))))), c_Divides_Opdivmod(_1463911, _1463913)))))], (36189 ^ _777959) ^ [] : [_1463913 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1463911, _1463913) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1463911))]]], (1210 ^ _777959) ^ [_795808, _795810] : [-(class_Groups_Oabs__if(_795808)), _795810 = _795808, class_Groups_Oabs__if(_795810)], (29958 ^ _777959) ^ [_1344245, _1344247, _1344249, _1344251] : [class_Divides_Osemiring__div(_1344245), -(c_Divides_Odiv__class_Omod(_1344245, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344245), _1344247), _1344249), _1344251) = c_Divides_Odiv__class_Omod(_1344245, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344245), c_Divides_Odiv__class_Omod(_1344245, _1344247, _1344251)), _1344249), _1344251))], (36688 ^ _777959) ^ [_1473973, _1473975, _1473977, _1473979, _1473981] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1473973, _1473975, _1473977), _1473979), _1473981) = hAPP(hAPP(_1473979, hAPP(c_Product__Type_Ofst(_1473973, _1473975), _1473981)), hAPP(c_Product__Type_Osnd(_1473973, _1473975), _1473981)))], (1670 ^ _777959) ^ [_801558, _801560] : [-(class_Orderings_Opreorder(_801558)), _801560 = _801558, class_Orderings_Opreorder(_801560)], (31164 ^ _777959) ^ [_1366555, _1366557, _1366559, _1366561, _1366563] : [class_Rings_Olinordered__idom(_1366555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366555), hAPP(c_Groups_Oabs__class_Oabs(_1366555), _1366557)), _1366559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366555), hAPP(c_Groups_Oabs__class_Oabs(_1366555), _1366561)), _1366563)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366555), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366555), hAPP(c_Groups_Oabs__class_Oabs(_1366555), _1366557)), hAPP(c_Groups_Oabs__class_Oabs(_1366555), _1366561))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366555), _1366559), _1366563))))], (12010 ^ _777959) ^ [_995970, _995972] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995970), _995972))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995970), _995972)), -(_995970 = _995972)], (43909 ^ _777959) ^ [_1650791, _1650793, _1650795] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1650791)), _1650793), c_List_Olists(_1650791, _1650795)))), 43910 ^ _777959 : [(43913 ^ _777959) ^ [_1650919, _1650921] : [_1650793 = hAPP(hAPP(c_List_Olist_OCons(_1650791), _1650921), _1650919), hBOOL(hAPP(hAPP(c_member(_1650791), _1650921), _1650795)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1650791)), _1650919), c_List_Olists(_1650791, _1650795)))], (43911 ^ _777959) ^ [] : [_1650793 = c_List_Olist_ONil(_1650791)]]], (14875 ^ _777959) ^ [_1059043, _1059045, _1059047, _1059049] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1059043), hAPP(c_Set_OCollect(_1059043), _1059045))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1059047), hAPP(c_Set_OCollect(_1059047), hAPP(hAPP(c_COMBB(tc_fun(_1059043, tc_HOL_Obool), tc_HOL_Obool, _1059047), c_HOL_OEx(_1059043)), hAPP(hAPP(c_COMBC(_1059047, tc_fun(_1059043, tc_HOL_Obool), tc_fun(_1059043, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1059043, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1059043, tc_HOL_Obool), tc_fun(_1059043, tc_HOL_Obool)), _1059047), c_COMBS(_1059043, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1059043, tc_HOL_Obool), tc_fun(_1059043, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1059047), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1059043), c_fconj)), hAPP(hAPP(c_COMBC(_1059047, tc_fun(_1059043, _1059047), tc_fun(_1059043, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1059047, tc_HOL_Obool), tc_fun(tc_fun(_1059043, _1059047), tc_fun(_1059043, tc_HOL_Obool)), _1059047), c_COMBB(_1059047, tc_HOL_Obool, _1059043)), c_fequal)), _1059049)))), _1059045))))))], (47301 ^ _777959) ^ [_1727570, _1727572, _1727574] : [c_Wellfounded_Owf(_1727570, _1727572), c_Wellfounded_Owf(_1727570, _1727574), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1727570, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1727570, _1727570), _1727572)), hAPP(c_Relation_ORange(_1727570, _1727570), _1727574)) = c_Orderings_Obot__class_Obot(tc_fun(_1727570, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1727570, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1727570, _1727570), tc_HOL_Obool)), _1727572), _1727574)))], (37072 ^ _777959) ^ [_1483128] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1483128)), -(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))), _1483128)), c_FunDef_Omax__weak)))], (21238 ^ _777959) ^ [_1181562, _1181564, _1181566, _1181568] : [class_Groups_Oordered__comm__monoid__add(_1181562), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181562), c_Groups_Ozero__class_Ozero(_1181562)), _1181564)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181562), _1181566), _1181568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181562), _1181566), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181562), _1181564), _1181568))))], (17091 ^ _777959) ^ [_1104856, _1104858, _1104860, _1104862] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1104856, _1104858, _1104860, _1104862, c_Orderings_Obot__class_Obot(tc_fun(_1104856, tc_HOL_Obool))), _1104862)))], (22112 ^ _777959) ^ [_1198697, _1198699, _1198701, _1198703] : [class_Groups_Ocomm__monoid__add(_1198697), hBOOL(hAPP(c_Finite__Set_Ofinite(_1198699), _1198701)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198699, _1198697), _1198703), _1198701) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1198697, _1198699, c_Groups_Oplus__class_Oplus(_1198697)), _1198703), c_Groups_Ozero__class_Ozero(_1198697)), _1198701))], (6103 ^ _777959) ^ [_875717, _875719, _875721] : [_875717 = _875719, 6106 ^ _777959 : [(6109 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875721, tc_HOL_Obool)), _875719), _875717)))], (6107 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875721, tc_HOL_Obool)), _875717), _875719)))]]], (16977 ^ _777959) ^ [_1102726, _1102728, _1102730, _1102732] : [class_Orderings_Olinorder(_1102726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102726), _1102728), _1102730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102726), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1102726), _1102728), _1102732)), _1102730)))], (29064 ^ _777959) ^ [_1325636, _1325638] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1325636, _1325638) = 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), _1325636), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1325638))))], (40288 ^ _777959) ^ [_1559687, _1559689, _1559691] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1559687, tc_HOL_Obool)), hAPP(c_List_Oset(_1559687), c_List_Osublist(_1559687, _1559689, _1559691))), hAPP(c_List_Oset(_1559687), _1559689))))], (12397 ^ _777959) ^ [_1003092, _1003094, _1003096] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003092), _1003094)), 12400 ^ _777959 : [(12407 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003096), _1003092)), _1003094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003096), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003094), _1003092))))], (12401 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003096), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003094), _1003092))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003096), _1003092)), _1003094)))]]], (49649 ^ _777959) ^ [_1784489, _1784491, _1784493, _1784495, _1784497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1784489, tc_HOL_Obool)), _1784491), _1784493)), 49655 ^ _777959 : [(49660 ^ _777959) ^ [] : [hBOOL(hAPP(_1784497, 49654 ^ [_1784489, _1784491, _1784493, _1784495, _1784497]))], (49658 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1784495, 49654 ^ [_1784489, _1784491, _1784493, _1784495, _1784497])))], (49656 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1784489), 49654 ^ [_1784489, _1784491, _1784493, _1784495, _1784497]), _1784491)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1784489, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1784489, tc_HOL_Obool)), _1784491), hAPP(c_Set_OCollect(_1784489), _1784495))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1784489, tc_HOL_Obool)), _1784493), hAPP(c_Set_OCollect(_1784489), _1784497)))))], (45600 ^ _777959) ^ [_1687984, _1687986] : [-(c_Enum_Oenum__the(_1687984, _1687986) = c_HOL_OThe(_1687984, _1687986))], (51470 ^ _777959) ^ [] : [-(hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))], (1730 ^ _777959) ^ [_802308, _802310] : [-(class_Rings_Omult__zero(_802308)), _802310 = _802308, class_Rings_Omult__zero(_802310)], (31470 ^ _777959) ^ [_1372433, _1372435, _1372437] : [31472 ^ _777959 : [(31475 ^ _777959) ^ [] : [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(_1372435, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 31471 ^ [_1372433, _1372435, _1372437]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1372435, 31471 ^ [_1372433, _1372435, _1372437])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (31473 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31471 ^ [_1372433, _1372435, _1372437]), _1372433)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1372435, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1372437)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372437), hAPP(_1372435, _1372433))), 31485 ^ _777959 : [(31488 ^ _777959) ^ [] : [-(hAPP(_1372435, 31484 ^ [_1372433, _1372435, _1372437]) = _1372437)], (31486 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 31484 ^ [_1372433, _1372435, _1372437]), _1372433)))]]], (21872 ^ _777959) ^ [_1193477, _1193479, _1193481, _1193483, _1193485] : [class_Groups_Ocomm__monoid__mult(_1193477), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193479), _1193481)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193479), _1193483)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193477), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1193479, _1193477), _1193485), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1193479, tc_HOL_Obool)), _1193481), _1193483))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1193479, _1193477), _1193485), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1193479, tc_HOL_Obool)), _1193481), _1193483))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193477), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1193479, _1193477), _1193485), _1193481)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1193479, _1193477), _1193485), _1193483)))], (19028 ^ _777959) ^ [_1143395, _1143397, _1143399, _1143401, _1143403] : [-(hAPP(hAPP(c_Option_Omap(_1143395, _1143397), _1143399), _1143401) = hAPP(c_Option_Ooption_OSome(_1143397), _1143403)), 19029 ^ _777959 : [(19030 ^ _777959) ^ [_1143463] : [_1143401 = hAPP(c_Option_Ooption_OSome(_1143395), _1143463), hAPP(_1143399, _1143463) = _1143403]]], (49458 ^ _777959) ^ [_1779367, _1779369, _1779371, _1779373, _1779375] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779367, _1779367)), hAPP(hAPP(c_Product__Type_OPair(_1779367, _1779367), _1779369), _1779371)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1779367, _1779367), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1779373)), _1779375))), 49462 ^ _777959 : [(49465 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779367, _1779367)), hAPP(hAPP(c_Product__Type_OPair(_1779367, _1779367), 49461 ^ [_1779367, _1779369, _1779371, _1779373, _1779375]), _1779371)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1779367, _1779367), tc_HOL_Obool), _1779373), _1779375))))], (49463 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779367, _1779367)), hAPP(hAPP(c_Product__Type_OPair(_1779367, _1779367), _1779369), 49461 ^ [_1779367, _1779369, _1779371, _1779373, _1779375])), _1779375)))]]], (9148 ^ _777959) ^ [_934952, _934954, _934956, _934958] : [class_Lattices_Osemilattice__sup(_934952), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934952), _934954), _934956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934952), _934954), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_934952), _934958), _934956))))], (36686 ^ _777959) ^ [_1473938, _1473940] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1473938, _1473940) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1473938, _1473940)))], (44831 ^ _777959) ^ [_1669699, _1669701] : [_1669701 = c_List_Olist_ONil(_1669699), -(hAPP(c_List_Orev(_1669699), _1669701) = c_List_Olist_ONil(_1669699))], (14672 ^ _777959) ^ [_1053637, _1053639, _1053641, _1053643] : [hBOOL(hAPP(hAPP(_1053641, _1053639), _1053643)), -(hBOOL(hAPP(hAPP(c_member(_1053637), _1053639), c_SetInterval_Oord_OatMost(_1053637, _1053641, _1053643))))], (12936 ^ _777959) ^ [_1013167, _1013169, _1013171] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013167, tc_HOL_Obool)), _1013169), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1013167, tc_HOL_Obool), _1013171)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1013167, tc_HOL_Obool), tc_fun(_1013167, tc_HOL_Obool)), _1013171), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013167, tc_HOL_Obool)), _1013169)))], (23104 ^ _777959) ^ [_1218371, _1218373] : [class_Int_Oring__char__0(_1218371), hBOOL(hAPP(hAPP(c_member(_1218371), _1218373), c_Int_Oring__1__class_OInts(_1218371))), 23111 ^ _777959 : [(23118 ^ _777959) ^ [] : [_1218373 = c_Groups_Ozero__class_Ozero(_1218371), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218371), _1218373), _1218373) = c_Groups_Ozero__class_Ozero(_1218371))], (23112 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218371), _1218373), _1218373) = c_Groups_Ozero__class_Ozero(_1218371), -(_1218373 = c_Groups_Ozero__class_Ozero(_1218371))]]], (1170 ^ _777959) ^ [_795308, _795310] : [-(class_Divides_Oring__div(_795308)), _795310 = _795308, class_Divides_Oring__div(_795310)], (35559 ^ _777959) ^ [_1451815, _1451817, _1451819, _1451821, _1451823, _1451825, _1451827] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451815, _1451817), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1451819), _1451821))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1451823, _1451817), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1451825), _1451827))), -(_1451817 = 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), _1451815), _1451823), _1451817), 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), _1451819), _1451825)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1451821), _1451827)), _1451817))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1451821), _1451827), _1451817)))))], (44881 ^ _777959) ^ [_1670651, _1670653] : [-(hAPP(c_List_Orev(_1670651), hAPP(c_List_Orev(_1670651), _1670653)) = _1670653)], (6387 ^ _777959) ^ [_881092, _881094, _881096, _881098] : [_881092 = _881094, hBOOL(hAPP(hAPP(c_member(_881096), _881094), _881098)), -(hBOOL(hAPP(hAPP(c_member(_881096), _881092), _881098)))], (35083 ^ _777959) ^ [_1438087] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1438087) = c_Int_Opred(_1438087))], (31190 ^ _777959) ^ [_1367182, _1367184, _1367186] : [class_Groups_Oordered__ab__group__add__abs(_1367182), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1367182), hAPP(c_Groups_Oabs__class_Oabs(_1367182), _1367184)), hAPP(c_Groups_Oabs__class_Oabs(_1367182), _1367186))), hAPP(c_Groups_Oabs__class_Oabs(_1367182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1367182), _1367186), _1367184)))))], (30052 ^ _777959) ^ [_1346294, _1346296, _1346298] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1346294), _1346296), _1346298) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1346294), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1346296, _1346298)), _1346298))], (24468 ^ _777959) ^ [_1242710] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1242710) = _1242710)], (42188 ^ _777959) ^ [_1609413, _1609415, _1609417, _1609419, _1609421, _1609423] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609413, _1609415)), hAPP(hAPP(c_Product__Type_OPair(_1609413, _1609415), _1609417), _1609419)), hAPP(hAPP(c_Product__Type_OSigma(_1609413, _1609415), _1609421), _1609423))), -(hBOOL(hAPP(hAPP(c_member(_1609413), _1609417), _1609421)))], (26090 ^ _777959) ^ [_1272733, _1272735, _1272737] : [class_Fields_Olinordered__field__inverse__zero(_1272733), 26093 ^ _777959 : [(26108 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272733), c_Groups_Ozero__class_Ozero(_1272733)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272733), _1272735), _1272737)))), 26109 ^ _777959 : [(26116 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272733), _1272735), c_Groups_Ozero__class_Ozero(_1272733))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272733), _1272737), c_Groups_Ozero__class_Ozero(_1272733)))], (26110 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272733), c_Groups_Ozero__class_Ozero(_1272733)), _1272735)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272733), c_Groups_Ozero__class_Ozero(_1272733)), _1272737))]]], (26094 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272733), c_Groups_Ozero__class_Ozero(_1272733)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272733), _1272735), _1272737))), 26099 ^ _777959 : [(26102 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272733), c_Groups_Ozero__class_Ozero(_1272733)), _1272737)))], (26100 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272733), c_Groups_Ozero__class_Ozero(_1272733)), _1272735)))]], 26103 ^ _777959 : [(26106 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272733), _1272737), c_Groups_Ozero__class_Ozero(_1272733))))], (26104 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1272733), _1272735), c_Groups_Ozero__class_Ozero(_1272733))))]]]]], (5470 ^ _777959) ^ [_861575, _861577] : [_861577 = _861575, -(c_List_Oset(_861577) = c_List_Oset(_861575))], (45392 ^ _777959) ^ [_1682790, _1682792, _1682794] : [hBOOL(hAPP(c_List_Odistinct(_1682790), _1682792)), -(hBOOL(hAPP(c_List_Odistinct(_1682790), c_List_OdropWhile(_1682790, _1682794, _1682792))))], (30195 ^ _777959) ^ [_1348902, _1348904] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1348902, _1348904)), _1348904) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37156 ^ _777959) ^ [_1485299, _1485301, _1485303, _1485305, _1485307] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1485303, _1485299)), hAPP(hAPP(c_Product__Type_OPair(_1485303, _1485299), _1485307), _1485301)), _1485305)), -(hBOOL(hAPP(hAPP(c_member(_1485299), _1485301), hAPP(c_Relation_OImage(_1485303, _1485299, _1485305), hAPP(hAPP(c_Set_Oinsert(_1485303), _1485307), c_Orderings_Obot__class_Obot(tc_fun(_1485303, tc_HOL_Obool)))))))], (5514 ^ _777959) ^ [_862213, _862215] : [_862215 = _862213, -(c_COMBI(_862215) = c_COMBI(_862213))], (12413 ^ _777959) ^ [_1003381, _1003383, _1003385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003381), _1003383)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003385), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003383), _1003381)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003385), _1003383)), _1003381))], (44936 ^ _777959) ^ [_1671891, _1671893] : [44938 ^ _777959 : [(44941 ^ _777959) ^ [] : [44937 ^ [_1671891, _1671893] = c_List_Olist_ONil(_1671891)], (44939 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1671891)), 44937 ^ [_1671891, _1671893]), hAPP(c_List_Oset(tc_List_Olist(_1671891)), _1671893))))]], -(c_List_Olist_ONil(_1671891) = c_List_Oconcat(_1671891, _1671893))], (17085 ^ _777959) ^ [_1104707, _1104709] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104707)), hAPP(c_Nat_OSuc, _1104709)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1104707), _1104709)))], (16187 ^ _777959) ^ [_1086847, _1086849, _1086851] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086847), _1086849)), _1086851) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086849), _1086851)))], (14568 ^ _777959) ^ [_1051619, _1051621, _1051623, _1051625, _1051627, _1051629] : [hBOOL(hAPP(hAPP(c_member(_1051619), _1051621), _1051623)), -(hAPP(c_Fun_Ooverride__on(_1051619, _1051625, _1051627, _1051629, _1051623), _1051621) = hAPP(_1051629, _1051621))], (16485 ^ _777959) ^ [_1093597, _1093599, _1093601, _1093603] : [class_Orderings_Olinorder(_1093597), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093597), _1093599), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093597), _1093601), _1093603)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093597), _1093601), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093597), _1093599), _1093603)))], (44907 ^ _777959) ^ [_1671273, _1671275] : [c_List_Oconcat(_1671273, _1671275) = c_List_Olist_ONil(_1671273), 44910 ^ _777959 : [(44911 ^ _777959) ^ [_1671364] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1671273)), _1671364), hAPP(c_List_Oset(tc_List_Olist(_1671273)), _1671275))), -(_1671364 = c_List_Olist_ONil(_1671273))]]], (46884 ^ _777959) ^ [_1717993, _1717995] : [c_Wellfounded_Owf(_1717993, _1717995), -(c_Wellfounded_Owf(tc_List_Olist(_1717993), c_List_Olenlex(_1717993, _1717995)))], (8728 ^ _777959) ^ [_928610, _928612, _928614, _928616, _928618, _928620] : [-(_928610 = _928612), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928614, _928616), _928618), _928612), _928620), _928610) = hAPP(_928618, _928610))], (48266 ^ _777959) ^ [_1749450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1749450)), _1749450 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (16347 ^ _777959) ^ [_1090867, _1090869, _1090871] : [class_Orderings_Olinorder(_1090867), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090867), _1090869)), hBOOL(hAPP(hAPP(c_member(_1090867), _1090871), _1090869)), 16358 ^ _777959 : [(16365 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090867, tc_HOL_Obool)), _1090869), hAPP(hAPP(c_Set_Oinsert(_1090867), _1090871), c_Orderings_Obot__class_Obot(tc_fun(_1090867, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1090867, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1090867, _1090869) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1090867), _1090871), c_Big__Operators_Olinorder__class_OMax(_1090867, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090867, tc_HOL_Obool)), _1090869), hAPP(hAPP(c_Set_Oinsert(_1090867), _1090871), c_Orderings_Obot__class_Obot(tc_fun(_1090867, tc_HOL_Obool)))))))], (16359 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090867, tc_HOL_Obool)), _1090869), hAPP(hAPP(c_Set_Oinsert(_1090867), _1090871), c_Orderings_Obot__class_Obot(tc_fun(_1090867, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1090867, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1090867, _1090869) = _1090871)]]], (50220 ^ _777959) ^ [_1795726] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1795726))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1795726)))], (34083 ^ _777959) ^ [_1419907, _1419909] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1419907)), _1419909) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1419907), _1419909)))], (22790 ^ _777959) ^ [_1212656, _1212658] : [class_Rings_Ocomm__semiring__1(_1212656), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1212656), _1212658), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1212658)], (21061 ^ _777959) ^ [_1178130, _1178132, _1178134] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1178130), _1178132)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1178134), _1178132))), 21064 ^ _777959 : [(21067 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1178130), _1178134)))], (21065 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1178132)))]]], (13667 ^ _777959) ^ [_1030117, _1030119, _1030121, _1030123, _1030125] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030117, tc_fun(_1030119, tc_HOL_Obool)), _1030121), hAPP(hAPP(c_COMBS(_1030117, tc_fun(_1030119, tc_HOL_Obool), tc_fun(_1030119, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1030119, tc_HOL_Obool), tc_fun(tc_fun(_1030119, tc_HOL_Obool), tc_fun(_1030119, tc_HOL_Obool)), _1030117), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1030119, tc_HOL_Obool))), _1030123)), _1030125)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1030119, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030117, tc_fun(_1030119, tc_HOL_Obool)), _1030121), _1030123)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030117, tc_fun(_1030119, tc_HOL_Obool)), _1030121), _1030125)))], (11776 ^ _777959) ^ [_990930, _990932, _990934, _990936, _990938, _990940] : [class_Complete__Lattice_Ocomplete__lattice(_990930), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990932, tc_fun(_990934, _990930)), _990936), _990938), _990940) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990932, _990930), _990936), hAPP(hAPP(c_COMBC(_990932, _990934, _990930), _990938), _990940)))], (49712 ^ _777959) ^ [_1786153, _1786155] : [-(c_Nitpick_Ouminus__frac(_1786153, _1786155) = c_Nitpick_OAbs__Frac(_1786153, 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(_1786153), _1786155))), hAPP(c_Nitpick_Odenom(_1786153), _1786155))))], (28744 ^ _777959) ^ [_1319417, _1319419, _1319421] : [class_Orderings_Oorder(_1319417), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319417, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1319417), _1319419)), c_SetInterval_Oord__class_OatLeastAtMost(_1319417, _1319419, _1319421)) = c_Orderings_Obot__class_Obot(tc_fun(_1319417, tc_HOL_Obool)))], (50978 ^ _777959) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (5354 ^ _777959) ^ [_859865, _859867, _859869, _859871] : [-(c_List_Ofilter(_859871, _859867) = c_List_Ofilter(_859869, _859865)), _859871 = _859869, _859867 = _859865], (47352 ^ _777959) ^ [_1728874, _1728876] : [-(hAPP(c_Relation_ODomain(_1728874, _1728874), c_Relation_OId__on(_1728874, _1728876)) = _1728876)], (30671 ^ _777959) ^ [_1357582, _1357584, _1357586] : [class_Rings_Olinordered__idom(_1357582), -(c_Groups_Osgn__class_Osgn(_1357582, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357582), _1357584), _1357586)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357582), c_Groups_Osgn__class_Osgn(_1357582, _1357584)), c_Groups_Osgn__class_Osgn(_1357582, _1357586)))], (34195 ^ _777959) ^ [_1421800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1421800), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1421800)), c_Int_OPls)))], (33797 ^ _777959) ^ [_1414142, _1414144] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1414142)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414144)) = 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)))), _1414142)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414144)))], (13085 ^ _777959) ^ [_1016503, _1016505, _1016507] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1016503, tc_HOL_Obool)), _1016505), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1016503, tc_HOL_Obool)), _1016507)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1016503, tc_HOL_Obool)), _1016505), _1016507))], (25398 ^ _777959) ^ [_1259276, _1259278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259276)), -(c_SMT_Oz3div(_1259278, _1259276) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1259278), _1259276))], (47057 ^ _777959) ^ [_1721398, _1721400] : [47059 ^ _777959 : [(47060 ^ _777959) ^ [_1721423] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1721398, _1721398)), hAPP(hAPP(c_Product__Type_OPair(_1721398, _1721398), hAPP(47058 ^ [_1721398, _1721400], hAPP(c_Nat_OSuc, _1721423))), hAPP(47058 ^ [_1721398, _1721400], _1721423))), _1721400)))]], -(c_Wellfounded_Owf(_1721398, _1721400))], (10160 ^ _777959) ^ [_955801] : [class_Lattices_Osemilattice__inf(_955801), -(c_Finite__Set_Ofun__left__comm__idem(_955801, _955801, c_Lattices_Osemilattice__inf__class_Oinf(_955801)))], (47916 ^ _777959) ^ [_1742745, _1742747, _1742749] : [class_Orderings_Olinorder(_1742745), 47922 ^ _777959 : [(47925 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1742745), _1742749), 47921 ^ [_1742745, _1742747, _1742749]))], (47923 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742745), 47921 ^ [_1742745, _1742747, _1742749]), hAPP(c_List_Oset(_1742745), _1742747))))]], c_List_Olinorder__class_Osorted(_1742745, _1742747), -(c_List_Olinorder__class_Osorted(_1742745, hAPP(hAPP(c_List_Olist_OCons(_1742745), _1742749), _1742747)))], (40730 ^ _777959) ^ [_1569319, _1569321] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1569319), _1569321)), -(c_Nitpick_Ocard_H(_1569319, _1569321) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1569319)), c_Hilbert__Choice_OEps(tc_List_Olist(_1569319), hAPP(hAPP(c_COMBS(tc_List_Olist(_1569319), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1569319)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1569319), tc_fun(_1569319, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1569319, tc_HOL_Obool), tc_fun(tc_fun(_1569319, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1569319)), c_fequal), c_List_Oset(_1569319))), _1569321))), c_List_Odistinct(_1569319)))))], (51292 ^ _777959) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (46770 ^ _777959) ^ [_1713725, _1713727, _1713729, _1713731, _1713733, _1713735, _1713737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1713725, _1713727), tc_HOL_Obool)), _1713729), _1713731)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1713727, _1713733), tc_HOL_Obool)), _1713735), _1713737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1713725, _1713733), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1713725, _1713727, _1713733), _1713729), _1713735)), hAPP(hAPP(c_Relation_Orel__comp(_1713725, _1713727, _1713733), _1713731), _1713737))))], (34207 ^ _777959) ^ [_1422017, _1422019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1422017), _1422019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1422017)), c_Int_OBit1(_1422019))))], (37351 ^ _777959) ^ [_1490911, _1490913] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490911), c_Orderings_Obot__class_Obot(tc_fun(_1490911, tc_HOL_Obool))), _1490913) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1490911, tc_HOL_Obool), tc_HOL_Obool)))], (8930 ^ _777959) ^ [_931713, _931715, _931717] : [class_Orderings_Olinorder(_931713), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931713), _931715), _931717))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931713), _931717), _931715)))], (31386 ^ _777959) ^ [_1370891, _1370893, _1370895] : [class_Rings_Olinordered__idom(_1370891), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370891), c_Groups_Ozero__class_Ozero(_1370891)), hAPP(hAPP(c_Power_Opower__class_Opower(_1370891), hAPP(c_Groups_Oabs__class_Oabs(_1370891), _1370893)), _1370895))))], (23739 ^ _777959) ^ [_1229417, _1229419] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1229417), c_Groups_Ozero__class_Ozero(_1229417)), hAPP(c_Nat_OSuc, _1229419)) = c_Groups_Ozero__class_Ozero(_1229417)), class_Power_Opower(_1229417), class_Rings_Osemiring__0(_1229417)], (23072 ^ _777959) ^ [_1217913, _1217915, _1217917] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(_1217913, _1217915, _1217917)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45410 ^ _777959) ^ [_1683080, _1683082, _1683084, _1683086] : [hBOOL(hAPP(_1683080, _1683082)), -(c_List_OdropWhile(_1683084, _1683080, hAPP(hAPP(c_List_Olist_OCons(_1683084), _1683082), _1683086)) = c_List_OdropWhile(_1683084, _1683080, _1683086))], (36179 ^ _777959) ^ [_1463833, _1463835] : [_1463833 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1463833, _1463835) = 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)))], (50120 ^ _777959) ^ [_1793960] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1793960)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1793960), c_Int_OMin)))], (51330 ^ _777959) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (41880 ^ _777959) ^ [_1602350, _1602352, _1602354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1602350, _1602350), tc_HOL_Obool)), _1602352), hAPP(hAPP(c_Product__Type_OSigma(_1602350, _1602350), _1602354), hAPP(c_COMBK(tc_fun(_1602350, tc_HOL_Obool), _1602350), _1602354)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1602350), tc_List_Olist(_1602350)), tc_HOL_Obool)), c_List_Olistrel(_1602350, _1602352)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1602350), tc_List_Olist(_1602350)), c_List_Olists(_1602350, _1602354)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1602350), tc_HOL_Obool), tc_List_Olist(_1602350)), c_List_Olists(_1602350, _1602354))))))], (37190 ^ _777959) ^ [_1486533, _1486535, _1486537, _1486539, _1486541, _1486543] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486539, _1486539)), hAPP(hAPP(c_Product__Type_OPair(_1486539, _1486539), hAPP(_1486543, _1486535)), hAPP(_1486543, _1486537))), _1486541)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486533, _1486533)), hAPP(hAPP(c_Product__Type_OPair(_1486533, _1486533), _1486535), _1486537)), hAPP(hAPP(c_Relation_Oinv__image(_1486539, _1486533), _1486541), _1486543))))], (6847 ^ _777959) ^ [_889669, _889671, _889673, _889675, _889677] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889669, tc_HOL_Obool)), _889671), hAPP(c_Set_Oimage(_889673, _889669, _889675), _889677)))), 6848 ^ _777959 : [(6849 ^ _777959) ^ [_889749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889673, tc_HOL_Obool)), _889749), _889677)), _889671 = hAPP(c_Set_Oimage(_889673, _889669, _889675), _889749)]]], (42483 ^ _777959) ^ [_1617246, _1617248, _1617250, _1617252, _1617254] : [-(hAPP(hAPP(c_List_Ozip(_1617246, _1617248), _1617250), hAPP(hAPP(c_List_Olist_OCons(_1617248), _1617252), _1617254)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1617246, _1617248)), _1617246, c_List_Olist_ONil(tc_prod(_1617246, _1617248)), hAPP(hAPP(c_COMBC(_1617246, tc_fun(tc_List_Olist(_1617246), tc_List_Olist(tc_prod(_1617246, _1617248))), tc_fun(tc_List_Olist(_1617246), tc_List_Olist(tc_prod(_1617246, _1617248)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1617246, _1617248)), tc_List_Olist(tc_prod(_1617246, _1617248))), tc_fun(tc_fun(tc_List_Olist(_1617246), tc_List_Olist(tc_prod(_1617246, _1617248))), tc_fun(tc_List_Olist(_1617246), tc_List_Olist(tc_prod(_1617246, _1617248)))), _1617246), c_COMBB(tc_List_Olist(tc_prod(_1617246, _1617248)), tc_List_Olist(tc_prod(_1617246, _1617248)), tc_List_Olist(_1617246))), hAPP(hAPP(c_COMBB(tc_prod(_1617246, _1617248), tc_fun(tc_List_Olist(tc_prod(_1617246, _1617248)), tc_List_Olist(tc_prod(_1617246, _1617248))), _1617246), c_List_Olist_OCons(tc_prod(_1617246, _1617248))), hAPP(hAPP(c_COMBC(_1617246, _1617248, tc_prod(_1617246, _1617248)), c_Product__Type_OPair(_1617246, _1617248)), _1617252)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1617246), tc_List_Olist(_1617248), tc_List_Olist(tc_prod(_1617246, _1617248))), c_List_Ozip(_1617246, _1617248)), _1617254))), _1617250))], (28420 ^ _777959) ^ [_1313630, _1313632] : [c_Nat__Transfer_Ois__nat(_1313630), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1313630), _1313632)))], (15671 ^ _777959) ^ [_1076285, _1076287] : [15672 ^ _777959 : [(15673 ^ _777959) ^ [_1076338] : [_1076287 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076285), _1076338))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076285), _1076287)))], (39982 ^ _777959) ^ [_1552112, _1552114, _1552116] : [hBOOL(hAPP(c_List_Odistinct(_1552112), _1552114)), -(c_List_Oremove1(_1552112, _1552116, _1552114) = hAPP(c_List_OremoveAll(_1552112, _1552116), _1552114))], (51240 ^ _777959) ^ [_1812516, _1812518] : [-(class_Enum_Oenum(tc_prod(_1812516, _1812518))), class_Enum_Oenum(_1812516), class_Enum_Oenum(_1812518)], (39141 ^ _777959) ^ [_1531908, _1531910, _1531912, _1531914, _1531916] : [c_Fun_Oinj__on(_1531908, _1531910, _1531912, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1531908, tc_HOL_Obool)), hAPP(c_List_Oset(_1531908), _1531914)), hAPP(c_List_Oset(_1531908), _1531916))), 39144 ^ _777959 : [(39151 ^ _777959) ^ [] : [_1531914 = _1531916, -(hAPP(hAPP(c_List_Omap(_1531908, _1531910), _1531912), _1531914) = hAPP(hAPP(c_List_Omap(_1531908, _1531910), _1531912), _1531916))], (39145 ^ _777959) ^ [] : [hAPP(hAPP(c_List_Omap(_1531908, _1531910), _1531912), _1531914) = hAPP(hAPP(c_List_Omap(_1531908, _1531910), _1531912), _1531916), -(_1531914 = _1531916)]]], (42754 ^ _777959) ^ [_1624871, _1624873, _1624875, _1624877] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1624871)), hAPP(hAPP(c_List_Oappend(_1624871), _1624873), _1624875)), c_List_Olists(_1624871, _1624877))), 42757 ^ _777959 : [(42760 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1624871)), _1624875), c_List_Olists(_1624871, _1624877))))], (42758 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1624871)), _1624873), c_List_Olists(_1624871, _1624877))))]]], (10502 ^ _777959) ^ [_963668, _963670, _963672, _963674, _963676, _963678] : [hBOOL(hAPP(hAPP(c_member(_963668), _963670), _963672)), -(c_Map_Orestrict__map(_963668, _963674, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_963668, tc_Option_Ooption(_963674)), _963676), _963670), _963678), _963672) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_963668, tc_Option_Ooption(_963674)), c_Map_Orestrict__map(_963668, _963674, _963676, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963668, tc_HOL_Obool)), _963672), hAPP(hAPP(c_Set_Oinsert(_963668), _963670), c_Orderings_Obot__class_Obot(tc_fun(_963668, tc_HOL_Obool)))))), _963670), _963678))], (37976 ^ _777959) ^ [_1505613, _1505615, _1505617, _1505619, _1505621, _1505623] : [c_Fun_Oinj__on(_1505613, _1505615, _1505617, _1505619), -(_1505621 = _1505623), hBOOL(hAPP(hAPP(c_member(_1505613), _1505621), _1505619)), hBOOL(hAPP(hAPP(c_member(_1505613), _1505623), _1505619)), hAPP(_1505617, _1505621) = hAPP(_1505617, _1505623)], (32951 ^ _777959) ^ [_1400362, _1400364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400362), _1400364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1400362)), c_Int_OBit1(_1400364))))], (39876 ^ _777959) ^ [_1549665, _1549667, _1549669] : [class_Orderings_Olinorder(_1549665), hBOOL(hAPP(c_Finite__Set_Ofinite(_1549665), _1549667)), -(c_List_Olinorder__class_Osorted__list__of__set(_1549665, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1549665, tc_HOL_Obool)), _1549667), hAPP(hAPP(c_Set_Oinsert(_1549665), _1549669), c_Orderings_Obot__class_Obot(tc_fun(_1549665, tc_HOL_Obool))))) = c_List_Oremove1(_1549665, _1549669, c_List_Olinorder__class_Osorted__list__of__set(_1549665, _1549667)))], (19272 ^ _777959) ^ [_1147902, _1147904, _1147906] : [class_Rings_Ono__zero__divisors(_1147902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1147902), _1147904), _1147906) = c_Groups_Ozero__class_Ozero(_1147902), -(_1147904 = c_Groups_Ozero__class_Ozero(_1147902)), -(_1147906 = c_Groups_Ozero__class_Ozero(_1147902))], (35171 ^ _777959) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (50384 ^ _777959) ^ [_1799707, _1799709, _1799711, _1799713] : [-(c_Lazy__Sequence_Ohb__bind(_1799707, _1799709, _1799711, _1799713) = c_Lazy__Sequence_Ohb__flat(_1799709, c_Lazy__Sequence_Ohb__map(_1799707, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1799709)), _1799713, _1799711)))], (6073 ^ _777959) ^ [_875175, _875177, _875179] : [hBOOL(hAPP(_875179, _875177)), -(hBOOL(hAPP(hAPP(c_member(_875175), _875177), _875179)))], (21608 ^ _777959) ^ [_1188526, _1188528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1188526), _1188528))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1188526), _1188528)))], (42742 ^ _777959) ^ [_1624580, _1624582, _1624584, _1624586, _1624588, _1624590] : [hAPP(hAPP(c_List_Olist_OCons(_1624580), _1624582), _1624584) = _1624586, _1624588 = hAPP(hAPP(c_List_Oappend(_1624580), _1624584), _1624590), -(hAPP(hAPP(c_List_Olist_OCons(_1624580), _1624582), _1624588) = hAPP(hAPP(c_List_Oappend(_1624580), _1624586), _1624590))], (4694 ^ _777959) ^ [_849241, _849243, _849245, _849247, _849249, _849251, _849253, _849255] : [-(c_New__Random__Sequence_Opos__bind(_849255, _849251, _849247, _849243) = c_New__Random__Sequence_Opos__bind(_849253, _849249, _849245, _849241)), _849255 = _849253, _849251 = _849249, _849247 = _849245, _849243 = _849241], (5296 ^ _777959) ^ [_859036, _859038] : [_859038 = _859036, -(c_List_Ohd(_859038) = c_List_Ohd(_859036))], (37898 ^ _777959) ^ [_1503863, _1503865, _1503867] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1503863), _1503865)), c_Fun_Oinj__on(_1503863, tc_fun(tc_fun(_1503863, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1503863, tc_fun(tc_prod(_1503863, _1503863), tc_HOL_Obool), tc_fun(tc_fun(_1503863, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1503863, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1503863, _1503863), tc_HOL_Obool), tc_fun(tc_fun(_1503863, tc_HOL_Obool), tc_HOL_Obool)), _1503863), c_Equiv__Relations_Oquotient(_1503863)), hAPP(hAPP(c_COMBC(_1503863, tc_fun(_1503863, tc_HOL_Obool), tc_fun(_1503863, tc_HOL_Obool)), c_Set_Oinsert(_1503863)), c_Orderings_Obot__class_Obot(tc_fun(_1503863, tc_HOL_Obool))))), _1503867), _1503865), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1503863, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1503863), _1503865), _1503867)) = hAPP(c_Finite__Set_Ocard(_1503863), _1503865))], (11170 ^ _777959) ^ [_976816, _976818, _976820] : [class_Lattices_Olattice(_976816), hBOOL(hAPP(c_Finite__Set_Ofinite(_976816), _976818)), hBOOL(hAPP(hAPP(c_member(_976816), _976820), _976818)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_976816), _976820), c_Big__Operators_Olattice__class_OInf__fin(_976816, _976818)) = c_Big__Operators_Olattice__class_OInf__fin(_976816, _976818))], (50648 ^ _777959) ^ [_1805311, _1805313, _1805315, _1805317] : [-(hBOOL(hAPP(hAPP(c_member(_1805311), _1805313), hAPP(c_List_Oset(_1805311), c_List_Oreplicate(_1805311, _1805315, _1805317))))), _1805313 = _1805317, -(_1805315 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43434 ^ _777959) ^ [_1641508, _1641510, _1641512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641508), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641510)), _1641512))), -(hAPP(hAPP(c_List_Oappend(_1641510), hAPP(hAPP(c_List_Otake(_1641510), _1641508), _1641512)), hAPP(hAPP(c_List_Olist_OCons(_1641510), hAPP(c_List_Ohd(_1641510), hAPP(hAPP(c_List_Odrop(_1641510), _1641508), _1641512))), c_List_Olist_ONil(_1641510))) = hAPP(hAPP(c_List_Otake(_1641510), hAPP(c_Nat_OSuc, _1641508)), _1641512))], (33485 ^ _777959) ^ [_1409095, _1409097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409095)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409097))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409095), _1409097))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409095), c_Int_OPls)))], (23555 ^ _777959) ^ [_1226267, _1226269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226267), _1226269)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226267), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1226269)))], (29382 ^ _777959) ^ [_1331884, _1331886, _1331888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331884)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1331886), _1331888)), 29389 ^ _777959 : [(29390 ^ _777959) ^ [_1332080] : [29392 ^ _777959 : [(29398 ^ _777959) ^ [] : [-(_1332080 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 29394 ^ [_1331884, _1331886, _1331888, _1332080]), 29391 ^ [_1331884, _1331886, _1331888, _1332080]))], (29396 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29394 ^ [_1331884, _1331886, _1331888, _1332080]), _1331888)))], (29393 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29391 ^ [_1331884, _1331886, _1331888, _1332080]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1331884))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331886), _1332080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1331886), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1332080), _1331884))))]]], (30639 ^ _777959) ^ [_1357080, _1357082, _1357084] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1357080, _1357082)), _1357084) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1357080), _1357084), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1357082), _1357084)))], (44658 ^ _777959) ^ [_1665458, _1665460, _1665462, _1665464] : [class_Orderings_Olinorder(_1665458), c_List_Olinorder__class_Osorted(_1665458, _1665460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1665462), _1665464)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665464), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665458)), _1665460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1665458), hAPP(hAPP(c_List_Onth(_1665458), _1665460), _1665462)), hAPP(hAPP(c_List_Onth(_1665458), _1665460), _1665464))))], (38018 ^ _777959) ^ [_1506327, _1506329, _1506331, _1506333, _1506335, _1506337] : [c_Fun_Oinj__on(_1506327, _1506329, _1506331, _1506333), hAPP(_1506331, _1506335) = hAPP(_1506331, _1506337), hBOOL(hAPP(hAPP(c_member(_1506327), _1506335), _1506333)), hBOOL(hAPP(hAPP(c_member(_1506327), _1506337), _1506333)), -(_1506335 = _1506337)], (10032 ^ _777959) ^ [_952608, _952610, _952612, _952614] : [hBOOL(hAPP(hAPP(c_member(_952608), _952610), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952608, tc_HOL_Obool)), _952612), _952614))), 10035 ^ _777959 : [(10038 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_952608), _952610), _952614)))], (10036 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_952608), _952610), _952612)))]]], (20879 ^ _777959) ^ [_1175254, _1175256] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175254), _1175256) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 20880 ^ _777959 : [(20887 ^ _777959) ^ [] : [_1175254 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1175256 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20881 ^ _777959) ^ [] : [_1175254 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (51366 ^ _777959) ^ [_1813788, _1813790, _1813792, _1813794, _1813796, _1813798] : [-(hAPP(hAPP(hAPP(c_COMBC(_1813788, _1813790, _1813792), _1813794), _1813796), _1813798) = hAPP(hAPP(_1813794, _1813798), _1813796))], (31839 ^ _777959) ^ [_1379349, _1379351, _1379353] : [hBOOL(hAPP(c_Com_OWT, _1379349)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OLocal(_1379351, _1379353, _1379349))))], (39027 ^ _777959) ^ [_1529437, _1529439, _1529441, _1529443, _1529445, _1529447, _1529449] : [-(hAPP(c_Product__Type_Oapsnd(_1529437, _1529439, _1529441, _1529443), hAPP(c_Product__Type_Oapsnd(_1529445, _1529437, _1529441, _1529447), _1529449)) = hAPP(c_Product__Type_Oapsnd(_1529445, _1529439, _1529441, hAPP(c_Fun_Ocomp(_1529437, _1529439, _1529445, _1529443), _1529447)), _1529449))], (29717 ^ _777959) ^ [_1338696, _1338698, _1338700] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1338696, tc_HOL_Obool)), _1338698), hAPP(c_Set_OPow(_1338696), _1338700))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338696, tc_HOL_Obool)), _1338698), _1338700)))], (41509 ^ _777959) ^ [_1591688, _1591690, _1591692, _1591694] : [-(_1591688 = _1591690), -(c_List_Oremove1(_1591692, _1591688, hAPP(hAPP(c_List_Olist_OCons(_1591692), _1591690), _1591694)) = hAPP(hAPP(c_List_Olist_OCons(_1591692), _1591690), c_List_Oremove1(_1591692, _1591688, _1591694)))], (48278 ^ _777959) ^ [_1749639, _1749641] : [-(c_Random_Oselect(_1749639, _1749641) = 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(_1749639, 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(_1749639)), _1749641)))), hAPP(hAPP(c_COMBB(_1749639, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1749639, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1749639, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1749639, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1749639), _1749641)), c_Code__Numeral_Onat__of))))], (37608 ^ _777959) ^ [_1496708, _1496710, _1496712, _1496714, _1496716] : [c_Equiv__Relations_Oequiv(_1496708, _1496710, _1496712), hBOOL(hAPP(hAPP(c_member(_1496708), _1496714), _1496710)), hBOOL(hAPP(hAPP(c_member(_1496708), _1496716), _1496710)), 37619 ^ _777959 : [(37626 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1496708, _1496708)), hAPP(hAPP(c_Product__Type_OPair(_1496708, _1496708), _1496714), _1496716)), _1496712)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1496708), hAPP(hAPP(c_Set_Oinsert(_1496708), _1496714), c_Orderings_Obot__class_Obot(tc_fun(_1496708, tc_HOL_Obool)))), _1496712) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1496708), hAPP(hAPP(c_Set_Oinsert(_1496708), _1496716), c_Orderings_Obot__class_Obot(tc_fun(_1496708, tc_HOL_Obool)))), _1496712))], (37620 ^ _777959) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1496708), hAPP(hAPP(c_Set_Oinsert(_1496708), _1496714), c_Orderings_Obot__class_Obot(tc_fun(_1496708, tc_HOL_Obool)))), _1496712) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1496708), hAPP(hAPP(c_Set_Oinsert(_1496708), _1496716), c_Orderings_Obot__class_Obot(tc_fun(_1496708, tc_HOL_Obool)))), _1496712), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1496708, _1496708)), hAPP(hAPP(c_Product__Type_OPair(_1496708, _1496708), _1496714), _1496716)), _1496712)))]]], (17095 ^ _777959) ^ [_1104940, _1104942, _1104944, _1104946, _1104948] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1104940, _1104942, _1104944, _1104946, c_Orderings_Obot__class_Obot(tc_fun(_1104940, tc_HOL_Obool))), _1104948)), -(_1104948 = _1104946)], (33905 ^ _777959) ^ [_1416644, _1416646, _1416648, _1416650, _1416652] : [-(c_Nat_Onat_Onat__case(_1416644, _1416646, _1416648, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416650)), _1416652)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1416644), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1416650))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1416644, _1416644), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1416644, tc_fun(_1416644, _1416644)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1416644, tc_fun(_1416644, _1416644)), tc_Int_Oint), c_If(_1416644)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1416644, _1416646, _1416648, _1416652))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1416644, tc_Int_Oint), _1416648), 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)), _1416652)))))], (33895 ^ _777959) ^ [_1416454] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416454)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416454)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1416454)))], (29723 ^ _777959) ^ [_1338821, _1338823, _1338825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338821, tc_HOL_Obool)), _1338823), _1338825)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1338821, tc_HOL_Obool)), _1338823), hAPP(c_Set_OPow(_1338821), _1338825))))], (6710 ^ _777959) ^ [_886959, _886961] : [-(_886961 = c_Orderings_Obot__class_Obot(tc_fun(_886959, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_886959), 6713 ^ [_886959, _886961]), _886961)))], (5202 ^ _777959) ^ [_857567, _857569, _857571, _857573, _857575, _857577] : [-(c_Predicate_Oconversep(_857577, _857573, _857569) = c_Predicate_Oconversep(_857575, _857571, _857567)), _857577 = _857575, _857573 = _857571, _857569 = _857567], (42461 ^ _777959) ^ [_1616434, _1616436, _1616438, _1616440, _1616442] : [_1616434 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1616436, _1616438, _1616440), _1616434), _1616442) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616438), _1616436), c_List_Olist_ONil(_1616438)), _1616442))], (48601 ^ _777959) ^ [_1757330, _1757332, _1757334, _1757336, _1757338] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1757330, _1757330)), hAPP(hAPP(c_Product__Type_OPair(_1757330, _1757330), _1757332), _1757334)), c_Transitive__Closure_Ortrancl(_1757330, _1757336))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1757330, _1757330)), hAPP(hAPP(c_Product__Type_OPair(_1757330, _1757330), _1757334), _1757338)), _1757336)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1757330, _1757330)), hAPP(hAPP(c_Product__Type_OPair(_1757330, _1757330), _1757332), _1757338)), c_Transitive__Closure_Otrancl(_1757330, _1757336))))], (13943 ^ _777959) ^ [_1036271, _1036273, _1036275, _1036277, _1036279] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1036271, tc_fun(_1036273, tc_HOL_Obool)), _1036275), hAPP(hAPP(c_COMBB(tc_fun(_1036273, tc_HOL_Obool), tc_fun(_1036273, tc_HOL_Obool), _1036271), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1036273, tc_HOL_Obool)), _1036277)), _1036279)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1036273, tc_HOL_Obool)), _1036277), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1036271, tc_fun(_1036273, tc_HOL_Obool)), _1036275), _1036279)))], (28952 ^ _777959) ^ [_1323702] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1323702) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1323702))], (31440 ^ _777959) ^ [_1371801, _1371803] : [31441 ^ _777959 : [(31444 ^ _777959) ^ [] : [_1371803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31442 ^ _777959) ^ [] : [-(_1371801 = 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), _1371801)), _1371803))))], (39484 ^ _777959) ^ [_1539804, _1539806, _1539808, _1539810, _1539812] : [c_Hoare__Mirabelle_Ohoare__valids(_1539804, _1539806, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1539804)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1539804), c_Hoare__Mirabelle_Opeek__and(_1539804, _1539808, _1539810)), _1539812), _1539808)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1539804), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__valids(_1539804, _1539806, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1539804)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1539804), _1539808), c_Com_Ocom_OWhile(_1539810, _1539812)), c_Hoare__Mirabelle_Opeek__and(_1539804, _1539808, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1539810)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1539804), tc_HOL_Obool)))))], (45246 ^ _777959) ^ [_1679877, _1679879, _1679881, _1679883, _1679885] : [class_Orderings_Olinorder(_1679877), c_List_Olinorder__class_Osorted(_1679877, hAPP(c_List_Orev(_1679877), hAPP(hAPP(c_List_Omap(_1679879, _1679877), _1679881), _1679883))), -(hAPP(c_List_Ofilter(_1679879, hAPP(hAPP(c_COMBB(_1679877, tc_HOL_Obool, _1679879), hAPP(c_Orderings_Oord__class_Oless(_1679877), _1679885)), _1679881)), _1679883) = c_List_OtakeWhile(_1679879, hAPP(hAPP(c_COMBB(_1679877, tc_HOL_Obool, _1679879), hAPP(c_Orderings_Oord__class_Oless(_1679877), _1679885)), _1679881), _1679883))], (25188 ^ _777959) ^ [_1255306, _1255308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1255306), _1255308)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1255306), hAPP(c_Nat_OSuc, _1255308)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1255308), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1255306), _1255308)))], (45113 ^ _777959) ^ [_1676902, _1676904] : [-(c_List_Oconcat(tc_List_Olist(_1676902), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1676902), tc_List_Olist(tc_List_Olist(_1676902))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1676902)), _1676902, c_List_Olist_ONil(tc_List_Olist(_1676902)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1676902), tc_List_Olist(tc_List_Olist(_1676902))), _1676902), hAPP(hAPP(c_COMBC(tc_List_Olist(_1676902), tc_List_Olist(tc_List_Olist(_1676902)), tc_List_Olist(tc_List_Olist(_1676902))), c_List_Olist_OCons(tc_List_Olist(_1676902))), c_List_Olist_ONil(tc_List_Olist(_1676902)))))), _1676904)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1676902), tc_List_Olist(_1676902)), c_List_Otl(_1676902)), hAPP(c_List_Ofilter(tc_List_Olist(_1676902), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1676902)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1676902), tc_List_Olist(_1676902), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1676902)))), _1676904)))], (42592 ^ _777959) ^ [_1620727, _1620729, _1620731, _1620733, _1620735, _1620737] : [class_Groups_Ocomm__monoid__mult(_1620727), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620729), _1620731)), 42602 ^ _777959 : [(42605 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1620733), hAPP(_1620735, 42601 ^ [_1620727, _1620729, _1620731, _1620733, _1620735, _1620737])))], (42603 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620729), 42601 ^ [_1620727, _1620729, _1620731, _1620733, _1620735, _1620737]), _1620731)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1620729, _1620727), hAPP(hAPP(c_COMBS(_1620729, tc_fun(_1620733, tc_HOL_Obool), _1620727), hAPP(hAPP(c_COMBB(tc_fun(_1620733, _1620727), tc_fun(tc_fun(_1620733, tc_HOL_Obool), _1620727), _1620729), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1620733, _1620727)), _1620737)), _1620735)), _1620731) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1620729, _1620733), _1620727), hAPP(c_Product__Type_Oprod_Oprod__case(_1620729, _1620733, _1620727), _1620737)), hAPP(hAPP(c_Product__Type_OSigma(_1620729, _1620733), _1620731), _1620735)))], (40540 ^ _777959) ^ [_1564895, _1564897, _1564899] : [class_Groups_Omonoid__add(_1564895), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1564895), hAPP(hAPP(c_List_Omap(_1564897, _1564895), hAPP(c_COMBK(_1564895, _1564897), c_Groups_Ozero__class_Ozero(_1564895))), _1564899)) = c_Groups_Ozero__class_Ozero(_1564895))], (42521 ^ _777959) ^ [_1619358] : [-(hAPP(c_List_Omap(_1619358, _1619358), c_COMBI(_1619358)) = c_Fun_Oid(tc_List_Olist(_1619358)))], (7972 ^ _777959) ^ [_913971, _913973, _913975] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913971, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913971, tc_HOL_Obool)), _913973), _913975)), _913975) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913971, tc_HOL_Obool)), _913973), _913975))], (50958 ^ _777959) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (48511 ^ _777959) ^ [_1754447, _1754449, _1754451, _1754453] : [-(c_Transitive__Closure_Otrancl(_1754447, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1754447, _1754447)), hAPP(hAPP(c_Product__Type_OPair(_1754447, _1754447), _1754449), _1754451)), _1754453)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1754447, _1754447), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1754447, _1754453)), hAPP(c_Set_OCollect(tc_prod(_1754447, _1754447)), hAPP(c_Product__Type_Oprod_Oprod__case(_1754447, _1754447, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1754447, tc_fun(_1754447, tc_HOL_Obool), tc_fun(_1754447, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1754447, tc_HOL_Obool), tc_fun(_1754447, tc_HOL_Obool)), _1754447), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1754447)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1754447), c_fconj), hAPP(hAPP(c_COMBC(_1754447, tc_fun(tc_prod(_1754447, _1754447), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1754447, _1754447), tc_fun(tc_fun(tc_prod(_1754447, _1754447), tc_HOL_Obool), tc_HOL_Obool), _1754447), c_member(tc_prod(_1754447, _1754447))), hAPP(hAPP(c_COMBC(_1754447, _1754447, tc_prod(_1754447, _1754447)), c_Product__Type_OPair(_1754447, _1754447)), _1754449))), c_Transitive__Closure_Ortrancl(_1754447, _1754453))))), hAPP(hAPP(c_COMBC(_1754447, tc_fun(tc_prod(_1754447, _1754447), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1754447, _1754447), tc_fun(tc_fun(tc_prod(_1754447, _1754447), tc_HOL_Obool), tc_HOL_Obool), _1754447), c_member(tc_prod(_1754447, _1754447))), hAPP(c_Product__Type_OPair(_1754447, _1754447), _1754451))), c_Transitive__Closure_Ortrancl(_1754447, _1754453)))))))], (5564 ^ _777959) ^ [_862974, _862976, _862978, _862980, _862982, _862984] : [-(c_Set_Oimage(_862984, _862980, _862976) = c_Set_Oimage(_862982, _862978, _862974)), _862984 = _862982, _862980 = _862978, _862976 = _862974], (50834 ^ _777959) ^ [_1808425, _1808427] : [class_Groups_Ouminus(_1808425), -(class_Groups_Ouminus(tc_fun(_1808427, _1808425)))], (51368 ^ _777959) ^ [_1813840, _1813842, _1813844, _1813846, _1813848, _1813850] : [-(hAPP(hAPP(hAPP(c_COMBS(_1813840, _1813842, _1813844), _1813846), _1813848), _1813850) = hAPP(hAPP(_1813846, _1813850), hAPP(_1813848, _1813850)))], (31909 ^ _777959) ^ [_1380484, _1380486, _1380488] : [class_Int_Onumber__ring(_1380484), class_Int_Oring__char__0(_1380484), 31916 ^ _777959 : [(31923 ^ _777959) ^ [] : [_1380486 = _1380488, -(hAPP(c_Int_Onumber__class_Onumber__of(_1380484), _1380486) = hAPP(c_Int_Onumber__class_Onumber__of(_1380484), _1380488))], (31917 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1380484), _1380486) = hAPP(c_Int_Onumber__class_Onumber__of(_1380484), _1380488), -(_1380486 = _1380488)]]], (43378 ^ _777959) ^ [_1639904, _1639906, _1639908, _1639910, _1639912] : [-(hAPP(hAPP(c_List_Oappend(_1639904), _1639906), _1639908) = hAPP(hAPP(c_List_Oappend(_1639904), _1639910), _1639912)), 43381 ^ _777959 : [(43384 ^ _777959) ^ [] : [_1639906 = hAPP(hAPP(c_List_Otake(_1639904), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639904)), _1639906)), _1639910), _1639908 = hAPP(hAPP(c_List_Oappend(_1639904), hAPP(hAPP(c_List_Odrop(_1639904), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639904)), _1639906)), _1639910)), _1639912)], (43382 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639904)), _1639906)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639904)), _1639910))))]], 43389 ^ _777959 : [(43392 ^ _777959) ^ [] : [hAPP(hAPP(c_List_Otake(_1639904), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639904)), _1639910)), _1639906) = _1639910, hAPP(hAPP(c_List_Oappend(_1639904), hAPP(hAPP(c_List_Odrop(_1639904), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639904)), _1639910)), _1639906)), _1639908) = _1639912], (43390 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639904)), _1639906)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1639904)), _1639910)))]]], (37682 ^ _777959) ^ [_1498847, _1498849] : [c_Equiv__Relations_Oequivp(_1498847, _1498849), 37685 ^ _777959 : [(37692 ^ _777959) ^ [_1499040, _1499042] : [hAPP(_1498849, _1499042) = hAPP(_1498849, _1499040), -(hBOOL(hAPP(hAPP(_1498849, _1499042), _1499040)))], (37686 ^ _777959) ^ [_1498941, _1498943] : [hBOOL(hAPP(hAPP(_1498849, _1498943), _1498941)), -(hAPP(_1498849, _1498943) = hAPP(_1498849, _1498941))]]], (32253 ^ _777959) ^ [_1387005, _1387007, _1387009, _1387011] : [class_Fields_Ofield__inverse__zero(_1387005), class_Int_Onumber(_1387005), 32260 ^ _777959 : [(32261 ^ _777959) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387005), _1387007), _1387009) = hAPP(c_Int_Onumber__class_Onumber__of(_1387005), _1387011), 32264 ^ _777959 : [(32271 ^ _777959) ^ [] : [_1387009 = c_Groups_Ozero__class_Ozero(_1387005), -(hAPP(c_Int_Onumber__class_Onumber__of(_1387005), _1387011) = c_Groups_Ozero__class_Ozero(_1387005))], (32265 ^ _777959) ^ [] : [-(_1387009 = c_Groups_Ozero__class_Ozero(_1387005)), -(_1387007 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387005), hAPP(c_Int_Onumber__class_Onumber__of(_1387005), _1387011)), _1387009))]]], (32277 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1387005), _1387007), _1387009) = hAPP(c_Int_Onumber__class_Onumber__of(_1387005), _1387011)), 32280 ^ _777959 : [(32283 ^ _777959) ^ [] : [_1387007 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387005), hAPP(c_Int_Onumber__class_Onumber__of(_1387005), _1387011)), _1387009)], (32281 ^ _777959) ^ [] : [_1387009 = c_Groups_Ozero__class_Ozero(_1387005)]], 32284 ^ _777959 : [(32287 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1387005), _1387011) = c_Groups_Ozero__class_Ozero(_1387005)], (32285 ^ _777959) ^ [] : [-(_1387009 = c_Groups_Ozero__class_Ozero(_1387005))]]]]], (51122 ^ _777959) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (32921 ^ _777959) ^ [_1399815, _1399817] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1399815)), c_Int_OBit1(_1399817))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1399815), _1399817)))], (19981 ^ _777959) ^ [_1159478, _1159480, _1159482, _1159484] : [class_Rings_Oordered__semiring(_1159478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159478), _1159480), _1159482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159478), c_Groups_Ozero__class_Ozero(_1159478)), _1159484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159478), _1159484), _1159480)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159478), _1159484), _1159482))))], (46892 ^ _777959) ^ [_1718110, _1718112] : [hAPP(hAPP(c_Relation_Orel__comp(_1718110, _1718110, _1718110), _1718112), _1718112) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1718110, _1718110), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1718110, _1718112))], (25744 ^ _777959) ^ [_1266365, _1266367, _1266369, _1266371] : [class_Rings_Odivision__ring(_1266365), -(_1266367 = c_Groups_Ozero__class_Ozero(_1266365)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266365), _1266369), _1266367) = _1266371, -(_1266369 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266365), _1266371), _1266367))], (27798 ^ _777959) ^ [_1303142, _1303144, _1303146, _1303148] : [class_Orderings_Olinorder(_1303142), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303142), _1303144), _1303146)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1303142), _1303146), _1303148)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1303142, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1303142, _1303144, _1303146)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1303142, _1303146, _1303148)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1303142, _1303144, _1303148))], (41541 ^ _777959) ^ [_1592423, _1592425, _1592427] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1592423, tc_HOL_Obool)), hAPP(c_List_Oset(_1592423), _1592425)), hAPP(c_List_Oset(_1592423), hAPP(hAPP(c_List_Olist_OCons(_1592423), _1592427), _1592425)))))], (3740 ^ _777959) ^ [_834520, _834522, _834524, _834526] : [-(c_Nitpick_Onumber__of__frac(_834526, _834522) = c_Nitpick_Onumber__of__frac(_834524, _834520)), _834526 = _834524, _834522 = _834520], (36876 ^ _777959) ^ [_1477699] : [c_Code__Numeral_OSuc__code__numeral(_1477699) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (11758 ^ _777959) ^ [_990030, _990032, _990034, _990036, _990038] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990030, tc_fun(_990032, tc_HOL_Obool)), _990034), hAPP(hAPP(c_COMBB(tc_fun(_990032, tc_HOL_Obool), tc_fun(_990032, tc_HOL_Obool), _990030), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990032, tc_HOL_Obool)), _990036)), _990038)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990032, tc_HOL_Obool)), _990036), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990030, tc_fun(_990032, tc_HOL_Obool)), _990034), _990038)))], (22655 ^ _777959) ^ [_1210148, _1210150] : [class_Rings_Oring__1(_1210148), -(hBOOL(hAPP(hAPP(c_member(_1210148), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210148), _1210150)), c_Int_Oring__1__class_OInts(_1210148))))], (36443 ^ _777959) ^ [_1468778, _1468780, _1468782] : [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), _1468778), _1468780))), -(hBOOL(hAPP(hAPP(_1468782, _1468778), _1468780))), 36450 ^ _777959 : [(36453 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1468782, 36448 ^ [_1468778, _1468780, _1468782]), 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)))), 36449 ^ [_1468778, _1468780, _1468782])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 36448 ^ [_1468778, _1468780, _1468782]), 36449 ^ [_1468778, _1468780, _1468782]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 36449 ^ [_1468778, _1468780, _1468782]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36463 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1468782, 36448 ^ [_1468778, _1468780, _1468782]), 36449 ^ [_1468778, _1468780, _1468782]))], (36451 ^ _777959) ^ [] : [-(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), 36448 ^ [_1468778, _1468780, _1468782]), 36449 ^ [_1468778, _1468780, _1468782]))))]]], (24229 ^ _777959) ^ [_1238526, _1238528, _1238530, _1238532] : [class_Rings_Osemiring__1(_1238526), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1238526, _1238528, hAPP(c_Nat_OSuc, _1238530), _1238532) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1238526, _1238528, _1238530, hAPP(_1238528, _1238532)))], (34721 ^ _777959) ^ [_1431157, _1431159, _1431161] : [class_Rings_Olinordered__idom(_1431157), 34724 ^ _777959 : [(34733 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431157), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1431157), hAPP(hAPP(c_Power_Opower__class_Opower(_1431157), _1431159), 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(_1431157), 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c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1609934))], (11756 ^ _777959) ^ [_989941, _989943, _989945, _989947, _989949] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989941, tc_fun(_989943, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_989941, tc_HOL_Obool)), _989945), _989947)), _989949) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_989943, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989941, tc_fun(_989943, tc_HOL_Obool)), _989945), _989949)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989941, tc_fun(_989943, tc_HOL_Obool)), _989947), _989949)))], (6297 ^ _777959) ^ [_879527, _879529, _879531, _879533] : [hBOOL(hAPP(hAPP(c_member(_879527), _879529), _879531)), -(hBOOL(hAPP(hAPP(c_member(_879527), _879529), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_879527, tc_HOL_Obool)), _879533), _879531))))], (33029 ^ _777959) ^ [_1401806, _1401808] : [-(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), _1401806)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1401808), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1401806))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (41749 ^ _777959) ^ [_1599017, _1599019, _1599021, _1599023, _1599025] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599017), tc_List_Olist(_1599017))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599017), tc_List_Olist(_1599017)), hAPP(hAPP(c_List_Olist_OCons(_1599017), _1599019), _1599021)), _1599023)), c_List_Olistrel(_1599017, _1599025))), 41754 ^ _777959 : [(41759 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1599017), tc_List_Olist(_1599017))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1599017), tc_List_Olist(_1599017)), _1599021), 41753 ^ [_1599017, _1599019, _1599021, _1599023, _1599025])), c_List_Olistrel(_1599017, _1599025))))], (41757 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599017, _1599017)), hAPP(hAPP(c_Product__Type_OPair(_1599017, _1599017), _1599019), 41752 ^ [_1599017, _1599019, _1599021, _1599023, _1599025])), _1599025)))], (41755 ^ _777959) ^ [] : [-(_1599023 = hAPP(hAPP(c_List_Olist_OCons(_1599017), 41752 ^ [_1599017, _1599019, _1599021, _1599023, _1599025]), 41753 ^ [_1599017, _1599019, _1599021, _1599023, _1599025]))]]], (21584 ^ _777959) ^ [_1188097] : [class_Rings_Olinordered__semidom(_1188097), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1188097), c_Groups_Ozero__class_Ozero(_1188097)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1188097), c_Groups_Oone__class_Oone(_1188097)), c_Groups_Oone__class_Oone(_1188097)))))], (11631 ^ _777959) ^ [_986577, _986579, _986581, _986583, _986585, _986587] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986577, tc_fun(_986579, tc_HOL_Obool)), _986581), hAPP(hAPP(c_COMBC(_986577, tc_fun(_986583, tc_fun(_986579, tc_HOL_Obool)), tc_fun(_986579, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_986583, tc_HOL_Obool), tc_fun(tc_fun(_986583, tc_fun(_986579, tc_HOL_Obool)), tc_fun(_986579, tc_HOL_Obool)), _986577), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986583, tc_fun(_986579, tc_HOL_Obool))), _986585)), _986587)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986583, tc_fun(_986579, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_986577, tc_fun(_986583, tc_HOL_Obool)), _986581), _986585)), _986587))], (41811 ^ _777959) ^ [_1600598, _1600600, _1600602, _1600604] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1600598)), hAPP(hAPP(c_List_Olist_OCons(_1600598), _1600600), _1600602)), c_List_Olists(_1600598, _1600604)))), hBOOL(hAPP(hAPP(c_member(_1600598), _1600600), _1600604)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1600598)), _1600602), c_List_Olists(_1600598, _1600604)))], (51358 ^ _777959) ^ [_1813644] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1813644)))], (13937 ^ _777959) ^ [_1036046, _1036048] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1036046, tc_HOL_Obool)), _1036048), c_Orderings_Otop__class_Otop(tc_fun(_1036046, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1036046, tc_HOL_Obool)))], (35451 ^ _777959) ^ [_1448572, _1448574, _1448576, _1448578, _1448580, _1448582] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1448572, tc_fun(_1448574, tc_fun(_1448576, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1448572, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1448574, _1448576), tc_HOL_Obool), tc_fun(_1448574, tc_fun(_1448576, tc_HOL_Obool)), _1448572), hAPP(c_COMBC(_1448574, tc_fun(tc_prod(_1448574, _1448576), tc_HOL_Obool), tc_fun(_1448576, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1448576, tc_fun(tc_fun(tc_prod(_1448574, _1448576), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1448574, _1448576), tc_HOL_Obool), tc_fun(_1448576, tc_HOL_Obool)), _1448574), c_COMBC(_1448576, tc_fun(tc_prod(_1448574, _1448576), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1448576, tc_prod(_1448574, _1448576)), tc_fun(_1448576, tc_fun(tc_fun(tc_prod(_1448574, _1448576), tc_HOL_Obool), tc_HOL_Obool)), _1448574), hAPP(c_COMBB(tc_prod(_1448574, _1448576), tc_fun(tc_fun(tc_prod(_1448574, _1448576), tc_HOL_Obool), tc_HOL_Obool), _1448576), c_member(tc_prod(_1448574, _1448576)))), c_Product__Type_OPair(_1448574, _1448576))))), _1448578)), _1448580), _1448582)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1448574, _1448576)), hAPP(hAPP(c_Product__Type_OPair(_1448574, _1448576), _1448580), _1448582)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1448572, tc_fun(tc_prod(_1448574, _1448576), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1448572, tc_HOL_Obool))), _1448578))))], (15334 ^ _777959) ^ [_1069757, _1069759] : [class_Groups_Omonoid__mult(_1069757), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069757), c_Groups_Oone__class_Oone(_1069757)), _1069759) = _1069759)], (34389 ^ _777959) ^ [_1425293, _1425295, _1425297] : [class_Int_Onumber__ring(_1425293), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1425293), _1425295), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1425297))) = hAPP(hAPP(c_HOL_OLet(_1425293, _1425293), hAPP(hAPP(c_Power_Opower__class_Opower(_1425293), _1425295), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425297))), hAPP(hAPP(c_COMBS(_1425293, _1425293, _1425293), c_Groups_Otimes__class_Otimes(_1425293)), c_COMBI(_1425293))))], (41940 ^ _777959) ^ [_1604021, _1604023, _1604025, _1604027] : [-(c_Map_Omap__upds(_1604021, _1604023, _1604025, _1604027, c_List_Olist_ONil(_1604023)) = _1604025)], (40073 ^ _777959) ^ [_1554170, _1554172, _1554174, _1554176] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554170)), _1554172) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554174)), _1554176), hBOOL(hAPP(c_List_Odistinct(_1554170), _1554172)), -(c_Map_Odom(_1554170, _1554174, hAPP(c_Map_Omap__of(_1554170, _1554174), hAPP(hAPP(c_List_Ozip(_1554170, _1554174), _1554172), _1554176))) = hAPP(c_List_Oset(_1554170), _1554172))], (10910 ^ _777959) ^ [_971840, _971842, _971844, _971846] : [class_Groups_Oordered__cancel__ab__semigroup__add(_971840), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971840), _971842), _971844)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971840), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971840), _971846), _971842)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971840), _971846), _971844))))], (38230 ^ _777959) ^ [_1510304, _1510306] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1510304), c_Orderings_Otop__class_Otop(tc_fun(_1510304, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1510304, _1510304, _1510306), c_Orderings_Otop__class_Otop(tc_fun(_1510304, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1510304, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1510304, _1510304, _1510306, c_Orderings_Otop__class_Otop(tc_fun(_1510304, tc_HOL_Obool))))], (50972 ^ _777959) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (28199 ^ _777959) ^ [_1309734, _1309736] : [class_Rings_Olinordered__idom(_1309734), 28202 ^ _777959 : [(28209 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1309736), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309734), hAPP(c_Int_Oring__1__class_Oof__int(_1309734), _1309736)), c_Groups_Ozero__class_Ozero(_1309734))))], (28203 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1309734), hAPP(c_Int_Oring__1__class_Oof__int(_1309734), _1309736)), c_Groups_Ozero__class_Ozero(_1309734))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1309736), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (41950 ^ _777959) ^ [_1604197, _1604199, _1604201] : [-(hAPP(hAPP(c_List_Ozip(_1604197, _1604199), c_List_Olist_ONil(_1604197)), _1604201) = c_List_Olist_ONil(tc_prod(_1604197, _1604199)))], (37265 ^ _777959) ^ [_1488724, _1488726, _1488728, _1488730] : [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), _1488724), _1488726)), 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), _1488728), _1488730)), 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), _1488724), _1488730)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1488728), _1488726))))], (17623 ^ _777959) ^ [_1114656, _1114658, _1114660] : [class_Orderings_Olinorder(_1114656), hBOOL(hAPP(c_Finite__Set_Ofinite(_1114656), _1114658)), -(_1114658 = c_Orderings_Obot__class_Obot(tc_fun(_1114656, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1114656), _1114660)), -(_1114660 = c_Orderings_Obot__class_Obot(tc_fun(_1114656, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1114656, tc_HOL_Obool)), _1114658), _1114660) = c_Orderings_Obot__class_Obot(tc_fun(_1114656, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1114656, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1114656, tc_HOL_Obool)), _1114658), _1114660)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1114656), c_Big__Operators_Olinorder__class_OMax(_1114656, _1114658)), c_Big__Operators_Olinorder__class_OMax(_1114656, _1114660)))], (15660 ^ _777959) ^ [_1076079, _1076081] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1076079), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1076079), _1076081)))))], (48417 ^ _777959) ^ [_1752078, _1752080] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1752078, _1752078), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1752078, _1752080)), hAPP(hAPP(c_Product__Type_OSigma(_1752078, _1752078), hAPP(c_Relation_OField(_1752078), _1752080)), hAPP(c_COMBK(tc_fun(_1752078, tc_HOL_Obool), _1752078), hAPP(c_Relation_OField(_1752078), _1752080))))))], (10002 ^ _777959) ^ [_951848, _951850, _951852, _951854] : [class_Lattices_Odistrib__lattice(_951848), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_951848), _951850), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951848), _951852), _951854)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951848), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_951848), _951850), _951852)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_951848), _951850), _951854)))], (30002 ^ _777959) ^ [_1345211, _1345213, _1345215, _1345217] : [class_Divides_Osemiring__div(_1345211), -(c_Divides_Odiv__class_Omod(_1345211, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345211), _1345213), _1345215), _1345217) = c_Divides_Odiv__class_Omod(_1345211, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345211), c_Divides_Odiv__class_Omod(_1345211, _1345213, _1345217)), _1345215), _1345217))], (51266 ^ _777959) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (6577 ^ _777959) ^ [_884390, _884392, _884394] : [class_Orderings_Olinorder(_884390), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884390), _884392), _884394))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884390), _884394), _884392)))], (19704 ^ _777959) ^ [_1154333, _1154335, _1154337] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1154333), _1154335)), 19707 ^ _777959 : [(19708 ^ _777959) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1154333, tc_Nat_Onat), _1154337), _1154335) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 19711 ^ _777959 : [(19712 ^ _777959) ^ [_1154495] : [hBOOL(hAPP(hAPP(c_member(_1154333), _1154495), _1154335)), -(hAPP(_1154337, _1154495) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (19718 ^ _777959) ^ [] : [19720 ^ _777959 : [(19723 ^ _777959) ^ [] : [hAPP(_1154337, 19719 ^ [_1154333, _1154335, _1154337]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (19721 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1154333), 19719 ^ [_1154333, _1154335, _1154337]), _1154335)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1154333, tc_Nat_Onat), _1154337), _1154335) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (11108 ^ _777959) ^ [_975562, _975564] : [c_Option_Oset(_975562, _975564) = c_Orderings_Obot__class_Obot(tc_fun(_975562, tc_HOL_Obool)), -(_975564 = c_Option_Ooption_ONone(_975562))], (45700 ^ _777959) ^ [_1689857, _1689859, _1689861, _1689863] : [class_Orderings_Olinorder(_1689857), -(hAPP(c_List_Oset(_1689859), c_List_Olinorder__class_Osort__key(_1689859, _1689857, _1689861, _1689863)) = hAPP(c_List_Oset(_1689859), _1689863))], (43282 ^ _777959) ^ [_1637578, _1637580, _1637582, _1637584, _1637586] : [hAPP(hAPP(c_List_Odrop(_1637578), _1637580), _1637582) = hAPP(hAPP(c_List_Olist_OCons(_1637578), _1637584), _1637586), -(hAPP(hAPP(c_List_Onth(_1637578), _1637582), _1637580) = _1637584)], (45443 ^ _777959) ^ [_1683715, _1683717, _1683719] : [-(hAPP(hAPP(c_List_Oappend(_1683715), c_List_OtakeWhile(_1683715, _1683717, _1683719)), c_List_OdropWhile(_1683715, _1683717, _1683719)) = _1683719)], (1940 ^ _777959) ^ [_806026, _806028, _806030, _806032] : [-(c_Option_Oset(_806032, _806028) = c_Option_Oset(_806030, _806026)), _806032 = _806030, _806028 = _806026], (33051 ^ _777959) ^ [_1402148, _1402150] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1402148) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402150)), _1402148 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402150)), 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), _1402150)))], (41233 ^ _777959) ^ [_1584997, _1584999] : [-(c_List_Olex(_1584997, _1584999) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1584997), tc_List_Olist(_1584997)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1584997, _1584999)))], (26450 ^ _777959) ^ [_1278950, _1278952, _1278954] : [class_Fields_Olinordered__field(_1278950), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278950), c_Groups_Ozero__class_Ozero(_1278950)), _1278952)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1278950), c_Groups_Ozero__class_Ozero(_1278950)), _1278954)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1278950), c_Groups_Ozero__class_Ozero(_1278950)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278950), _1278952), _1278954))))], (7178 ^ _777959) ^ [_898083, _898085, _898087, _898089] : [class_Lattices_Olattice(_898083), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898083), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898083), _898085), _898087)), _898089) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898083), _898085), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898083), _898087), _898089)))], (28426 ^ _777959) ^ [_1313730, _1313732] : [28434 ^ _777959 : [(28437 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1313732, 28433 ^ [_1313730, _1313732])))], (28435 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 28433 ^ [_1313730, _1313732]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1313730))))]], 28427 ^ _777959 : [(28428 ^ _777959) ^ [_1313799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1313799), _1313730)), hBOOL(hAPP(_1313732, _1313799))]]], (2148 ^ _777959) ^ [_809534, _809536, _809538, _809540] : [-(c_Orderings_Oord_Omax(_809540, _809536) = c_Orderings_Oord_Omax(_809538, _809534)), _809540 = _809538, _809536 = _809534], (47174 ^ _777959) ^ [] : [-(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))))], (34495 ^ _777959) ^ [_1427262] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1427262), 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), _1427262), _1427262))], (10998 ^ _777959) ^ [_973366, _973368] : [10999 ^ _777959 : [(11000 ^ _777959) ^ [_973414] : [_973366 = hAPP(c_Option_Ooption_OSome(_973368), _973414)]], _973366 = c_Option_Ooption_ONone(_973368)], (21520 ^ _777959) ^ [_1186932, _1186934, _1186936] : [class_Rings_Olinordered__ring__strict(_1186932), 21523 ^ _777959 : [(21524 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186932), c_Groups_Ozero__class_Ozero(_1186932)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186932), _1186934), _1186934)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186932), _1186936), _1186936)))), _1186934 = c_Groups_Ozero__class_Ozero(_1186932), _1186936 = c_Groups_Ozero__class_Ozero(_1186932)], (21534 ^ _777959) ^ [] : [21535 ^ _777959 : [(21538 ^ _777959) ^ [] : [-(_1186936 = c_Groups_Ozero__class_Ozero(_1186932))], (21536 ^ _777959) ^ [] : [-(_1186934 = c_Groups_Ozero__class_Ozero(_1186932))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1186932), c_Groups_Ozero__class_Ozero(_1186932)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186932), _1186934), _1186934)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186932), _1186936), _1186936)))))]]], (18338 ^ _777959) ^ [_1129756, _1129758] : [class_Orderings_Olinorder(_1129756), hBOOL(hAPP(c_Finite__Set_Ofinite(_1129756), _1129758)), -(_1129758 = c_Orderings_Obot__class_Obot(tc_fun(_1129756, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1129756), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1129756), 18351 ^ [_1129756, _1129758]), 18352 ^ [_1129756, _1129758])), hAPP(hAPP(c_Set_Oinsert(_1129756), 18351 ^ [_1129756, _1129758]), hAPP(hAPP(c_Set_Oinsert(_1129756), 18352 ^ [_1129756, _1129758]), c_Orderings_Obot__class_Obot(tc_fun(_1129756, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1129756), c_Big__Operators_Olattice_OSup__fin(_1129756, c_Orderings_Oord__class_Omax(_1129756), _1129758)), _1129758)))], (41336 ^ _777959) ^ [_1587653, _1587655, _1587657] : [hBOOL(hAPP(hAPP(c_member(_1587653), _1587655), hAPP(c_List_Oset(_1587653), c_List_Obutlast(_1587653, _1587657)))), -(hBOOL(hAPP(hAPP(c_member(_1587653), _1587655), hAPP(c_List_Oset(_1587653), _1587657))))], (50492 ^ _777959) ^ [_1802544, _1802546, _1802548, _1802550, _1802552] : [-(hAPP(hAPP(c_List_Omap(_1802544, _1802546), _1802548), c_List_Oreplicate(_1802544, _1802550, _1802552)) = c_List_Oreplicate(_1802546, _1802550, hAPP(_1802548, _1802552)))], (16105 ^ _777959) ^ [_1084727, _1084729, _1084731] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1084727), _1084729)), -(hAPP(c_Finite__Set_Ocard(_1084727), hAPP(hAPP(c_Set_Oinsert(_1084727), _1084731), _1084729)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1084727), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1084727, tc_HOL_Obool)), _1084729), hAPP(hAPP(c_Set_Oinsert(_1084727), _1084731), c_Orderings_Obot__class_Obot(tc_fun(_1084727, tc_HOL_Obool)))))))], (46670 ^ _777959) ^ [_1710749, _1710751, _1710753] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1710749, _1710749)), hAPP(hAPP(c_Product__Type_OPair(_1710749, _1710749), _1710751), _1710753)), c_List_Omeasures(_1710749, c_List_Olist_ONil(tc_fun(_1710749, tc_Nat_Onat)))))], (20147 ^ _777959) ^ [_1162471, _1162473] : [class_Rings_Olinordered__ring(_1162471), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1162471), c_Groups_Ozero__class_Ozero(_1162471)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1162471), _1162473), _1162473))))], (9260 ^ _777959) ^ [_937098, _937100, _937102, _937104, _937106] : [hAPP(_937098, _937100) = hAPP(c_Option_Ooption_OSome(_937102), _937104), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_937106, tc_Option_Ooption(_937102)), _937098), _937100), hAPP(c_Option_Ooption_OSome(_937102), _937104)) = _937098)], (34777 ^ _777959) ^ [_1432287, _1432289, _1432291] : [class_Rings_Olinordered__idom(_1432287), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1432287), c_Groups_Ozero__class_Ozero(_1432287)), hAPP(hAPP(c_Power_Opower__class_Opower(_1432287), _1432289), 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)))), _1432291)))))], (30697 ^ _777959) ^ [_1358017, _1358019] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1358017, _1358019) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1358017 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1358019), 30700 ^ [_1358017, _1358019]))], (48707 ^ _777959) ^ [_1760082, _1760084] : [-(c_Transitive__Closure_Ortrancl(_1760082, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1760082, _1760082), tc_HOL_Obool)), _1760084), c_Relation_OId(_1760082))) = c_Transitive__Closure_Ortrancl(_1760082, _1760084))], (24299 ^ _777959) ^ [_1239769, _1239771, _1239773, _1239775] : [c_Sum__Type_OPlus(_1239769, _1239771, _1239773, _1239775) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1239769, _1239771), tc_HOL_Obool)), 24302 ^ _777959 : [(24305 ^ _777959) ^ [] : [-(_1239775 = c_Orderings_Obot__class_Obot(tc_fun(_1239771, tc_HOL_Obool)))], (24303 ^ _777959) ^ [] : [-(_1239773 = c_Orderings_Obot__class_Obot(tc_fun(_1239769, tc_HOL_Obool)))]]], (48282 ^ _777959) ^ [] : [-(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))))], (51114 ^ _777959) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (3192 ^ _777959) ^ [_825910, _825912] : [_825912 = _825910, -(c_SetInterval_Oord__class_OatMost(_825912) = c_SetInterval_Oord__class_OatMost(_825910))], (35818 ^ _777959) ^ [_1457272, _1457274, _1457276] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1457272, tc_HOL_Obool), tc_fun(_1457272, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1457272, tc_HOL_Obool), tc_fun(_1457272, tc_HOL_Obool)), _1457274), _1457276)), c_Wellfounded_Ofinite__psubset(_1457272)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1457272, tc_HOL_Obool)), _1457274), _1457276)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1457272), _1457276))], (44955 ^ _777959) ^ [_1672370, _1672372, _1672374, _1672376] : [_1672372 = hAPP(hAPP(c_List_Oappend(_1672370), hAPP(c_List_Orev(_1672370), _1672376)), hAPP(hAPP(c_List_Olist_OCons(_1672370), _1672374), c_List_Olist_ONil(_1672370))), -(hAPP(c_List_Orev(_1672370), _1672372) = hAPP(hAPP(c_List_Olist_OCons(_1672370), _1672374), _1672376))], (37098 ^ _777959) ^ [_1483438, _1483440] : [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), _1483438), _1483440)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1483438), _1483440)))], (35854 ^ _777959) ^ [_1458343, _1458345, _1458347, _1458349, _1458351] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1458343, _1458345)), hAPP(hAPP(c_Product__Type_OPair(_1458343, _1458345), _1458349), _1458351)), _1458347)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1458343, _1458345, _1458347), _1458349), _1458351)))], (50064 ^ _777959) ^ [_1793096] : [class_HOL_Oequal(_1793096), -(c_fequal = c_HOL_Oequal__class_Oequal(_1793096))], (48108 ^ _777959) ^ [_1746725, _1746727] : [-(c_Random_Olog(_1746725, _1746727) = 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(_1746725, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1746727), _1746725)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1746725), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1746727), _1746725)))], (34529 ^ _777959) ^ [_1427884, _1427886] : [class_Fields_Olinordered__field__inverse__zero(_1427884), class_Int_Onumber__ring(_1427884), 34536 ^ _777959 : [(34543 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427884), c_Groups_Ozero__class_Ozero(_1427884)), _1427886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427884), c_Groups_Ozero__class_Ozero(_1427884)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1427884), _1427886), hAPP(c_Int_Onumber__class_Onumber__of(_1427884), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34537 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427884), c_Groups_Ozero__class_Ozero(_1427884)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1427884), _1427886), hAPP(c_Int_Onumber__class_Onumber__of(_1427884), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1427884), c_Groups_Ozero__class_Ozero(_1427884)), _1427886)))]]], (22685 ^ _777959) ^ [_1210726, _1210728] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210726)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210728), 22688 ^ _777959 : [(22691 ^ _777959) ^ [] : [-(_1210728 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22689 ^ _777959) ^ [] : [-(_1210726 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (17217 ^ _777959) ^ [_1107173, _1107175, _1107177] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1107173, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1107173, tc_HOL_Obool)), _1107175), _1107177)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1107173, tc_HOL_Obool)), _1107175), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1107173, tc_HOL_Obool), _1107177)))], (2444 ^ _777959) ^ [_814160, _814162, _814164, _814166, _814168, _814170] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(_814170, _814166, _814162) = c_Smallcheck_Ofull__small__class_Ofull__small(_814168, _814164, _814160)), _814170 = _814168, _814166 = _814164, _814162 = _814160], (45372 ^ _777959) ^ [_1682202, _1682204, _1682206] : [hBOOL(hAPP(c_List_Odistinct(_1682202), _1682204)), hBOOL(hAPP(hAPP(c_member(_1682202), _1682206), hAPP(c_List_Oset(_1682202), _1682204))), -(c_List_OtakeWhile(_1682202, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1682202), c_fNot), hAPP(hAPP(c_COMBC(_1682202, _1682202, tc_HOL_Obool), c_fequal), _1682206)), hAPP(c_List_Orev(_1682202), _1682204)) = hAPP(c_List_Orev(_1682202), hAPP(c_List_Otl(_1682202), c_List_OdropWhile(_1682202, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1682202), c_fNot), hAPP(hAPP(c_COMBC(_1682202, _1682202, tc_HOL_Obool), c_fequal), _1682206)), _1682204))))], (22325 ^ _777959) ^ [_1203125, _1203127] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1203125), hAPP(c_Nat_OSuc, _1203127)) = 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)), _1203127)), _1203125))], (6497 ^ _777959) ^ [_882913, _882915, _882917, _882919] : [class_Orderings_Opreorder(_882913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882913), _882915), _882917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882913), _882917), _882919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882913), _882915), _882919)))], (41916 ^ _777959) ^ [_1603639, _1603641] : [-(hAPP(hAPP(c_List_Otake(_1603639), _1603641), c_List_Olist_ONil(_1603639)) = c_List_Olist_ONil(_1603639))], (34475 ^ _777959) ^ [] : [-(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))))))], (29693 ^ _777959) ^ [_1338087, _1338089, _1338091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338087, tc_HOL_Obool)), _1338089), _1338091)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1338087, tc_HOL_Obool)), _1338089), hAPP(c_Set_OPow(_1338087), _1338091))))], (46966 ^ _777959) ^ [_1719730, _1719732, _1719734] : [c_Wellfounded_Owf(_1719730, _1719732), -(c_Wellfounded_Owf(tc_List_Olist(_1719730), hAPP(c_List_Olexn(_1719730, _1719732), _1719734)))], (28672 ^ _777959) ^ [_1318091, _1318093, _1318095, _1318097] : [class_Orderings_Oorder(_1318091), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1318091, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1318091, _1318093), _1318095)), c_SetInterval_Oord__class_OatLeastAtMost(_1318091, _1318095, _1318097)) = c_Orderings_Obot__class_Obot(tc_fun(_1318091, tc_HOL_Obool)))], (30229 ^ _777959) ^ [_1349753, _1349755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1349753), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1349755), _1349753)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1349753, _1349755) = _1349753)], (17411 ^ _777959) ^ [_1110759, _1110761, _1110763] : [class_Orderings_Olinorder(_1110759), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110759), _1110761)), -(_1110763 = c_Orderings_Obot__class_Obot(tc_fun(_1110759, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1110759, tc_HOL_Obool)), _1110763), _1110761)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1110759), c_Big__Operators_Olinorder__class_OMin(_1110759, _1110763)), c_Big__Operators_Olinorder__class_OMin(_1110759, _1110761)) = c_Big__Operators_Olinorder__class_OMin(_1110759, _1110761))], (40769 ^ _777959) ^ [_1570439, _1570441, _1570443, _1570445, _1570447, _1570449, _1570451] : [-(hBOOL(hAPP(hAPP(c_member(_1570439), _1570441), hAPP(c_List_Oset(_1570439), hAPP(hAPP(c_List_Otake(_1570439), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1570443)), _1570445)), _1570447))))), -(c_Map_Omap__upds(_1570439, _1570443, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1570439, tc_Option_Ooption(_1570443)), _1570449), _1570441), hAPP(c_Option_Ooption_OSome(_1570443), _1570451)), _1570447, _1570445) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1570439, tc_Option_Ooption(_1570443)), c_Map_Omap__upds(_1570439, _1570443, _1570449, _1570447, _1570445)), _1570441), hAPP(c_Option_Ooption_OSome(_1570443), _1570451)))], (27692 ^ _777959) ^ [_1301087, _1301089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301089)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1301087)), hAPP(c_Int_Onat, _1301089)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1301087), _1301089)))], (16551 ^ _777959) ^ [_1095182, _1095184] : [class_Orderings_Olinorder(_1095182), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095182), _1095184), _1095184) = _1095184)], (35247 ^ _777959) ^ [_1440571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1440571)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1440571) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (47412 ^ _777959) ^ [_1730844, _1730846, _1730848, _1730850] : [hBOOL(hAPP(c_Predicate_ODomainP(_1730844, _1730846, _1730848), _1730850)), -(hBOOL(hAPP(hAPP(_1730848, _1730850), 47415 ^ [_1730844, _1730846, _1730848, _1730850])))], (49897 ^ _777959) ^ [_1789816, _1789818, _1789820, _1789822] : [-(c_List_Olist__ex1(_1789816, _1789818, hAPP(hAPP(c_List_Olist_OCons(_1789816), _1789820), _1789822))), 49900 ^ _777959 : [(49903 ^ _777959) ^ [] : [c_List_Olist__all(_1789816, hAPP(hAPP(c_COMBS(_1789816, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1789816), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1789816), c_fNot), _1789818))), hAPP(c_fequal, _1789820)), _1789822)], (49901 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1789818, _1789820)))]], 49904 ^ _777959 : [(49907 ^ _777959) ^ [] : [c_List_Olist__ex1(_1789816, _1789818, _1789822)], (49905 ^ _777959) ^ [] : [hBOOL(hAPP(_1789818, _1789820))]]], (13895 ^ _777959) ^ [_1035125, _1035127, _1035129, _1035131, _1035133] : [hBOOL(hAPP(hAPP(c_member(_1035125), _1035127), _1035129)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1035131, tc_HOL_Obool)), hAPP(_1035133, _1035127)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1035125, tc_fun(_1035131, tc_HOL_Obool)), _1035129), _1035133)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1035125, tc_fun(_1035131, tc_HOL_Obool)), _1035129), _1035133))], (28652 ^ _777959) ^ [_1317699, _1317701] : [hAPP(_1317699, 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), _1317699), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1317701)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1317699), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1317701)))], (19596 ^ _777959) ^ [_1152710] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152710), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51414 ^ _777959) ^ [_1814452, _1814454] : [hBOOL(hAPP(hAPP(c_fconj, _1814452), _1814454)), -(hBOOL(_1814454))], (30395 ^ _777959) ^ [_1352638, _1352640, _1352642, _1352644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352640)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1352640), _1352642)), -(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), _1352642), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1352644, _1352638))), _1352640))))], (8132 ^ _777959) ^ [_917638, _917640, _917642] : [hBOOL(hAPP(hAPP(c_member(_917638), _917640), _917642)), -(hAPP(hAPP(c_Set_Oinsert(_917638), _917640), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917638, tc_HOL_Obool)), _917642), hAPP(hAPP(c_Set_Oinsert(_917638), _917640), c_Orderings_Obot__class_Obot(tc_fun(_917638, tc_HOL_Obool))))) = _917642)], (15858 ^ _777959) ^ [_1079584, _1079586, _1079588, _1079590, _1079592, _1079594] : [class_Rings_Oordered__ring(_1079584), 15861 ^ _777959 : [(15868 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079584), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079584), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1079584), _1079586), _1079592)), _1079588)), _1079590)), _1079594)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079584), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079584), _1079586), _1079588)), _1079590)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079584), _1079592), _1079588)), _1079594))))], (15862 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079584), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079584), _1079586), _1079588)), _1079590)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079584), _1079592), _1079588)), _1079594))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1079584), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1079584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079584), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1079584), _1079586), _1079592)), _1079588)), _1079590)), _1079594)))]]], (6719 ^ _777959) ^ [_887065, _887067, _887069] : [_887065 = c_Orderings_Obot__class_Obot(tc_fun(_887067, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_887067), _887069), _887065))], (38824 ^ _777959) ^ [_1523626, _1523628, _1523630, _1523632, _1523634] : [-(hAPP(c_Set_Ovimage(_1523626, _1523628, _1523630), hAPP(hAPP(c_Set_Oinsert(_1523628), _1523632), _1523634)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1523626, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1523626, _1523628, _1523630), hAPP(hAPP(c_Set_Oinsert(_1523628), _1523632), c_Orderings_Obot__class_Obot(tc_fun(_1523628, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1523626, _1523628, _1523630), _1523634)))], (41611 ^ _777959) ^ [_1594016, _1594018, _1594020, _1594022] : 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hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072188), _1072190))], (12654 ^ _777959) ^ [_1007623, _1007625, _1007627] : [_1007625 = _1007627, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1007623, tc_HOL_Obool)), _1007625) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1007623, tc_HOL_Obool)), _1007627))], (25956 ^ _777959) ^ [_1270037, _1270039] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1270037, _1270039)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1270039), hAPP(c_Nat_OSuc, _1270037)))], (7432 ^ _777959) ^ [_902625, _902627, _902629] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902625), _902629)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_902625), hAPP(hAPP(c_Set_Oinsert(_902625), _902627), _902629))))], (15584 ^ _777959) ^ [_1074087, _1074089, _1074091, _1074093, _1074095] : [class_Rings_Osemiring__0(_1074087), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074087), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1074089, _1074087), _1074091), _1074093)), _1074095) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1074089, _1074087), hAPP(hAPP(c_COMBC(_1074089, _1074087, _1074087), hAPP(hAPP(c_COMBB(_1074087, tc_fun(_1074087, _1074087), _1074089), c_Groups_Otimes__class_Otimes(_1074087)), _1074091)), _1074095)), _1074093))], (42194 ^ _777959) ^ [_1609568, _1609570, _1609572, _1609574, _1609576, _1609578] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609568, _1609570)), hAPP(hAPP(c_Product__Type_OPair(_1609568, _1609570), _1609572), _1609574)), hAPP(hAPP(c_Product__Type_OSigma(_1609568, _1609570), _1609576), _1609578))), -(hBOOL(hAPP(hAPP(c_member(_1609570), _1609574), hAPP(_1609578, _1609572))))], (31292 ^ _777959) ^ [_1369024, _1369026] : [class_Rings_Olinordered__idom(_1369024), -(hAPP(c_Groups_Oabs__class_Oabs(_1369024), _1369026) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369024), _1369026), c_Groups_Osgn__class_Osgn(_1369024, _1369026)))], (47342 ^ _777959) ^ [_1728607, _1728609] : [-(hAPP(c_Relation_ODomain(_1728607, _1728609), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1728607, _1728609), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1728607, tc_HOL_Obool)))], (46056 ^ _777959) ^ [_1696860, _1696862, _1696864] : [class_Enum_Oenum(_1696860), class_Enum_Oenum(_1696862), class_HOL_Oequal(_1696862), 46067 ^ _777959 : [(46074 ^ _777959) ^ [] : [c_Enum_Oex__n__lists(_1696860, hAPP(hAPP(c_COMBB(tc_fun(_1696862, _1696860), tc_HOL_Obool, tc_List_Olist(_1696860)), _1696864), hAPP(hAPP(c_COMBB(tc_fun(_1696862, tc_Option_Ooption(_1696860)), tc_fun(_1696862, _1696860), tc_List_Olist(_1696860)), c_Fun_Ocomp(tc_Option_Ooption(_1696860), _1696860, _1696862, c_Option_Othe(_1696860))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1696862, _1696860)), tc_fun(_1696862, tc_Option_Ooption(_1696860)), tc_List_Olist(_1696860)), c_Map_Omap__of(_1696862, _1696860)), hAPP(c_List_Ozip(_1696862, _1696860), c_Enum_Oenum__class_Oenum(_1696862))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696862)), c_Enum_Oenum__class_Oenum(_1696862))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1696862, _1696860)), _1696864)))], (46068 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1696862, _1696860)), _1696864)), -(c_Enum_Oex__n__lists(_1696860, hAPP(hAPP(c_COMBB(tc_fun(_1696862, _1696860), tc_HOL_Obool, tc_List_Olist(_1696860)), _1696864), hAPP(hAPP(c_COMBB(tc_fun(_1696862, tc_Option_Ooption(_1696860)), tc_fun(_1696862, _1696860), tc_List_Olist(_1696860)), c_Fun_Ocomp(tc_Option_Ooption(_1696860), _1696860, _1696862, c_Option_Othe(_1696860))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1696862, _1696860)), tc_fun(_1696862, tc_Option_Ooption(_1696860)), tc_List_Olist(_1696860)), c_Map_Omap__of(_1696862, _1696860)), hAPP(c_List_Ozip(_1696862, _1696860), c_Enum_Oenum__class_Oenum(_1696862))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696862)), c_Enum_Oenum__class_Oenum(_1696862))))]]], (24235 ^ _777959) ^ [_1238652, _1238654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1238652), _1238654)), -(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)), _1238652)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238654))))], (37339 ^ _777959) ^ [_1490671, _1490673, _1490675] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1490671, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490671), _1490673), _1490675), -(_1490673 = c_Orderings_Obot__class_Obot(tc_fun(_1490671, tc_HOL_Obool)))], (40912 ^ _777959) ^ [_1574489, _1574491, _1574493, _1574495] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1574489), tc_List_Olist(_1574489))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1574489), tc_List_Olist(_1574489)), _1574491), _1574493)), c_List_Olex(_1574489, _1574495))), 40915 ^ _777959 : [(40918 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1574489)), _1574491) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1574489)), _1574493))], (40916 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1574489), tc_List_Olist(_1574489))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1574489), tc_List_Olist(_1574489)), _1574491), _1574493)), c_List_Olexord(_1574489, _1574495))))]]], (51012 ^ _777959) ^ [] : [-(class_HOL_Oequal(tc_Int_Oint))], (38808 ^ _777959) ^ [_1523185, _1523187, _1523189, _1523191] : [-(hAPP(c_Set_Ovimage(_1523185, _1523187, _1523189), _1523191) = hAPP(c_Set_OCollect(_1523185), hAPP(hAPP(c_COMBC(_1523185, tc_fun(_1523187, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1523187, tc_fun(tc_fun(_1523187, tc_HOL_Obool), tc_HOL_Obool), _1523185), c_member(_1523187)), _1523189)), _1523191)))], (24047 ^ _777959) ^ [_1235170, _1235172, _1235174] : [-(hBOOL(hAPP(_1235170, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1235172), _1235174))))), 24050 ^ _777959 : [(24053 ^ _777959) ^ [] : [hBOOL(hAPP(_1235170, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1235172)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1235174))))], (24051 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1235174), _1235172)))]], 24054 ^ _777959 : [(24057 ^ _777959) ^ [] : [hBOOL(hAPP(_1235170, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (24055 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1235172), _1235174)))]]], (46377 ^ _777959) ^ [_1704288, _1704290, _1704292, _1704294, _1704296, _1704298, _1704300] : [c_List_Olist__all2(_1704288, _1704296, hAPP(hAPP(c_COMBC(_1704288, tc_fun(_1704296, _1704290), tc_fun(_1704296, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1704290, tc_HOL_Obool), tc_fun(tc_fun(_1704296, _1704290), tc_fun(_1704296, tc_HOL_Obool)), _1704288), c_COMBB(_1704290, tc_HOL_Obool, _1704296)), _1704292)), _1704298), _1704294, _1704300), -(c_List_Olist__all2(_1704288, _1704290, _1704292, _1704294, hAPP(hAPP(c_List_Omap(_1704296, _1704290), _1704298), _1704300)))], (15934 ^ _777959) ^ [_1081638, _1081640, _1081642, _1081644, _1081646] : [-(c_Map_Omap__comp(_1081638, _1081640, _1081642, _1081644, hAPP(c_COMBK(tc_Option_Ooption(_1081638), _1081642), c_Option_Ooption_ONone(_1081638)), _1081646) = c_Option_Ooption_ONone(_1081640))], (29946 ^ _777959) ^ [_1344001, _1344003, _1344005] : [class_Divides_Osemiring__div(_1344001), -(c_Divides_Odiv__class_Omod(_1344001, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344001), _1344003), _1344005), _1344003) = c_Divides_Odiv__class_Omod(_1344001, _1344005, _1344003))], (28151 ^ _777959) ^ [_1308966, _1308968] : 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_1254597))))), -(_1254597 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1254599), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1254599), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1254597))))], (4310 ^ _777959) ^ [_843211, _843213] : [_843213 = _843211, -(c_Divides_Odiv__class_Odiv(_843213) = c_Divides_Odiv__class_Odiv(_843211))], (19106 ^ _777959) ^ [_1145203] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1145203), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25068 ^ _777959) ^ [_1252763, _1252765, _1252767, _1252769, _1252771] : [class_Groups_Ocomm__monoid__add(_1252763), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1252765), _1252767)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1252767), _1252769)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1252763), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1252763), _1252771), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1252765), _1252767))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1252763), _1252771), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1252767), _1252769))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1252763), _1252771), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1252765), _1252769)))], (7438 ^ _777959) ^ [_902738, _902740, _902742] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902738), _902740)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902738, tc_HOL_Obool)), _902742), _902740)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_902738), _902742)))], (23597 ^ _777959) ^ [_1226914, _1226916, _1226918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1226914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1226914), _1226916)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1226914), _1226918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1226916), _1226918)))], (41519 ^ _777959) ^ [_1591905, _1591907, _1591909, _1591911, _1591913, _1591915] : [class_Orderings_Olinorder(_1591905), 41522 ^ _777959 : [(41529 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1591905), hAPP(_1591907, _1591909)), hAPP(_1591907, _1591911)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1591913, _1591905, _1591907), _1591909), hAPP(hAPP(c_List_Olist_OCons(_1591913), _1591911), _1591915)) = hAPP(hAPP(c_List_Olist_OCons(_1591913), _1591911), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1591913, _1591905, _1591907), _1591909), _1591915)))], (41523 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1591905), hAPP(_1591907, _1591909)), hAPP(_1591907, _1591911))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1591913, _1591905, _1591907), _1591909), hAPP(hAPP(c_List_Olist_OCons(_1591913), _1591911), _1591915)) = hAPP(hAPP(c_List_Olist_OCons(_1591913), _1591909), hAPP(hAPP(c_List_Olist_OCons(_1591913), _1591911), _1591915)))]]], (40443 ^ _777959) ^ [_1562970, _1562972, _1562974, _1562976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1562970), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562972)), _1562974))), -(hAPP(hAPP(c_List_Onth(_1562972), hAPP(hAPP(c_List_Olist__update(_1562972, _1562974), _1562970), _1562976)), _1562970) = _1562976)], (36660 ^ _777959) ^ [_1473401, _1473403] : [_1473401 = _1473403, -(hAPP(c_Int_ORep__Integ, _1473401) = hAPP(c_Int_ORep__Integ, _1473403))], (44811 ^ _777959) ^ [_1669358] : [-(hAPP(c_List_Orev(_1669358), c_List_Olist_ONil(_1669358)) = c_List_Olist_ONil(_1669358))], (43093 ^ _777959) ^ [_1632550, _1632552, _1632554, _1632556, _1632558, _1632560, _1632562, _1632564] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632550, _1632550)), hAPP(hAPP(c_Product__Type_OPair(_1632550, _1632550), _1632552), _1632554)), _1632556)), _1632558 = hAPP(hAPP(c_List_Oappend(_1632550), _1632560), hAPP(hAPP(c_List_Olist_OCons(_1632550), _1632552), _1632562)), _1632564 = hAPP(hAPP(c_List_Oappend(_1632550), _1632560), hAPP(hAPP(c_List_Olist_OCons(_1632550), _1632554), _1632562)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632550), tc_List_Olist(_1632550))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632550), tc_List_Olist(_1632550)), _1632558), _1632564)), c_List_Olistrel1(_1632550, _1632556))))], (20701 ^ _777959) ^ [_1172416, _1172418] : [class_Groups_Olinordered__ab__group__add(_1172416), 20704 ^ _777959 : [(20711 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172416), c_Groups_Ozero__class_Ozero(_1172416)), _1172418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172416), hAPP(c_Groups_Ouminus__class_Ouminus(_1172416), _1172418)), _1172418)))], (20705 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172416), hAPP(c_Groups_Ouminus__class_Ouminus(_1172416), _1172418)), _1172418)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1172416), c_Groups_Ozero__class_Ozero(_1172416)), _1172418)))]]], (8076 ^ _777959) ^ [_916129, _916131, _916133, _916135] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916129, tc_HOL_Obool)), _916131), hAPP(hAPP(c_Set_Oinsert(_916129), _916133), _916135)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916129, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916129, tc_HOL_Obool)), _916131), hAPP(hAPP(c_Set_Oinsert(_916129), _916133), c_Orderings_Obot__class_Obot(tc_fun(_916129, tc_HOL_Obool))))), _916135))], (35097 ^ _777959) ^ [_1438266] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1438266), c_Int_OMin) = c_Int_Osucc(_1438266))], (42843 ^ _777959) ^ [_1626912, _1626914, _1626916, _1626918] : [-(hAPP(c_List_OremoveAll(_1626912, _1626914), hAPP(hAPP(c_List_Oappend(_1626912), _1626916), _1626918)) = hAPP(hAPP(c_List_Oappend(_1626912), hAPP(c_List_OremoveAll(_1626912, _1626914), _1626916)), hAPP(c_List_OremoveAll(_1626912, _1626914), _1626918)))], (13215 ^ _777959) ^ [_1019148, _1019150, _1019152] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1019148), _1019150)), hBOOL(hAPP(hAPP(c_member(_1019148), _1019152), _1019150)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1019148), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1019148, tc_HOL_Obool)), _1019150), hAPP(hAPP(c_Set_Oinsert(_1019148), _1019152), c_Orderings_Obot__class_Obot(tc_fun(_1019148, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1019148), _1019150))))], (47768 ^ _777959) ^ [_1738850, _1738852, _1738854, _1738856, _1738858] : [-(hAPP(c_List_Ofilter(_1738850, _1738852), _1738854) = hAPP(hAPP(c_List_Olist_OCons(_1738850), _1738856), _1738858)), 47769 ^ _777959 : [(47770 ^ _777959) ^ [_1738978, _1738980] : [_1738854 = hAPP(hAPP(c_List_Oappend(_1738850), _1738980), hAPP(hAPP(c_List_Olist_OCons(_1738850), _1738856), _1738978)), 47776 ^ _777959 : [(47779 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1738852, 47775 ^ [_1738850, _1738852, _1738854, _1738856, _1738858, _1738978, _1738980])))], (47777 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1738850), 47775 ^ [_1738850, _1738852, _1738854, _1738856, _1738858, _1738978, _1738980]), hAPP(c_List_Oset(_1738850), _1738980))))]], hBOOL(hAPP(_1738852, _1738856)), _1738858 = hAPP(c_List_Ofilter(_1738850, _1738852), _1738978)]]], (9286 ^ _777959) ^ [_937609, _937611, _937613, _937615, _937617, _937619] : [-(hBOOL(hAPP(hAPP(c_member(_937609), _937611), _937613))), -(hAPP(c_Set_Oimage(_937609, tc_Option_Ooption(_937615), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_937609, tc_Option_Ooption(_937615)), _937617), _937611), hAPP(c_Option_Ooption_OSome(_937615), _937619))), _937613) = hAPP(c_Set_Oimage(_937609, tc_Option_Ooption(_937615), _937617), _937613))], (41501 ^ _777959) ^ [_1591515, _1591517, _1591519, _1591521, _1591523, _1591525] : [-(c_List_Ofoldr(_1591515, _1591517, _1591519, hAPP(hAPP(c_List_Olist_OCons(_1591515), _1591521), _1591523), _1591525) = hAPP(hAPP(_1591519, _1591521), c_List_Ofoldr(_1591515, _1591517, _1591519, _1591523, _1591525)))], (16823 ^ _777959) ^ [_1100109, _1100111, _1100113] : [class_Orderings_Olinorder(_1100109), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100109), _1100111), _1100113)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100109), _1100113), _1100111) = _1100111)], (22996 ^ _777959) ^ [_1216464, _1216466, _1216468] : [class_Rings_Oring__1(_1216464), hBOOL(hAPP(hAPP(c_member(_1216464), _1216466), c_Int_Oring__1__class_OInts(_1216464))), hBOOL(hAPP(hAPP(c_member(_1216464), _1216468), c_Int_Oring__1__class_OInts(_1216464))), -(hBOOL(hAPP(hAPP(c_member(_1216464), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1216464), _1216466), _1216468)), c_Int_Oring__1__class_OInts(_1216464))))], (2524 ^ _777959) ^ [_815368, _815370] : [_815370 = _815368, -(c_Divides_Oadjust(_815370) = c_Divides_Oadjust(_815368))], (25458 ^ _777959) ^ [_1260636, _1260638] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1260636)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1260638)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260636), _1260638)))], (41713 ^ _777959) ^ [_1597737, _1597739, _1597741, _1597743, _1597745, _1597747, _1597749, _1597751, _1597753] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597737, _1597739)), hAPP(hAPP(c_Product__Type_OPair(_1597737, _1597739), _1597741), _1597743)), _1597745)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597747, _1597749)), hAPP(hAPP(c_Product__Type_OPair(_1597747, _1597749), hAPP(_1597751, _1597741)), hAPP(_1597753, _1597743))), hAPP(c_Set_Oimage(tc_prod(_1597737, _1597739), tc_prod(_1597747, _1597749), c_Product__Type_Omap__pair(_1597737, _1597747, _1597739, _1597749, _1597751, _1597753)), _1597745))))], (41491 ^ _777959) ^ [_1591340, _1591342, _1591344, _1591346, _1591348] : [-(hAPP(hAPP(c_List_Olist_OCons(_1591340), _1591342), _1591344) = hAPP(hAPP(c_List_Olist_OCons(_1591340), _1591346), _1591348)), _1591342 = _1591346, _1591344 = _1591348], (43149 ^ _777959) ^ [_1634276, _1634278, _1634280, _1634282] : [-(c_List_Osublist(_1634276, hAPP(hAPP(c_List_Olist_OCons(_1634276), _1634278), _1634280), _1634282) = hAPP(hAPP(c_List_Oappend(_1634276), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1634276)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1634282)), hAPP(hAPP(c_List_Olist_OCons(_1634276), _1634278), c_List_Olist_ONil(_1634276))), c_List_Olist_ONil(_1634276))), c_List_Osublist(_1634276, _1634280, 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)), _1634282)))))], (47350 ^ _777959) ^ [_1728802, _1728804, _1728806, _1728808] : [-(hAPP(c_Relation_ODomain(_1728802, _1728804), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1728802, _1728804), tc_HOL_Obool)), _1728806), _1728808)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1728802, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1728802, _1728804), _1728806)), hAPP(c_Relation_ODomain(_1728802, _1728804), _1728808)))], (34507 ^ _777959) ^ [_1427464, _1427466] : [class_Rings_Olinordered__idom(_1427464), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427464), hAPP(c_Groups_Oabs__class_Oabs(_1427464), _1427466)), 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(_1427464), _1427466), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (16687 ^ _777959) ^ [_1097739, _1097741, _1097743, _1097745] : [class_Orderings_Olinorder(_1097739), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097739), _1097741), _1097743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097739), _1097741), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1097739), _1097743), _1097745))))], (27642 ^ _777959) ^ [_1300138, _1300140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300140)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1300138)), hAPP(c_Int_Onat, _1300140)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1300138), _1300140)))], (33609 ^ _777959) ^ [_1410951, _1410953] : [class_Groups_Omonoid__mult(_1410951), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1410951), _1410953), 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(_1410951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1410951), _1410953), _1410953)), _1410953))], (27836 ^ _777959) ^ [_1303789, _1303791] : [c_Nat__Transfer_Onat__set(_1303789), c_Nat__Transfer_Onat__set(_1303791), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1303789), _1303791) = 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), _1303789)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1303791))))], (27888 ^ _777959) ^ [_1304573, _1304575] : [c_Nat__Transfer_Onat__set(_1304573), c_Nat__Transfer_Onat__set(_1304575), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1304573), _1304575)))], (7630 ^ _777959) ^ [_906626] : [c_Com_Ocom_OSKIP = hAPP(c_Com_Ocom_OBODY, _906626)], (49911 ^ _777959) ^ [_1790124, _1790126, _1790128] : [-(c_Product__Type_Ointernal__split(_1790124, _1790126, _1790128) = c_Product__Type_Oprod_Oprod__case(_1790124, _1790126, _1790128))], (34249 ^ _777959) ^ [_1422754, _1422756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1422754)), c_Int_OBit0(_1422756))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422754), _1422756)))], (17507 ^ _777959) ^ [_1112531, _1112533, _1112535] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1112531, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1112531, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1112531, tc_HOL_Obool), _1112533)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1112531, tc_HOL_Obool), _1112535))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1112531, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_1112531, tc_HOL_Obool), tc_HOL_Obool)), _1112533), _1112535)))))], (29833 ^ _777959) ^ [_1341909, _1341911, _1341913, _1341915, _1341917] : [class_Groups_Ocomm__monoid__add(_1341909), class_Groups_Ocomm__monoid__mult(_1341909), _1341911 = _1341913, c_Nat__Transfer_Onat__set(_1341913), 29851 ^ _777959 : [(29854 ^ _777959) ^ [] : [hAPP(_1341915, 29850 ^ [_1341909, _1341911, _1341913, _1341915, _1341917]) = hAPP(_1341917, 29850 ^ [_1341909, _1341911, _1341913, _1341915, _1341917])], (29852 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 29850 ^ [_1341909, _1341911, _1341913, _1341915, _1341917])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1341909), _1341915), _1341911) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1341909), _1341917), _1341913))], (13749 ^ _777959) ^ [_1032156, _1032158] : [-(hAPP(c_Set_OCollect(_1032156), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1032156), c_fNot), _1032158)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1032156, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1032156), _1032158)))], (48100 ^ _777959) ^ [_1746590, _1746592] : [48101 ^ _777959 : [(48104 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1746592), _1746590))], (48102 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1746590), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))]], -(c_Random_Olog(_1746590, _1746592) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (7154 ^ _777959) ^ [_897511, _897513, _897515, _897517] : [class_Lattices_Osemilattice__sup(_897511), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897511), _897513), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897511), _897515), _897517)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897511), _897515), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897511), _897513), _897517)))], (10272 ^ _777959) ^ [_958654, _958656, _958658, _958660] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958654, tc_HOL_Obool)), _958656), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958654, tc_HOL_Obool)), _958658), _958660)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958654, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958654, tc_HOL_Obool)), _958656), _958658)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958654, tc_HOL_Obool)), _958656), _958660)))], (8086 ^ _777959) ^ [_916469, _916471, _916473, _916475] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_916469), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916469, tc_HOL_Obool)), _916471), _916475))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_916469), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916469, tc_HOL_Obool)), _916471), hAPP(hAPP(c_Set_Oinsert(_916469), _916473), _916475)))))], (15108 ^ _777959) ^ [_1065371, _1065373, _1065375, _1065377] : [class_Rings_Ocomm__semiring__1(_1065371), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065371), _1065373), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065371), _1065375), _1065377)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065371), _1065373), _1065375)), _1065377))], (13375 ^ _777959) ^ [_1022753, _1022755] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1022753), _1022755)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1022753, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1022753, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1022753, tc_HOL_Obool), tc_fun(_1022753, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1022753, tc_HOL_Obool))), _1022755)))))], (33791 ^ _777959) ^ [_1414001, _1414003] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1414001))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414003)) = 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)))), _1414001), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414003)))], (25878 ^ _777959) ^ [_1268415, _1268417, _1268419, _1268421] : [class_Fields_Ofield(_1268415), -(_1268417 = c_Groups_Ozero__class_Ozero(_1268415)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1268415), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268415), _1268419), _1268417)), _1268421) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268415), hAPP(hAPP(c_Power_Opower__class_Opower(_1268415), _1268419), _1268421)), hAPP(hAPP(c_Power_Opower__class_Opower(_1268415), _1268417), _1268421)))], (22138 ^ _777959) ^ [_1199164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1199164)), -(_1199164 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1199164), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (5320 ^ _777959) ^ [_859376, _859378, _859380, _859382] : [-(c_List_Oconcat(_859382, _859378) = c_List_Oconcat(_859380, _859376)), _859382 = _859380, _859378 = _859376], (6929 ^ _777959) ^ [_891361, _891363, _891365, _891367, _891369] : [hAPP(_891361, _891363) = hAPP(c_Option_Ooption_OSome(_891365), _891367), -(hBOOL(hAPP(hAPP(c_member(_891369), _891363), c_Map_Odom(_891369, _891365, _891361))))], (48320 ^ _777959) ^ [_1750410, _1750412] : [hAPP(c_Code__Numeral_Onat__of, _1750410) = hAPP(c_Code__Numeral_Onat__of, _1750412), -(_1750410 = _1750412)], (31869 ^ _777959) ^ [_1379873, _1379875, _1379877, _1379879, _1379881, _1379883] : [c_Com_Ocom_OLocal(_1379873, _1379875, _1379877) = c_Com_Ocom_OLocal(_1379879, _1379881, _1379883), 31872 ^ _777959 : [(31877 ^ _777959) ^ [] : [-(_1379877 = _1379883)], (31875 ^ _777959) ^ [] : [-(_1379875 = _1379881)], (31873 ^ _777959) ^ [] : [-(_1379873 = _1379879)]]], (23475 ^ _777959) ^ [_1224847, _1224849] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1224847), _1224849) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224847), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1224849)))], (26894 ^ _777959) ^ [_1287240, _1287242, _1287244, _1287246, _1287248] : [class_Fields_Ofield(_1287240), -(_1287242 = c_Groups_Ozero__class_Ozero(_1287240)), -(_1287244 = c_Groups_Ozero__class_Ozero(_1287240)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1287240), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287240), _1287246), _1287242)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287240), _1287248), _1287244)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287240), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1287240), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287240), _1287246), _1287244)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287240), _1287248), _1287242))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287240), _1287242), _1287244)))], (51008 ^ _777959) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (41976 ^ _777959) ^ [_1605095, _1605097, _1605099, _1605101, _1605103] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1605095, _1605097), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605095, tc_HOL_Obool)), _1605099), _1605101)), hAPP(c_COMBK(tc_fun(_1605097, tc_HOL_Obool), _1605095), _1605103)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1605095, _1605097), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1605095, _1605097), _1605099), hAPP(c_COMBK(tc_fun(_1605097, tc_HOL_Obool), _1605095), _1605103))), hAPP(hAPP(c_Product__Type_OSigma(_1605095, _1605097), _1605101), hAPP(c_COMBK(tc_fun(_1605097, tc_HOL_Obool), _1605095), _1605103))))], (43632 ^ _777959) ^ [_1645326, _1645328, _1645330, _1645332, _1645334, _1645336, _1645338] : [-(hAPP(c_List_Ofoldl(_1645326, _1645328, _1645330, _1645332), hAPP(hAPP(c_List_Omap(_1645334, _1645328), _1645336), _1645338)) = hAPP(c_List_Ofoldl(_1645326, _1645334, hAPP(hAPP(c_COMBC(_1645326, tc_fun(_1645334, _1645328), tc_fun(_1645334, _1645326)), hAPP(hAPP(c_COMBB(tc_fun(_1645328, _1645326), tc_fun(tc_fun(_1645334, _1645328), tc_fun(_1645334, _1645326)), _1645326), c_COMBB(_1645328, _1645326, _1645334)), _1645330)), _1645336), _1645332), _1645338))], (24546 ^ _777959) ^ [_1244055, _1244057] : [class_Divides_Osemiring__div(_1244055), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1244055), _1244057), c_Groups_Oone__class_Oone(_1244055)) = _1244057)], (36546 ^ _777959) ^ [_1471165, _1471167, _1471169, _1471171, _1471173] : [-(hAPP(c_Product__Type_Osnd(_1471165, _1471167), hAPP(c_Product__Type_Oapsnd(_1471169, _1471167, _1471165, _1471171), _1471173)) = hAPP(_1471171, hAPP(c_Product__Type_Osnd(_1471165, _1471169), _1471173)))], (51420 ^ _777959) ^ [_1814539, _1814541] : [hBOOL(_1814539), -(hBOOL(hAPP(hAPP(c_fdisj, _1814539), _1814541)))], (50482 ^ _777959) ^ [_1802405, _1802407, _1802409] : [-(c_List_Osplice(_1802405, hAPP(hAPP(c_List_Olist_OCons(_1802405), _1802407), _1802409), c_List_Olist_ONil(_1802405)) = hAPP(hAPP(c_List_Olist_OCons(_1802405), _1802407), _1802409))], (29713 ^ _777959) ^ [_1338551, _1338553, _1338555, _1338557] : [-(hAPP(c_Set_OPow(_1338551), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1338553, tc_fun(_1338551, tc_HOL_Obool)), _1338555), _1338557)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1338553, tc_fun(tc_fun(_1338551, tc_HOL_Obool), tc_HOL_Obool)), _1338555), hAPP(hAPP(c_COMBB(tc_fun(_1338551, tc_HOL_Obool), tc_fun(tc_fun(_1338551, tc_HOL_Obool), tc_HOL_Obool), _1338553), c_Set_OPow(_1338551)), _1338557)))], (12969 ^ _777959) ^ [_1013962, _1013964, _1013966] : [class_Complete__Lattice_Ocomplete__lattice(_1013962), class_Orderings_Olinorder(_1013962), 12976 ^ _777959 : [(12986 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1013962), _1013964), c_Complete__Lattice_OSup__class_OSup(_1013962, _1013966)))), 12987 ^ _777959 : [(12988 ^ _777959) ^ [_1014268] : [hBOOL(hAPP(hAPP(c_member(_1013962), _1014268), _1013966)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1013962), _1013964), _1014268))]]], (12977 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1013962), _1013964), c_Complete__Lattice_OSup__class_OSup(_1013962, _1013966))), 12981 ^ _777959 : [(12984 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1013962), _1013964), 12980 ^ [_1013962, _1013964, _1013966])))], (12982 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1013962), 12980 ^ [_1013962, _1013964, _1013966]), _1013966)))]]]]], (30026 ^ _777959) ^ [_1345775, _1345777, _1345779, _1345781] : [class_Divides_Osemiring__div(_1345775), -(c_Divides_Odiv__class_Omod(_1345775, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345775), c_Divides_Odiv__class_Omod(_1345775, _1345777, _1345779)), _1345781), _1345779) = c_Divides_Odiv__class_Omod(_1345775, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345775), _1345777), _1345781), _1345779))], (25708 ^ _777959) ^ [_1265523, _1265525, _1265527, _1265529] : [class_Rings_Odivision__ring(_1265523), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265523), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265523), _1265525), _1265527)), _1265529) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1265523), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265523), _1265525), _1265529)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265523), _1265527), _1265529)))], (14666 ^ _777959) ^ [_1053528, _1053530, _1053532, _1053534] : [hBOOL(hAPP(hAPP(c_member(_1053528), _1053530), c_SetInterval_Oord_OatMost(_1053528, _1053532, _1053534))), -(hBOOL(hAPP(hAPP(_1053532, _1053530), _1053534)))], (35745 ^ _777959) ^ [_1455688, _1455690, _1455692, _1455694, _1455696, _1455698] : [hBOOL(hAPP(hAPP(_1455688, _1455690), _1455692)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1455694, tc_fun(_1455696, tc_HOL_Obool))), _1455688), _1455698), _1455690), _1455692)))], (33495 ^ _777959) ^ [_1409225, _1409227] : [33496 ^ _777959 : [(33499 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409225), c_Int_OPls))], (33497 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409225), _1409227))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409225)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1409227))))], (1220 ^ _777959) ^ [_795933, _795935] : [-(class_Rings_Oring__1(_795933)), _795935 = _795933, class_Rings_Oring__1(_795935)], (4742 ^ _777959) ^ [_850131, _850133, _850135, _850137, _850139, _850141, _850143, _850145] : [-(c_New__DSequence_Oneg__decr__bind(_850145, _850141, _850137, _850133) = c_New__DSequence_Oneg__decr__bind(_850143, _850139, _850135, _850131)), _850145 = _850143, _850141 = _850139, _850137 = _850135, _850133 = _850131], (16603 ^ _777959) ^ [_1096246, _1096248, _1096250, _1096252] : [class_Orderings_Olinorder(_1096246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096246), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1096246), _1096248), _1096250)), _1096252)), 16610 ^ _777959 : [(16613 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096246), _1096250), _1096252)))], (16611 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096246), _1096248), _1096252)))]]], (22784 ^ _777959) ^ [_1212513, _1212515, _1212517] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1212513), _1212515)), _1212517) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1212513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1212515), _1212517)))], (26764 ^ _777959) ^ [_1284826, _1284828, _1284830, _1284832] : [class_Fields_Olinordered__field(_1284826), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284826), _1284828), c_Groups_Ozero__class_Ozero(_1284826))), 26771 ^ _777959 : [(26778 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284826), _1284832), _1284828)), _1284830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284826), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1284826), _1284830), _1284828)), _1284832)))], (26772 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284826), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1284826), _1284830), _1284828)), _1284832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284826), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284826), _1284832), _1284828)), _1284830)))]]], (9778 ^ _777959) ^ [_947630, _947632, _947634, _947636, _947638, _947640] : [class_Groups_Ocomm__monoid__add(_947630), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_947632, _947630), hAPP(hAPP(c_COMBC(_947632, tc_fun(_947634, tc_HOL_Obool), _947630), hAPP(hAPP(c_COMBB(tc_fun(_947634, _947630), tc_fun(tc_fun(_947634, tc_HOL_Obool), _947630), _947632), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_947634, _947630)), _947636)), _947638)), _947640) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_947634, _947630), hAPP(hAPP(c_COMBC(_947634, tc_fun(_947632, tc_HOL_Obool), _947630), hAPP(hAPP(c_COMBB(tc_fun(_947632, _947630), tc_fun(tc_fun(_947632, tc_HOL_Obool), _947630), _947634), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_947632, _947630)), hAPP(c_COMBC(_947632, _947634, _947630), _947636))), _947640)), _947638))], (36335 ^ _777959) ^ [_1466821, _1466823, _1466825, _1466827, _1466829, _1466831, _1466833] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1466821, _1466823), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1466825), _1466827))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1466829, _1466823), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1466831), _1466833))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1466823)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1466821), _1466829), _1466823), 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), _1466825), _1466831)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1466827), _1466833)), _1466823))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1466827), _1466833), _1466823)))))], (22729 ^ _777959) ^ [_1211374] : [-(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, _1211374)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (8062 ^ _777959) ^ [_915820, _915822, _915824, _915826] : [-(hBOOL(hAPP(hAPP(c_member(_915820), _915822), _915824))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915820, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_915820), _915822), _915826)), _915824) = hAPP(hAPP(c_Set_Oinsert(_915820), _915822), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915820, tc_HOL_Obool)), _915826), _915824)))], (43849 ^ _777959) ^ [_1649735, _1649737, _1649739] : [-(c_List_Olast(_1649735, hAPP(hAPP(c_List_Oappend(_1649735), _1649737), hAPP(hAPP(c_List_Olist_OCons(_1649735), _1649739), c_List_Olist_ONil(_1649735)))) = _1649739)], (50102 ^ _777959) ^ [_1793607, _1793609] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1793607)), _1793609) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1793607, tc_Lazy__Sequence_Olazy__sequence(_1793607)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1793607, tc_Lazy__Sequence_Olazy__sequence(_1793607), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1793607), tc_Nat_Onat), _1793607), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1793607), 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(_1793607)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1793607)))), c_Groups_Oone__class_Oone(tc_Nat_Onat))))), hAPP(c_Lazy__Sequence_Oyield(_1793607), _1793609)))], (5831 ^ _777959) ^ [_870405, _870407, _870409, _870411, _870413, _870415] : [-(hAPP(c_Set_Oimage(_870405, _870407, _870409), hAPP(c_Set_Oimage(_870411, _870405, _870413), _870415)) = hAPP(c_Set_Oimage(_870411, _870407, hAPP(hAPP(c_COMBB(_870405, _870407, _870411), _870409), _870413)), _870415))], (32885 ^ _777959) ^ [_1399131, _1399133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1399131), _1399133)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399131)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399133))))], (45272 ^ _777959) ^ [_1680444, _1680446] : [class_Orderings_Olinorder(_1680444), c_List_Olinorder__class_Osorted(_1680444, _1680446), -(c_List_Olinorder__class_Osorted(_1680444, c_List_Oremdups(_1680444, _1680446)))], (35237 ^ _777959) ^ [_1440406, _1440408] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1440406), hAPP(hAPP(c_Power_Opower__class_Opower(_1440406), hAPP(c_Int_Onumber__class_Onumber__of(_1440406), c_Int_OMin)), _1440408)) = c_Groups_Oone__class_Oone(_1440406)), class_Int_Onumber__ring(_1440406), class_Rings_Olinordered__idom(_1440406)], (12375 ^ _777959) ^ [_1002722, _1002724, _1002726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1002722), _1002724)), 12378 ^ _777959 : [(12385 ^ _777959) ^ [] : [_1002724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1002726), _1002722), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002724), _1002722) = _1002726)], (12379 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002724), _1002722) = _1002726, -(_1002724 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1002726), _1002722))]]], (23321 ^ _777959) ^ [_1222309] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1222309)))], (14263 ^ _777959) ^ [_1043624, _1043626, _1043628, _1043630] : [hAPP(c_Set_Oimage(_1043624, _1043626, _1043628), c_Orderings_Otop__class_Otop(tc_fun(_1043624, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1043626, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1043626, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043626, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1043624, _1043626, _1043628), _1043630))), hAPP(c_Set_Oimage(_1043624, _1043626, _1043628), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1043624, tc_HOL_Obool)), _1043630)))))], (33507 ^ _777959) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (51104 ^ _777959) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (28634 ^ _777959) ^ [_1317390, _1317392] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1317390, _1317392)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1317392)), _1317390))], (24670 ^ _777959) ^ [_1246078, _1246080, _1246082] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1246078), _1246080)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1246078), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1246080), _1246082)) = 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, _1246078), _1246080)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1246080), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1246080), _1246082))))], (49782 ^ _777959) ^ [_1787649, _1787651, _1787653, _1787655] : [-(c_List_Olist__all(_1787649, _1787651, hAPP(hAPP(c_List_Olist_OCons(_1787649), _1787653), _1787655))), hBOOL(hAPP(_1787651, _1787653)), c_List_Olist__all(_1787649, _1787651, _1787655)], (6623 ^ _777959) ^ [_885207, _885209, _885211, _885213] : [-(hBOOL(hAPP(hAPP(c_member(_885207), _885209), _885211))), 6626 ^ _777959 : [(6633 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885207, tc_HOL_Obool)), _885211), _885213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885207, tc_HOL_Obool)), _885211), hAPP(hAPP(c_Set_Oinsert(_885207), _885209), _885213))))], (6627 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885207, tc_HOL_Obool)), _885211), hAPP(hAPP(c_Set_Oinsert(_885207), _885209), _885213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885207, tc_HOL_Obool)), _885211), _885213)))]]], (29246 ^ _777959) ^ [_1329350, _1329352, _1329354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329350)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1329352), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1329354)), 29253 ^ _777959 : [(29254 ^ _777959) ^ [_1329558] : [29256 ^ _777959 : [(29262 ^ _777959) ^ [] : [-(_1329558 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 29258 ^ [_1329350, _1329352, _1329354, _1329558]), 29255 ^ [_1329350, _1329352, _1329354, _1329558]))], (29260 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29258 ^ [_1329350, _1329352, _1329354, _1329558]), _1329354)))], (29257 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29255 ^ [_1329350, _1329352, _1329354, _1329558]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1329350))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1329352), _1329558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1329352), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1329558), _1329350))))]]], (6739 ^ _777959) ^ [_887479, _887481, _887483, _887485] : [hBOOL(hAPP(hAPP(c_member(_887479), _887481), hAPP(hAPP(c_Set_Oinsert(_887479), _887483), _887485))), -(_887481 = _887483), -(hBOOL(hAPP(hAPP(c_member(_887479), _887481), _887485)))], (3830 ^ _777959) ^ [_835931, _835933, _835935, _835937, _835939, _835941] : [-(c_List_OdropWhile(_835941, _835937, _835933) = c_List_OdropWhile(_835939, _835935, _835931)), _835941 = _835939, _835937 = _835935, _835933 = _835931], (2824 ^ _777959) ^ [_820128, _820130] : [_820130 = _820128, -(c_Set_OBall(_820130) = c_Set_OBall(_820128))], (51198 ^ _777959) ^ [_1811979] : [-(class_HOL_Oequal(tc_Option_Ooption(_1811979)))], (18139 ^ _777959) ^ [_1124411, _1124413, _1124415] : [class_Orderings_Olinorder(_1124411), hBOOL(hAPP(c_Finite__Set_Ofinite(_1124411), _1124413)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1124411), _1124415)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1124411, tc_HOL_Obool)), _1124413), _1124415) = c_Orderings_Obot__class_Obot(tc_fun(_1124411, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1124411), c_Big__Operators_Olattice_OInf__fin(_1124411, c_Orderings_Oord__class_Omin(_1124411), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1124411, tc_HOL_Obool)), _1124413), _1124415))), c_Big__Operators_Olattice_OInf__fin(_1124411, c_Orderings_Oord__class_Omin(_1124411), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1124411, tc_HOL_Obool)), _1124413), _1124415))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1124411), c_Big__Operators_Olattice_OInf__fin(_1124411, c_Orderings_Oord__class_Omin(_1124411), _1124413)), c_Big__Operators_Olattice_OInf__fin(_1124411, c_Orderings_Oord__class_Omin(_1124411), _1124415)))], (47140 ^ _777959) ^ [_1723261, _1723263, _1723265, _1723267] : [47142 ^ _777959 : [(47145 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1723263, hAPP(_1723265, 47141 ^ [_1723261, _1723263, _1723265, _1723267]))), hAPP(_1723263, 47141 ^ [_1723261, _1723263, _1723265, _1723267])))], (47143 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1723261, 47141 ^ [_1723261, _1723263, _1723265, _1723267])))]], -(c_Wellfounded_Owf(_1723267, hAPP(c_Set_OCollect(tc_prod(_1723267, _1723267)), hAPP(c_Product__Type_Oprod_Oprod__case(_1723267, _1723267, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1723267, tc_HOL_Obool), tc_fun(_1723267, tc_HOL_Obool), _1723267), hAPP(c_COMBS(_1723267, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1723267), c_fconj), _1723261))), hAPP(hAPP(c_COMBC(_1723267, tc_fun(_1723267, _1723267), tc_fun(_1723267, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1723267, tc_HOL_Obool), tc_fun(tc_fun(_1723267, _1723267), tc_fun(_1723267, tc_HOL_Obool)), _1723267), c_COMBB(_1723267, tc_HOL_Obool, _1723267)), c_fequal)), _1723265))))))], (37908 ^ _777959) ^ [_1504212, _1504214, _1504216] : [-(c_Fun_Oinj__on(_1504212, _1504214, _1504216, c_Orderings_Obot__class_Obot(tc_fun(_1504212, tc_HOL_Obool))))], (40509 ^ _777959) ^ [_1564386] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1564386) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 40512 ^ _777959 : [(40513 ^ _777959) ^ [_1564461] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1564461), hAPP(c_List_Oset(tc_Nat_Onat), _1564386))), -(_1564461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (46860 ^ _777959) ^ [_1717623] : [-(c_Wellfounded_Owf(_1717623, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1717623, _1717623), tc_HOL_Obool))))], (46245 ^ _777959) ^ [_1701174, _1701176, _1701178, _1701180] : [-(hBOOL(hAPP(c_List_Olistsp(_1701174, _1701176), hAPP(hAPP(c_List_Olist_OCons(_1701174), _1701178), _1701180)))), hBOOL(hAPP(_1701176, _1701178)), hBOOL(hAPP(c_List_Olistsp(_1701174, _1701176), _1701180))], (34879 ^ _777959) ^ [_1434403, _1434405] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1434403)), -(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)))), _1434405)), 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)))), _1434403)) = 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, _1434405, _1434403))))], (38726 ^ _777959) ^ [_1521194, _1521196, _1521198, _1521200, _1521202] : [hAPP(hAPP(c_List_Omap(_1521194, _1521196), _1521198), _1521200) = hAPP(hAPP(c_List_Omap(_1521194, _1521196), _1521198), _1521202), c_Fun_Oinj__on(_1521194, _1521196, _1521198, c_Orderings_Otop__class_Otop(tc_fun(_1521194, tc_HOL_Obool))), -(_1521200 = _1521202)], (50178 ^ _777959) ^ [_1794969, _1794971] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1794969)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1794971))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1794969), _1794971)))], (24333 ^ _777959) ^ [_1240341, _1240343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240343)), -(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), _1240341), _1240343))))], (7076 ^ _777959) ^ [_896164, _896166, _896168] : [c_Hoare__Mirabelle_Ohoare__derivs(_896164, _896166, _896168), -(c_Hoare__Mirabelle_Ohoare__valids(_896164, _896166, _896168))], (14560 ^ _777959) ^ [_1051515, _1051517] : [-(hAPP(c_Finite__Set_Ocard(_1051515), _1051517) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1051515, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1051515), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1051517))], (20153 ^ _777959) ^ [_1162580, _1162582, _1162584] : [class_Groups_Oordered__comm__monoid__add(_1162580), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162580), _1162582), c_Groups_Ozero__class_Ozero(_1162580))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162580), _1162584), c_Groups_Ozero__class_Ozero(_1162580))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162580), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162580), _1162582), _1162584)), c_Groups_Ozero__class_Ozero(_1162580))))], (42423 ^ _777959) ^ [_1615704, _1615706, _1615708, _1615710] : [-(_1615704 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1615706), _1615704), hAPP(hAPP(c_List_Olist_OCons(_1615706), _1615708), _1615710)) = hAPP(hAPP(c_List_Olist_OCons(_1615706), _1615708), hAPP(hAPP(c_List_Otake(_1615706), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1615704), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1615710)))], (39460 ^ _777959) ^ [_1539224, _1539226, _1539228, _1539230, _1539232, _1539234] : [c_Finite__Set_Ofolding(_1539224, _1539226, _1539228, _1539230), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539224), _1539232)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539224), _1539234)), -(hAPP(c_Fun_Ocomp(_1539226, _1539226, _1539226, hAPP(_1539230, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1539224, tc_HOL_Obool)), _1539232), _1539234))), hAPP(_1539230, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1539224, tc_HOL_Obool)), _1539232), _1539234))) = hAPP(c_Fun_Ocomp(_1539226, _1539226, _1539226, hAPP(_1539230, _1539232)), hAPP(_1539230, _1539234)))], (5815 ^ _777959) ^ [_870102, _870104, _870106, _870108] : [-(hAPP(hAPP(c_Set_Oinsert(_870102), _870104), hAPP(hAPP(c_Set_Oinsert(_870102), _870106), _870108)) = hAPP(hAPP(c_Set_Oinsert(_870102), _870106), hAPP(hAPP(c_Set_Oinsert(_870102), _870104), _870108)))], (42300 ^ _777959) ^ [_1612058, _1612060, _1612062] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612058), tc_List_Olist(_1612058))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612058), tc_List_Olist(_1612058)), c_List_Olist_ONil(_1612058)), _1612060)), c_List_Olistrel1(_1612058, _1612062)))], (37500 ^ _777959) ^ [_1494302, _1494304, _1494306, _1494308, _1494310, _1494312, _1494314] : [c_Equiv__Relations_Oequiv(_1494302, _1494304, _1494306), hBOOL(hAPP(hAPP(c_member(tc_fun(_1494302, tc_HOL_Obool)), _1494308), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1494302), _1494304), _1494306))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1494302, tc_HOL_Obool)), _1494310), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1494302), _1494304), _1494306))), hBOOL(hAPP(hAPP(c_member(_1494302), _1494312), _1494308)), hBOOL(hAPP(hAPP(c_member(_1494302), _1494314), _1494310)), 37519 ^ _777959 : [(37526 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494302, _1494302)), hAPP(hAPP(c_Product__Type_OPair(_1494302, _1494302), _1494312), _1494314)), _1494306)), -(_1494308 = _1494310)], (37520 ^ _777959) ^ [] : [_1494308 = _1494310, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494302, _1494302)), hAPP(hAPP(c_Product__Type_OPair(_1494302, _1494302), _1494312), _1494314)), _1494306)))]]], (38810 ^ _777959) ^ [_1523257, _1523259, _1523261, _1523263] : [-(hAPP(c_Set_Ovimage(_1523257, _1523259, _1523261), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1523259, tc_HOL_Obool), _1523263)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1523259, tc_HOL_Obool), tc_fun(_1523257, tc_HOL_Obool)), _1523263), c_Set_Ovimage(_1523257, _1523259, _1523261)))], (7854 ^ _777959) ^ [_911489, _911491, _911493, _911495] : [c_Com_Ocom_OSemi(_911489, _911491) = c_Com_Ocom_OSemi(_911493, _911495), 7857 ^ _777959 : [(7860 ^ _777959) ^ [] : [-(_911491 = _911495)], (7858 ^ _777959) ^ [] : [-(_911489 = _911493)]]], (23343 ^ _777959) ^ [] : [-(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))))], (23052 ^ _777959) ^ [_1217510, _1217512, _1217514, _1217516] : [class_Groups_Ocomm__monoid__mult(_1217510), hBOOL(hAPP(c_Finite__Set_Ofinite(_1217512), _1217514)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1217512, _1217510), hAPP(c_COMBK(_1217510, _1217512), _1217516)), _1217514) = hAPP(hAPP(c_Power_Opower__class_Opower(_1217510), _1217516), hAPP(c_Finite__Set_Ocard(_1217512), _1217514)))], (23281 ^ _777959) ^ [_1221630, _1221632] : [23282 ^ _777959 : [(23283 ^ _777959) ^ [_1221683] : [_1221632 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1221630), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221683))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1221630), _1221632)))], (5891 ^ _777959) ^ [_871529, _871531] : [-(c_Set_Othe__elem(_871529, hAPP(hAPP(c_Set_Oinsert(_871529), _871531), c_Orderings_Obot__class_Obot(tc_fun(_871529, tc_HOL_Obool)))) = _871531)], (14213 ^ _777959) ^ [_1042408, _1042410] : [class_Lattices_Oboolean__algebra(_1042408), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1042408), hAPP(c_Groups_Ouminus__class_Ouminus(_1042408), _1042410)), _1042410) = c_Orderings_Otop__class_Otop(_1042408))], (49843 ^ _777959) ^ [_1788757, _1788759, _1788761] : [49845 ^ _777959 : [(49848 ^ _777959) ^ [] : [hBOOL(hAPP(_1788761, 49844 ^ [_1788757, _1788759, _1788761]))], (49846 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1788757), 49844 ^ [_1788757, _1788759, _1788761]), hAPP(c_List_Oset(_1788757), _1788759))))]], -(c_List_Olist__all(_1788757, _1788761, _1788759))], (16323 ^ _777959) ^ [_1090361, _1090363, _1090365] : [class_Orderings_Olinorder(_1090361), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090361), _1090363)), hBOOL(hAPP(hAPP(c_member(_1090361), _1090365), _1090363)), 16334 ^ _777959 : [(16341 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090361, tc_HOL_Obool)), _1090363), hAPP(hAPP(c_Set_Oinsert(_1090361), _1090365), c_Orderings_Obot__class_Obot(tc_fun(_1090361, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1090361, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1090361, _1090363) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1090361), _1090365), c_Big__Operators_Olinorder__class_OMin(_1090361, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090361, tc_HOL_Obool)), _1090363), hAPP(hAPP(c_Set_Oinsert(_1090361), _1090365), c_Orderings_Obot__class_Obot(tc_fun(_1090361, tc_HOL_Obool)))))))], (16335 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1090361, tc_HOL_Obool)), _1090363), hAPP(hAPP(c_Set_Oinsert(_1090361), _1090365), c_Orderings_Obot__class_Obot(tc_fun(_1090361, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1090361, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1090361, _1090363) = _1090365)]]], (50458 ^ _777959) ^ [_1801379, _1801381, _1801383, _1801385, _1801387] : [hBOOL(hAPP(hAPP(_1801383, _1801387), _1801385)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1801379, _1801381, _1801383), _1801385), _1801387)))], (12040 ^ _777959) ^ [_996436, _996438] : [_996436 = _996438, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996436), _996438)))], (34813 ^ _777959) ^ [_1433076] : [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, _1433076, 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, _1433076, 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))], (21113 ^ _777959) ^ [_1179072, _1179074] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1179072), _1179074)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1179072), _1179074) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19038 ^ _777959) ^ [_1143607, _1143609, _1143611, _1143613, _1143615] : [-(c_Map_Odom(_1143607, _1143609, hAPP(hAPP(c_COMBS(_1143607, tc_Option_Ooption(_1143611), tc_Option_Ooption(_1143609)), hAPP(hAPP(c_COMBB(tc_fun(_1143611, _1143609), tc_fun(tc_Option_Ooption(_1143611), tc_Option_Ooption(_1143609)), _1143607), c_Option_Omap(_1143611, _1143609)), _1143613)), _1143615)) = c_Map_Odom(_1143607, _1143611, _1143615))], (22922 ^ _777959) ^ [_1215076, _1215078, _1215080] : [class_Rings_Olinordered__semidom(_1215076), 22925 ^ _777959 : [(22932 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1215078), _1215080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215076), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215076), _1215078)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215076), _1215080))))], (22926 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1215076), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215076), _1215078)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215076), _1215080))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1215078), _1215080)))]]], (10588 ^ _777959) ^ [_965551, _965553, _965555, _965557, _965559, _965561] : [c_Finite__Set_Ofun__left__comm(_965551, _965553, _965555), hBOOL(hAPP(c_Finite__Set_Ofinite(_965551), _965557)), -(hBOOL(hAPP(hAPP(c_member(_965551), _965559), _965557))), -(hAPP(hAPP(c_Finite__Set_Ofold(_965551, _965553, _965555), _965561), hAPP(hAPP(c_Set_Oinsert(_965551), _965559), _965557)) = hAPP(hAPP(c_Finite__Set_Ofold(_965551, _965553, _965555), hAPP(hAPP(_965555, _965559), _965561)), _965557))], (42443 ^ _777959) ^ [_1616087, _1616089] : [-(c_List_Oset__Cons(_1616087, _1616089, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1616087)), c_List_Olist_ONil(_1616087)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1616087), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1616087, tc_List_Olist(_1616087), hAPP(hAPP(c_COMBC(_1616087, tc_List_Olist(_1616087), tc_List_Olist(_1616087)), c_List_Olist_OCons(_1616087)), c_List_Olist_ONil(_1616087))), _1616089))], (2478 ^ _777959) ^ [_814687, _814689] : [_814689 = _814687, -(c_Nat_Osemiring__1__class_ONats(_814689) = c_Nat_Osemiring__1__class_ONats(_814687))], (20267 ^ _777959) ^ [_1164625, _1164627, _1164629, _1164631] : [class_Rings_Olinordered__ring__strict(_1164625), 20270 ^ _777959 : [(20285 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164625), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164625), _1164627), _1164629)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164625), _1164627), _1164631)))), 20286 ^ _777959 : [(20293 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164625), _1164627), c_Groups_Ozero__class_Ozero(_1164625))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164625), _1164631), _1164629))], (20287 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164625), c_Groups_Ozero__class_Ozero(_1164625)), _1164627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164625), _1164629), _1164631))]]], (20271 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164625), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164625), _1164627), _1164629)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164625), _1164627), _1164631))), 20276 ^ _777959 : [(20279 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164625), _1164629), _1164631)))], (20277 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164625), c_Groups_Ozero__class_Ozero(_1164625)), _1164627)))]], 20280 ^ _777959 : [(20283 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164625), _1164631), _1164629)))], (20281 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164625), _1164627), c_Groups_Ozero__class_Ozero(_1164625))))]]]]], (22786 ^ _777959) ^ [_1212564, _1212566] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212564)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212566)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1212564), _1212566)))], (18055 ^ _777959) ^ [_1122691, _1122693, _1122695] : [class_Orderings_Olinorder(_1122691), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122691), _1122693)), -(hBOOL(hAPP(hAPP(c_member(_1122691), _1122695), _1122693))), -(_1122693 = c_Orderings_Obot__class_Obot(tc_fun(_1122691, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1122691, c_Orderings_Oord__class_Omax(_1122691), hAPP(hAPP(c_Set_Oinsert(_1122691), _1122695), _1122693)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1122691), _1122695), c_Big__Operators_Olattice_OSup__fin(_1122691, c_Orderings_Oord__class_Omax(_1122691), _1122693)))], (31158 ^ _777959) ^ [_1366402, _1366404, _1366406] : [class_Groups_Oordered__ab__group__add__abs(_1366402), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366402), hAPP(c_Groups_Oabs__class_Oabs(_1366402), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1366402), _1366404), _1366406))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1366402), hAPP(c_Groups_Oabs__class_Oabs(_1366402), _1366404)), hAPP(c_Groups_Oabs__class_Oabs(_1366402), _1366406)))))], (22471 ^ _777959) ^ [_1206379] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1206379))))], (49332 ^ _777959) ^ [_1775932, _1775934, _1775936, _1775938] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775932, _1775932)), hAPP(hAPP(c_Product__Type_OPair(_1775932, _1775932), _1775934), _1775936)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775932, _1775932), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1775938))), -(_1775934 = _1775936)], (8078 ^ _777959) ^ [_916212, _916214, _916216, _916218] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916212, tc_HOL_Obool)), _916214), hAPP(hAPP(c_Set_Oinsert(_916212), _916216), _916218)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916212, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916212, tc_HOL_Obool)), _916214), _916218)), hAPP(hAPP(c_Set_Oinsert(_916212), _916216), c_Orderings_Obot__class_Obot(tc_fun(_916212, tc_HOL_Obool)))))], (35789 ^ _777959) ^ [_1456609, _1456611, _1456613] : [hBOOL(hAPP(_1456609, 35790 ^ [_1456609, _1456611, _1456613])), 35793 ^ _777959 : [(35794 ^ _777959) ^ [_1456720, _1456722] : [-(hBOOL(hAPP(_1456609, hAPP(hAPP(c_Product__Type_OPair(_1456611, _1456613), _1456722), _1456720))))]]], (22832 ^ _777959) ^ [] : [-(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))], (10026 ^ _777959) ^ [_952456, _952458, _952460, _952462] : [hBOOL(hAPP(hAPP(c_member(_952456), _952458), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952456, tc_HOL_Obool)), _952460), _952462))), -(hBOOL(hAPP(hAPP(c_member(_952456), _952458), _952460)))], (13661 ^ _777959) ^ [_1029828, _1029830, _1029832, _1029834, _1029836] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029828, tc_HOL_Obool)), _1029830), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029832, tc_fun(_1029828, tc_HOL_Obool)), _1029834), _1029836)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029832, tc_fun(_1029828, tc_HOL_Obool)), _1029834), hAPP(hAPP(c_COMBB(tc_fun(_1029828, tc_HOL_Obool), tc_fun(_1029828, tc_HOL_Obool), _1029832), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029828, tc_HOL_Obool)), _1029830)), _1029836)))], (15522 ^ _777959) ^ [_1073059, _1073061, _1073063] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073059), _1073061)), _1073063) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073059), _1073063)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073061), _1073063)))], (1050 ^ _777959) ^ [_793808, _793810] : [-(class_Rings_Oring__1__no__zero__divisors(_793808)), _793810 = _793808, class_Rings_Oring__1__no__zero__divisors(_793810)], (2250 ^ _777959) ^ [_811185, _811187, _811189, _811191, _811193, _811195, _811197, _811199] : [-(c_Sum__Type_OPlus(_811199, _811195, _811191, _811187) = c_Sum__Type_OPlus(_811197, _811193, _811189, _811185)), _811199 = _811197, _811195 = _811193, _811191 = _811189, _811187 = _811185], (1640 ^ _777959) ^ [_801183, _801185] : [-(class_Rings_Ocomm__semiring(_801183)), _801185 = _801183, class_Rings_Ocomm__semiring(_801185)], (42913 ^ _777959) ^ [_1628507, _1628509, _1628511] : [_1628507 = hAPP(hAPP(c_List_Oappend(_1628509), _1628507), _1628511), -(_1628511 = c_List_Olist_ONil(_1628509))], (22206 ^ _777959) ^ [_1200576, _1200578] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1200576), _1200578)), -(hAPP(c_Finite__Set_Ocard(_1200576), _1200578) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1200576, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1200576), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1200578))], (5769 ^ _777959) ^ [_869246, _869248, _869250, _869252] : [c_Orderings_Obot__class_Obot(tc_fun(_869246, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_869248, _869246, _869250), _869252), -(_869252 = c_Orderings_Obot__class_Obot(tc_fun(_869248, tc_HOL_Obool)))], (8308 ^ _777959) ^ [_921534] : [-(c_Finite__Set_Ofun__left__comm__idem(_921534, tc_fun(_921534, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_921534, tc_HOL_Obool), tc_fun(tc_fun(_921534, tc_HOL_Obool), tc_fun(_921534, tc_HOL_Obool)), _921534), hAPP(c_COMBC(tc_fun(_921534, tc_HOL_Obool), tc_fun(_921534, tc_HOL_Obool), tc_fun(_921534, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_921534, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_921534, tc_fun(_921534, tc_HOL_Obool), tc_fun(_921534, tc_HOL_Obool)), c_Set_Oinsert(_921534)), c_Orderings_Obot__class_Obot(tc_fun(_921534, tc_HOL_Obool))))))], (5000 ^ _777959) ^ [_854268, _854270, _854272, _854274, _854276, _854278, _854280, _854282] : [-(c_Option_Ooption_Ooption__case(_854282, _854278, _854274, _854270) = c_Option_Ooption_Ooption__case(_854280, _854276, _854272, _854268)), _854282 = _854280, _854278 = _854276, _854274 = _854272, _854270 = _854268], (13489 ^ _777959) ^ [_1025417, _1025419] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1025417), hAPP(c_Set_OCollect(_1025417), _1025419))), 13492 ^ _777959 : [(13499 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1025417), c_Orderings_Otop__class_Otop(tc_fun(_1025417, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1025417), hAPP(c_Set_OCollect(_1025417), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1025417), c_fNot), _1025419)))))], (13493 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1025417), hAPP(c_Set_OCollect(_1025417), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1025417), c_fNot), _1025419)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1025417), c_Orderings_Otop__class_Otop(tc_fun(_1025417, tc_HOL_Obool)))))]]], (11150 ^ _777959) ^ [_976545] : [-(hAPP(c_Com_Obody, _976545) = c_Option_Ooption_ONone(tc_Com_Ocom)), -(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _976545))))], (41148 ^ _777959) ^ [_1583103, _1583105, _1583107] : [c_Hoare__Mirabelle_Ohoare__valids(_1583103, _1583105, _1583107), 41151 ^ _777959 : [(41152 ^ _777959) ^ [_1583212] : [41154 ^ _777959 : [(41157 ^ _777959) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1583103, _1583212, 41153 ^ [_1583103, _1583105, _1583107, _1583212])], (41155 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1583103)), 41153 ^ [_1583103, _1583105, _1583107, _1583212]), _1583105)))]], 41158 ^ _777959 : [(41159 ^ _777959) ^ [_1583384] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1583103)), _1583384), _1583107)), -(c_Hoare__Mirabelle_Otriple__valid(_1583103, _1583212, _1583384))]]]]], (17231 ^ _777959) ^ [_1107441, _1107443, _1107445] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1107441, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1107441, tc_HOL_Obool), tc_HOL_Obool)), _1107443), _1107445)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1107441, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1107441, tc_HOL_Obool), _1107443)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1107441, tc_HOL_Obool), _1107445)))], (48547 ^ _777959) ^ [_1756080, _1756082] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1756080, _1756080), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1756080, _1756082)), c_Relation_OId(_1756080)) = c_Transitive__Closure_Ortrancl(_1756080, _1756082))], (45570 ^ _777959) ^ [_1686652, _1686654] : [-(c_Enum_On__lists(_1686652, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1686654) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1686652)), c_List_Olist_ONil(_1686652)), c_List_Olist_ONil(tc_List_Olist(_1686652))))], (50596 ^ _777959) ^ [_1804389, _1804391] : [-(c_List_Oconcat(_1804389, c_List_Oreplicate(tc_List_Olist(_1804389), _1804391, c_List_Olist_ONil(_1804389))) = c_List_Olist_ONil(_1804389))], (3976 ^ _777959) ^ [_838180, _838182, _838184, _838186] : [-(c_Random_Opick(_838186, _838182) = c_Random_Opick(_838184, _838180)), _838186 = _838184, _838182 = _838180], (570 ^ _777959) ^ [_786750, _786752, _786754, _786756, _786758, _786760] : [-(c_Enum_Oall__n__lists(_786758, _786754, _786750)), c_Enum_Oall__n__lists(_786760, _786756, _786752), _786760 = _786758, _786756 = _786754, _786752 = _786750], (50092 ^ _777959) ^ [_1793494] : [class_HOL_Oequal(_1793494), -(c_HOL_Oequal__class_Oequal(_1793494) = c_fequal)], (13357 ^ _777959) ^ [_1022373] : [-(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)), _1022373)))))], (8144 ^ _777959) ^ [_917868, _917870, _917872, _917874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917868, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917868, tc_HOL_Obool)), _917870), hAPP(hAPP(c_Set_Oinsert(_917868), _917872), c_Orderings_Obot__class_Obot(tc_fun(_917868, tc_HOL_Obool))))), _917874)), hBOOL(hAPP(hAPP(c_member(_917868), _917872), _917870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917868, tc_HOL_Obool)), _917870), hAPP(hAPP(c_Set_Oinsert(_917868), _917872), _917874))))], (4186 ^ _777959) ^ [_841319, _841321] : [_841321 = _841319, -(c_List_Orotate1(_841321) = c_List_Orotate1(_841319))], (534 ^ _777959) ^ [_786212, _786214, _786216, _786218, _786220, _786222] : [-(c_Finite__Set_Ofun__left__comm(_786220, _786216, _786212)), c_Finite__Set_Ofun__left__comm(_786222, _786218, _786214), _786222 = _786220, _786218 = _786216, _786214 = _786212], (18017 ^ _777959) ^ [_1122060, _1122062, _1122064] : [class_Orderings_Olinorder(_1122060), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122060), _1122062)), -(c_Big__Operators_Olattice_OInf__fin(_1122060, c_Orderings_Oord__class_Omin(_1122060), hAPP(hAPP(c_Set_Oinsert(_1122060), _1122064), _1122062)) = hAPP(hAPP(c_Finite__Set_Ofold(_1122060, _1122060, c_Orderings_Oord__class_Omin(_1122060)), _1122064), _1122062))], (33607 ^ _777959) ^ [] : [-(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)))], (49834 ^ _777959) ^ [_1788557, _1788559, _1788561] : [49836 ^ _777959 : [(49839 ^ _777959) ^ [] : [hBOOL(hAPP(_1788559, 49835 ^ [_1788557, _1788559, _1788561]))], (49837 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1788557), 49835 ^ [_1788557, _1788559, _1788561]), hAPP(c_List_Oset(_1788557), _1788561))))]], -(c_List_Olist__all(_1788557, _1788559, _1788561))], (49294 ^ _777959) ^ [_1774830, _1774832, _1774834] : [c_Wellfounded_Owf(_1774830, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1774830, _1774830), tc_HOL_Obool), _1774832), _1774834)), -(c_Wellfounded_Owf(_1774830, _1774834))], (23026 ^ _777959) ^ [_1216987, _1216989, _1216991, _1216993] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1216987), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1216989, tc_Nat_Onat), _1216991), _1216993)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1216989, _1216987), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1216987, _1216989), c_Nat_Osemiring__1__class_Oof__nat(_1216987)), _1216991)), _1216993)), class_Groups_Ocomm__monoid__mult(_1216987), class_Rings_Osemiring__1(_1216987)], (8112 ^ _777959) ^ [_917204, _917206, _917208, _917210, _917212, _917214] : [c_Finite__Set_Ofolding__image__simple(_917204, _917206, _917208, _917210, _917212, _917214), -(hAPP(_917214, c_Orderings_Obot__class_Obot(tc_fun(_917206, tc_HOL_Obool))) = _917210)], (51258 ^ _777959) ^ [] : [-(class_HOL_Oequal(tc_Product__Type_Ounit))], (14073 ^ _777959) ^ [_1039374, _1039376, _1039378, _1039380] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1039374, tc_fun(_1039376, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1039374, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1039376, tc_HOL_Obool), tc_fun(_1039376, tc_HOL_Obool), _1039374), hAPP(c_COMBC(_1039376, tc_fun(_1039376, tc_HOL_Obool), tc_HOL_Obool), c_member(_1039376))), _1039378)), _1039380)), -(hBOOL(hAPP(hAPP(c_member(_1039376), _1039380), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1039374, tc_fun(_1039376, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1039374, tc_HOL_Obool))), _1039378))))], (33291 ^ _777959) ^ [_1406027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1406027), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1406027)), c_Int_OPls)))], (16044 ^ _777959) ^ [_1083624, _1083626, _1083628, _1083630, _1083632, _1083634] : [c_Map_Omap__comp(_1083624, _1083626, _1083628, _1083630, _1083632, _1083634) = c_Option_Ooption_ONone(_1083626), -(hAPP(_1083632, _1083634) = c_Option_Ooption_ONone(_1083624)), 16052 ^ _777959 : [(16055 ^ _777959) ^ [] : [-(hAPP(_1083630, 16051 ^ [_1083624, _1083626, _1083628, _1083630, _1083632, _1083634]) = c_Option_Ooption_ONone(_1083626))], (16053 ^ _777959) ^ [] : [-(hAPP(_1083632, _1083634) = hAPP(c_Option_Ooption_OSome(_1083624), 16051 ^ [_1083624, _1083626, _1083628, _1083630, _1083632, _1083634]))]]], (51056 ^ _777959) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (48765 ^ _777959) ^ [_1761481, _1761483, _1761485] : [_1761483 = _1761485, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1761481, _1761481)), hAPP(hAPP(c_Product__Type_OPair(_1761481, _1761481), _1761483), _1761485)), c_Relation_OId(_1761481))))], (9978 ^ _777959) ^ [_951372, _951374] : [class_Lattices_Obounded__lattice__bot(_951372), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951372), c_Orderings_Obot__class_Obot(_951372)), _951374) = c_Orderings_Obot__class_Obot(_951372))], (46371 ^ _777959) ^ [_1704091, _1704093, _1704095, _1704097, _1704099, _1704101, _1704103] : [c_List_Olist__all2(_1704091, _1704093, _1704095, _1704097, hAPP(hAPP(c_List_Omap(_1704099, _1704093), _1704101), _1704103)), -(c_List_Olist__all2(_1704091, _1704099, hAPP(hAPP(c_COMBC(_1704091, tc_fun(_1704099, _1704093), tc_fun(_1704099, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1704093, tc_HOL_Obool), tc_fun(tc_fun(_1704099, _1704093), tc_fun(_1704099, tc_HOL_Obool)), _1704091), c_COMBB(_1704093, tc_HOL_Obool, _1704099)), _1704095)), _1704101), _1704097, _1704103))], (29699 ^ _777959) ^ [_1338216, _1338218, _1338220, _1338222, _1338224] : [hAPP(c_Set_Oimage(_1338216, _1338218, _1338220), _1338222) = _1338224, -(hAPP(c_Set_Oimage(tc_fun(_1338216, tc_HOL_Obool), tc_fun(_1338218, tc_HOL_Obool), c_Set_Oimage(_1338216, _1338218, _1338220)), hAPP(c_Set_OPow(_1338216), _1338222)) = hAPP(c_Set_OPow(_1338218), _1338224))], (49002 ^ _777959) ^ [_1767897, _1767899, _1767901] : [c_Relation_Orefl__on(_1767897, _1767899, hAPP(c_Relation_Oconverse(_1767897, _1767897), _1767901)), -(c_Relation_Orefl__on(_1767897, _1767899, _1767901))], (40455 ^ _777959) ^ [_1563256, _1563258, _1563260] : [class_Orderings_Olinorder(_1563256), hBOOL(hAPP(hAPP(c_member(_1563256), _1563258), hAPP(c_List_Oset(_1563256), _1563260))), -(c_List_Olinorder__class_Oinsort__insert__key(_1563256, _1563256, c_COMBI(_1563256), _1563258, _1563260) = _1563260)], (43893 ^ _777959) ^ [_1650508, _1650510, _1650512] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1650508)), _1650510), c_List_Olists(_1650508, _1650512))), -(_1650510 = c_List_Olist_ONil(_1650508)), 43902 ^ _777959 : [(43907 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1650508)), 43901 ^ [_1650508, _1650510, _1650512]), c_List_Olists(_1650508, _1650512))))], (43905 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1650508), 43900 ^ [_1650508, _1650510, _1650512]), _1650512)))], (43903 ^ _777959) ^ [] : [-(_1650510 = hAPP(hAPP(c_List_Olist_OCons(_1650508), 43900 ^ [_1650508, _1650510, _1650512]), 43901 ^ [_1650508, _1650510, _1650512]))]]], (35495 ^ _777959) ^ [_1450785, _1450787, _1450789, _1450791] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1450785, _1450787), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1450789), _1450791))), -(_1450787 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1450785), _1450787) = _1450789)], (30603 ^ _777959) ^ [_1356471, _1356473] : [class_Rings_Olinordered__idom(_1356471), 30606 ^ _777959 : [(30613 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356471), _1356473), c_Groups_Ozero__class_Ozero(_1356471))), -(c_Groups_Osgn__class_Osgn(_1356471, _1356473) = hAPP(c_Groups_Ouminus__class_Ouminus(_1356471), c_Groups_Oone__class_Oone(_1356471)))], (30607 ^ _777959) ^ [] : [c_Groups_Osgn__class_Osgn(_1356471, _1356473) = hAPP(c_Groups_Ouminus__class_Ouminus(_1356471), c_Groups_Oone__class_Oone(_1356471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356471), _1356473), c_Groups_Ozero__class_Ozero(_1356471))))]]], (5845 ^ _777959) ^ [_870721, _870723, _870725, _870727, _870729] : [hAPP(hAPP(c_Set_Oinsert(_870721), _870723), hAPP(hAPP(c_Set_Oinsert(_870721), _870725), c_Orderings_Obot__class_Obot(tc_fun(_870721, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_870721), _870727), hAPP(hAPP(c_Set_Oinsert(_870721), _870729), c_Orderings_Obot__class_Obot(tc_fun(_870721, tc_HOL_Obool)))), 5850 ^ _777959 : [(5853 ^ _777959) ^ [] : [-(_870725 = _870729)], (5851 ^ _777959) ^ [] : [-(_870723 = _870727)]], 5854 ^ _777959 : [(5857 ^ _777959) ^ [] : [-(_870725 = _870727)], (5855 ^ _777959) ^ [] : [-(_870723 = _870729)]]], (43990 ^ _777959) ^ [_1652581, _1652583] : [-(c_List_OremoveAll(_1652581, _1652583) = c_List_Ofilter(_1652581, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1652581), c_fNot), hAPP(c_fequal, _1652583))))], (51084 ^ _777959) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (24702 ^ _777959) ^ [_1246639, _1246641, _1246643] : [class_Divides_Osemiring__div(_1246639), -(_1246641 = c_Groups_Ozero__class_Ozero(_1246639)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1246639), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246639), _1246643), _1246641)), _1246641) = _1246643)], (2982 ^ _777959) ^ [_822617, _822619, _822621, _822623] : [-(c_Big__Operators_Olattice__class_OSup__fin(_822623, _822619) = c_Big__Operators_Olattice__class_OSup__fin(_822621, _822617)), _822623 = _822621, _822619 = _822617], (27179 ^ _777959) ^ [_1292771, _1292773] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1292771, _1292773)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1292773), _1292771)))], (22014 ^ _777959) ^ [_1196617, _1196619, _1196621] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1196617)), hAPP(c_Set_Oimage(_1196619, tc_Option_Ooption(_1196617), hAPP(c_Map_Omap__of(_1196619, _1196617), _1196621)), c_Orderings_Otop__class_Otop(tc_fun(_1196619, tc_HOL_Obool))))))], (43426 ^ _777959) ^ [_1641212, _1641214, _1641216, _1641218, _1641220] : [-(hAPP(hAPP(c_List_Ozip(_1641212, _1641214), _1641216), hAPP(hAPP(c_List_Oappend(_1641214), _1641218), _1641220)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1641212, _1641214)), hAPP(hAPP(c_List_Ozip(_1641212, _1641214), hAPP(hAPP(c_List_Otake(_1641212), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641214)), _1641218)), _1641216)), _1641218)), hAPP(hAPP(c_List_Ozip(_1641212, _1641214), hAPP(hAPP(c_List_Odrop(_1641212), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641214)), _1641218)), _1641216)), _1641220)))], (41623 ^ _777959) ^ [_1594243, _1594245, _1594247, _1594249, _1594251, _1594253] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594243), tc_List_Olist(_1594243))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594243), tc_List_Olist(_1594243)), hAPP(hAPP(c_List_Olist_OCons(_1594243), _1594245), _1594247)), hAPP(hAPP(c_List_Olist_OCons(_1594243), _1594249), _1594251))), c_List_Olistrel1(_1594243, _1594253))), 41628 ^ _777959 : [(41631 ^ _777959) ^ [] : [-(_1594247 = _1594251)], (41629 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594243, _1594243)), hAPP(hAPP(c_Product__Type_OPair(_1594243, _1594243), _1594245), _1594249)), _1594253)))]], 41632 ^ _777959 : [(41635 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594243), tc_List_Olist(_1594243))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594243), tc_List_Olist(_1594243)), _1594247), _1594251)), c_List_Olistrel1(_1594243, _1594253))))], (41633 ^ _777959) ^ [] : [-(_1594245 = _1594249)]]], (19608 ^ _777959) ^ [_1152852, _1152854] : [19609 ^ _777959 : [(19612 ^ _777959) ^ [] : [_1152854 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (19610 ^ _777959) ^ [] : [_1152852 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152852), _1152854) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40757 ^ _777959) ^ [_1570003, _1570005, _1570007] : [-(c_Hilbert__Choice_OEps(tc_prod(_1570003, _1570005), _1570007) = c_Hilbert__Choice_OEps(tc_prod(_1570003, _1570005), hAPP(c_Product__Type_Oprod_Oprod__case(_1570003, _1570005, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1570005, tc_prod(_1570003, _1570005)), tc_fun(_1570005, tc_HOL_Obool), _1570003), hAPP(c_COMBB(tc_prod(_1570003, _1570005), tc_HOL_Obool, _1570005), _1570007)), c_Product__Type_OPair(_1570003, _1570005)))))], (4482 ^ _777959) ^ [_845775, _845777, _845779, _845781] : [-(c_Product__Type_Ofst(_845781, _845777) = c_Product__Type_Ofst(_845779, _845775)), _845781 = _845779, _845777 = _845775], (22144 ^ _777959) ^ [_1199261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1199261)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1199261), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1199261)], (28800 ^ _777959) ^ [_1320613, _1320615, _1320617, _1320619] : [class_Groups_Ocomm__monoid__add(_1320613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1320615), _1320617)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1320613), _1320619), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1320615, _1320617)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320613), hAPP(_1320619, _1320615)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1320613), _1320619), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1320615, _1320617))))], (32709 ^ _777959) ^ [_1395741, _1395743, _1395745, _1395747] : [class_Fields_Olinordered__field__inverse__zero(_1395741), class_Int_Onumber(_1395741), 32716 ^ _777959 : [(32717 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395741), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1395741), _1395743), _1395745)), hAPP(c_Int_Onumber__class_Onumber__of(_1395741), _1395747))), 32720 ^ _777959 : [(32727 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395741), c_Groups_Ozero__class_Ozero(_1395741)), _1395745))), 32730 ^ _777959 : [(32737 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395741), _1395745), c_Groups_Ozero__class_Ozero(_1395741)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395741), c_Groups_Ozero__class_Ozero(_1395741)), hAPP(c_Int_Onumber__class_Onumber__of(_1395741), _1395747))))], (32731 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395741), _1395745), c_Groups_Ozero__class_Ozero(_1395741))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395741), hAPP(c_Int_Onumber__class_Onumber__of(_1395741), _1395747)), _1395745)), _1395743)))]]], (32721 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395741), c_Groups_Ozero__class_Ozero(_1395741)), _1395745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395741), _1395743), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395741), hAPP(c_Int_Onumber__class_Onumber__of(_1395741), _1395747)), _1395745))))]]], (32743 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395741), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1395741), _1395743), _1395745)), hAPP(c_Int_Onumber__class_Onumber__of(_1395741), _1395747)))), 32746 ^ _777959 : [(32749 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395741), _1395743), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395741), hAPP(c_Int_Onumber__class_Onumber__of(_1395741), _1395747)), _1395745)))], (32747 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395741), c_Groups_Ozero__class_Ozero(_1395741)), _1395745)))]], 32750 ^ _777959 : [(32753 ^ _777959) ^ [] : [32754 ^ _777959 : [(32757 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1395741), hAPP(c_Int_Onumber__class_Onumber__of(_1395741), _1395747)), _1395745)), _1395743))], (32755 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395741), _1395745), c_Groups_Ozero__class_Ozero(_1395741))))]], 32758 ^ _777959 : [(32761 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1395741), c_Groups_Ozero__class_Ozero(_1395741)), hAPP(c_Int_Onumber__class_Onumber__of(_1395741), _1395747)))], (32759 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395741), _1395745), c_Groups_Ozero__class_Ozero(_1395741)))]]], (32751 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1395741), c_Groups_Ozero__class_Ozero(_1395741)), _1395745))]]]]], (33453 ^ _777959) ^ [_1408568, _1408570] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408568)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408570)))), 33456 ^ _777959 : [(33459 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1408570))], (33457 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408568), _1408570)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408568), _1408570))], (38256 ^ _777959) ^ [_1510840, _1510842, _1510844, _1510846, _1510848, _1510850] : [c_Fun_Oinj__on(_1510840, _1510842, _1510844, _1510846), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510840, tc_HOL_Obool)), _1510848), _1510846)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1510840, tc_HOL_Obool)), _1510850), _1510846)), -(hAPP(c_Set_Oimage(_1510840, _1510842, _1510844), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1510840, tc_HOL_Obool)), _1510848), _1510850)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1510842, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1510840, _1510842, _1510844), _1510848)), hAPP(c_Set_Oimage(_1510840, _1510842, _1510844), _1510850)))], (14607 ^ _777959) ^ [_1052359] : [14609 ^ _777959 : [(14612 ^ _777959) ^ [_1052469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 14608 ^ [_1052359, _1052469]), _1052469))], (14610 ^ _777959) ^ [_1052435] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 14608 ^ [_1052359, _1052435]), _1052359)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1052359)))], (50872 ^ _777959) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (16461 ^ _777959) ^ [_1093061, _1093063, _1093065] : [class_Orderings_Olinorder(_1093061), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093061), _1093063), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093061), _1093063), _1093065)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093061), _1093063), _1093065))], (37744 ^ _777959) ^ [_1499949, _1499951, _1499953, _1499955, _1499957, _1499959, _1499961, _1499963] : [c_Equiv__Relations_Oequiv(_1499949, _1499951, _1499953), c_Equiv__Relations_Ocongruent2(_1499949, _1499955, _1499957, _1499953, _1499959, _1499961), hBOOL(hAPP(hAPP(c_member(_1499949), _1499963), _1499951)), -(c_Equiv__Relations_Ocongruent(_1499955, _1499957, _1499959, hAPP(_1499961, _1499963)))], (19496 ^ _777959) ^ [_1151170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151170), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (37148 ^ _777959) ^ [_1485001, _1485003, _1485005, _1485007] : [-(hAPP(c_Relation_OImage(_1485001, _1485003, _1485005), hAPP(hAPP(c_Set_Oinsert(_1485001), _1485007), c_Orderings_Obot__class_Obot(tc_fun(_1485001, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1485003), hAPP(hAPP(c_COMBC(_1485003, tc_fun(tc_prod(_1485001, _1485003), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1485001, _1485003), tc_fun(tc_fun(tc_prod(_1485001, _1485003), tc_HOL_Obool), tc_HOL_Obool), _1485003), c_member(tc_prod(_1485001, _1485003))), hAPP(c_Product__Type_OPair(_1485001, _1485003), _1485007))), _1485005)))], (44426 ^ _777959) ^ [_1660955, _1660957] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1660955, _1660957)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1660955), _1660957))], (51128 ^ _777959) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (51070 ^ _777959) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (38752 ^ _777959) ^ [_1521835, _1521837, _1521839, _1521841, _1521843] : [-(hAPP(c_Set_Ovimage(_1521835, _1521837, _1521839), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1521837, tc_HOL_Obool)), _1521841), _1521843)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1521835, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1521835, _1521837, _1521839), _1521841)), hAPP(c_Set_Ovimage(_1521835, _1521837, _1521839), _1521843)))], (48919 ^ _777959) ^ [_1765417, _1765419, _1765421, _1765423, _1765425] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1765417, _1765417)), hAPP(hAPP(c_Product__Type_OPair(_1765417, _1765417), hAPP(_1765419, hAPP(c_Nat_OSuc, 48920 ^ [_1765417, _1765419, _1765421, _1765423, _1765425]))), hAPP(_1765419, 48920 ^ [_1765417, _1765419, _1765421, _1765423, _1765425]))), c_Transitive__Closure_Ortrancl(_1765417, _1765421))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765417, _1765417)), hAPP(hAPP(c_Product__Type_OPair(_1765417, _1765417), hAPP(_1765419, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1765423), _1765425))), hAPP(_1765419, _1765423))), c_Transitive__Closure_Ortrancl(_1765417, _1765421))))], (13395 ^ _777959) ^ [_1023423, _1023425, _1023427, _1023429] : [hBOOL(hAPP(hAPP(c_member(_1023425), _1023429), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023423, tc_fun(_1023425, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1023423, tc_HOL_Obool))), _1023427))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023423, tc_fun(_1023425, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1023423, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1023425, tc_HOL_Obool), tc_fun(_1023425, tc_HOL_Obool), _1023423), hAPP(c_COMBC(_1023425, tc_fun(_1023425, tc_HOL_Obool), tc_HOL_Obool), c_member(_1023425))), _1023427)), _1023429)))], (40465 ^ _777959) ^ [_1563427, _1563429, _1563431] : [class_Orderings_Olinorder(_1563427), -(hAPP(c_List_Oset(_1563427), c_List_Olinorder__class_Oinsort__insert__key(_1563427, _1563427, c_COMBI(_1563427), _1563429, _1563431)) = hAPP(hAPP(c_Set_Oinsert(_1563427), _1563429), hAPP(c_List_Oset(_1563427), _1563431)))], (11906 ^ _777959) ^ [_994033, _994035] : [class_Lattices_Olattice(_994033), hBOOL(hAPP(c_Finite__Set_Ofinite(_994033), _994035)), -(_994035 = c_Orderings_Obot__class_Obot(tc_fun(_994033, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_994033), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_994033), 11919 ^ [_994033, _994035]), 11920 ^ [_994033, _994035])), hAPP(hAPP(c_Set_Oinsert(_994033), 11919 ^ [_994033, _994035]), hAPP(hAPP(c_Set_Oinsert(_994033), 11920 ^ [_994033, _994035]), c_Orderings_Obot__class_Obot(tc_fun(_994033, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_994033), c_Big__Operators_Olattice__class_OInf__fin(_994033, _994035)), _994035)))], (44184 ^ _777959) ^ [_1657073, _1657075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657073), _1657075)), -(c_List_Oupt(_1657073, _1657075) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1657073), c_List_Oupt(hAPP(c_Nat_OSuc, _1657073), _1657075)))], (5984 ^ _777959) ^ [_873483, _873485, _873487, _873489] : [hBOOL(hAPP(hAPP(c_member(_873483), _873485), hAPP(hAPP(c_Set_Oinsert(_873483), _873487), _873489))), -(_873485 = _873487), -(hBOOL(hAPP(hAPP(c_member(_873483), _873485), _873489)))], (51048 ^ _777959) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (34957 ^ _777959) ^ [] : [c_Int_OPls = c_Int_OMin], (27652 ^ _777959) ^ [_1300317, _1300319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300317)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300319)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1300317), _1300319)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1300317)), hAPP(c_Int_Onat, _1300319)))], (50382 ^ _777959) ^ [_1799659, _1799661, _1799663, _1799665] : [-(hAPP(c_New__DSequence_Oneg__union(_1799659, _1799661, _1799663), _1799665) = c_Lazy__Sequence_Oappend(tc_Option_Ooption(_1799659), hAPP(_1799661, _1799665), hAPP(_1799663, _1799665)))], (36694 ^ _777959) ^ [_1474192, _1474194, _1474196] : [-(c_HOL_OThe(tc_prod(_1474192, _1474194), hAPP(c_Product__Type_Oprod_Oprod__case(_1474192, _1474194, tc_HOL_Obool), _1474196)) = c_HOL_OThe(tc_prod(_1474192, _1474194), hAPP(hAPP(c_COMBS(tc_prod(_1474192, _1474194), _1474194, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1474192, tc_fun(_1474194, tc_HOL_Obool), tc_prod(_1474192, _1474194)), _1474196), c_Product__Type_Ofst(_1474192, _1474194))), c_Product__Type_Osnd(_1474192, _1474194))))], (19092 ^ _777959) ^ [_1144869, _1144871, _1144873, _1144875, _1144877] : [class_Groups_Ocomm__monoid__mult(_1144869), hBOOL(hAPP(c_Finite__Set_Ofinite(_1144871), _1144873)), hBOOL(hAPP(hAPP(c_member(_1144871), _1144875), _1144873)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1144871, _1144869), _1144877), _1144873) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144869), hAPP(_1144877, _1144875)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1144871, _1144869), _1144877), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1144871, tc_HOL_Obool)), _1144873), hAPP(hAPP(c_Set_Oinsert(_1144871), _1144875), c_Orderings_Obot__class_Obot(tc_fun(_1144871, tc_HOL_Obool)))))))], (4848 ^ _777959) ^ [_851870, _851872] : [_851872 = _851870, -(c_If(_851872) = c_If(_851870))], (44779 ^ _777959) ^ [_1668596, _1668598] : [-(hAPP(c_List_Orev(_1668596), _1668598) = hAPP(c_List_Ofoldl(tc_List_Olist(_1668596), _1668596, hAPP(c_COMBC(_1668596, tc_List_Olist(_1668596), tc_List_Olist(_1668596)), c_List_Olist_OCons(_1668596)), c_List_Olist_ONil(_1668596)), _1668598))], (6145 ^ _777959) ^ [_876420, _876422, _876424, _876426] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876420, tc_HOL_Obool)), _876422), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876420, tc_HOL_Obool)), _876424), _876426)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876420, tc_HOL_Obool)), _876424), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876420, tc_HOL_Obool)), _876422), _876426)))], (17451 ^ _777959) ^ [_1111422, _1111424, _1111426] : [class_Orderings_Olinorder(_1111422), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111422), _1111424)), -(_1111424 = c_Orderings_Obot__class_Obot(tc_fun(_1111422, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111422), _1111426)), -(_1111426 = c_Orderings_Obot__class_Obot(tc_fun(_1111422, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1111422, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1111422, tc_HOL_Obool)), _1111424), _1111426)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1111422), c_Big__Operators_Olinorder__class_OMin(_1111422, _1111424)), c_Big__Operators_Olinorder__class_OMin(_1111422, _1111426)))], (38457 ^ _777959) ^ [_1515319, _1515321, _1515323, _1515325] : [c_Fun_Oinj__on(_1515319, tc_fun(tc_fun(_1515319, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1515319, tc_fun(tc_prod(_1515319, _1515319), tc_HOL_Obool), tc_fun(tc_fun(_1515319, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1515319, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1515319, _1515319), tc_HOL_Obool), tc_fun(tc_fun(_1515319, tc_HOL_Obool), tc_HOL_Obool)), _1515319), c_Equiv__Relations_Oquotient(_1515319)), hAPP(hAPP(c_COMBC(_1515319, tc_fun(_1515319, tc_HOL_Obool), tc_fun(_1515319, tc_HOL_Obool)), c_Set_Oinsert(_1515319)), c_Orderings_Obot__class_Obot(tc_fun(_1515319, tc_HOL_Obool))))), _1515321), _1515323), hBOOL(hAPP(hAPP(c_member(_1515319), _1515325), _1515323)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1515319), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1515319, tc_HOL_Obool)), _1515323), hAPP(hAPP(c_Set_Oinsert(_1515319), _1515325), c_Orderings_Obot__class_Obot(tc_fun(_1515319, tc_HOL_Obool))))), _1515321) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1515319, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1515319), _1515323), _1515321)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1515319), hAPP(hAPP(c_Set_Oinsert(_1515319), _1515325), c_Orderings_Obot__class_Obot(tc_fun(_1515319, tc_HOL_Obool)))), _1515321)))], (25904 ^ _777959) ^ [_1269009, _1269011, _1269013] : [class_Orderings_Oorder(_1269009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1269009), _1269011), _1269013)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_1269009, _1269013, _1269011) = c_Orderings_Obot__class_Obot(tc_fun(_1269009, tc_HOL_Obool)))], (11806 ^ _777959) ^ [_991886, _991888, _991890, _991892, _991894] : [_991886 = c_Orderings_Obot__class_Obot(tc_fun(_991888, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_991890), _991892), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991888, tc_fun(_991890, tc_HOL_Obool)), _991886), _991894)) = hAPP(hAPP(c_Set_Oinsert(_991890), _991892), c_Orderings_Obot__class_Obot(tc_fun(_991890, tc_HOL_Obool))))], (27708 ^ _777959) ^ [_1301389, _1301391, _1301393, _1301395, _1301397] : [class_Orderings_Olinorder(_1301389), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301389, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1301389, _1301391, _1301393)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1301389, _1301395, _1301397)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1301389, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1301389), _1301391), _1301395), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1301389), _1301393), _1301397)))], (30852 ^ _777959) ^ [_1360906, _1360908] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360906)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1360908)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1360906), hAPP(c_Int_Onat, _1360908)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1360906, _1360908)))], (48913 ^ _777959) ^ [_1765231, _1765233, _1765235] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1765231, _1765231), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1765231, _1765231), _1765233)), c_Transitive__Closure_Ortrancl(_1765231, _1765233)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1765231, _1765231), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1765231, _1765231)), hAPP(hAPP(c_Product__Type_OPair(_1765231, _1765231), _1765235), _1765235)), c_Transitive__Closure_Otrancl(_1765231, _1765233)))], (15080 ^ _777959) ^ [_1064741, _1064743] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064741), hAPP(c_Nat_OSuc, _1064743)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1064741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1064741), _1064743)))], (50640 ^ _777959) ^ [_1805168, _1805170, _1805172, _1805174] : [hBOOL(hAPP(hAPP(c_member(_1805168), _1805170), hAPP(c_List_Oset(_1805168), c_List_Oreplicate(_1805168, _1805172, _1805174)))), 50643 ^ _777959 : [(50646 ^ _777959) ^ [] : [_1805172 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50644 ^ _777959) ^ [] : [-(_1805170 = _1805174)]]], (31508 ^ _777959) ^ [_1373152] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1373152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373152)))], (48364 ^ _777959) ^ [_1751184, _1751186] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1751184), _1751186) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1751184), _1751186))], (11569 ^ _777959) ^ [_984871, _984873, _984875, _984877, _984879] : [-(_984871 = c_Orderings_Obot__class_Obot(tc_fun(_984873, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_984873, tc_fun(_984875, tc_HOL_Obool)), _984871), hAPP(hAPP(c_COMBC(_984873, tc_fun(_984875, tc_HOL_Obool), tc_fun(_984875, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_984875, tc_HOL_Obool), tc_fun(tc_fun(_984875, tc_HOL_Obool), tc_fun(_984875, tc_HOL_Obool)), _984873), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984875, tc_HOL_Obool))), _984877)), _984879)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984875, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_984873, tc_fun(_984875, tc_HOL_Obool)), _984871), _984877)), _984879))], (5606 ^ _777959) ^ [_863637, _863639] : [_863639 = _863637, -(c_Set_Oinsert(_863639) = c_Set_Oinsert(_863637))], (8758 ^ _777959) ^ [_929056, _929058, _929060, _929062, _929064] : [class_Groups_Oordered__ab__group__add(_929056), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_929056), _929058), _929060) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_929056), _929062), _929064), 8765 ^ _777959 : [(8772 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929056), _929062), _929064)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929056), _929058), _929060)))], (8766 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929056), _929058), _929060)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_929056), _929062), _929064)))]]], (14516 ^ _777959) ^ [_1050538, _1050540, _1050542, _1050544, _1050546] : [14518 ^ _777959 : [(14521 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1050544, 14517 ^ [_1050538, _1050540, _1050542, _1050544, _1050546]), _1050546))], (14519 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1050538), 14517 ^ [_1050538, _1050540, _1050542, _1050544, _1050546]), _1050542)))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1050538, tc_fun(_1050540, tc_HOL_Obool)), _1050542), _1050544), _1050546)))], (26730 ^ _777959) ^ [_1284176, _1284178, _1284180, _1284182] : [class_Fields_Olinordered__field(_1284176), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284176), c_Groups_Ozero__class_Ozero(_1284176)), _1284178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284176), _1284180), _1284178)), _1284182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284176), _1284180), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1284176), _1284182), _1284178))))], (19232 ^ _777959) ^ [_1147281, _1147283] : [class_Groups_Ocomm__monoid__add(_1147281), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1147281), c_Groups_Ozero__class_Ozero(_1147281)), _1147283) = _1147283)], (37196 ^ _777959) ^ [_1486726, _1486728, _1486730, _1486732, _1486734, _1486736] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1486726, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1486728, _1486726, _1486730), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486732, tc_fun(_1486728, tc_HOL_Obool)), _1486734), _1486736))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1486732, tc_fun(_1486726, tc_HOL_Obool)), _1486734), hAPP(hAPP(c_COMBB(tc_fun(_1486728, tc_HOL_Obool), tc_fun(_1486726, tc_HOL_Obool), _1486732), c_Relation_OImage(_1486728, _1486726, _1486730)), _1486736)))))], (17759 ^ _777959) ^ [_1117145] : [class_Orderings_Oord(_1117145), -(c_Orderings_Oord__class_Omin(_1117145) = c_Orderings_Oord_Omin(_1117145, c_Orderings_Oord__class_Oless__eq(_1117145)))], (3440 ^ _777959) ^ [_829828, _829830, _829832, _829834, _829836, _829838, _829840, _829842] : [-(c_List_Olinorder__class_Osort__key(_829842, _829838, _829834, _829830) = c_List_Olinorder__class_Osort__key(_829840, _829836, _829832, _829828)), _829842 = _829840, _829838 = _829836, _829834 = _829832, _829830 = _829828], (11677 ^ _777959) ^ [_987820, _987822, _987824, _987826] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_987820, tc_fun(_987822, tc_HOL_Obool)), _987824), _987826) = c_Orderings_Obot__class_Obot(tc_fun(_987822, tc_HOL_Obool)), 11680 ^ _777959 : [(11681 ^ _777959) ^ [_987936] : [hBOOL(hAPP(hAPP(c_member(_987820), _987936), _987824)), -(hAPP(_987826, _987936) = c_Orderings_Obot__class_Obot(tc_fun(_987822, tc_HOL_Obool)))]]], (31977 ^ _777959) ^ [_1381717, _1381719, _1381721] : [class_Int_Onumber(_1381717), class_Orderings_Olinorder(_1381717), 31984 ^ _777959 : [(31991 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381717), hAPP(c_Int_Onumber__class_Onumber__of(_1381717), _1381721)), hAPP(c_Int_Onumber__class_Onumber__of(_1381717), _1381719)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1381717), hAPP(c_Int_Onumber__class_Onumber__of(_1381717), _1381719)), hAPP(c_Int_Onumber__class_Onumber__of(_1381717), _1381721))))], (31985 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1381717), hAPP(c_Int_Onumber__class_Onumber__of(_1381717), _1381719)), hAPP(c_Int_Onumber__class_Onumber__of(_1381717), _1381721))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1381717), hAPP(c_Int_Onumber__class_Onumber__of(_1381717), _1381721)), hAPP(c_Int_Onumber__class_Onumber__of(_1381717), _1381719)))]]], (19081 ^ _777959) ^ [_1144717, _1144719, _1144721] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1144717), c_Map_Odom(_1144717, _1144719, _1144721))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1144717), c_Orderings_Otop__class_Otop(tc_fun(_1144717, tc_HOL_Obool))))), -(hAPP(_1144721, 19088 ^ [_1144717, _1144719, _1144721]) = c_Option_Ooption_ONone(_1144719))], (42016 ^ _777959) ^ [_1605948, _1605950, _1605952, _1605954] : [c_List_Olist_ONil(_1605948) = hAPP(hAPP(c_List_Omap(_1605950, _1605948), _1605952), _1605954), -(_1605954 = c_List_Olist_ONil(_1605950))], (29090 ^ _777959) ^ [_1326152, _1326154] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1326152), _1326154))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1326154, _1326152) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1326154), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1326154), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1326152)))], (41275 ^ _777959) ^ [_1585945, _1585947, _1585949, _1585951] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1585945), tc_List_Olist(_1585945))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1585945), tc_List_Olist(_1585945)), _1585947), _1585949)), c_List_Olistrel1(_1585945, _1585951))), 41280 ^ _777959 : [(41285 ^ _777959) ^ [] : [-(_1585949 = hAPP(hAPP(c_List_Olist__update(_1585945, _1585947), 41279 ^ [_1585945, _1585947, _1585949, _1585951]), 41278 ^ [_1585945, _1585947, _1585949, _1585951]))], (41283 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41279 ^ [_1585945, _1585947, _1585949, _1585951]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1585945)), _1585947))))], (41281 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585945, _1585945)), hAPP(hAPP(c_Product__Type_OPair(_1585945, _1585945), hAPP(hAPP(c_List_Onth(_1585945), _1585947), 41279 ^ [_1585945, _1585947, _1585949, _1585951])), 41278 ^ [_1585945, _1585947, _1585949, _1585951])), _1585951)))]]], (19478 ^ _777959) ^ [_1150945] : [hAPP(c_Nat_OSuc, _1150945) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5246 ^ _777959) ^ [_858243, _858245] : [_858245 = _858243, -(c_Groups_Oone__class_Oone(_858245) = c_Groups_Oone__class_Oone(_858243))], (47112 ^ _777959) ^ [_1722669, _1722671, _1722673, _1722675] : [c_FunDef_Oreduction__pair(_1722669, _1722671), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1722669, _1722669), tc_HOL_Obool)), _1722673), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1722669, _1722669), tc_HOL_Obool), tc_fun(tc_prod(_1722669, _1722669), tc_HOL_Obool)), _1722671))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1722669, _1722669), tc_HOL_Obool)), _1722675), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1722669, _1722669), tc_HOL_Obool), tc_fun(tc_prod(_1722669, _1722669), tc_HOL_Obool)), _1722671))), c_Wellfounded_Owf(_1722669, _1722675), -(c_Wellfounded_Owf(_1722669, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1722669, _1722669), tc_HOL_Obool)), _1722673), _1722675)))], (9632 ^ _777959) ^ [_944536, _944538, _944540, _944542] : [hBOOL(hAPP(hAPP(c_member(_944536), _944538), _944540)), hBOOL(hAPP(hAPP(c_member(_944536), _944538), _944542)), -(hBOOL(hAPP(hAPP(c_member(_944536), _944538), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944536, tc_HOL_Obool)), _944540), _944542))))], (26522 ^ _777959) ^ [_1280306, _1280308, _1280310, _1280312, _1280314] : [class_Fields_Olinordered__field(_1280306), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280306), c_Groups_Ozero__class_Ozero(_1280306)), _1280308)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280306), _1280308), _1280310)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280306), c_Groups_Ozero__class_Ozero(_1280306)), _1280312)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280306), _1280312), _1280314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280306), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280306), _1280308), _1280314)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280306), _1280310), _1280312))))], (50304 ^ _777959) ^ [_1797927, _1797929] : [class_Lazy__Sequence_Osmall__lazy(_1797927), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1797927), _1797929) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1797927), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1797927)), c_List_Olist_ONil(_1797927)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1797927))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1797929)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1797927, tc_List_Olist(_1797927)), tc_List_Olist(_1797927), c_Lazy__Sequence_Oproduct(_1797927, tc_List_Olist(_1797927), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1797927, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1797929), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1797927), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1797929), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1797927, tc_List_Olist(_1797927), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1797927))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1797927), tc_List_Olist(_1797927)), tc_fun(tc_List_Olist(_1797927), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1797927))), _1797927), hAPP(c_COMBB(tc_List_Olist(_1797927), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1797927)), tc_List_Olist(_1797927)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1797927)))), c_List_Olist_OCons(_1797927))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1797927)))))], (47023 ^ _777959) ^ [_1720740, _1720742] : [c_Wellfounded_Owf(_1720740, _1720742), 47026 ^ _777959 : [(47027 ^ _777959) ^ [_1720809] : [-(hBOOL(hAPP(hAPP(c_member(_1720740), _1720809), c_Wellfounded_Oacc(_1720740, _1720742))))]]], (14201 ^ _777959) ^ [_1042167, _1042169, _1042171, _1042173, _1042175] : [_1042167 = c_Orderings_Obot__class_Obot(tc_fun(_1042169, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042171, tc_HOL_Obool)), _1042173), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1042169, tc_fun(_1042171, tc_HOL_Obool)), _1042167), _1042175)) = _1042173)], (40795 ^ _777959) ^ [_1571060, _1571062, _1571064, _1571066, _1571068] : [-(hAPP(hAPP(c_List_Otake(_1571060), _1571062), hAPP(hAPP(c_List_Omap(_1571064, _1571060), _1571066), _1571068)) = hAPP(hAPP(c_List_Omap(_1571064, _1571060), _1571066), hAPP(hAPP(c_List_Otake(_1571064), _1571062), _1571068)))], (48240 ^ _777959) ^ [_1749024, _1749026] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1749024), _1749026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1749024)), hAPP(c_Code__Numeral_Oof__nat, _1749026))))], (44436 ^ _777959) ^ [_1661192, _1661194] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1661192, _1661194)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1661194), _1661192))], (18600 ^ _777959) ^ [_1135414, _1135416] : [class_Orderings_Olinorder(_1135414), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135414), _1135416)), -(c_Big__Operators_Olinorder__class_OMax(_1135414, _1135416) = hAPP(c_Finite__Set_Ofold1(_1135414, c_Orderings_Oord__class_Omax(_1135414)), _1135416))], (11894 ^ _777959) ^ [_993792, _993794, _993796, _993798, _993800] : [_993792 = c_Orderings_Obot__class_Obot(tc_fun(_993794, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_993796, tc_HOL_Obool)), _993798), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993794, tc_fun(_993796, tc_HOL_Obool)), _993792), _993800)) = _993798)], (34165 ^ _777959) ^ [_1421313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1421313)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1421313), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (12183 ^ _777959) ^ [_999124, _999126, _999128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999124), _999126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999124), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999128), _999126))))], (45463 ^ _777959) ^ [_1684126, _1684128, _1684130, _1684132, _1684134] : [c_List_OdropWhile(_1684126, _1684128, _1684130) = hAPP(hAPP(c_List_Olist_OCons(_1684126), _1684132), _1684134), 45466 ^ _777959 : [(45469 ^ _777959) ^ [] : [hBOOL(hAPP(_1684128, _1684132))], (45467 ^ _777959) ^ [] : [-(_1684130 = hAPP(hAPP(c_List_Oappend(_1684126), c_List_OtakeWhile(_1684126, _1684128, _1684130)), hAPP(hAPP(c_List_Olist_OCons(_1684126), _1684132), _1684134)))]]], (28926 ^ _777959) ^ [_1323196, _1323198] : [class_Groups_Oordered__ab__group__add(_1323196), -(hAPP(c_Set_Oimage(_1323196, _1323196, c_Groups_Ouminus__class_Ouminus(_1323196)), hAPP(c_SetInterval_Oord__class_OatMost(_1323196), _1323198)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1323196), hAPP(c_Groups_Ouminus__class_Ouminus(_1323196), _1323198)))], (50746 ^ _777959) ^ [_1807269, _1807271] : [class_Complete__Lattice_Ocomplete__lattice(_1807269), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1807271, _1807269)))], (39946 ^ _777959) ^ [_1551298, _1551300] : [hBOOL(hAPP(c_List_Odistinct(_1551298), _1551300)), -(hAPP(c_Finite__Set_Ocard(_1551298), hAPP(c_List_Oset(_1551298), _1551300)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551298)), _1551300))], (31624 ^ _777959) ^ [_1375064, _1375066, _1375068, _1375070, _1375072, _1375074] : [-(c_Com_Ocom_OCond(_1375064, _1375066, _1375068) = c_Com_Ocom_OCond(_1375070, _1375072, _1375074)), _1375064 = _1375070, _1375066 = _1375072, _1375068 = _1375074], (38999 ^ _777959) ^ [_1528720, _1528722, _1528724, _1528726, _1528728, _1528730] : [-(hAPP(hAPP(c_Fun_Ocomp(_1528720, _1528722, _1528724, _1528726), _1528728), _1528730) = hAPP(_1528726, hAPP(_1528728, _1528730)))], (17741 ^ _777959) ^ [_1116856] : [class_Orderings_Olinorder(_1116856), -(c_Orderings_Oord_Omin(_1116856, hAPP(c_COMBC(_1116856, _1116856, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1116856))) = c_Orderings_Oord__class_Omax(_1116856))], (13445 ^ _777959) ^ [_1024582] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1024582)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1024582), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1024582), c_Orderings_Otop__class_Otop(tc_fun(_1024582, tc_HOL_Obool)))))], (42533 ^ _777959) ^ [_1619560, _1619562] : [-(c_Product__Type_Oapfst(_1619560, _1619560, _1619562, c_Fun_Oid(_1619560)) = c_Fun_Oid(tc_prod(_1619560, _1619562)))], (17215 ^ _777959) ^ [_1107131] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1107131, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1107131, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1107131, tc_HOL_Obool)))], (35407 ^ _777959) ^ [_1447986, _1447988, _1447990, _1447992, _1447994, _1447996] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1447986, _1447988), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1447990), _1447992))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1447986, _1447988), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1447994), _1447996))), -(_1447988 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1447992 = _1447996)], (43715 ^ _777959) ^ [_1647014, _1647016, _1647018] : [class_Orderings_Olinorder(_1647014), -(c_Big__Operators_Olinorder__class_OMin(_1647014, hAPP(c_List_Oset(_1647014), hAPP(hAPP(c_List_Olist_OCons(_1647014), _1647016), _1647018))) = hAPP(c_List_Ofoldl(_1647014, _1647014, c_Orderings_Oord__class_Omin(_1647014), _1647016), _1647018))], (41457 ^ _777959) ^ [_1590651, _1590653, _1590655] : [class_Groups_Omonoid__add(_1590651), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1590651), hAPP(hAPP(c_List_Olist_OCons(_1590651), _1590653), _1590655)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1590651), _1590653), hAPP(c_List_Omonoid__add__class_Olistsum(_1590651), _1590655)))], (4454 ^ _777959) ^ [_845371, _845373] : [_845373 = _845371, -(c_HOL_Obool_Obool__size(_845373) = c_HOL_Obool_Obool__size(_845371))], (48729 ^ _777959) ^ [_1760619, _1760621] : [-(hAPP(c_Relation_ORange(_1760619, _1760619), c_Transitive__Closure_Ortrancl(_1760619, _1760621)) = c_Orderings_Otop__class_Otop(tc_fun(_1760619, tc_HOL_Obool)))], (3402 ^ _777959) ^ [_829229, _829231, _829233, _829235] : [-(c_HOL_OThe(_829235, _829231) = c_HOL_OThe(_829233, _829229)), _829235 = _829233, _829231 = _829229], (40186 ^ _777959) ^ [_1557148, _1557150, _1557152] : [40188 ^ _777959 : [(40191 ^ _777959) ^ [] : [hBOOL(hAPP(_1557152, 40187 ^ [_1557148, _1557150, _1557152]))], (40189 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1557148), 40187 ^ [_1557148, _1557150, _1557152]), hAPP(c_List_Oset(_1557148), _1557150))))]], 40192 ^ _777959 : [(40193 ^ _777959) ^ [_1557332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1557332), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1557148)), _1557150))), -(hBOOL(hAPP(_1557152, hAPP(hAPP(c_List_Onth(_1557148), _1557150), _1557332))))]]], (23469 ^ _777959) ^ [_1224733] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224733), _1224733)))], (38740 ^ _777959) ^ [_1521482, _1521484, _1521486] : [-(hAPP(c_Set_Ovimage(_1521482, _1521484, _1521486), c_Orderings_Obot__class_Obot(tc_fun(_1521484, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1521482, tc_HOL_Obool)))], (2504 ^ _777959) ^ [_815070, _815072, _815074, _815076] : [-(c_Groups_Osgn__class_Osgn(_815076, _815072) = c_Groups_Osgn__class_Osgn(_815074, _815070)), _815076 = _815074, _815072 = _815070], (25641 ^ _777959) ^ [_1264009, _1264011, _1264013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264009, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1264009, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25642 ^ [_1264009, _1264011, _1264013])), _1264011)), _1264013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1264009, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1264009, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1264011)), _1264013)))], (50464 ^ _777959) ^ [_1801492, _1801494, _1801496] : [-(c_Predicate_Oconversep(_1801492, _1801494, c_Predicate_Oconversep(_1801494, _1801492, _1801496)) = _1801496)], (12287 ^ _777959) ^ [_1001032, _1001034, _1001036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001032), _1001034)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001032), _1001036)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001034), _1001032)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001036), _1001032)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001034), _1001036))], (40349 ^ _777959) ^ [_1561023, _1561025, _1561027, _1561029] : [hBOOL(hAPP(c_List_Odistinct(_1561023), _1561025)), -(hBOOL(hAPP(hAPP(c_member(_1561023), _1561027), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1561023, tc_HOL_Obool)), hAPP(c_List_Oset(_1561023), _1561025)), hAPP(hAPP(c_Set_Oinsert(_1561023), hAPP(hAPP(c_List_Onth(_1561023), _1561025), _1561029)), c_Orderings_Obot__class_Obot(tc_fun(_1561023, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1561023), hAPP(hAPP(c_List_Olist__update(_1561023, _1561025), _1561029), _1561027))))], (29102 ^ _777959) ^ [_1326346, _1326348, _1326350, _1326352] : [class_Orderings_Olinorder(_1326346), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326346, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1326346), _1326348)), c_SetInterval_Oord__class_OatLeastAtMost(_1326346, _1326350, _1326352)) = c_SetInterval_Oord__class_OatLeastAtMost(_1326346, _1326350, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1326346), _1326348), _1326352)))], (21386 ^ _777959) ^ [_1184362, _1184364, _1184366, _1184368, _1184370] : [class_Rings_Olinordered__semiring__strict(_1184362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184362), _1184364), _1184366)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184362), _1184368), _1184370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184362), c_Groups_Ozero__class_Ozero(_1184362)), _1184364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184362), c_Groups_Ozero__class_Ozero(_1184362)), _1184368)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184362), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184362), _1184364), _1184368)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184362), _1184366), _1184370))))], (1460 ^ _777959) ^ [_798933, _798935] : [-(class_Rings_Olinordered__semiring__strict(_798933)), _798935 = _798933, class_Rings_Olinordered__semiring__strict(_798935)], (27471 ^ _777959) ^ [_1297406, _1297408, _1297410] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1297406), _1297408), _1297410) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1297406), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1297406, tc_Int_Oint), _1297408), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1297410))), class_Groups_Ocomm__monoid__add(_1297406), class_Groups_Ocomm__monoid__mult(_1297406)], (15733 ^ _777959) ^ [_1077274, _1077276] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077274), _1077276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077274), hAPP(c_Nat_OSuc, _1077276))))], (3098 ^ _777959) ^ [_824403, _824405, _824407, _824409, _824411, _824413] : [-(c_List_Osublist(_824413, _824409, _824405) = c_List_Osublist(_824411, _824407, _824403)), _824413 = _824411, _824409 = _824407, _824405 = _824403], (11551 ^ _777959) ^ [_984369, _984371, _984373, _984375, _984377] : [_984369 = c_Orderings_Obot__class_Obot(tc_fun(_984371, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_984371, tc_fun(_984373, tc_HOL_Obool)), _984369), hAPP(hAPP(c_COMBB(tc_fun(_984373, tc_HOL_Obool), tc_fun(_984373, tc_HOL_Obool), _984371), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984373, tc_HOL_Obool)), _984375)), _984377)) = c_Orderings_Obot__class_Obot(tc_fun(_984373, tc_HOL_Obool)))], (32989 ^ _777959) ^ [_1400993] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400993))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1400993)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43270 ^ _777959) ^ [_1637221, _1637223] : [-(hAPP(hAPP(c_List_Odrop(_1637221), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1637223) = _1637223)], (50017 ^ _777959) ^ [_1792272, _1792274] : [-(c_FunDef_Ois__measure(_1792272, _1792274))], (30491 ^ _777959) ^ [_1354492, _1354494, _1354496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1354492)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1354494, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1354496), _1354492)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1354496), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1354494), _1354496), _1354492))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1354494, _1354496)))], (18568 ^ _777959) ^ [_1134903, _1134905, _1134907] : [-(hAPP(c_Finite__Set_Ofold1(_1134903, _1134905), _1134907) = c_HOL_OThe(_1134903, c_Finite__Set_Ofold1Set(_1134903, _1134905, _1134907)))], (33229 ^ _777959) ^ [_1405149] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1405149), c_Int_OPls) = _1405149)], (39344 ^ _777959) ^ [_1536557, _1536559, _1536561, _1536563, _1536565, _1536567, _1536569, _1536571, _1536573, _1536575, _1536577] : [c_Finite__Set_Ofolding(_1536557, _1536559, _1536561, _1536563), -(hAPP(c_Fun_Ocomp(_1536565, _1536567, _1536569, _1536571), hAPP(c_Fun_Ocomp(_1536573, _1536565, _1536569, _1536575), _1536577)) = hAPP(c_Fun_Ocomp(_1536573, _1536567, _1536569, hAPP(c_Fun_Ocomp(_1536565, _1536567, _1536573, _1536571), _1536575)), _1536577))], (15520 ^ _777959) ^ [_1073025] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1073025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073025), _1073025))))], (48218 ^ _777959) ^ [_1748692, _1748694] : [hAPP(c_Code__Numeral_Oof__nat, _1748692) = hAPP(c_Code__Numeral_Oof__nat, _1748694), -(_1748692 = _1748694)], (7998 ^ _777959) ^ [_914494, _914496, _914498, _914500, _914502] : [c_Com_Ocom_OCall(_914494, _914496, _914498) = c_Com_Ocom_OWhile(_914500, _914502)], (49361 ^ _777959) ^ [_1776676, _1776678] : [-(hAPP(hAPP(c_Nat_Ocompow(_1776676, _1776676), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1776678) = c_Fun_Oid(_1776676))], (5761 ^ _777959) ^ [_869064, _869066, _869068] : [class_Orderings_Obot(_869064), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_869066, _869064)), _869068) = c_Orderings_Obot__class_Obot(_869064))], (39932 ^ _777959) ^ [_1551080, _1551082] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1551080), hAPP(c_List_Oset(_1551080), _1551082))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551080)), _1551082))))], (47399 ^ _777959) ^ [_1730553, _1730555, _1730557, _1730559] : [hBOOL(hAPP(hAPP(c_member(_1730553), _1730555), hAPP(c_Relation_ODomain(_1730553, _1730557), _1730559))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1730553, _1730557)), hAPP(hAPP(c_Product__Type_OPair(_1730553, _1730557), _1730555), 47402 ^ [_1730553, _1730555, _1730557, _1730559])), _1730559)))], (13603 ^ _777959) ^ [_1027916, _1027918] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1027916, tc_HOL_Obool)), _1027918), c_Orderings_Otop__class_Otop(tc_fun(_1027916, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1027916, tc_HOL_Obool)))], (13457 ^ _777959) ^ [_1024818, _1024820] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1024818), c_Orderings_Otop__class_Otop(tc_fun(_1024818, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024820), c_Orderings_Otop__class_Otop(tc_fun(_1024820, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1024818, _1024820)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1024818, _1024820), tc_HOL_Obool)))))], (45936 ^ _777959) ^ [_1694576, _1694578] : [class_Enum_Oenum(_1694576), 45939 ^ _777959 : [(45946 ^ _777959) ^ [] : [hBOOL(hAPP(_1694578, 45947 ^ [_1694576, _1694578])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1694576), _1694578)))], (45940 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1694576), _1694578)), 45943 ^ _777959 : [(45944 ^ _777959) ^ [_1694702] : [-(hBOOL(hAPP(_1694578, _1694702)))]]]]], (37365 ^ _777959) ^ [_1491309, _1491311, _1491313, _1491315] : [_1491309 = _1491311, hBOOL(hAPP(hAPP(c_member(_1491313), _1491309), _1491315)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1491313, _1491313)), hAPP(hAPP(c_Product__Type_OPair(_1491313, _1491313), _1491309), _1491311)), c_Relation_OId__on(_1491313, _1491315))))], (42519 ^ _777959) ^ [_1619323] : [-(hAPP(c_List_Omap(_1619323, _1619323), c_Fun_Oid(_1619323)) = c_Fun_Oid(tc_List_Olist(_1619323)))], (5655 ^ _777959) ^ [_867194] : [c_Hoare__Mirabelle_Ostate__not__singleton, c_Com_OWT__bodies, hBOOL(hAPP(c_Com_OWT, _867194)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _867194)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (1540 ^ _777959) ^ [_799933, _799935] : [-(class_Rings_Olinordered__semidom(_799933)), _799935 = _799933, class_Rings_Olinordered__semidom(_799935)], (9666 ^ _777959) ^ [_945303, _945305] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945303, tc_HOL_Obool)), _945305), _945305) = _945305)], (6698 ^ _777959) ^ [_886719, _886721] : [_886721 = c_Orderings_Obot__class_Obot(tc_fun(_886719, tc_HOL_Obool)), 6701 ^ _777959 : [(6702 ^ _777959) ^ [_886799] : [hBOOL(hAPP(hAPP(c_member(_886719), _886799), _886721))]]], (33677 ^ _777959) ^ [_1412110, _1412112] : [class_Int_Onumber__ring(_1412110), class_Rings_Olinordered__idom(_1412110), 33684 ^ _777959 : [(33691 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412112), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412110), hAPP(c_Int_Onumber__class_Onumber__of(_1412110), _1412112)), c_Groups_Oone__class_Oone(_1412110))))], (33685 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1412110), hAPP(c_Int_Onumber__class_Onumber__of(_1412110), _1412112)), c_Groups_Oone__class_Oone(_1412110))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1412112), c_Int_OBit1(c_Int_OPls))))]]], (7124 ^ _777959) ^ [_896918, _896920, _896922] : [class_Lattices_Olattice(_896918), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896918), _896920), _896922) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896918), _896922), _896920))], (190 ^ _777959) ^ [_781106, _781108] : [-(class_Rings_Odivision__ring__inverse__zero(_781106)), _781108 = _781106, class_Rings_Odivision__ring__inverse__zero(_781108)], (14031 ^ _777959) ^ [_1038506, _1038508, _1038510, _1038512] : [_1038506 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1038508, _1038510), 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)), _1038512))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1038508), _1038506)))], (47446 ^ _777959) ^ [_1731447, _1731449, _1731451] : [c_Wellfounded_OwfP(_1731447, _1731449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1731447, tc_fun(_1731447, tc_HOL_Obool))), _1731451), _1731449)), -(c_Wellfounded_OwfP(_1731447, _1731451))], (22122 ^ _777959) ^ [_1198892, _1198894, _1198896, _1198898] : [class_Groups_Ocomm__monoid__add(_1198892), 22125 ^ _777959 : [(22132 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1198894), _1198896))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198894, _1198892), _1198898), _1198896) = c_Groups_Ozero__class_Ozero(_1198892))], (22126 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1198894), _1198896)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1198894, _1198892), _1198898), _1198896) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1198892, _1198894, c_Groups_Oplus__class_Oplus(_1198892)), _1198898), c_Groups_Ozero__class_Ozero(_1198892)), _1198896))]]], (31402 ^ _777959) ^ [_1371225] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1371225)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1371225 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36906 ^ _777959) ^ [_1478640, _1478642, _1478644, _1478646, _1478648, _1478650, _1478652, _1478654] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1478640, _1478642), tc_prod(_1478640, _1478642))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1478640, _1478642), tc_prod(_1478640, _1478642)), hAPP(hAPP(c_Product__Type_OPair(_1478640, _1478642), _1478644), _1478646)), hAPP(hAPP(c_Product__Type_OPair(_1478640, _1478642), _1478648), _1478650))), c_Wellfounded_Olex__prod(_1478640, _1478642, _1478652, _1478654)))), 36907 ^ _777959 : [(36910 ^ _777959) ^ [] : [_1478644 = _1478648, hBOOL(hAPP(hAPP(c_member(tc_prod(_1478642, _1478642)), hAPP(hAPP(c_Product__Type_OPair(_1478642, _1478642), _1478646), _1478650)), _1478654))], (36908 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1478640, _1478640)), hAPP(hAPP(c_Product__Type_OPair(_1478640, _1478640), _1478644), _1478648)), _1478652))]]], (39388 ^ _777959) ^ [_1537739, _1537741, _1537743, _1537745, _1537747, _1537749, _1537751, _1537753] : [c_Finite__Set_Ofolding(_1537739, _1537741, _1537743, _1537745), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537739), _1537747)), -(hAPP(c_Fun_Ocomp(_1537741, _1537741, _1537749, hAPP(_1537743, _1537751)), hAPP(c_Fun_Ocomp(_1537741, _1537741, _1537749, hAPP(_1537745, _1537747)), _1537753)) = hAPP(c_Fun_Ocomp(_1537741, _1537741, _1537749, hAPP(_1537745, _1537747)), hAPP(c_Fun_Ocomp(_1537741, _1537741, _1537749, hAPP(_1537743, _1537751)), _1537753)))], (35263 ^ _777959) ^ [_1440823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1440823)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1440823) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1440823), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (48785 ^ _777959) ^ [_1762035, _1762037, _1762039, _1762041] : [-(hBOOL(hAPP(hAPP(c_member(_1762035), _1762037), hAPP(c_Relation_ODomain(_1762035, _1762035), _1762039)))), 48788 ^ _777959 : [(48795 ^ _777959) ^ [] : [_1762037 = _1762041, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1762035, _1762035)), hAPP(hAPP(c_Product__Type_OPair(_1762035, _1762035), _1762037), _1762041)), c_Transitive__Closure_Ortrancl(_1762035, _1762039))))], (48789 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1762035, _1762035)), hAPP(hAPP(c_Product__Type_OPair(_1762035, _1762035), _1762037), _1762041)), c_Transitive__Closure_Ortrancl(_1762035, _1762039))), -(_1762037 = _1762041)]]], (25658 ^ _777959) ^ [_1264448, _1264450] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSemi(_1264448, _1264450)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1264448)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1264450))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43091 ^ _777959) ^ [_1632471, _1632473, _1632475, _1632477] : [-(c_List_Osublist(_1632471, hAPP(hAPP(c_List_Oappend(_1632471), _1632473), _1632475), _1632477) = hAPP(hAPP(c_List_Oappend(_1632471), c_List_Osublist(_1632471, _1632473, _1632477)), c_List_Osublist(_1632471, _1632475, 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(_1632471)), _1632473)))), _1632477)))))], (32141 ^ _777959) ^ [_1385070, _1385072, _1385074] : [class_Int_Onumber__ring(_1385070), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1385070), hAPP(c_Int_Onumber__class_Onumber__of(_1385070), _1385072)), hAPP(c_Int_Onumber__class_Onumber__of(_1385070), _1385074)) = hAPP(c_Int_Onumber__class_Onumber__of(_1385070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1385072), _1385074)))], (42989 ^ _777959) ^ [_1629880, _1629882, _1629884, _1629886] : [-(hAPP(hAPP(c_List_Otake(_1629880), _1629882), hAPP(hAPP(c_List_Oappend(_1629880), _1629884), _1629886)) = hAPP(hAPP(c_List_Oappend(_1629880), hAPP(hAPP(c_List_Otake(_1629880), _1629882), _1629884)), hAPP(hAPP(c_List_Otake(_1629880), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1629882), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629880)), _1629884))), _1629886)))], (10514 ^ _777959) ^ [_963962, _963964, _963966, _963968, _963970, _963972] : [c_Finite__Set_Ofun__left__comm(_963962, _963964, _963966), hBOOL(hAPP(c_Finite__Set_Ofinite(_963962), _963968)), hBOOL(hAPP(hAPP(c_member(_963962), _963970), _963968)), -(hAPP(hAPP(c_Finite__Set_Ofold(_963962, _963964, _963966), _963972), _963968) = hAPP(hAPP(_963966, _963970), hAPP(hAPP(c_Finite__Set_Ofold(_963962, _963964, _963966), _963972), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_963962, tc_HOL_Obool)), _963968), hAPP(hAPP(c_Set_Oinsert(_963962), _963970), c_Orderings_Obot__class_Obot(tc_fun(_963962, tc_HOL_Obool)))))))], (39926 ^ _777959) ^ [_1550973, _1550975, _1550977] : [hBOOL(hAPP(c_List_Odistinct(_1550973), _1550975)), -(hBOOL(hAPP(c_List_Odistinct(_1550973), hAPP(c_List_OremoveAll(_1550973, _1550977), _1550975))))], (10741 ^ _777959) ^ [_968592, _968594, _968596, _968598] : [class_Groups_Ocancel__ab__semigroup__add(_968592), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968592), _968594), _968596) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968592), _968594), _968598), -(_968596 = _968598)], (13014 ^ _777959) ^ [_1014779, _1014781] : [class_Lattices_Oboolean__algebra(_1014779), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1014779), _1014781), hAPP(c_Groups_Ouminus__class_Ouminus(_1014779), _1014781)) = c_Orderings_Obot__class_Obot(_1014779))], (24516 ^ _777959) ^ [_1243527, _1243529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1243527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243529)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1243529), _1243527)), _1243529) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1243529), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1243527), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (25472 ^ _777959) ^ [_1260891, _1260893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1260891)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1260893), _1260891)), _1260891) = _1260893)], (42375 ^ _777959) ^ [_1614445, _1614447, _1614449, _1614451] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1614445, _1614447), _1614449), _1614451) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1614445, tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool)), _1614449), hAPP(hAPP(c_COMBS(_1614445, tc_fun(_1614447, tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool)), tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1614447, tc_HOL_Obool), tc_fun(tc_fun(_1614447, tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool)), tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool)), _1614445), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1614447, tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool))), _1614451)), hAPP(hAPP(c_COMBC(_1614445, tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool), tc_fun(_1614447, tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1614447, tc_fun(tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool), tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool), tc_fun(_1614447, tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool))), _1614445), c_COMBC(_1614447, tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool), tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1614447, tc_prod(_1614445, _1614447)), tc_fun(_1614447, tc_fun(tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool), tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool))), _1614445), hAPP(c_COMBB(tc_prod(_1614445, _1614447), tc_fun(tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool), tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool)), _1614447), c_Set_Oinsert(tc_prod(_1614445, _1614447)))), c_Product__Type_OPair(_1614445, _1614447)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1614445, _1614447), tc_HOL_Obool))))))], (16581 ^ _777959) ^ [_1095897, _1095899, _1095901, _1095903] : [class_Orderings_Olinorder(_1095897), 16584 ^ _777959 : [(16585 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095897), _1095899), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095897), _1095901), _1095903))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095897), _1095899), _1095901))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095897), _1095899), _1095903)))], (16595 ^ _777959) ^ [] : [16596 ^ _777959 : [(16599 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095897), _1095899), _1095903))], (16597 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095897), _1095899), _1095901))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095897), _1095899), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095897), _1095901), _1095903))))]]], (44853 ^ _777959) ^ [_1670127, _1670129, _1670131] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1670127), tc_List_Olist(_1670127), c_List_Oappend(_1670127), 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hAPP(c_Product__Type_Oprod_Oprod__case(_1597057, tc_List_Olist(_1597057), tc_List_Olist(_1597057)), c_List_Olist_OCons(_1597057)), hAPP(c_Product__Type_Oprod_Oprod__case(_1597057, tc_List_Olist(_1597057), tc_List_Olist(_1597057)), c_List_Olist_OCons(_1597057)))), c_Wellfounded_Olex__prod(_1597057, tc_List_Olist(_1597057), _1597059, hAPP(c_List_Olexn(_1597057, _1597059), _1597061)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1597057), tc_List_Olist(_1597057))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1597057), tc_List_Olist(_1597057), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1597057), tc_fun(tc_List_Olist(_1597057), tc_HOL_Obool), tc_fun(tc_List_Olist(_1597057), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1597057), tc_HOL_Obool), tc_fun(tc_List_Olist(_1597057), tc_HOL_Obool)), tc_List_Olist(_1597057)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1597057))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1597057)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1597057), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1597057)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1597057)))), hAPP(c_Nat_OSuc, _1597061))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1597057), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1597057)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1597057)))), hAPP(c_Nat_OSuc, _1597061)))))))], (48733 ^ _777959) ^ [_1760697, _1760699, _1760701, _1760703, _1760705] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1760697), tc_List_Olist(_1760697))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1760697), tc_List_Olist(_1760697)), _1760699), _1760701)), c_List_Olistrel(_1760697, c_Transitive__Closure_Ortrancl(_1760697, _1760703)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1760697), tc_List_Olist(_1760697))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1760697), tc_List_Olist(_1760697)), _1760701), _1760705)), c_List_Olistrel(_1760697, c_Transitive__Closure_Ortrancl(_1760697, _1760703)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1760697), tc_List_Olist(_1760697))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1760697), tc_List_Olist(_1760697)), _1760699), _1760705)), c_List_Olistrel(_1760697, c_Transitive__Closure_Ortrancl(_1760697, _1760703)))))], (40067 ^ _777959) ^ [_1554100, _1554102, _1554104] : [-(hBOOL(hAPP(hAPP(c_member(_1554100), _1554102), hAPP(c_List_Oset(_1554100), _1554104)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554100)), c_List_Oremove1(_1554100, _1554102, _1554104)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554100)), _1554104))], (16163 ^ _777959) ^ [_1086218, _1086220, _1086222, _1086224, _1086226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1086218), _1086220)), 16166 ^ _777959 : [(16173 ^ _777959) ^ [] : [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), _1086220), _1086218)), _1086222)), _1086224)), _1086226)), -(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), _1086220), _1086222)), _1086224)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086218), _1086222)), _1086226))))], (16167 ^ _777959) ^ [] : [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), _1086220), _1086222)), _1086224)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086218), _1086222)), _1086226))), -(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), _1086220), _1086218)), _1086222)), _1086224)), _1086226)))]]], (6469 ^ _777959) ^ [_882481, _882483, _882485, _882487] : [class_Orderings_Oorder(_882481), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882481), _882483), _882485)), _882483 = _882487, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882481), _882487), _882485)))], (41988 ^ _777959) ^ [_1605426, _1605428] : [_1605428 = c_List_Olist_ONil(_1605426), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605426)), _1605428) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30994 ^ _777959) ^ [_1363532, _1363534, _1363536] : [class_Groups_Oordered__ab__group__add__abs(_1363532), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363532), hAPP(c_Groups_Oabs__class_Oabs(_1363532), _1363534)), _1363536)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363532), _1363534), _1363536)))], (2288 ^ _777959) ^ [_811792, _811794, _811796, _811798] : [-(c_SMT_Oz3div(_811798, _811794) = c_SMT_Oz3div(_811796, _811792)), _811798 = _811796, _811794 = _811792], (3002 ^ _777959) ^ [_822915, _822917, _822919, _822921] : [-(c_Big__Operators_Olinorder__class_OMin(_822921, _822917) = c_Big__Operators_Olinorder__class_OMin(_822919, _822915)), _822921 = _822919, _822917 = _822915], (37229 ^ _777959) ^ [_1487642, _1487644, _1487646] : [class_Rings_Oring__1(_1487642), -(hAPP(c_Int_Oring__1__class_Oof__int(_1487642), 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), _1487644), _1487646)), 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(_1487642), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1487642), _1487644)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1487642), _1487646)))], (37247 ^ _777959) ^ [_1488099, _1488101, _1488103, _1488105] : [-(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), _1488099), _1488101)), 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), _1488103), _1488105)), 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), _1488099), _1488103)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1488101), _1488105))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (40797 ^ _777959) ^ [_1571125, _1571127, _1571129] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1571125, tc_HOL_Obool)), hAPP(c_List_Oset(_1571125), hAPP(hAPP(c_List_Otake(_1571125), _1571127), _1571129))), hAPP(c_List_Oset(_1571125), _1571129))))], (8528 ^ _777959) ^ [_925351, _925353, _925355] : [class_Orderings_Opreorder(_925351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925351), _925353), _925355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925351), _925355), _925353))], (34183 ^ _777959) ^ [_1421604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1421604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1421604))))], (42290 ^ _777959) ^ [_1611838, _1611840, _1611842, _1611844] : [-(_1611838 = c_Orderings_Obot__class_Obot(tc_fun(_1611840, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1611840, _1611842), _1611842, c_Product__Type_Osnd(_1611840, _1611842)), hAPP(hAPP(c_Product__Type_OSigma(_1611840, _1611842), _1611838), hAPP(c_COMBK(tc_fun(_1611842, tc_HOL_Obool), _1611840), _1611844))) = _1611844)], (12247 ^ _777959) ^ [_1000326, _1000328, _1000330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000326), _1000328)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1000326), _1000330)), 12254 ^ _777959 : [(12261 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000328), _1000330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1000328), _1000326)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1000330), _1000326))))], (12255 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1000328), _1000326)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1000330), _1000326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1000328), _1000330)))]]], (31350 ^ _777959) ^ [_1370321, _1370323] : [class_Groups_Oordered__ab__group__add__abs(_1370321), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1370321), _1370323), c_Groups_Ozero__class_Ozero(_1370321))), -(hAPP(c_Groups_Oabs__class_Oabs(_1370321), _1370323) = hAPP(c_Groups_Ouminus__class_Ouminus(_1370321), _1370323))], (43193 ^ _777959) ^ [_1635573, _1635575] : [hBOOL(hAPP(c_List_Odistinct(_1635573), hAPP(c_List_Orotate1(_1635573), _1635575))), -(hBOOL(hAPP(c_List_Odistinct(_1635573), _1635575)))], (51316 ^ _777959) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (19352 ^ _777959) ^ [_1149083, _1149085] : [class_Groups_Ogroup__add(_1149083), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149083), _1149085), _1149085) = c_Groups_Ozero__class_Ozero(_1149083))], (22212 ^ _777959) ^ [_1200709, _1200711, _1200713, _1200715, _1200717, _1200719] : [class_Rings_Olinordered__semiring__1__strict(_1200709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200709), _1200711), _1200713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200709), _1200715), _1200713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1200709), c_Groups_Ozero__class_Ozero(_1200709)), _1200717)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1200709), c_Groups_Ozero__class_Ozero(_1200709)), _1200719)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200709), _1200717), _1200719) = c_Groups_Oone__class_Oone(_1200709), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1200709), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1200709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200709), _1200717), _1200711)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1200709), _1200719), _1200715))), _1200713)))], (172 ^ _777959) ^ [_780837, _780839, _780841, _780843, _780845, _780847] : [-(c_Big__Operators_Osemilattice__big(_780845, _780841, _780837)), c_Big__Operators_Osemilattice__big(_780847, _780843, _780839), _780847 = _780845, _780843 = _780841, _780839 = _780837], (44374 ^ _777959) ^ [_1660149, _1660151] : [c_List_Oupt(_1660149, _1660151) = c_List_Olist_ONil(tc_Nat_Onat), -(_1660151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1660151), _1660149)))], (11832 ^ _777959) ^ [_992484, _992486, _992488, _992490, _992492] : [class_Complete__Lattice_Ocomplete__lattice(_992484), 11835 ^ _777959 : [(11836 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992484), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992486, _992484), _992488), _992490)), _992492)), 11839 ^ _777959 : [(11840 ^ _777959) ^ [_992665] : [hBOOL(hAPP(hAPP(c_member(_992486), _992665), _992488)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992484), hAPP(_992490, _992665)), _992492)))]]], (11846 ^ _777959) ^ [] : [11848 ^ _777959 : [(11851 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992484), hAPP(_992490, 11847 ^ [_992484, _992486, _992488, _992490, _992492])), _992492))], (11849 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_992486), 11847 ^ [_992484, _992486, _992488, _992490, _992492]), _992488)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992484), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992486, _992484), _992488), _992490)), _992492)))]]], (7118 ^ _777959) ^ [_896809, _896811, _896813] : [class_Lattices_Osemilattice__sup(_896809), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896809), _896811), _896813) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896809), _896813), _896811))], (29952 ^ _777959) ^ [_1344110, _1344112, _1344114, _1344116] : [class_Divides_Osemiring__div(_1344110), -(c_Divides_Odiv__class_Omod(_1344110, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344110), _1344112), _1344114), _1344116) = c_Divides_Odiv__class_Omod(_1344110, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344110), _1344112), c_Divides_Odiv__class_Omod(_1344110, _1344114, _1344116)), _1344116))], (44037 ^ _777959) ^ [_1653492, _1653494, _1653496] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1653492, tc_HOL_Obool)), hAPP(c_List_Oset(_1653492), _1653494)), hAPP(hAPP(c_Set_Oinsert(_1653492), _1653496), c_Orderings_Obot__class_Obot(tc_fun(_1653492, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1653492), hAPP(c_List_Ofilter(_1653492, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1653492), c_fNot), hAPP(hAPP(c_COMBC(_1653492, _1653492, tc_HOL_Obool), c_fequal), _1653496))), _1653494)))], (10761 ^ _777959) ^ [_968926, _968928, _968930, _968932, _968934] : [c_Finite__Set_Ofun__left__comm(_968926, _968928, _968930), -(c_Finite__Set_Ofun__left__comm(_968932, _968928, hAPP(hAPP(c_COMBB(_968926, tc_fun(_968928, _968928), _968932), _968930), _968934)))], (11314 ^ _777959) ^ [_979282, _979284, _979286, _979288, _979290] : [class_Groups_Ocomm__monoid__add(_979282), hBOOL(hAPP(c_Finite__Set_Ofinite(_979284), _979286)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_979284, _979282), _979288), hAPP(hAPP(c_Set_Oinsert(_979284), _979290), _979286)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979282), hAPP(_979288, _979290)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_979284, _979282), _979288), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_979284, tc_HOL_Obool)), _979286), hAPP(hAPP(c_Set_Oinsert(_979284), _979290), c_Orderings_Obot__class_Obot(tc_fun(_979284, tc_HOL_Obool)))))))], (4504 ^ _777959) ^ [_846094, _846096] : [_846096 = _846094, -(c_Int_Onumber__class_Onumber__of(_846096) = c_Int_Onumber__class_Onumber__of(_846094))], (49104 ^ _777959) ^ [_1770285, _1770287, _1770289] : [-(hAPP(c_Relation_Oconverse(_1770285, _1770287), _1770289) = hAPP(c_Set_OCollect(tc_prod(_1770287, _1770285)), hAPP(c_Product__Type_Oprod_Oprod__case(_1770287, _1770285, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1770287, tc_fun(tc_prod(_1770285, _1770287), tc_HOL_Obool), tc_fun(_1770285, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1770285, tc_fun(tc_fun(tc_prod(_1770285, _1770287), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1770285, _1770287), tc_HOL_Obool), tc_fun(_1770285, tc_HOL_Obool)), _1770287), c_COMBC(_1770285, tc_fun(tc_prod(_1770285, _1770287), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1770285, tc_prod(_1770285, _1770287)), tc_fun(_1770285, tc_fun(tc_fun(tc_prod(_1770285, _1770287), tc_HOL_Obool), tc_HOL_Obool)), _1770287), hAPP(c_COMBB(tc_prod(_1770285, _1770287), tc_fun(tc_fun(tc_prod(_1770285, _1770287), tc_HOL_Obool), tc_HOL_Obool), _1770285), c_member(tc_prod(_1770285, _1770287)))), hAPP(c_COMBC(_1770285, _1770287, tc_prod(_1770285, _1770287)), c_Product__Type_OPair(_1770285, _1770287))))), _1770289))))], (27032 ^ _777959) ^ [_1289823, _1289825, _1289827, _1289829] : [class_Fields_Olinordered__field(_1289823), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1289823), c_Groups_Ozero__class_Ozero(_1289823)), _1289825)), 27039 ^ _777959 : [(27046 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289823), _1289827), _1289825)), _1289829)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289823), _1289827), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289823), _1289829), _1289825))))], (27040 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289823), _1289827), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1289823), _1289829), _1289825))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1289823), _1289827), _1289825)), _1289829)))]]], (43982 ^ _777959) ^ [_1652407, _1652409, _1652411, _1652413] : [-(hAPP(c_List_Ofilter(_1652407, _1652409), hAPP(c_List_Ofilter(_1652407, _1652411), _1652413)) = hAPP(c_List_Ofilter(_1652407, hAPP(hAPP(c_COMBS(_1652407, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1652407), c_fconj), _1652411)), _1652409)), _1652413))], (39705 ^ _777959) ^ [_1545290, _1545292, _1545294, _1545296, _1545298] : [c_Finite__Set_Ofolding__idem(_1545290, _1545292, _1545294, _1545296), -(hAPP(c_Fun_Ocomp(_1545292, _1545292, _1545292, hAPP(_1545294, _1545298)), hAPP(_1545294, _1545298)) = hAPP(_1545294, _1545298))], (35757 ^ _777959) ^ [_1455954, _1455956, _1455958, _1455960, _1455962, _1455964] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455954, tc_fun(_1455956, tc_HOL_Obool))), _1455958), _1455960), _1455962), _1455964)), -(hBOOL(hAPP(hAPP(_1455958, _1455962), _1455964)))], (39081 ^ _777959) ^ [_1530615, _1530617, _1530619, _1530621, _1530623, _1530625] : [c_Fun_Oinj__on(_1530615, _1530617, hAPP(c_Fun_Ocomp(_1530619, _1530617, _1530615, _1530621), _1530623), _1530625), -(c_Fun_Oinj__on(_1530619, _1530617, _1530621, hAPP(c_Set_Oimage(_1530615, _1530619, _1530623), _1530625)))], (6445 ^ _777959) ^ [_882065, _882067, _882069, _882071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882065, tc_HOL_Obool)), _882067), _882069)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882065, tc_HOL_Obool)), _882069), _882071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_882065, tc_HOL_Obool)), _882067), _882071)))], (49714 ^ _777959) ^ [_1786221, _1786223, _1786225] : [c_Nitpick_Oless__frac(_1786221, _1786223, _1786225), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1786221), c_Nitpick_Oplus__frac(_1786221, _1786223, c_Nitpick_Ouminus__frac(_1786221, _1786225)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (7466 ^ _777959) ^ [_903241, _903243, _903245] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_903241), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903241, tc_HOL_Obool)), _903243), _903245)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_903241), _903243)), hBOOL(hAPP(c_Finite__Set_Ofinite(_903241), _903245))], (24089 ^ _777959) ^ [_1235903, _1235905, _1235907, _1235909, _1235911, _1235913] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235903), _1235905)), _1235907) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235909), _1235911)), _1235913), 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), _1235909), _1235911)), _1235913)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1235907), _1235903)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235913)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235909)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1235909), _1235903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1235911), _1235905)))], (2182 ^ _777959) ^ [_810053, _810055, _810057, _810059, _810061, _810063, _810065, _810067, _810069, _810071] : [-(c_Finite__Set_Ofold__graph(_810071, _810067, _810063, _810059, _810055) = c_Finite__Set_Ofold__graph(_810069, _810065, _810061, _810057, _810053)), _810071 = _810069, _810067 = _810065, _810063 = _810061, _810059 = _810057, _810055 = _810053], (46627 ^ _777959) ^ [_1709552, _1709554, _1709556, _1709558] : [-(c_List_Oconcat(_1709552, hAPP(hAPP(c_List_Omap(_1709554, tc_List_Olist(_1709552)), _1709556), _1709558)) = c_List_Omaps(_1709554, _1709552, _1709556, _1709558))], (41783 ^ _777959) ^ [_1600025, _1600027, _1600029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1600025, tc_HOL_Obool)), _1600027), _1600029)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1600025), tc_HOL_Obool)), c_List_Olists(_1600025, _1600027)), c_List_Olists(_1600025, _1600029))))], (17525 ^ _777959) ^ [_1112937, _1112939] : [class_Complete__Lattice_Ocomplete__lattice(_1112937), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112937), _1112939)), -(_1112939 = c_Orderings_Obot__class_Obot(tc_fun(_1112937, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1112937, _1112939) = c_Complete__Lattice_OInf__class_OInf(_1112937, _1112939))], (20363 ^ _777959) ^ [_1166377, _1166379, _1166381] : [class_Rings_Olinordered__semiring__strict(_1166377), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166377), c_Groups_Ozero__class_Ozero(_1166377)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166377), _1166379), _1166381))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166377), c_Groups_Ozero__class_Ozero(_1166377)), _1166379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166377), c_Groups_Ozero__class_Ozero(_1166377)), _1166381)))], (7566 ^ _777959) ^ [_905037, _905039, _905041, _905043] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_905037), _905039)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_905037, tc_HOL_Obool)), _905039), _905041)), hBOOL(hAPP(_905043, c_Orderings_Obot__class_Obot(tc_fun(_905037, tc_HOL_Obool)))), 7581 ^ _777959 : [(7582 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_905037), 7580 ^ [_905037, _905039, _905041, _905043])))], (7586 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_905037), 7579 ^ [_905037, _905039, _905041, _905043]), 7580 ^ [_905037, _905039, _905041, _905043]))], (7590 ^ _777959) ^ [] : [hBOOL(hAPP(_905043, hAPP(hAPP(c_Set_Oinsert(_905037), 7579 ^ [_905037, _905039, _905041, _905043]), 7580 ^ [_905037, _905039, _905041, _905043])))], (7588 ^ _777959) ^ [] : [-(hBOOL(hAPP(_905043, 7580 ^ [_905037, _905039, _905041, _905043])))], (7584 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_905037), 7579 ^ [_905037, _905039, _905041, _905043]), _905041)))]], -(hBOOL(hAPP(_905043, _905039)))], (13530 ^ _777959) ^ [_1026223, _1026225] : [hAPP(c_Set_OCollect(_1026223), _1026225) = c_Orderings_Obot__class_Obot(tc_fun(_1026223, tc_HOL_Obool)), 13533 ^ _777959 : [(13534 ^ _777959) ^ [_1026308] : [hBOOL(hAPP(_1026225, _1026308))]]], (15196 ^ _777959) ^ [_1067578, _1067580, _1067582, _1067584, _1067586] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1067578), 15199 ^ _777959 : [(15200 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^ _777959 : [(24664 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1245821), 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), _1245821), _1245819)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24658 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1245821), _1245819)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1245821), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (47288 ^ _777959) ^ [_1727337, _1727339, _1727341, _1727343] : [hBOOL(hAPP(c_Predicate_ORangeP(_1727337, _1727339, _1727341), _1727343)), -(hBOOL(hAPP(hAPP(_1727341, 47291 ^ [_1727337, _1727339, _1727341, _1727343]), _1727343)))], (15260 ^ _777959) ^ [_1068650, _1068652] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068650), _1068652))), 15263 ^ _777959 : [(15270 ^ _777959) ^ [] : [_1068650 = _1068652, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068650), hAPP(c_Nat_OSuc, _1068652))))], (15264 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068650), hAPP(c_Nat_OSuc, _1068652))), -(_1068650 = _1068652)]]], (23405 ^ _777959) ^ [_1223733, _1223735, _1223737] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223733), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1223735), _1223737)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223733), _1223735)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223733), _1223737)))], (37446 ^ _777959) ^ [_1493186, _1493188, _1493190, _1493192, _1493194] : [c_Equiv__Relations_Oequiv(_1493186, _1493188, _1493190), hBOOL(hAPP(hAPP(c_member(tc_fun(_1493186, tc_HOL_Obool)), _1493192), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1493186), _1493188), _1493190))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1493186, tc_HOL_Obool)), _1493194), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1493186), _1493188), _1493190))), -(_1493192 = _1493194), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1493186, tc_HOL_Obool)), _1493192), _1493194) = c_Orderings_Obot__class_Obot(tc_fun(_1493186, tc_HOL_Obool)))], (23531 ^ _777959) ^ [_1225805, _1225807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225805), _1225807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225805), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1225807), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (15642 ^ _777959) ^ [_1075658, _1075660] : [class_Rings_Ocomm__semiring__1(_1075658), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075658), _1075660), _1075660) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075658), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075658), c_Groups_Oone__class_Oone(_1075658)), c_Groups_Oone__class_Oone(_1075658))), _1075660))], (46273 ^ _777959) ^ [_1701814, _1701816, _1701818, _1701820, _1701822] : [c_List_Olist__all2(_1701814, _1701816, _1701818, _1701820, _1701822), 46276 ^ _777959 : [(46279 ^ _777959) ^ [_1701980] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1701814, _1701816)), _1701980), hAPP(c_List_Oset(tc_prod(_1701814, _1701816)), hAPP(hAPP(c_List_Ozip(_1701814, _1701816), _1701820), _1701822)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1701814, _1701816, tc_HOL_Obool), _1701818), _1701980)))], (46277 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701814)), _1701820) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1701816)), _1701822))]]], (51068 ^ _777959) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (20467 ^ _777959) ^ [_1168316, _1168318, _1168320, _1168322] : [class_Rings_Olinordered__comm__semiring__strict(_1168316), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168316), _1168318), _1168320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168316), c_Groups_Ozero__class_Ozero(_1168316)), _1168322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168316), _1168322), _1168318)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168316), _1168322), _1168320))))], (28400 ^ _777959) ^ [_1313360, _1313362] : [c_Nat__Transfer_Ois__nat(_1313360), c_Nat__Transfer_Ois__nat(_1313362), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1313360), _1313362)))], (45880 ^ _777959) ^ [_1693719, _1693721] : [class_Enum_Oenum(_1693719), 45883 ^ _777959 : [(45892 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1693719)), _1693721))), hBOOL(hAPP(_1693721, c_Option_Ooption_ONone(_1693719))), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1693719), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1693719), tc_HOL_Obool, _1693719), _1693721), c_Option_Ooption_OSome(_1693719))))], (45884 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(_1693719)), _1693721)), 45887 ^ _777959 : [(45890 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1693719), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1693719), tc_HOL_Obool, _1693719), _1693721), c_Option_Ooption_OSome(_1693719)))))], (45888 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1693721, c_Option_Ooption_ONone(_1693719))))]]]]], (50926 ^ _777959) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (4088 ^ _777959) ^ [_839864, _839866] : [_839866 = _839864, -(c_Relation_OField(_839866) = c_Relation_OField(_839864))], (24798 ^ _777959) ^ [_1248036, _1248038, _1248040, _1248042, _1248044] : [class_Orderings_Olinorder(_1248036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1248036, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1248036, _1248038), _1248040)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1248036, _1248042), _1248044))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248036), _1248040), _1248038))), 24809 ^ _777959 : [(24812 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248036), _1248040), _1248044)))], (24810 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248036), _1248042), _1248038)))]]], (51082 ^ _777959) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (44049 ^ _777959) ^ [_1653916, _1653918] : [-(c_List_Ofoldr(tc_List_Olist(_1653916), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1653916)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1653916))), c_List_Otranspose(_1653916, _1653918), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1653916))), hAPP(c_List_Ofilter(tc_List_Olist(_1653916), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1653916)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1653916), tc_List_Olist(_1653916), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1653916)))), _1653918)))], (1820 ^ _777959) ^ [_803433, _803435] : [-(class_HOL_Oequal(_803433)), _803435 = _803433, class_HOL_Oequal(_803435)], (12227 ^ _777959) ^ [_999952, _999954, _999956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999952), _999954)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999952), _999956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999956), _999954)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999956), _999952))))], (41033 ^ _777959) ^ [_1579867, _1579869] : [class_Complete__Lattice_Ocomplete__lattice(_1579867), -(c_Complete__Lattice_OInf__class_OInf(_1579867, _1579869) = c_Complete__Lattice_OSup__class_OSup(_1579867, hAPP(c_Set_OCollect(_1579867), hAPP(hAPP(c_COMBB(tc_fun(_1579867, tc_HOL_Obool), tc_HOL_Obool, _1579867), c_HOL_OAll(_1579867)), hAPP(hAPP(c_COMBB(tc_fun(_1579867, tc_HOL_Obool), tc_fun(_1579867, tc_HOL_Obool), _1579867), hAPP(c_COMBS(_1579867, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1579867), c_fimplies), hAPP(hAPP(c_COMBC(_1579867, tc_fun(_1579867, tc_HOL_Obool), tc_HOL_Obool), c_member(_1579867)), _1579869)))), c_Orderings_Oord__class_Oless__eq(_1579867))))))], (38526 ^ _777959) ^ [_1517030, _1517032, _1517034] : [-(c_Fun_Oinj__on(tc_prod(_1517030, _1517032), tc_prod(_1517032, _1517030), hAPP(c_Product__Type_Oprod_Oprod__case(_1517030, _1517032, tc_prod(_1517032, _1517030)), hAPP(c_COMBC(_1517032, _1517030, tc_prod(_1517032, _1517030)), c_Product__Type_OPair(_1517032, _1517030))), _1517034))], (35043 ^ _777959) ^ [_1437487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437487), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1437487)), c_Int_OMin)))], (9686 ^ _777959) ^ [_945698, _945700, _945702, _945704] : [class_Lattices_Osemilattice__inf(_945698), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945698), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945698), _945700), _945702)), _945704) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945698), _945700), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945698), _945702), _945704)))], (42877 ^ _777959) ^ [_1627854, _1627856, _1627858, _1627860, _1627862] : [-(hAPP(hAPP(c_List_Omap(_1627854, _1627856), _1627858), hAPP(hAPP(c_List_Oappend(_1627854), _1627860), _1627862)) = hAPP(hAPP(c_List_Oappend(_1627856), hAPP(hAPP(c_List_Omap(_1627854, _1627856), _1627858), _1627860)), hAPP(hAPP(c_List_Omap(_1627854, _1627856), _1627858), _1627862)))], (860 ^ _777959) ^ [_791099, _791101, _791103, _791105, _791107, _791109] : [-(c_Nitpick_Oless__frac(_791107, _791103, _791099)), c_Nitpick_Oless__frac(_791109, _791105, _791101), _791109 = _791107, _791105 = _791103, _791101 = _791099], (5994 ^ _777959) ^ [_873623, _873625, _873627, _873629] : [5995 ^ _777959 : [(5998 ^ _777959) ^ [] : [_873625 = _873629], (5996 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_873623), _873625), _873627))]], -(hBOOL(hAPP(hAPP(c_member(_873623), _873625), hAPP(hAPP(c_Set_Oinsert(_873623), _873629), _873627))))], (11770 ^ _777959) ^ [_990721, _990723, _990725, _990727, _990729, _990731] : [class_Complete__Lattice_Ocomplete__lattice(_990721), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990723, _990721), _990725), hAPP(hAPP(c_COMBB(tc_fun(_990727, _990721), _990721, _990723), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990727, _990721), _990729)), _990731)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990727, _990721), _990729), hAPP(hAPP(c_COMBB(tc_fun(_990723, _990721), _990721, _990727), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990723, _990721), _990725)), hAPP(c_COMBC(_990723, _990727, _990721), _990731))))], (21542 ^ _777959) ^ [_1187307, _1187309, _1187311] : [class_Rings_Olinordered__ring(_1187307), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1187307), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1187307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187307), _1187309), _1187309)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187307), _1187311), _1187311))), c_Groups_Ozero__class_Ozero(_1187307)))], (41956 ^ _777959) ^ [_1604316, _1604318, _1604320, _1604322] : [-(c_List_Ofoldr(_1604316, _1604318, _1604320, c_List_Olist_ONil(_1604316), _1604322) = _1604322)], (46631 ^ _777959) ^ [_1709648, _1709650, _1709652] : [-(c_List_Omaps(_1709648, _1709650, _1709652, c_List_Olist_ONil(_1709648)) = c_List_Olist_ONil(_1709650))], (30455 ^ _777959) ^ [_1353780, _1353782, _1353784] : [-(hBOOL(hAPP(_1353780, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1353782, _1353784)))), 30458 ^ _777959 : [(30461 ^ _777959) ^ [] : [hBOOL(hAPP(_1353780, _1353782))], (30459 ^ _777959) ^ [] : [-(_1353784 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 30464 ^ _777959 : [(30465 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1353784)))], (30471 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 30467 ^ [_1353780, _1353782, _1353784]), _1353784)))], (30475 ^ _777959) ^ [] : [hBOOL(hAPP(_1353780, 30467 ^ [_1353780, _1353782, _1353784]))], (30473 ^ _777959) ^ [] : [-(_1353782 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1353784), 30466 ^ [_1353780, _1353782, _1353784])), 30467 ^ [_1353780, _1353782, _1353784]))], (30469 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30467 ^ [_1353780, _1353782, _1353784])))]], 30476 ^ _777959 : [(30477 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1353784), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30483 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 30479 ^ [_1353780, _1353782, _1353784]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30487 ^ _777959) ^ [] : [hBOOL(hAPP(_1353780, 30479 ^ [_1353780, _1353782, _1353784]))], (30485 ^ _777959) ^ [] : [-(_1353782 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1353784), 30478 ^ [_1353780, _1353782, _1353784])), 30479 ^ [_1353780, _1353782, _1353784]))], (30481 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1353784), 30479 ^ [_1353780, _1353782, _1353784])))]]], (41595 ^ _777959) ^ [_1593692, _1593694, _1593696] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593692)), hAPP(hAPP(c_List_Olist_OCons(_1593692), _1593694), _1593696)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1593692)), _1593696)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (22238 ^ _777959) ^ [_1201238, _1201240, _1201242, _1201244, _1201246] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_1201238, _1201240, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1201238), _1201242), _1201244), _1201246)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (17829 ^ _777959) ^ [_1118775, _1118777, _1118779] : [class_Orderings_Olinorder(_1118775), hBOOL(hAPP(c_Finite__Set_Ofinite(_1118775), _1118777)), hBOOL(hAPP(hAPP(c_member(_1118775), _1118779), _1118777)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1118775), _1118779), c_Big__Operators_Olattice_OInf__fin(_1118775, c_Orderings_Oord__class_Omin(_1118775), _1118777)) = c_Big__Operators_Olattice_OInf__fin(_1118775, c_Orderings_Oord__class_Omin(_1118775), _1118777))], (24217 ^ _777959) ^ [_1238312, _1238314] : [class_Rings_Osemiring__1(_1238312), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1238312), _1238314) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1238312, hAPP(hAPP(c_COMBC(_1238312, _1238312, _1238312), c_Groups_Oplus__class_Oplus(_1238312)), c_Groups_Oone__class_Oone(_1238312)), _1238314, c_Groups_Ozero__class_Ozero(_1238312)))], (35253 ^ _777959) ^ [_1440656, _1440658] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1440656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1440656), _1440658)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1440656), _1440658) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (31496 ^ _777959) ^ [_1372997, _1372999] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1372997))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1372999)), hAPP(c_Int_Onat, _1372997)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1372999), _1372997)), 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)))], (10 ^ _777959) ^ [_778082, _778084, _778086] : [-(_778086 = _778082), _778086 = _778084, _778084 = _778082], (13789 ^ _777959) ^ [_1032962, _1032964] : [class_Lattices_Obounded__lattice__top(_1032962), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1032962), _1032964), c_Orderings_Otop__class_Otop(_1032962)) = _1032964)], (50158 ^ _777959) ^ [_1794606, _1794608] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1794606), _1794608)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1794606)), c_Int_OBit0(_1794608))))], (23487 ^ _777959) ^ [_1225058, _1225060] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225058), _1225060))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225058), _1225060)), -(_1225058 = _1225060)], (46591 ^ _777959) ^ [_1708964, _1708966, _1708968] : [-(hBOOL(hAPP(hAPP(c_member(_1708964), _1708966), hAPP(c_List_Oset(_1708964), _1708968)))), -(c_List_Oinsert(_1708964, _1708966, _1708968) = hAPP(hAPP(c_List_Olist_OCons(_1708964), _1708966), _1708968))], (37316 ^ _777959) ^ [_1490015, _1490017, _1490019] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490015), _1490017), _1490019) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1490015, tc_fun(tc_fun(_1490015, tc_HOL_Obool), tc_HOL_Obool)), _1490017), hAPP(hAPP(c_COMBC(_1490015, tc_fun(tc_fun(_1490015, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1490015, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1490015, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1490015, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1490015, tc_HOL_Obool), tc_HOL_Obool)), _1490015), c_Set_Oinsert(tc_fun(_1490015, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1490015, tc_HOL_Obool), tc_fun(_1490015, tc_HOL_Obool), _1490015), c_Relation_OImage(_1490015, _1490015, _1490019)), hAPP(hAPP(c_COMBC(_1490015, tc_fun(_1490015, tc_HOL_Obool), tc_fun(_1490015, tc_HOL_Obool)), c_Set_Oinsert(_1490015)), c_Orderings_Obot__class_Obot(tc_fun(_1490015, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1490015, tc_HOL_Obool), tc_HOL_Obool)))))], (34437 ^ _777959) ^ [_1426343, _1426345] : [class_Rings_Oring__1__no__zero__divisors(_1426343), 34440 ^ _777959 : [(34447 ^ _777959) ^ [] : [_1426345 = c_Groups_Ozero__class_Ozero(_1426343), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1426343), _1426345), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1426343))], (34441 ^ _777959) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1426343), _1426345), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1426343), -(_1426345 = c_Groups_Ozero__class_Ozero(_1426343))]]], (28730 ^ _777959) ^ [_1319152, _1319154, _1319156, _1319158] : [class_Orderings_Olinorder(_1319152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319152), _1319154), _1319156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1319152), _1319156), _1319158)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1319152, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1319152, _1319154, _1319156)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1319152, _1319156, _1319158)) = c_SetInterval_Oord__class_OatLeastAtMost(_1319152, _1319154, _1319158))], (22962 ^ _777959) ^ [_1215859] : [class_Rings_Oring__1(_1215859), -(hBOOL(hAPP(hAPP(c_member(_1215859), c_Groups_Ozero__class_Ozero(_1215859)), c_Int_Oring__1__class_OInts(_1215859))))], (41012 ^ _777959) ^ [_1578951, _1578953, _1578955, _1578957] : [c_Equiv__Relations_Ocongruent(_1578951, _1578953, _1578955, _1578957), 41015 ^ _777959 : [(41016 ^ _777959) ^ [_1579096] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1578951, _1578951)), _1579096), _1578955)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1578951, _1578951, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1578951, tc_fun(_1578951, _1578953), tc_fun(_1578951, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1578953, tc_HOL_Obool), tc_fun(tc_fun(_1578951, _1578953), tc_fun(_1578951, tc_HOL_Obool)), _1578951), c_COMBB(_1578953, tc_HOL_Obool, _1578951)), hAPP(hAPP(c_COMBB(_1578953, tc_fun(_1578953, tc_HOL_Obool), _1578951), c_fequal), _1578957))), _1578957)), _1579096)))]]], (31749 ^ _777959) ^ [_1377493, _1377495, _1377497] : [31751 ^ _777959 : [(31754 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1377493), _1377497), 31750 ^ [_1377493, _1377495, _1377497]))], (31752 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1377493, tc_HOL_Obool)), 31750 ^ [_1377493, _1377495, _1377497]), _1377495)))]], -(hBOOL(hAPP(hAPP(c_member(_1377493), _1377497), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1377493, tc_HOL_Obool), _1377495))))], (36125 ^ _777959) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (2308 ^ _777959) ^ [_812090, _812092, _812094, _812096] : [-(c_Nat__Transfer_Otsub(_812096, _812092) = c_Nat__Transfer_Otsub(_812094, _812090)), _812096 = _812094, _812092 = _812090], (36321 ^ _777959) ^ [_1466549, _1466551, _1466553, _1466555] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1466549, _1466551), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1466553), _1466555))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1466549, _1466551) = _1466555)], (20599 ^ _777959) ^ [_1170688] : [class_Rings_Olinordered__semidom(_1170688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170688), c_Groups_Oone__class_Oone(_1170688)), c_Groups_Ozero__class_Ozero(_1170688)))], (43165 ^ _777959) ^ [_1634768, _1634770, _1634772, _1634774] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1634768), _1634770)), 43171 ^ _777959 : [(43174 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1634772), hAPP(_1634774, 43170 ^ [_1634768, _1634770, _1634772, _1634774])))], (43172 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1634768), 43170 ^ [_1634768, _1634770, _1634772, _1634774]), _1634770)))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1634768, _1634772)), hAPP(hAPP(c_Product__Type_OSigma(_1634768, _1634772), _1634770), _1634774)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1634768, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1634772, tc_HOL_Obool), tc_Nat_Onat, _1634768), c_Finite__Set_Ocard(_1634772)), _1634774)), _1634770))], (37910 ^ _777959) ^ [_1504246, _1504248] : [class_Groups_Oordered__ab__group__add(_1504246), -(c_Fun_Oinj__on(_1504246, _1504246, c_Groups_Ouminus__class_Ouminus(_1504246), _1504248))], (22766 ^ _777959) ^ [_1212158, _1212160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212158)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212160))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1212158), _1212160)))], (1740 ^ _777959) ^ [_802433, _802435] : [-(class_Orderings_Oorder(_802433)), _802435 = _802433, class_Orderings_Oorder(_802435)], (13385 ^ _777959) ^ [_1023051, _1023053, _1023055, _1023057] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1023051, tc_HOL_Obool), tc_fun(_1023053, tc_HOL_Obool)), _1023055), hAPP(hAPP(c_COMBC(tc_fun(_1023051, tc_HOL_Obool), tc_fun(_1023051, tc_fun(_1023053, tc_HOL_Obool)), tc_fun(_1023053, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023051, tc_fun(_1023053, tc_HOL_Obool))), _1023057)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023051, tc_fun(_1023053, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1023051, tc_HOL_Obool), _1023055)), _1023057))], (12942 ^ _777959) ^ [_1013348, _1013350, _1013352, _1013354] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1013348, tc_fun(_1013350, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1013348, tc_HOL_Obool), _1013352)), _1013354) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1013348, tc_HOL_Obool), tc_fun(_1013350, tc_HOL_Obool)), _1013352), hAPP(hAPP(c_COMBC(tc_fun(_1013348, tc_HOL_Obool), tc_fun(_1013348, tc_fun(_1013350, tc_HOL_Obool)), tc_fun(_1013350, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1013348, tc_fun(_1013350, tc_HOL_Obool))), _1013354)))], (30185 ^ _777959) ^ [_1348758, _1348760] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1348758), _1348760) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, 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c_Orderings_Oord__class_Omax(_1125278), _1125280)), c_Big__Operators_Olattice_OSup__fin(_1125278, c_Orderings_Oord__class_Omax(_1125278), _1125282)))], (3658 ^ _777959) ^ [_833181, _833183] : [_833183 = _833181, -(c_Int_Oint__ge__less__than2(_833183) = c_Int_Oint__ge__less__than2(_833181))], (20993 ^ _777959) ^ [_1176933, _1176935, _1176937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176933)), 20996 ^ _777959 : [(21003 ^ _777959) ^ [] : [_1176935 = _1176937, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176933), _1176935) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176933), _1176937))], (20997 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176933), _1176935) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176933), _1176937), -(_1176935 = _1176937)]]], (31304 ^ _777959) ^ [_1369238, _1369240, _1369242] : [class_Rings_Oordered__ring__abs(_1369238), -(hAPP(c_Groups_Oabs__class_Oabs(_1369238), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369238), _1369240), _1369242)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369238), hAPP(c_Groups_Oabs__class_Oabs(_1369238), _1369240)), hAPP(c_Groups_Oabs__class_Oabs(_1369238), _1369242))), 31311 ^ _777959 : [(31314 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369238), _1369240), c_Groups_Ozero__class_Ozero(_1369238)))], (31312 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369238), c_Groups_Ozero__class_Ozero(_1369238)), _1369240))]], 31315 ^ _777959 : [(31318 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369238), _1369242), c_Groups_Ozero__class_Ozero(_1369238)))], (31316 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369238), c_Groups_Ozero__class_Ozero(_1369238)), _1369242))]]], (31965 ^ _777959) ^ [_1381392, _1381394, _1381396] : [c_Com_Ocom_OLocal(_1381392, _1381394, _1381396) = c_Com_Ocom_OSKIP], (25462 ^ _777959) ^ [_1260710, _1260712, _1260714] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1260710)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1260710), _1260712)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260714), _1260712)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260714), _1260710))))], (14133 ^ _777959) ^ [_1040865, _1040867, _1040869] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040865), _1040867)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1040865), _1040867)), hAPP(c_Finite__Set_Ocard(_1040865), hAPP(hAPP(c_Set_Oinsert(_1040865), _1040869), _1040867)))))], (10132 ^ _777959) ^ [_955043, _955045, _955047, _955049] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_955043, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_955043, tc_HOL_Obool)), _955045), _955047)), _955049) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_955043, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_955043, tc_HOL_Obool)), _955045), _955049)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_955043, tc_HOL_Obool)), _955047), _955049)))], (14091 ^ _777959) ^ [_1039985, _1039987, _1039989, _1039991, _1039993, _1039995] : [hAPP(c_Map_Omap__add(_1039985, _1039987, _1039989, _1039991), _1039993) = hAPP(c_Option_Ooption_OSome(_1039987), _1039995), -(hAPP(_1039991, _1039993) = hAPP(c_Option_Ooption_OSome(_1039987), _1039995)), 14098 ^ _777959 : [(14101 ^ _777959) ^ [] : [-(hAPP(_1039989, _1039993) = hAPP(c_Option_Ooption_OSome(_1039987), _1039995))], (14099 ^ _777959) ^ [] : [-(hAPP(_1039991, _1039993) = c_Option_Ooption_ONone(_1039987))]]], (27449 ^ _777959) ^ [_1297061] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1297061))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1297061)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (37345 ^ _777959) ^ [_1490788, _1490790, _1490792] : [_1490790 = c_Orderings_Obot__class_Obot(tc_fun(_1490788, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1490788, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490788), _1490790), _1490792))], (18580 ^ _777959) ^ [_1135100, _1135102] : [class_Lattices_Olattice(_1135100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135100), _1135102)), -(c_Big__Operators_Olattice__class_OInf__fin(_1135100, _1135102) = hAPP(c_Finite__Set_Ofold1(_1135100, c_Lattices_Osemilattice__inf__class_Oinf(_1135100)), _1135102))], (51386 ^ _777959) ^ [_1814115] : [hBOOL(hAPP(c_fNot, _1814115)), hBOOL(_1814115)], (23977 ^ _777959) ^ [_1233888, _1233890, _1233892, _1233894] : [class_Rings_Olinordered__semidom(_1233888), hAPP(hAPP(c_Power_Opower__class_Opower(_1233888), _1233890), _1233892) = hAPP(hAPP(c_Power_Opower__class_Opower(_1233888), _1233894), _1233892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233888), c_Groups_Ozero__class_Ozero(_1233888)), _1233890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1233888), c_Groups_Ozero__class_Ozero(_1233888)), _1233894)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1233892)), -(_1233890 = _1233894)], (10751 ^ _777959) ^ [_968759, _968761, _968763, _968765] : [class_Groups_Ocancel__semigroup__add(_968759), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968759), _968761), _968763) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968759), _968765), _968763), -(_968761 = _968765)], (588 ^ _777959) ^ [_787019, _787021, _787023, _787025, _787027, _787029, _787031, _787033] : [-(c_Wellfounded_Omax__extp(_787031, _787027, _787023, _787019)), c_Wellfounded_Omax__extp(_787033, _787029, _787025, _787021), _787033 = _787031, _787029 = _787027, _787025 = _787023, _787021 = _787019], (35337 ^ _777959) ^ [_1442339, _1442341, _1442343, _1442345, _1442347, _1442349] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442339, tc_fun(_1442341, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1442339, tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_fun(_1442341, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1442341, tc_fun(tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_fun(_1442341, tc_HOL_Obool)), _1442339), c_COMBC(_1442341, tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1442341, tc_prod(_1442339, _1442341)), tc_fun(_1442341, tc_fun(tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_HOL_Obool)), _1442339), hAPP(c_COMBB(tc_prod(_1442339, _1442341), tc_fun(tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_HOL_Obool), _1442341), c_member(tc_prod(_1442339, _1442341)))), c_Product__Type_OPair(_1442339, _1442341)))), _1442343)), hAPP(hAPP(c_COMBC(_1442339, tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_fun(_1442341, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1442341, tc_fun(tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_fun(_1442341, tc_HOL_Obool)), _1442339), c_COMBC(_1442341, tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1442341, tc_prod(_1442339, _1442341)), tc_fun(_1442341, tc_fun(tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_HOL_Obool)), _1442339), hAPP(c_COMBB(tc_prod(_1442339, _1442341), tc_fun(tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool), tc_HOL_Obool), _1442341), c_member(tc_prod(_1442339, _1442341)))), c_Product__Type_OPair(_1442339, _1442341)))), _1442345)), _1442347), _1442349)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1442339, _1442341)), hAPP(hAPP(c_Product__Type_OPair(_1442339, _1442341), _1442347), _1442349)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1442339, _1442341), tc_HOL_Obool)), _1442343), _1442345))))], (26124 ^ _777959) ^ [_1273323, _1273325, _1273327] : [class_Fields_Olinordered__field__inverse__zero(_1273323), 26127 ^ _777959 : [(26142 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273323), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273323), _1273325), _1273327)), c_Groups_Ozero__class_Ozero(_1273323)))), 26143 ^ _777959 : [(26150 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273323), _1273325), c_Groups_Ozero__class_Ozero(_1273323))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273323), c_Groups_Ozero__class_Ozero(_1273323)), _1273327))], (26144 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273323), c_Groups_Ozero__class_Ozero(_1273323)), _1273325)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273323), _1273327), c_Groups_Ozero__class_Ozero(_1273323)))]]], (26128 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273323), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1273323), _1273325), _1273327)), c_Groups_Ozero__class_Ozero(_1273323))), 26133 ^ _777959 : [(26136 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273323), _1273327), c_Groups_Ozero__class_Ozero(_1273323))))], (26134 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273323), c_Groups_Ozero__class_Ozero(_1273323)), _1273325)))]], 26137 ^ _777959 : [(26140 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273323), c_Groups_Ozero__class_Ozero(_1273323)), _1273327)))], (26138 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1273323), _1273325), c_Groups_Ozero__class_Ozero(_1273323))))]]]]], (21051 ^ _777959) ^ [_1177929, _1177931, _1177933] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177929), _1177931)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177929), _1177933)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1177929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1177931), _1177933))], (17807 ^ _777959) ^ [_1118420, _1118422, _1118424, _1118426] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1118420, _1118422, _1118424), _1118426)), _1118424 = c_Orderings_Obot__class_Obot(tc_fun(_1118420, tc_HOL_Obool))], (35435 ^ _777959) ^ [_1448394, _1448396, _1448398] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1448394, _1448394), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1448396), _1448398))), -(_1448394 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1448398 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (45362 ^ _777959) ^ [_1681963, _1681965] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681963)), c_List_Oremdups(_1681963, _1681965)) = hAPP(c_Finite__Set_Ocard(_1681963), hAPP(c_List_Oset(_1681963), _1681965)))], (30305 ^ _777959) ^ [_1350987, _1350989, _1350991] : [-(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), _1350987), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1350989), _1350987))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350989, _1350987))), _1350991) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1350989), _1350991))], (49913 ^ _777959) ^ [_1790159, _1790161] : [class_Enum_Oenum(_1790159), 49916 ^ _777959 : [(49930 ^ _777959) ^ [] : [c_List_Olist__ex1(_1790159, _1790161, c_Enum_Oenum__class_Oenum(_1790159)), 49934 ^ _777959 : [(49937 ^ _777959) ^ [_1790558] : [hBOOL(hAPP(_1790161, _1790558)), -(_1790558 = 49933 ^ [_1790159, _1790161])], (49935 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1790161, 49933 ^ [_1790159, _1790161])))]]], (49917 ^ _777959) ^ [] : [-(c_List_Olist__ex1(_1790159, _1790161, c_Enum_Oenum__class_Oenum(_1790159))), 49918 ^ _777959 : [(49919 ^ _777959) ^ [_1790274] : [hBOOL(hAPP(_1790161, _1790274)), 49923 ^ _777959 : [(49926 ^ _777959) ^ [] : [49922 ^ [_1790159, _1790161, _1790274] = _1790274], (49924 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1790161, 49922 ^ [_1790159, _1790161, _1790274])))]]]]]]], (24912 ^ _777959) ^ [_1250298, _1250300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1250298), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 24915 ^ _777959 : [(24922 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1250300), 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), _1250300), _1250298))))], (24916 ^ _777959) ^ [] : [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), _1250300), _1250298))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1250300), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (15952 ^ _777959) ^ [_1081965, _1081967, _1081969] : [class_Orderings_Olinorder(_1081965), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081965), _1081967)), hBOOL(hAPP(hAPP(c_member(_1081965), _1081969), _1081967)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1081965), _1081969), c_Big__Operators_Olinorder__class_OMax(_1081965, _1081967))))], (22715 ^ _777959) ^ [] : [-(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))], (37020 ^ _777959) ^ [_1482096, _1482098, _1482100, _1482102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1482096), _1482098)), -(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), _1482096), _1482100)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1482098), _1482102))), c_FunDef_Opair__leq)))], (36722 ^ _777959) ^ [_1474716, _1474718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1474716)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1474718), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1474716), _1474718) = 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), _1474716), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1474718)))))], (19526 ^ _777959) ^ [_1151570, _1151572] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1151570), _1151572) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151570 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1151572 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (35963 ^ _777959) ^ [_1460347] : [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), _1460347))), 35966 ^ _777959 : [(35973 ^ _777959) ^ [] : [-(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), _1460347)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1460347)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1460347)), 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), _1460347)))))], (35967 ^ _777959) ^ [] : [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), _1460347))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1460347)) = 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)))]]], (46790 ^ _777959) ^ [_1714359, _1714361, _1714363, _1714365] : [hAPP(hAPP(c_Relation_Orel__comp(_1714359, _1714359, _1714359), _1714361), _1714363) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1714359, _1714359), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1714359, _1714359, _1714359), _1714365), _1714363) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1714359, _1714359), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1714359, _1714359, _1714359), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1714359, _1714359), tc_HOL_Obool)), _1714361), _1714365)), _1714363) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1714359, _1714359), tc_HOL_Obool)))], (47036 ^ _777959) ^ [_1720975, _1720977, _1720979] : [c_Wellfounded_Owf(_1720975, _1720977), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1720975, _1720975), tc_HOL_Obool)), _1720979), _1720977)), -(c_Wellfounded_Owf(_1720975, _1720979))], (2940 ^ _777959) ^ [_821946, _821948, _821950, _821952, _821954, _821956] : [-(c_Finite__Set_Ofold__image(_821956, _821952, _821948) = c_Finite__Set_Ofold__image(_821954, _821950, _821946)), _821956 = _821954, _821952 = _821950, _821948 = _821946], (27183 ^ _777959) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (14395 ^ _777959) ^ [_1047582, _1047584, _1047586] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047582), _1047584)), 14398 ^ _777959 : [(14405 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1047582), _1047586), _1047584))), -(hAPP(c_Finite__Set_Ocard(_1047582), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1047582, tc_HOL_Obool)), _1047584), hAPP(hAPP(c_Set_Oinsert(_1047582), _1047586), c_Orderings_Obot__class_Obot(tc_fun(_1047582, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1047582), _1047584))], (14399 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1047582), _1047586), _1047584)), -(hAPP(c_Finite__Set_Ocard(_1047582), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1047582, tc_HOL_Obool)), _1047584), hAPP(hAPP(c_Set_Oinsert(_1047582), _1047586), c_Orderings_Obot__class_Obot(tc_fun(_1047582, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1047582), _1047584)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))]]], (23305 ^ _777959) ^ [_1222067] : [-(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), _1222067))))], (33369 ^ _777959) ^ [_1407227, _1407229] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1407227), _1407229), hAPP(c_Int_Onumber__class_Onumber__of(_1407227), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1407227)), class_Fields_Ofield__inverse__zero(_1407227), class_Int_Onumber__ring(_1407227)], (19895 ^ _777959) ^ [_1157825, _1157827, _1157829, _1157831, _1157833] : [class_Rings_Oordered__semiring(_1157825), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157825), _1157827), _1157829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157825), _1157831), _1157833)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157825), c_Groups_Ozero__class_Ozero(_1157825)), _1157829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157825), c_Groups_Ozero__class_Ozero(_1157825)), _1157831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157825), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157825), _1157827), _1157831)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157825), _1157829), _1157833))))], (48839 ^ _777959) ^ [_1763215, _1763217, _1763219, _1763221, _1763223] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1763215), tc_List_Olist(_1763215))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1763215), tc_List_Olist(_1763215)), _1763217), _1763219)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1763215), c_List_Olistrel1(_1763215, _1763221)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1763215), tc_List_Olist(_1763215))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1763215), tc_List_Olist(_1763215)), hAPP(hAPP(c_List_Olist_OCons(_1763215), _1763223), _1763217)), hAPP(hAPP(c_List_Olist_OCons(_1763215), _1763223), _1763219))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1763215), c_List_Olistrel1(_1763215, _1763221)))))], (3674 ^ _777959) ^ [_833415, _833417, _833419, _833421, _833423, _833425, _833427, _833429, _833431, _833433, _833435, _833437] : [-(c_Product__Type_Omap__pair(_833437, _833433, _833429, _833425, _833421, _833417) = c_Product__Type_Omap__pair(_833435, _833431, _833427, _833423, _833419, _833415)), _833437 = _833435, _833433 = _833431, _833429 = _833427, _833425 = _833423, _833421 = _833419, _833417 = _833415], (51146 ^ _777959) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (36247 ^ _777959) ^ [_1465164, _1465166, _1465168] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1465164, _1465166), _1465168)), 36250 ^ _777959 : [(36251 ^ _777959) ^ [_1465249] : [hBOOL(hAPP(hAPP(_1465166, _1465249), _1465168)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1465164, _1465166), _1465249)))]]], (12594 ^ _777959) ^ [_1006680, _1006682, _1006684] : [class_Groups_Ogroup__add(_1006680), 12597 ^ _777959 : [(12604 ^ _777959) ^ [] : [_1006682 = _1006684, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1006680), _1006682) = hAPP(c_Groups_Ouminus__class_Ouminus(_1006680), _1006684))], (12598 ^ _777959) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1006680), _1006682) = hAPP(c_Groups_Ouminus__class_Ouminus(_1006680), _1006684), -(_1006682 = _1006684)]]], (35227 ^ _777959) ^ [_1440225, _1440227] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1440225), hAPP(c_Int_Onumber__class_Onumber__of(_1440225), c_Int_OMin)), _1440227) = hAPP(c_Groups_Ouminus__class_Ouminus(_1440225), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1440225), c_Groups_Oone__class_Oone(_1440225)), _1440227))), class_Fields_Ofield__inverse__zero(_1440225), class_Int_Onumber__ring(_1440225)], (49696 ^ _777959) ^ [_1785712, _1785714, _1785716] : [-(c_Nitpick_Oplus__frac(_1785712, _1785714, _1785716) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1785712), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1785712), _1785714), hAPP(c_Nitpick_Odenom(_1785712), _1785716))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1785712), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1785712), tc_Int_Oint), c_Nitpick_Ofrac(_1785712)), 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(_1785712), _1785714))), 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(_1785712), _1785714))))), 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(_1785712), _1785716))), 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(_1785712), _1785716)))))), c_COMBI(tc_Int_Oint))))], (34413 ^ _777959) ^ [_1425811, _1425813, _1425815] : [class_Int_Onumber__ring(_1425811), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1425811), hAPP(c_Int_Onumber__class_Onumber__of(_1425811), _1425813)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1425815))) = hAPP(hAPP(c_HOL_OLet(_1425811, _1425811), hAPP(hAPP(c_Power_Opower__class_Opower(_1425811), hAPP(c_Int_Onumber__class_Onumber__of(_1425811), _1425813)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425815))), hAPP(hAPP(c_COMBS(_1425811, _1425811, _1425811), c_Groups_Otimes__class_Otimes(_1425811)), c_COMBI(_1425811))))], (47344 ^ _777959) ^ [_1728651, _1728653, _1728655, _1728657] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1728651, _1728653), tc_HOL_Obool)), _1728655), _1728657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1728651, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1728651, _1728653), _1728655)), hAPP(c_Relation_ODomain(_1728651, _1728653), _1728657))))], (40652 ^ _777959) ^ [_1567748, _1567750, _1567752, _1567754] : [class_Groups_Ocomm__monoid__add(_1567748), 40655 ^ _777959 : [(40662 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1567750), _1567752))), -(c_Nitpick_Osetsum_H(_1567750, _1567748, _1567754, _1567752) = c_Groups_Ozero__class_Ozero(_1567748))], (40656 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1567750), _1567752)), -(c_Nitpick_Osetsum_H(_1567750, _1567748, _1567754, _1567752) = hAPP(c_List_Omonoid__add__class_Olistsum(_1567748), hAPP(hAPP(c_List_Omap(_1567750, _1567748), _1567754), c_Hilbert__Choice_OEps(tc_List_Olist(_1567750), hAPP(hAPP(c_COMBS(tc_List_Olist(_1567750), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1567750)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1567750), tc_fun(_1567750, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1567750, tc_HOL_Obool), tc_fun(tc_fun(_1567750, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1567750)), c_fequal), c_List_Oset(_1567750))), _1567752))), c_List_Odistinct(_1567750))))))]]], (42014 ^ _777959) ^ [_1605887, _1605889, _1605891] : [-(hAPP(hAPP(c_List_Olist__update(_1605887, c_List_Olist_ONil(_1605887)), _1605889), _1605891) = c_List_Olist_ONil(_1605887))], (44438 ^ _777959) ^ [_1661229, _1661231, _1661233] : [class_Orderings_Olinorder(_1661229), 44441 ^ _777959 : [(44454 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1661229, hAPP(hAPP(c_List_Olist_OCons(_1661229), _1661231), _1661233))), c_List_Olinorder__class_Osorted(_1661229, _1661233), 44460 ^ _777959 : [(44463 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1661229), _1661231), 44459 ^ [_1661229, _1661231, _1661233]))], (44461 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1661229), 44459 ^ [_1661229, _1661231, _1661233]), hAPP(c_List_Oset(_1661229), _1661233))))]]], (44442 ^ _777959) ^ [] : [c_List_Olinorder__class_Osorted(_1661229, hAPP(hAPP(c_List_Olist_OCons(_1661229), _1661231), _1661233)), 44445 ^ _777959 : [(44448 ^ _777959) ^ [_1661415] : [hBOOL(hAPP(hAPP(c_member(_1661229), _1661415), hAPP(c_List_Oset(_1661229), _1661233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1661229), _1661231), _1661415)))], (44446 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1661229, _1661233))]]]]], (7252 ^ _777959) ^ [_899536, _899538, _899540] : [class_Lattices_Osemilattice__sup(_899536), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899536), _899538), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_899536), _899540), _899538))))], (47046 ^ _777959) ^ [] : [-(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)))))], (50840 ^ _777959) ^ [_1808504, _1808506] : [class_Groups_Ominus(_1808504), -(class_Groups_Ominus(tc_fun(_1808506, _1808504)))], (10222 ^ _777959) ^ [_957350, _957352, _957354, _957356] : [-(hBOOL(hAPP(hAPP(c_member(_957350), _957352), _957354))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957350, tc_HOL_Obool)), _957354), hAPP(hAPP(c_Set_Oinsert(_957350), _957352), _957356)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957350, tc_HOL_Obool)), _957354), _957356))], (40598 ^ _777959) ^ [_1566512, _1566514, _1566516, _1566518] : [class_Groups_Ocomm__monoid__add(_1566512), hBOOL(hAPP(c_List_Odistinct(_1566514), _1566516)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1566512), hAPP(hAPP(c_List_Omap(_1566514, _1566512), _1566518), _1566516)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1566514, _1566512), _1566518), hAPP(c_List_Oset(_1566514), _1566516)))], (30223 ^ _777959) ^ [_1349586, _1349588, _1349590, _1349592] : [class_Divides_Osemiring__div(_1349586), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349586), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349586), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349586), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1349586), _1349588), _1349590)), _1349590)), c_Divides_Odiv__class_Omod(_1349586, _1349588, _1349590))), _1349592) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349586), _1349588), _1349592))], (47369 ^ _777959) ^ [_1729245, _1729247, _1729249, _1729251] : [47370 ^ _777959 : [(47371 ^ _777959) ^ [_1729320] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1729245, _1729249)), hAPP(hAPP(c_Product__Type_OPair(_1729245, _1729249), _1729247), _1729320)), _1729251))]], -(hBOOL(hAPP(hAPP(c_member(_1729245), _1729247), hAPP(c_Relation_ODomain(_1729245, _1729249), _1729251))))], (37217 ^ _777959) ^ [_1487326, _1487328, _1487330, _1487332, _1487334, _1487336] : [hBOOL(hAPP(hAPP(c_member(_1487326), _1487328), _1487330)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1487326, _1487332)), hAPP(hAPP(c_Product__Type_OPair(_1487326, _1487332), _1487328), _1487334)), _1487336)), -(hBOOL(hAPP(hAPP(c_member(_1487332), _1487334), hAPP(c_Relation_OImage(_1487326, _1487332, _1487336), _1487330))))], (44571 ^ _777959) ^ [_1663776, _1663778, _1663780, _1663782] : [class_Groups_Ocomm__monoid__add(_1663776), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1663776), _1663778), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1663780, _1663782))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1663776), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1663776), _1663778), c_List_Oupt(_1663780, _1663782))))], (28522 ^ _777959) ^ [_1315330, _1315332, _1315334] : [class_Orderings_Oorder(_1315330), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1315330), _1315332), _1315334)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1315330, _1315334, _1315332) = c_Orderings_Obot__class_Obot(tc_fun(_1315330, tc_HOL_Obool)))], (46359 ^ _777959) ^ [_1703777, _1703779, _1703781, _1703783, _1703785, _1703787, _1703789] : [c_List_Olist__all2(_1703777, _1703779, _1703781, hAPP(hAPP(c_List_Omap(_1703783, _1703777), _1703785), _1703787), _1703789), -(c_List_Olist__all2(_1703783, _1703779, hAPP(hAPP(c_COMBB(_1703777, tc_fun(_1703779, tc_HOL_Obool), _1703783), _1703781), _1703785), _1703787, _1703789))], (43753 ^ _777959) ^ [_1648191, _1648193] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1648191), hAPP(c_List_Oset(tc_Nat_Onat), _1648193))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1648191), 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)), _1648193))))], (29924 ^ _777959) ^ [_1343584, _1343586, _1343588] : [class_Divides_Oring__div(_1343584), -(c_Divides_Odiv__class_Omod(_1343584, hAPP(c_Groups_Ouminus__class_Ouminus(_1343584), _1343586), _1343588) = c_Divides_Odiv__class_Omod(_1343584, hAPP(c_Groups_Ouminus__class_Ouminus(_1343584), c_Divides_Odiv__class_Omod(_1343584, _1343586, _1343588)), _1343588))], (9740 ^ _777959) ^ [_946931, _946933, _946935] : [class_Lattices_Osemilattice__inf(_946931), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946931), _946933), _946935) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946931), _946935), _946933))], (41697 ^ _777959) ^ [_1596522, _1596524, _1596526] : [-(c_List_Oset__Cons(_1596522, _1596524, _1596526) = hAPP(c_Set_OCollect(tc_List_Olist(_1596522)), hAPP(hAPP(c_COMBB(tc_fun(_1596522, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1596522)), c_HOL_OEx(_1596522)), hAPP(hAPP(c_COMBB(tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool)), tc_fun(_1596522, tc_HOL_Obool), tc_List_Olist(_1596522)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool), tc_HOL_Obool, _1596522), c_HOL_OEx(tc_List_Olist(_1596522)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1596522), tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool)), tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1596522, tc_fun(tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool), tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool))), tc_fun(tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool)), tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool))), tc_List_Olist(_1596522)), c_COMBS(_1596522, tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool), tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1596522, tc_fun(tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool), tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool))), tc_List_Olist(_1596522)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1596522), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool), tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool)), _1596522), c_COMBS(tc_List_Olist(_1596522), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool)), tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1596522)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool), tc_fun(tc_List_Olist(_1596522), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1596522), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1596522)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1596522), tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_List_Olist(_1596522))), tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1596522), tc_List_Olist(_1596522)), tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool)), tc_fun(tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_List_Olist(_1596522))), tc_fun(_1596522, tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool))), tc_List_Olist(_1596522)), c_COMBB(tc_fun(tc_List_Olist(_1596522), tc_List_Olist(_1596522)), tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool), _1596522)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1596522), tc_List_Olist(_1596522)), tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool)), tc_List_Olist(_1596522)), c_COMBB(tc_List_Olist(_1596522), tc_HOL_Obool, tc_List_Olist(_1596522))), c_fequal))), c_List_Olist_OCons(_1596522)))))), hAPP(hAPP(c_COMBC(_1596522, tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool), tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool), tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool)), _1596522), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1596522))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1596522), c_fconj), hAPP(hAPP(c_COMBC(_1596522, tc_fun(_1596522, tc_HOL_Obool), tc_HOL_Obool), c_member(_1596522)), _1596524)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1596522), tc_fun(tc_List_Olist(_1596522), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1596522))), _1596526)))))))], (35173 ^ _777959) ^ [_1439489, _1439491] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1439489), _1439491) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1439489 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1439489 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (14690 ^ _777959) ^ [_1054018, _1054020, _1054022, _1054024] : [hBOOL(hAPP(hAPP(c_member(_1054018), _1054020), c_SetInterval_Oord_OlessThan(_1054018, _1054022, _1054024))), -(hBOOL(hAPP(hAPP(_1054022, _1054020), _1054024)))], (2472 ^ _777959) ^ [_814602, _814604] : [_814604 = _814602, -(c_Smallcheck_Osmall__class_Osmall(_814604) = c_Smallcheck_Osmall__class_Osmall(_814602))], (31656 ^ _777959) ^ [_1375713, _1375715] : [-(_1375713 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1375715, _1375713) = c_Nitpick_Onat__gcd(_1375713, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1375715, _1375713)))], (22321 ^ _777959) ^ [_1203035, _1203037] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1203035), hAPP(c_Nat_OSuc, _1203037)) = 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), _1203035), _1203037)))], (5819 ^ _777959) ^ [_870229, _870231] : [hAPP(c_Com_Ocom_OBODY, _870229) = hAPP(c_Com_Ocom_OBODY, _870231), -(_870229 = _870231)], (22778 ^ _777959) ^ [_1212374, _1212376, _1212378, _1212380] : [class_Rings_Ocomm__semiring__1(_1212374), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1212374), hAPP(hAPP(c_Power_Opower__class_Opower(_1212374), _1212376), _1212378)), _1212380) = hAPP(hAPP(c_Power_Opower__class_Opower(_1212374), _1212376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1212378), _1212380)))], (1010 ^ _777959) ^ [_793308, _793310] : [-(class_Lattices_Obounded__lattice(_793308)), _793310 = _793308, class_Lattices_Obounded__lattice(_793310)], (1350 ^ _777959) ^ [_797558, _797560] : [-(class_Orderings_Otop(_797558)), _797560 = _797558, class_Orderings_Otop(_797560)], (22366 ^ _777959) ^ [_1203987, _1203989, _1203991, _1203993, _1203995] : [class_Groups_Ocomm__monoid__add(_1203987), hBOOL(hAPP(c_Finite__Set_Ofinite(_1203989), _1203991)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1203989), _1203993)), 22380 ^ _777959 : [(22383 ^ _777959) ^ [] : [hAPP(_1203995, 22379 ^ [_1203987, _1203989, _1203991, _1203993, _1203995]) = c_Groups_Ozero__class_Ozero(_1203987)], (22381 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1203989), 22379 ^ [_1203987, _1203989, _1203991, _1203993, _1203995]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1203989, tc_HOL_Obool)), _1203991), _1203993))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1203989, _1203987), _1203995), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1203989, tc_HOL_Obool)), _1203991), _1203993)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1203987), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1203989, _1203987), _1203995), _1203991)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1203989, _1203987), _1203995), _1203993)))], (17473 ^ _777959) ^ [_1111771, _1111773, _1111775] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1111771, tc_HOL_Obool)), _1111773), _1111775) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1111771, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1111771, tc_HOL_Obool)), _1111773), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1111771, tc_HOL_Obool)), _1111775), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1111771, tc_HOL_Obool), tc_HOL_Obool))))))], (48286 ^ _777959) ^ [_1749837] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1749837)) = _1749837)], (14576 ^ _777959) ^ [_1051794] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1051794)), 14580 ^ _777959 : [(14581 ^ _777959) ^ [_1051874] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1051874), _1051794)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1051874), 14579 ^ [_1051794])))]]], (48990 ^ _777959) ^ [_1767530, _1767532, _1767534, _1767536, _1767538] : [-(hAPP(c_Relation_Oconverse(_1767530, _1767532), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1767534, tc_fun(tc_prod(_1767530, _1767532), tc_HOL_Obool)), _1767536), _1767538)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1767534, tc_fun(tc_prod(_1767532, _1767530), tc_HOL_Obool)), _1767536), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1767530, _1767532), tc_HOL_Obool), tc_fun(tc_prod(_1767532, _1767530), tc_HOL_Obool), _1767534), c_Relation_Oconverse(_1767530, _1767532)), _1767538)))], (29034 ^ _777959) ^ [_1325103, _1325105] : [class_Orderings_Olinorder(_1325103), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1325103, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1325103), _1325105)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1325103), _1325105))], (13881 ^ _777959) ^ [_1034800, _1034802, _1034804, _1034806, _1034808] : [_1034800 = hAPP(_1034802, _1034804), -(hBOOL(hAPP(hAPP(c_member(_1034806), _1034800), hAPP(c_Set_Oimage(_1034808, _1034806, _1034802), c_Orderings_Otop__class_Otop(tc_fun(_1034808, tc_HOL_Obool))))))], (12189 ^ _777959) ^ [_999235, _999237, _999239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999235), _999237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999235), _999239)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999237), _999239))))], (30957 ^ _777959) ^ [_1362681, _1362683, _1362685] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1362681), _1362683)), 30963 ^ _777959 : [(30966 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1362685, 30962 ^ [_1362681, _1362683, _1362685])))], (30964 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1362681), 30962 ^ [_1362681, _1362683, _1362685]), _1362683)))]], -(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(_1362681, tc_Nat_Onat), _1362685), _1362683))))], (43648 ^ _777959) ^ [_1645677, _1645679, _1645681] : [class_Groups_Omonoid__add(_1645677), -(hAPP(c_List_Ofoldl(_1645677, _1645677, c_Groups_Oplus__class_Oplus(_1645677), _1645679), _1645681) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1645677), _1645679), c_List_Ofoldr(_1645677, _1645677, c_Groups_Oplus__class_Oplus(_1645677), _1645681, c_Groups_Ozero__class_Ozero(_1645677))))], (29976 ^ _777959) ^ [_1344658, _1344660, _1344662, _1344664] : [class_Divides_Osemiring__div(_1344658), -(c_Divides_Odiv__class_Omod(_1344658, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344658), c_Divides_Odiv__class_Omod(_1344658, _1344660, _1344662)), _1344664), _1344662) = c_Divides_Odiv__class_Omod(_1344658, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344658), _1344660), _1344664), _1344662))], (44789 ^ _777959) ^ [_1668838, _1668840, _1668842] : [_1668842 = hAPP(hAPP(c_List_Olist_OCons(_1668838), _1668840), c_List_Olist_ONil(_1668838)), -(hAPP(hAPP(c_List_Olist_OCons(_1668838), _1668840), c_List_Olist_ONil(_1668838)) = hAPP(c_List_Orev(_1668838), _1668842))], (35277 ^ _777959) ^ [] : [-(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)))))], (6647 ^ _777959) ^ [_885709, _885711, _885713, _885715] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885709, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_885709), _885711), _885713)), _885715))), hBOOL(hAPP(hAPP(c_member(_885709), _885711), _885715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885709, tc_HOL_Obool)), _885713), _885715))], (31538 ^ _777959) ^ [_1373541] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1373541))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1373541)) = _1373541)], (29138 ^ _777959) ^ [_1327131, _1327133, _1327135, _1327137] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1327131, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1327133)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1327131, tc_HOL_Obool), tc_Nat_Onat), _1327135), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1327137))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1327131, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1327137, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1327133), _1327137))), _1327135))], (34063 ^ _777959) ^ [_1419512, _1419514, _1419516] : [-(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), _1419512)), 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))), _1419514))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1419516))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1419516)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1419512), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1419512), 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), _1419516), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1419514)))))], (688 ^ _777959) ^ [_788521, _788523, _788525, _788527] : [-(c_List_Olinorder__class_Osorted(_788525, _788521)), c_List_Olinorder__class_Osorted(_788527, _788523), _788527 = _788525, _788523 = _788521], (51376 ^ _777959) ^ [_1813984, _1813986] : [_1813984 = _1813986, -(hBOOL(hAPP(hAPP(c_fequal, _1813984), _1813986)))], (41479 ^ _777959) ^ [_1591094, _1591096, _1591098] : [_1591094 = hAPP(hAPP(c_List_Olist_OCons(_1591096), _1591098), _1591094)], (46874 ^ _777959) ^ [_1717840, _1717842, _1717844, _1717846] : [c_Wellfounded_Owf(_1717840, _1717842), c_Wellfounded_Owf(_1717844, _1717846), -(c_Wellfounded_Owf(tc_prod(_1717840, _1717844), c_Wellfounded_Olex__prod(_1717840, _1717844, _1717842, _1717846)))], (36890 ^ _777959) ^ [_1477997, _1477999, _1478001, _1478003] : [-(c_Map_Omap__add(_1477997, _1477999, _1478001, hAPP(c_Map_Omap__of(_1477997, _1477999), _1478003)) = c_List_Ofoldr(tc_prod(_1477997, _1477999), tc_fun(_1477997, tc_Option_Ooption(_1477999)), hAPP(c_Product__Type_Oprod_Oprod__case(_1477997, _1477999, tc_fun(tc_fun(_1477997, tc_Option_Ooption(_1477999)), tc_fun(_1477997, tc_Option_Ooption(_1477999)))), hAPP(hAPP(c_COMBC(_1477997, tc_fun(_1477999, tc_Option_Ooption(_1477999)), tc_fun(_1477999, tc_fun(tc_fun(_1477997, tc_Option_Ooption(_1477999)), tc_fun(_1477997, tc_Option_Ooption(_1477999))))), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1477999), tc_fun(tc_fun(_1477997, tc_Option_Ooption(_1477999)), tc_fun(_1477997, tc_Option_Ooption(_1477999)))), tc_fun(tc_fun(_1477999, tc_Option_Ooption(_1477999)), tc_fun(_1477999, tc_fun(tc_fun(_1477997, tc_Option_Ooption(_1477999)), tc_fun(_1477997, tc_Option_Ooption(_1477999))))), _1477997), c_COMBB(tc_Option_Ooption(_1477999), tc_fun(tc_fun(_1477997, tc_Option_Ooption(_1477999)), tc_fun(_1477997, tc_Option_Ooption(_1477999))), _1477999)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1477997, tc_Option_Ooption(_1477999)), tc_fun(tc_Option_Ooption(_1477999), tc_fun(_1477997, tc_Option_Ooption(_1477999)))), tc_fun(tc_Option_Ooption(_1477999), tc_fun(tc_fun(_1477997, tc_Option_Ooption(_1477999)), tc_fun(_1477997, tc_Option_Ooption(_1477999)))), _1477997), c_COMBC(tc_fun(_1477997, tc_Option_Ooption(_1477999)), tc_Option_Ooption(_1477999), tc_fun(_1477997, tc_Option_Ooption(_1477999)))), hAPP(c_COMBC(tc_fun(_1477997, tc_Option_Ooption(_1477999)), _1477997, tc_fun(tc_Option_Ooption(_1477999), tc_fun(_1477997, tc_Option_Ooption(_1477999)))), c_Fun_Ofun__upd(_1477997, tc_Option_Ooption(_1477999)))))), c_Option_Ooption_OSome(_1477999))), _1478003, _1478001))], (38292 ^ _777959) ^ [_1511642, _1511644, _1511646, _1511648] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1511642), _1511644)), hAPP(c_Finite__Set_Ocard(_1511646), hAPP(c_Set_Oimage(_1511642, _1511646, _1511648), _1511644)) = hAPP(c_Finite__Set_Ocard(_1511642), _1511644), -(c_Fun_Oinj__on(_1511642, _1511646, _1511648, _1511644))], (22609 ^ _777959) ^ [_1209377, _1209379, _1209381, _1209383] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1209377, _1209381)), c_Sum__Type_OPlus(_1209377, _1209381, _1209379, _1209383)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1209377), _1209379)), hAPP(c_Finite__Set_Ocard(_1209381), _1209383))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1209377), _1209379)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1209381), _1209383))], (41455 ^ _777959) ^ [_1590597, _1590599, _1590601, _1590603] : [-(hAPP(hAPP(c_List_Olist__update(_1590597, hAPP(hAPP(c_List_Olist_OCons(_1590597), _1590599), _1590601)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1590603) = hAPP(hAPP(c_List_Olist_OCons(_1590597), _1590603), _1590601))], (7806 ^ _777959) ^ [_910688, _910690, _910692, _910694] : [hBOOL(hAPP(hAPP(c_member(_910688), _910690), _910692)), -(hBOOL(hAPP(hAPP(c_member(_910688), _910690), _910694))), -(hBOOL(hAPP(hAPP(c_member(_910688), _910690), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_910688, tc_HOL_Obool)), _910692), _910694))))], (23164 ^ _777959) ^ [_1219428, _1219430, _1219432, _1219434] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1219428), _1219430)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219432), _1219434)), -(hAPP(c_Finite__Set_Ocard(tc_sum(_1219428, _1219432)), c_Sum__Type_OPlus(_1219428, _1219432, _1219430, _1219434)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1219428), _1219430)), hAPP(c_Finite__Set_Ocard(_1219432), _1219434)))], (17019 ^ _777959) ^ [_1103464, _1103466, _1103468, _1103470] : [class_Orderings_Olinorder(_1103464), 17022 ^ _777959 : [(17023 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103464), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1103464), _1103466), _1103468)), _1103470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103464), _1103466), _1103470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103464), _1103468), _1103470)))], (17033 ^ _777959) ^ [] : [17034 ^ _777959 : [(17037 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103464), _1103468), _1103470))], (17035 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103464), _1103466), _1103470))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103464), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1103464), _1103466), _1103468)), _1103470)))]]], (16539 ^ _777959) ^ [_1094932, _1094934, _1094936, _1094938] : [class_Orderings_Olinorder(_1094932), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094932), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094932), _1094934), _1094936)), _1094938) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094932), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094932), _1094934), _1094938)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094932), _1094936), _1094938)))], (38981 ^ _777959) ^ [_1528233, _1528235, _1528237, _1528239, _1528241, _1528243] : [-(hAPP(hAPP(c_Option_Omap(_1528233, _1528235), _1528237), hAPP(hAPP(c_Option_Omap(_1528239, _1528233), _1528241), _1528243)) = hAPP(hAPP(c_Option_Omap(_1528239, _1528235), hAPP(c_Fun_Ocomp(_1528233, _1528235, _1528239, _1528237), _1528241)), _1528243))], (35908 ^ _777959) ^ [_1459361, _1459363] : [-(c_Divides_OnegDivAlg(_1459361, _1459363) = hAPP(c_Divides_Oadjust(_1459363), c_Divides_OnegDivAlg(_1459361, 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)))), _1459363)))), -(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), _1459361), _1459363)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1459363), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (16313 ^ _777959) ^ [_1090192, _1090194] : [class_Complete__Lattice_Ocomplete__lattice(_1090192), hBOOL(hAPP(c_Finite__Set_Ofinite(_1090192), _1090194)), -(c_Complete__Lattice_OInf__class_OInf(_1090192, _1090194) = hAPP(hAPP(c_Finite__Set_Ofold(_1090192, _1090192, c_Lattices_Osemilattice__inf__class_Oinf(_1090192)), c_Orderings_Otop__class_Otop(_1090192)), _1090194))], (41001 ^ _777959) ^ [_1578616, _1578618, _1578620] : [41003 ^ _777959 : [(41006 ^ _777959) ^ [] : [hBOOL(hAPP(_1578618, 41002 ^ [_1578616, _1578618, _1578620]))], (41004 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1578616), 41002 ^ [_1578616, _1578618, _1578620]), _1578620)))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1578616, _1578618), _1578620)))], (34237 ^ _777959) ^ [_1422567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1422567))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1422567)))], (50104 ^ _777959) ^ [_1793723, _1793725, _1793727, _1793729, _1793731] : [_1793723 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1793725, _1793727, _1793729, _1793731), _1793723) = c_Lazy__Sequence_Oempty(_1793727))], (17805 ^ _777959) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (25572 ^ _777959) ^ [_1262720, _1262722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1262720)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1262720), _1262722)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1262722), _1262720) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1262722), _1262720)), _1262720)))], (28810 ^ _777959) ^ [_1320832, _1320834, _1320836, _1320838, _1320840] : [class_Groups_Ocomm__monoid__add(_1320832), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1320834), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1320836), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1320832), _1320838), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1320834, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1320836), _1320840))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320832), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1320832), _1320838), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1320834, _1320836))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1320832), _1320838), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1320836), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1320836), _1320840)))))], (7986 ^ _777959) ^ [_914293, _914295] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OWhile(_914293, _914295))), -(hBOOL(hAPP(c_Com_OWT, _914295)))], (40028 ^ _777959) ^ [_1553254, _1553256, _1553258, _1553260, _1553262] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553254)), _1553256) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553258)), _1553260), 40031 ^ _777959 : [(40038 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553254), _1553262), hAPP(c_List_Oset(_1553254), _1553256)))), -(hAPP(hAPP(c_Map_Omap__of(_1553254, _1553258), hAPP(hAPP(c_List_Ozip(_1553254, _1553258), _1553256), _1553260)), _1553262) = c_Option_Ooption_ONone(_1553258))], (40032 ^ _777959) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1553254, _1553258), hAPP(hAPP(c_List_Ozip(_1553254, _1553258), _1553256), _1553260)), _1553262) = c_Option_Ooption_ONone(_1553258), hBOOL(hAPP(hAPP(c_member(_1553254), _1553262), hAPP(c_List_Oset(_1553254), _1553256)))]]], (5458 ^ _777959) ^ [_861405, _861407] : [_861407 = _861405, -(c_member(_861407) = c_member(_861405))], (15906 ^ _777959) ^ [_1080901, _1080903, _1080905, _1080907, _1080909, _1080911] : [class_Rings_Oordered__ring(_1080901), 15909 ^ _777959 : [(15916 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080901), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080901), _1080903), _1080909)), _1080905)), _1080907)), _1080911)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080901), _1080903), _1080905)), _1080907)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080901), _1080909), _1080905)), _1080911))))], (15910 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080901), _1080903), _1080905)), _1080907)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080901), _1080909), _1080905)), _1080911))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1080901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080901), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080901), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080901), _1080903), _1080909)), _1080905)), _1080907)), _1080911)))]]], (48555 ^ _777959) ^ [_1756277, _1756279, _1756281, _1756283] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1756277, _1756277)), hAPP(hAPP(c_Product__Type_OPair(_1756277, _1756277), _1756279), _1756281)), c_Transitive__Closure_Ortrancl(_1756277, _1756283))), -(_1756279 = _1756281), 48562 ^ _777959 : [(48565 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1756277, _1756277)), hAPP(hAPP(c_Product__Type_OPair(_1756277, _1756277), _1756279), _1756281)), c_Transitive__Closure_Otrancl(_1756277, _1756283))))], (48563 ^ _777959) ^ [] : [_1756279 = _1756281]]], (47013 ^ _777959) ^ [_1720576] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1720576)))], (35325 ^ _777959) ^ [] : [-(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))], (43612 ^ _777959) ^ [_1644862, _1644864, _1644866, _1644868, _1644870, _1644872] : [-(hAPP(c_List_Ofoldl(_1644862, _1644864, _1644866, _1644868), hAPP(hAPP(c_List_Olist_OCons(_1644864), _1644870), _1644872)) = hAPP(c_List_Ofoldl(_1644862, _1644864, _1644866, hAPP(hAPP(_1644866, _1644868), _1644870)), _1644872))], (25726 ^ _777959) ^ [_1265984, _1265986] : [class_Rings_Odivision__ring__inverse__zero(_1265984), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265984), _1265986), c_Groups_Ozero__class_Ozero(_1265984)) = c_Groups_Ozero__class_Ozero(_1265984))], (6097 ^ _777959) ^ [_875576, _875578, _875580] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875576, tc_HOL_Obool)), _875578), _875580) = _875580, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875576, tc_HOL_Obool)), _875578), _875580)))], (9272 ^ _777959) ^ [_937398, _937400] : [class_Lattices_Olattice(_937398), -(c_Big__Operators_Olattice__class_OSup__fin(_937398, hAPP(hAPP(c_Set_Oinsert(_937398), _937400), c_Orderings_Obot__class_Obot(tc_fun(_937398, tc_HOL_Obool)))) = _937400)], (23252 ^ _777959) ^ [_1221073, _1221075, _1221077, _1221079] : [class_Rings_Olinordered__semidom(_1221073), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1221075), _1221077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221073), c_Groups_Ozero__class_Ozero(_1221073)), _1221079)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221073), _1221079), c_Groups_Oone__class_Oone(_1221073))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1221073), hAPP(hAPP(c_Power_Opower__class_Opower(_1221073), _1221079), _1221077)), hAPP(hAPP(c_Power_Opower__class_Opower(_1221073), _1221079), _1221075))))], (11006 ^ _777959) ^ [_973512, _973514, _973516, _973518, _973520] : [class_Groups_Ocomm__monoid__add(_973512), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_973514, _973512), hAPP(hAPP(c_COMBS(_973514, _973512, _973512), hAPP(hAPP(c_COMBB(_973512, tc_fun(_973512, _973512), _973514), c_Groups_Oplus__class_Oplus(_973512)), _973516)), _973518)), _973520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973512), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_973514, _973512), _973516), _973520)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_973514, _973512), _973518), _973520)))], (47728 ^ _777959) ^ [_1737792, _1737794, _1737796, _1737798, _1737800] : [class_Orderings_Olinorder(_1737792), 47734 ^ _777959 : [(47737 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1737792), hAPP(_1737798, _1737800)), hAPP(_1737798, 47733 ^ [_1737792, _1737794, _1737796, _1737798, _1737800])))], (47735 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737794), 47733 ^ [_1737792, _1737794, _1737796, _1737798, _1737800]), hAPP(c_List_Oset(_1737794), _1737796))))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1737794, _1737792, _1737798), _1737800), _1737796) = hAPP(hAPP(c_List_Olist_OCons(_1737794), _1737800), _1737796))], (48224 ^ _777959) ^ [_1748777, _1748779] : [_1748777 = _1748779, -(hAPP(c_Code__Numeral_Oof__nat, _1748777) = hAPP(c_Code__Numeral_Oof__nat, _1748779))], (22343 ^ _777959) ^ [_1203411, _1203413, _1203415, _1203417, _1203419] : [class_Groups_Ocomm__monoid__mult(_1203411), hBOOL(hAPP(c_Finite__Set_Ofinite(_1203413), _1203415)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1203413), _1203417)), 22357 ^ _777959 : [(22360 ^ _777959) ^ [] : [hAPP(_1203419, 22356 ^ [_1203411, _1203413, _1203415, _1203417, _1203419]) = c_Groups_Oone__class_Oone(_1203411)], (22358 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1203413), 22356 ^ [_1203411, _1203413, _1203415, _1203417, _1203419]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1203413, tc_HOL_Obool)), _1203415), _1203417))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1203413, _1203411), _1203419), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1203413, tc_HOL_Obool)), _1203415), _1203417)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1203411), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1203413, _1203411), _1203419), _1203415)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1203413, _1203411), _1203419), _1203417)))], (7642 ^ _777959) ^ [_906815, _906817, _906819, _906821] : [c_Finite__Set_Ofolding__one(_906815, _906817, _906819), -(hAPP(_906819, hAPP(hAPP(c_Set_Oinsert(_906815), _906821), c_Orderings_Obot__class_Obot(tc_fun(_906815, tc_HOL_Obool)))) = _906821)], (45602 ^ _777959) ^ [_1688015, _1688017, _1688019] : [-(c_Enum_Oproduct(_1688015, _1688017, c_List_Olist_ONil(_1688015), _1688019) = c_List_Olist_ONil(tc_prod(_1688015, _1688017)))], (47379 ^ _777959) ^ [_1729558, _1729560, _1729562, _1729564] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1729558, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1729558, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1729558, _1729560), _1729562)), hAPP(c_Relation_ODomain(_1729558, _1729560), _1729564))), hAPP(c_Relation_ODomain(_1729558, _1729560), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1729558, _1729560), tc_HOL_Obool)), _1729562), _1729564)))))], (50148 ^ _777959) ^ [_1794424] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1794424)), c_Int_OPls))], (47102 ^ _777959) ^ [_1722348, _1722350] : [-(c_FunDef_Oreduction__pair(_1722348, _1722350)), c_Wellfounded_Owf(_1722348, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1722348, _1722348), tc_HOL_Obool), tc_fun(tc_prod(_1722348, _1722348), tc_HOL_Obool)), _1722350)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1722348, _1722348), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1722348, _1722348, _1722348), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1722348, _1722348), tc_HOL_Obool), tc_fun(tc_prod(_1722348, _1722348), tc_HOL_Obool)), _1722350)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1722348, _1722348), tc_HOL_Obool), tc_fun(tc_prod(_1722348, _1722348), tc_HOL_Obool)), _1722350))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1722348, _1722348), tc_HOL_Obool), tc_fun(tc_prod(_1722348, _1722348), tc_HOL_Obool)), _1722350)))], (23649 ^ _777959) ^ [_1227877, _1227879, _1227881, _1227883] : [class_Groups_Omonoid__mult(_1227877), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1227877), _1227879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1227881), _1227883)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1227877), hAPP(hAPP(c_Power_Opower__class_Opower(_1227877), _1227879), _1227881)), _1227883))], (9786 ^ _777959) ^ [_947956, _947958, _947960, _947962] : [class_Lattices_Osemilattice__inf(_947956), hBOOL(hAPP(c_Finite__Set_Ofinite(_947956), _947958)), -(hAPP(hAPP(c_Finite__Set_Ofold(_947956, _947956, c_Lattices_Osemilattice__inf__class_Oinf(_947956)), _947960), hAPP(hAPP(c_Set_Oinsert(_947956), _947962), _947958)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_947956), _947962), hAPP(hAPP(c_Finite__Set_Ofold(_947956, _947956, c_Lattices_Osemilattice__inf__class_Oinf(_947956)), _947960), _947958)))], (50882 ^ _777959) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (27627 ^ _777959) ^ [_1299875, _1299877] : [-(hBOOL(hAPP(_1299875, hAPP(c_Int_Onat, _1299877)))), 27631 ^ _777959 : [(27634 ^ _777959) ^ [] : [hBOOL(hAPP(_1299875, 27630 ^ [_1299875, _1299877]))], (27632 ^ _777959) ^ [] : [-(_1299877 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 27630 ^ [_1299875, _1299877]))]], 27635 ^ _777959 : [(27638 ^ _777959) ^ [] : [hBOOL(hAPP(_1299875, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (27636 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299877), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (41263 ^ _777959) ^ [_1585604, _1585606, _1585608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585604, _1585604), tc_HOL_Obool)), _1585606), _1585608)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1585604), tc_List_Olist(_1585604)), tc_HOL_Obool)), c_List_Olistrel1(_1585604, _1585606)), c_List_Olistrel1(_1585604, _1585608))))], (30888 ^ _777959) ^ [_1361495, _1361497] : [class_Rings_Olinordered__idom(_1361495), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361495), c_Groups_Ozero__class_Ozero(_1361495)), _1361497)), -(c_Groups_Osgn__class_Osgn(_1361495, _1361497) = c_Groups_Oone__class_Oone(_1361495))], (7094 ^ _777959) ^ [_896461, _896463] : [class_Finite__Set_Ofinite(_896461), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_896461), _896463)))], (33773 ^ _777959) ^ [_1413737, _1413739] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413737), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413737)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413739)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1413737), _1413739)))], (44855 ^ _777959) ^ [_1670179, _1670181] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670179)), hAPP(c_List_Orev(_1670179), _1670181)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670179)), _1670181))], (13923 ^ _777959) ^ [_1035709, _1035711, _1035713, _1035715, _1035717] : [_1035709 = c_Orderings_Obot__class_Obot(tc_fun(_1035711, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1035713, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1035711, tc_fun(_1035713, tc_HOL_Obool)), _1035709), _1035715)), _1035717) = _1035717)], (34145 ^ _777959) ^ [_1421034] : [_1421034 = c_Int_OPls, -(c_Int_OBit0(_1421034) = c_Int_OPls)], (51466 ^ _777959) ^ [] : [-(c_Com_OWT__bodies)], (43428 ^ _777959) ^ [_1641319, _1641321, _1641323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641319), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641321)), _1641323))), -(_1641323 = hAPP(hAPP(c_List_Oappend(_1641321), hAPP(hAPP(c_List_Otake(_1641321), _1641319), _1641323)), hAPP(hAPP(c_List_Olist_OCons(_1641321), hAPP(hAPP(c_List_Onth(_1641321), _1641323), _1641319)), hAPP(hAPP(c_List_Odrop(_1641321), hAPP(c_Nat_OSuc, _1641319)), _1641323))))], (48170 ^ _777959) ^ [_1747747, _1747749, _1747751, _1747753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1747747), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1747749), _1747751))), -(hAPP(c_Random_Opick(_1747749, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1747749)), _1747751), _1747753)), _1747747) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1747749), _1747751))], (47257 ^ _777959) ^ [_1726082, _1726084, _1726086, _1726088, _1726090] : [-(hAPP(c_Relation_ORange(_1726082, _1726084), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1726082, _1726084)), hAPP(hAPP(c_Product__Type_OPair(_1726082, _1726084), _1726086), _1726088)), _1726090)) = hAPP(hAPP(c_Set_Oinsert(_1726084), _1726088), hAPP(c_Relation_ORange(_1726082, _1726084), _1726090)))], (50856 ^ _777959) ^ [_1808712, _1808714] : [-(class_Enum_Oenum(tc_fun(_1808712, _1808714))), class_Enum_Oenum(_1808712), class_Enum_Oenum(_1808714)], (47670 ^ _777959) ^ [_1736407, _1736409, _1736411, _1736413, _1736415, _1736417] : [hBOOL(hAPP(hAPP(c_member(_1736407), _1736409), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1736411, _1736413, tc_fun(_1736407, tc_HOL_Obool)), _1736415), _1736417))), 47675 ^ _777959 : [(47678 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1736407), _1736409), hAPP(hAPP(_1736415, 47673 ^ [_1736407, _1736409, _1736411, _1736413, _1736415, _1736417]), 47674 ^ [_1736407, _1736409, _1736411, _1736413, _1736415, _1736417]))))], (47676 ^ _777959) ^ [] : [-(_1736417 = hAPP(hAPP(c_Product__Type_OPair(_1736411, _1736413), 47673 ^ [_1736407, _1736409, _1736411, _1736413, _1736415, _1736417]), 47674 ^ [_1736407, _1736409, _1736411, _1736413, _1736415, _1736417]))]]], (22240 ^ _777959) ^ [_1201284, _1201286] : [class_Rings_Olinordered__idom(_1201284), 22243 ^ _777959 : [(22250 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201284), _1201286), c_Groups_Ozero__class_Ozero(_1201284))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201284), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201284), _1201286), _1201286)), c_Groups_Ozero__class_Ozero(_1201284))))], (22244 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201284), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1201284), _1201286), _1201286)), c_Groups_Ozero__class_Ozero(_1201284))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1201284), _1201286), c_Groups_Ozero__class_Ozero(_1201284))))]]], (28353 ^ _777959) ^ [_1312261, _1312263, _1312265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1312261, 28354 ^ [_1312261, _1312263, _1312265])), hAPP(_1312263, 28354 ^ [_1312261, _1312263, _1312265]))), -(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), _1312263), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1312265))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1312261), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1312265))) = 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)), _1312263)), _1312261)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1312265)))], (5958 ^ _777959) ^ [_872998, _873000, _873002, _873004] : [_872998 = _873000, 5963 ^ _777959 : [(5966 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_873002), _873004), _873000)))], (5964 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_873002), _873004), _872998)))]], 5967 ^ _777959 : [(5970 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_873002), _873004), _873000))], (5968 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_873002), _873004), _872998))]]], (10410 ^ _777959) ^ [_961727, _961729, _961731] : [class_Lattices_Olattice(_961727), hBOOL(hAPP(c_Finite__Set_Ofinite(_961727), _961729)), -(c_Big__Operators_Olattice__class_OSup__fin(_961727, hAPP(hAPP(c_Set_Oinsert(_961727), _961731), _961729)) = hAPP(hAPP(c_Finite__Set_Ofold(_961727, _961727, c_Lattices_Osemilattice__sup__class_Osup(_961727)), _961731), _961729))], (34277 ^ _777959) ^ [_1423271] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1423271)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1423271)))], (13269 ^ _777959) ^ [_1020492, _1020494, _1020496, _1020498, _1020500] : [class_Complete__Lattice_Ocomplete__lattice(_1020492), hBOOL(hAPP(c_Finite__Set_Ofinite(_1020494), _1020496)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1020492), _1020498), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1020494, _1020492), _1020496), _1020500)) = hAPP(hAPP(c_Finite__Set_Ofold(_1020494, _1020492, hAPP(hAPP(c_COMBB(_1020492, tc_fun(_1020492, _1020492), _1020494), c_Lattices_Osemilattice__inf__class_Oinf(_1020492)), _1020500)), _1020498), _1020496))], (19238 ^ _777959) ^ [_1147376, _1147378] : [class_Groups_Omonoid__add(_1147376), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1147376), c_Groups_Ozero__class_Ozero(_1147376)), _1147378) = _1147378)], (23327 ^ _777959) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (34469 ^ _777959) ^ [_1426824, _1426826] : [class_Groups_Omonoid__mult(_1426824), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1426824), _1426826), 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(_1426824), _1426826), _1426826))], (48641 ^ _777959) ^ [_1758416, _1758418, _1758420, _1758422, _1758424] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1758416, _1758416)), hAPP(hAPP(c_Product__Type_OPair(_1758416, _1758416), _1758418), _1758420)), c_Transitive__Closure_Ortrancl(_1758416, _1758422))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1758416, _1758416)), hAPP(hAPP(c_Product__Type_OPair(_1758416, _1758416), _1758420), _1758424)), _1758422)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1758416, _1758416)), hAPP(hAPP(c_Product__Type_OPair(_1758416, _1758416), _1758418), _1758424)), c_Transitive__Closure_Ortrancl(_1758416, _1758422))))], (13911 ^ _777959) ^ [_1035450, _1035452, _1035454, _1035456, _1035458] : [_1035450 = c_Orderings_Obot__class_Obot(tc_fun(_1035452, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1035454, tc_HOL_Obool)), _1035456), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1035452, tc_fun(_1035454, tc_HOL_Obool)), _1035450), _1035458)) = _1035456)], (49306 ^ _777959) ^ [_1775096, _1775098, _1775100] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1775096, _1775096, _1775096), _1775098), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775096, _1775096), tc_HOL_Obool), _1775100), _1775098)) = hAPP(hAPP(c_Relation_Orel__comp(_1775096, _1775096, _1775096), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775096, _1775096), tc_HOL_Obool), _1775100), _1775098)), _1775098))], (35285 ^ _777959) ^ [_1441205, _1441207, _1441209, _1441211] : [-(c_Nitpick_Oprod(_1441205, _1441207, _1441209, _1441211) = hAPP(c_Set_OCollect(tc_prod(_1441205, _1441207)), hAPP(c_Product__Type_Oprod_Oprod__case(_1441205, _1441207, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1441205, tc_fun(_1441207, tc_HOL_Obool), tc_fun(_1441207, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1441207, tc_HOL_Obool), tc_fun(_1441207, tc_HOL_Obool)), _1441205), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1441207)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1441205), c_fconj), hAPP(hAPP(c_COMBC(_1441205, tc_fun(_1441205, tc_HOL_Obool), tc_HOL_Obool), c_member(_1441205)), _1441209)))), hAPP(hAPP(c_COMBC(_1441207, tc_fun(_1441207, tc_HOL_Obool), tc_HOL_Obool), c_member(_1441207)), _1441211)))))], (30217 ^ _777959) ^ [_1349419, _1349421, _1349423, _1349425] : [class_Divides_Osemiring__div(_1349419), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349419), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349419), _1349421), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1349419), _1349423), _1349421))), c_Divides_Odiv__class_Omod(_1349419, _1349423, _1349421))), _1349425) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349419), _1349423), _1349425))], (4226 ^ _777959) ^ [_841939, _841941, _841943, _841945] : [-(c_Transitive__Closure_Otrancl(_841945, _841941) = c_Transitive__Closure_Otrancl(_841943, _841939)), _841945 = _841943, _841941 = _841939], (13605 ^ _777959) ^ [_1027962, _1027964] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1027962, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1027962, tc_HOL_Obool))), _1027964) = _1027964)], (25958 ^ _777959) ^ [_1270078, _1270080, _1270082, _1270084] : [class_Orderings_Olinorder(_1270078), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270078), _1270080), _1270082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270078), _1270082), _1270084)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1270078, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1270078, _1270080, _1270082)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1270078, _1270082), _1270084)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1270078, _1270080, _1270084))], (36926 ^ _777959) ^ [_1479311, _1479313, _1479315, _1479317, _1479319, _1479321] : [hAPP(c_Product__Type_Oapfst(_1479311, _1479313, _1479315, _1479317), _1479319) = hAPP(c_Product__Type_Oapfst(_1479311, _1479313, _1479315, _1479321), _1479319), -(hAPP(_1479317, hAPP(c_Product__Type_Ofst(_1479311, _1479315), _1479319)) = hAPP(_1479321, hAPP(c_Product__Type_Ofst(_1479311, _1479315), _1479319)))], (47176 ^ _777959) ^ [_1724303, _1724305, _1724307, _1724309] : [47178 ^ _777959 : [(47181 ^ _777959) ^ [] : [c_Wellfounded_Owf(_1724305, hAPP(_1724307, 47177 ^ [_1724303, _1724305, _1724307, _1724309]))], (47179 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1724303, 47177 ^ [_1724303, _1724305, _1724307, _1724309])))]], -(c_Wellfounded_Owf(tc_prod(_1724309, _1724305), c_Recdef_Osame__fst(_1724309, _1724305, _1724303, _1724307)))], (17509 ^ _777959) ^ [_1112611, _1112613, _1112615] : [class_Complete__Lattice_Ocomplete__lattice(_1112611), -(c_Complete__Lattice_OInf__class_OInf(_1112611, hAPP(hAPP(c_Set_Oinsert(_1112611), _1112613), hAPP(hAPP(c_Set_Oinsert(_1112611), _1112615), c_Orderings_Obot__class_Obot(tc_fun(_1112611, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1112611), _1112613), _1112615))], (10050 ^ _777959) ^ [_952978, _952980, _952982, _952984] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_952978, _952980, _952982), _952984), c_Orderings_Obot__class_Obot(tc_fun(_952978, tc_HOL_Obool))) = _952984)], (22944 ^ _777959) ^ [_1215488, _1215490, _1215492] : [class_Rings_Osemiring__1(_1215488), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215488), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1215490), _1215492)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1215488), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215488), _1215490)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215488), _1215492)))], (50740 ^ _777959) ^ [_1807190, _1807192] : [class_Lattices_Obounded__lattice(_1807190), -(class_Lattices_Obounded__lattice(tc_fun(_1807192, _1807190)))], (31642 ^ _777959) ^ [_1375429, _1375431, _1375433, _1375435, _1375437, _1375439] : [c_Com_Ocom_OCond(_1375429, _1375431, _1375433) = c_Com_Ocom_OCall(_1375435, _1375437, _1375439)], (31548 ^ _777959) ^ [_1373660, _1373662, _1373664, _1373666] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1373660, tc_Nat_Onat), _1373662), _1373664) = hAPP(c_Nat_OSuc, _1373666), 31552 ^ _777959 : [(31555 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1373662, 31551 ^ [_1373660, _1373662, _1373664, _1373666]))))], (31553 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1373660), 31551 ^ [_1373660, _1373662, _1373664, _1373666]), _1373664)))]]], (40152 ^ _777959) ^ [_1556468] : [class_Orderings_Olinorder(_1556468), -(c_Finite__Set_Ofun__left__comm(_1556468, tc_List_Olist(_1556468), c_List_Olinorder__class_Oinsort__key(_1556468, _1556468, c_COMBI(_1556468))))], (45520 ^ _777959) ^ [_1685524, _1685526, _1685528] : [-(c_Enum_On__lists(_1685524, hAPP(c_Nat_OSuc, _1685526), _1685528) = c_List_Oconcat(tc_List_Olist(_1685524), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1685524), tc_List_Olist(tc_List_Olist(_1685524))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1685524), tc_List_Olist(_1685524), tc_List_Olist(tc_List_Olist(_1685524))), hAPP(hAPP(c_COMBB(tc_fun(_1685524, tc_List_Olist(_1685524)), tc_fun(tc_List_Olist(_1685524), tc_List_Olist(tc_List_Olist(_1685524))), tc_List_Olist(_1685524)), c_List_Omap(_1685524, tc_List_Olist(_1685524))), hAPP(c_COMBC(_1685524, tc_List_Olist(_1685524), tc_List_Olist(_1685524)), c_List_Olist_OCons(_1685524)))), _1685528)), c_Enum_On__lists(_1685524, _1685526, _1685528))))], (17393 ^ _777959) ^ [_1110445, _1110447, _1110449] : [class_Orderings_Olinorder(_1110445), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110445), _1110447)), -(_1110449 = c_Orderings_Obot__class_Obot(tc_fun(_1110445, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1110445, tc_HOL_Obool)), _1110449), _1110447)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1110445), c_Big__Operators_Olinorder__class_OMax(_1110445, _1110449)), c_Big__Operators_Olinorder__class_OMax(_1110445, _1110447)) = c_Big__Operators_Olinorder__class_OMax(_1110445, _1110447))], (25436 ^ _777959) ^ [_1260277] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260277), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1260277)], (11888 ^ _777959) ^ [_993647, _993649, _993651, _993653, _993655] : [-(_993647 = c_Orderings_Obot__class_Obot(tc_fun(_993649, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_993651, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993649, tc_fun(_993651, tc_HOL_Obool)), _993647), _993653)), _993655) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_993649, tc_fun(_993651, tc_HOL_Obool)), _993647), hAPP(hAPP(c_COMBC(_993649, tc_fun(_993651, tc_HOL_Obool), tc_fun(_993651, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_993651, tc_HOL_Obool), tc_fun(tc_fun(_993651, tc_HOL_Obool), tc_fun(_993651, tc_HOL_Obool)), _993649), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_993651, tc_HOL_Obool))), _993653)), _993655)))], (42931 ^ _777959) ^ [_1628816, _1628818, _1628820] : [_1628820 = c_List_Olist_ONil(_1628818), -(_1628816 = hAPP(hAPP(c_List_Oappend(_1628818), _1628820), _1628816))], (33219 ^ _777959) ^ [_1405024] : [c_Int_OPls = c_Int_OBit1(_1405024)], (22505 ^ _777959) ^ [_1206942, _1206944, _1206946] : [class_Orderings_Oord(_1206942), 22508 ^ _777959 : [(22515 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206942), _1206944), _1206946)), -(hBOOL(hAPP(hAPP(c_member(_1206942), _1206944), hAPP(c_SetInterval_Oord__class_OlessThan(_1206942), _1206946))))], (22509 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1206942), _1206944), hAPP(c_SetInterval_Oord__class_OlessThan(_1206942), _1206946))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1206942), _1206944), _1206946)))]]], (14297 ^ _777959) ^ [_1044571, _1044573, _1044575] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1044571), _1044573)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1044571), _1044575)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1044571), _1044573)), hAPP(c_Finite__Set_Ocard(_1044571), _1044575)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1044571), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1044571, tc_HOL_Obool)), _1044573), _1044575))), hAPP(c_Finite__Set_Ocard(_1044571), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1044571, tc_HOL_Obool)), _1044573), _1044575))))], (20349 ^ _777959) ^ [_1166122, _1166124, _1166126] : [class_Rings_Olinordered__semiring__strict(_1166122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166122), c_Groups_Ozero__class_Ozero(_1166122)), _1166124)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166122), _1166126), c_Groups_Ozero__class_Ozero(_1166122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166122), _1166126), _1166124)), c_Groups_Ozero__class_Ozero(_1166122))))], (27920 ^ _777959) ^ [_1305013] : [class_Rings_Oring__1(_1305013), -(hAPP(c_Int_Oring__1__class_Oof__int(_1305013), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1305013))], (20509 ^ _777959) ^ [_1169123, _1169125, _1169127] : [class_Groups_Oordered__ab__group__add(_1169123), 20512 ^ _777959 : [(20519 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169123), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1169123), _1169125), _1169127)), c_Groups_Ozero__class_Ozero(_1169123))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169123), _1169125), _1169127)))], (20513 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169123), _1169125), _1169127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1169123), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1169123), _1169125), _1169127)), c_Groups_Ozero__class_Ozero(_1169123))))]]], (44166 ^ _777959) ^ [_1656743, _1656745] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656743), _1656745))), -(c_List_Oupt(_1656743, hAPP(c_Nat_OSuc, _1656745)) = c_List_Olist_ONil(tc_Nat_Onat))], (50386 ^ _777959) ^ [_1799753, _1799755, _1799757, _1799759, _1799761] : [-(c_Lazy__Sequence_Ohb__map(_1799753, _1799755, _1799757, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(_1799753), _1799759, _1799761)) = c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Option_Ooption(_1799755), hAPP(hAPP(c_Option_Omap(_1799753, _1799755), _1799757), _1799759), c_Lazy__Sequence_Ohb__map(_1799753, _1799755, _1799757, _1799761)))], (27816 ^ _777959) ^ [] : [-(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))))], (34837 ^ _777959) ^ [_1433574, _1433576, _1433578] : [class_Rings_Olinordered__idom(_1433574), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433574), c_Groups_Ozero__class_Ozero(_1433574)), hAPP(hAPP(c_Power_Opower__class_Opower(_1433574), _1433576), 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)))), _1433578))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1433574), c_Groups_Ozero__class_Ozero(_1433574)), _1433576)))], (10094 ^ _777959) ^ [_953927, _953929, _953931, _953933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953927, tc_HOL_Obool)), _953929), _953931)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953927, tc_HOL_Obool)), _953929), _953933)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953927, tc_HOL_Obool)), _953929), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953927, tc_HOL_Obool)), _953931), _953933))))], (43107 ^ _777959) ^ [_1632929, _1632931, _1632933, _1632935, _1632937, _1632939, _1632941] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632929, _1632929)), hAPP(hAPP(c_Product__Type_OPair(_1632929, _1632929), _1632931), _1632933)), _1632935)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632929), tc_List_Olist(_1632929))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632929), tc_List_Olist(_1632929)), hAPP(hAPP(c_List_Oappend(_1632929), _1632937), hAPP(hAPP(c_List_Olist_OCons(_1632929), _1632931), _1632939))), hAPP(hAPP(c_List_Oappend(_1632929), _1632937), hAPP(hAPP(c_List_Olist_OCons(_1632929), _1632933), _1632941)))), c_List_Olexord(_1632929, _1632935))))], (50198 ^ _777959) ^ [_1795313, _1795315] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1795313), _1795315) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1795313), _1795315)))], (29775 ^ _777959) ^ [_1340384, _1340386, _1340388] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1340384, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1340384, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1340384), _1340386)), hAPP(c_Set_OPow(_1340384), _1340388))), hAPP(c_Set_OPow(_1340384), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1340384, tc_HOL_Obool)), _1340386), _1340388)))))], (19576 ^ _777959) ^ [_1152429, _1152431, _1152433] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152429), _1152431) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152429), _1152433), -(_1152429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1152431 = _1152433)], (4176 ^ _777959) ^ [_841170, _841172, _841174, _841176] : [-(c_List_Orotate(_841176, _841172) = c_List_Orotate(_841174, _841170)), _841176 = _841174, _841172 = _841170], (11409 ^ _777959) ^ [_981436, _981438, _981440] : [class_Lattices_Olattice(_981436), hBOOL(hAPP(c_Finite__Set_Ofinite(_981436), _981438)), 11416 ^ _777959 : [(11423 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981436, tc_HOL_Obool)), _981438), hAPP(hAPP(c_Set_Oinsert(_981436), _981440), c_Orderings_Obot__class_Obot(tc_fun(_981436, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_981436, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_981436, hAPP(hAPP(c_Set_Oinsert(_981436), _981440), _981438)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981436), _981440), c_Big__Operators_Olattice__class_OInf__fin(_981436, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981436, tc_HOL_Obool)), _981438), hAPP(hAPP(c_Set_Oinsert(_981436), _981440), c_Orderings_Obot__class_Obot(tc_fun(_981436, tc_HOL_Obool)))))))], (11417 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981436, tc_HOL_Obool)), _981438), hAPP(hAPP(c_Set_Oinsert(_981436), _981440), c_Orderings_Obot__class_Obot(tc_fun(_981436, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_981436, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_981436, hAPP(hAPP(c_Set_Oinsert(_981436), _981440), _981438)) = _981440)]]], (34369 ^ _777959) ^ [_1424930, _1424932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1424930)), c_Int_OBit1(_1424932))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1424930), _1424932)))], (51320 ^ _777959) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (15466 ^ _777959) ^ [_1071985, _1071987] : [15467 ^ _777959 : [(15470 ^ _777959) ^ [] : [_1071985 = hAPP(c_Nat_OSuc, _1071987)], (15468 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071985), _1071987))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071985), hAPP(c_Nat_OSuc, _1071987))))], (48272 ^ _777959) ^ [_1749532, _1749534] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1749532)), -(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(_1749532), _1749534))), _1749532)))], (43851 ^ _777959) ^ [_1649783, _1649785, _1649787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649783), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649785)), _1649787))), -(c_List_Olast(_1649785, hAPP(hAPP(c_List_Odrop(_1649785), _1649783), _1649787)) = c_List_Olast(_1649785, _1649787))], (36572 ^ _777959) ^ [_1471628] : [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), _1471628))), -(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), _1471628)) = 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), _1471628))))], (19586 ^ _777959) ^ [_1152541, _1152543, _1152545] : [19587 ^ _777959 : [(19590 ^ _777959) ^ [] : [_1152543 = _1152545], (19588 ^ _777959) ^ [] : [_1152541 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152541), _1152543) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152541), _1152545))], (22723 ^ _777959) ^ [_1211291] : [_1211291 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211291) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20822 ^ _777959) ^ [_1174358] : [20823 ^ _777959 : [(20824 ^ _777959) ^ [_1174400] : [_1174358 = hAPP(c_Nat_OSuc, _1174400)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174358)))], (48493 ^ _777959) ^ [_1753912, _1753914] : [-(c_Transitive__Closure_Otrancl(_1753912, _1753914) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1753912, _1753912), tc_HOL_Obool)), _1753914), hAPP(hAPP(c_Relation_Orel__comp(_1753912, _1753912, _1753912), c_Transitive__Closure_Otrancl(_1753912, _1753914)), _1753914)))], (40174 ^ _777959) ^ [_1556858, _1556860, _1556862, _1556864, _1556866] : [class_Orderings_Olinorder(_1556858), -(hAPP(c_List_Oset(_1556860), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1556860, _1556858, _1556862), _1556864), _1556866)) = hAPP(hAPP(c_Set_Oinsert(_1556860), _1556864), hAPP(c_List_Oset(_1556860), _1556866)))], (44987 ^ _777959) ^ [_1673042, _1673044, _1673046, _1673048] : [-(c_List_Otranspose(_1673042, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1673042)), hAPP(hAPP(c_List_Olist_OCons(_1673042), _1673044), _1673046)), _1673048)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1673042)), hAPP(hAPP(c_List_Olist_OCons(_1673042), _1673044), c_List_Oconcat(_1673042, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1673042), tc_List_Olist(_1673042)), c_List_Olist_Olist__case(tc_List_Olist(_1673042), _1673042, c_List_Olist_ONil(_1673042), hAPP(hAPP(c_COMBB(tc_List_Olist(_1673042), tc_fun(tc_List_Olist(_1673042), tc_List_Olist(_1673042)), _1673042), c_COMBK(tc_List_Olist(_1673042), tc_List_Olist(_1673042))), hAPP(hAPP(c_COMBC(_1673042, tc_List_Olist(_1673042), tc_List_Olist(_1673042)), c_List_Olist_OCons(_1673042)), c_List_Olist_ONil(_1673042))))), _1673048)))), c_List_Otranspose(_1673042, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1673042)), _1673046), c_List_Oconcat(tc_List_Olist(_1673042), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1673042), tc_List_Olist(tc_List_Olist(_1673042))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1673042)), _1673042, c_List_Olist_ONil(tc_List_Olist(_1673042)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1673042), tc_List_Olist(tc_List_Olist(_1673042))), _1673042), hAPP(hAPP(c_COMBC(tc_List_Olist(_1673042), tc_List_Olist(tc_List_Olist(_1673042)), tc_List_Olist(tc_List_Olist(_1673042))), c_List_Olist_OCons(tc_List_Olist(_1673042))), c_List_Olist_ONil(tc_List_Olist(_1673042)))))), _1673048))))))], (38558 ^ _777959) ^ [_1517637, _1517639, _1517641, _1517643] : [c_Fun_Oinj__on(_1517637, _1517639, _1517641, _1517643), -(c_Fun_Oinj__on(_1517639, _1517637, c_Fun_Othe__inv__into(_1517637, _1517639, _1517643, _1517641), hAPP(c_Set_Oimage(_1517637, _1517639, _1517641), _1517643)))], (21430 ^ _777959) ^ [_1185208, _1185210, _1185212, _1185214, _1185216] : [class_Rings_Olinordered__semiring__strict(_1185208), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185208), _1185210), _1185212)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185208), _1185214), _1185216)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185208), c_Groups_Ozero__class_Ozero(_1185208)), _1185212)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1185208), c_Groups_Ozero__class_Ozero(_1185208)), _1185214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1185208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185208), _1185210), _1185214)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1185208), _1185212), _1185216))))], (46469 ^ _777959) ^ [_1706163, _1706165, _1706167, _1706169, _1706171, _1706173] : [c_List_Olist__all2(_1706163, _1706165, _1706167, _1706169, _1706171), -(c_List_Olist__all2(_1706163, _1706165, _1706167, hAPP(hAPP(c_List_Otake(_1706163), _1706173), _1706169), hAPP(hAPP(c_List_Otake(_1706165), _1706173), _1706171)))], (27926 ^ _777959) ^ [_1305100, _1305102] : [class_Int_Oring__char__0(_1305100), 27929 ^ _777959 : [(27936 ^ _777959) ^ [] : [_1305102 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1305100) = hAPP(c_Int_Oring__1__class_Oof__int(_1305100), _1305102))], (27930 ^ _777959) ^ [] : [c_Groups_Ozero__class_Ozero(_1305100) = hAPP(c_Int_Oring__1__class_Oof__int(_1305100), _1305102), -(_1305102 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (14817 ^ _777959) ^ [_1056798, _1056800] : [-(hBOOL(hAPP(hAPP(c_member(_1056798), _1056800), c_Orderings_Otop__class_Otop(tc_fun(_1056798, tc_HOL_Obool)))))], (11372 ^ _777959) ^ [_980729, _980731, _980733, _980735, _980737] : [-(_980729 = c_Option_Ooption_ONone(_980731)), -(c_Map_Odom(_980733, _980731, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_980733, tc_Option_Ooption(_980731)), _980735), _980737), _980729)) = hAPP(hAPP(c_Set_Oinsert(_980733), _980737), c_Map_Odom(_980733, _980731, _980735)))], (17047 ^ _777959) ^ [_1103972, _1103974, _1103976, _1103978] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1103972), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103972), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1103972), _1103974), _1103976)), _1103978) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1103972), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103972), _1103974), _1103978)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103972), _1103976), _1103978)))], (15928 ^ _777959) ^ [_1081489, _1081491, _1081493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1081489), _1081491)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1081493), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1081491), _1081489))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1081493), _1081489)), hAPP(c_Nat_OSuc, _1081491)))], (41966 ^ _777959) ^ [_1604732] : [-(hBOOL(hAPP(c_List_Odistinct(_1604732), c_List_Olist_ONil(_1604732))))], (14227 ^ _777959) ^ [_1042766, _1042768, _1042770, _1042772, _1042774] : [class_Rings_Ocomm__semiring__1(_1042766), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042766), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042766), _1042768), _1042770)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042766), _1042772), _1042774)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042766), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042766), _1042768), _1042772)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042766), _1042770), _1042774)))], (22317 ^ _777959) ^ [_1202939, _1202941] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1202939), hAPP(c_Nat_OSuc, _1202941)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1202941), 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)), _1202941)), _1202939))], (25016 ^ _777959) ^ [_1251947, _1251949] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1251947), _1251949) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1251949 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25025 ^ _777959 : [(25028 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251947), _1251949)))], (25026 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251947)))]], 25029 ^ _777959 : [(25032 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1251949), _1251947)))], (25030 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1251947), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (17959 ^ _777959) ^ [_1121091, _1121093, _1121095] : [class_Orderings_Olinorder(_1121091), hBOOL(hAPP(c_Finite__Set_Ofinite(_1121091), _1121093)), hBOOL(hAPP(hAPP(c_member(_1121091), _1121095), _1121093)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1121091), _1121095), c_Big__Operators_Olattice_OSup__fin(_1121091, c_Orderings_Oord__class_Omax(_1121091), _1121093)) = _1121095)], (12512 ^ _777959) ^ [_1005515, _1005517, _1005519, _1005521] : [-(c_Map_Orestrict__map(_1005515, _1005517, _1005519, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1005515, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1005515), _1005521), c_Orderings_Obot__class_Obot(tc_fun(_1005515, tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1005515, tc_Option_Ooption(_1005517)), _1005519), _1005521), c_Option_Ooption_ONone(_1005517)))], (31506 ^ _777959) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8092 ^ _777959) ^ [_916628, _916630, _916632, _916634, _916636] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916628, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916628, tc_HOL_Obool)), hAPP(c_Set_Oimage(_916630, _916628, _916632), _916634)), hAPP(c_Set_Oimage(_916630, _916628, _916632), _916636))), hAPP(c_Set_Oimage(_916630, _916628, _916632), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916630, tc_HOL_Obool)), _916634), _916636)))))], (36918 ^ _777959) ^ [_1479015, _1479017, _1479019, _1479021, _1479023, _1479025, _1479027] : [-(hAPP(c_Product__Type_Oapfst(_1479015, _1479017, _1479019, _1479021), hAPP(c_Product__Type_Oapsnd(_1479023, _1479019, _1479015, _1479025), _1479027)) = hAPP(hAPP(c_Product__Type_OPair(_1479017, _1479019), hAPP(_1479021, hAPP(c_Product__Type_Ofst(_1479015, _1479023), _1479027))), hAPP(_1479025, hAPP(c_Product__Type_Osnd(_1479015, _1479023), _1479027))))], (31054 ^ _777959) ^ [_1364663, _1364665] : [class_Groups_Oordered__ab__group__add__abs(_1364663), 31057 ^ _777959 : [(31064 ^ _777959) ^ [] : [_1364665 = c_Groups_Ozero__class_Ozero(_1364663), -(hAPP(c_Groups_Oabs__class_Oabs(_1364663), _1364665) = c_Groups_Ozero__class_Ozero(_1364663))], (31058 ^ _777959) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1364663), _1364665) = c_Groups_Ozero__class_Ozero(_1364663), -(_1364665 = c_Groups_Ozero__class_Ozero(_1364663))]]], (50788 ^ _777959) ^ [_1807822, _1807824] : [class_Orderings_Opreorder(_1807822), -(class_Orderings_Opreorder(tc_fun(_1807824, _1807822)))], (30132 ^ _777959) ^ [_1347880, _1347882, _1347884] : [class_Divides_Osemiring__div(_1347880), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1347880), c_Divides_Odiv__class_Omod(_1347880, _1347882, _1347884)), _1347884) = c_Groups_Ozero__class_Ozero(_1347880))], (8484 ^ _777959) ^ [_924811, _924813, _924815] : [class_Orderings_Olinorder(_924811), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924811), _924813), _924815))), 8491 ^ _777959 : [(8498 ^ _777959) ^ [] : [_924815 = _924813, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924811), _924815), _924813))], (8492 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924811), _924815), _924813))), -(_924815 = _924813)]]], (5330 ^ _777959) ^ [_859525, _859527] : [_859527 = _859525, -(c_List_Oappend(_859527) = c_List_Oappend(_859525))], (39272 ^ _777959) ^ [_1535015, _1535017, _1535019, _1535021, _1535023, _1535025, _1535027] : [class_Groups_Oab__semigroup__mult(_1535015), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535017), _1535019)), c_Fun_Oinj__on(_1535017, _1535021, _1535023, _1535019), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1535015, _1535021, c_Groups_Otimes__class_Otimes(_1535015)), _1535025), _1535027), hAPP(c_Set_Oimage(_1535017, _1535021, _1535023), _1535019)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1535015, _1535017, c_Groups_Otimes__class_Otimes(_1535015)), hAPP(c_Fun_Ocomp(_1535021, _1535015, _1535017, _1535025), _1535023)), _1535027), _1535019))], (3802 ^ _777959) ^ [_835489, _835491, _835493, _835495, _835497, _835499] : [-(c_Predicate_ODomainP(_835499, _835495, _835491) = c_Predicate_ODomainP(_835497, _835493, _835489)), _835499 = _835497, _835495 = _835493, _835491 = _835489], (15004 ^ _777959) ^ [_1063300, _1063302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063300), _1063302)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1063300)), hAPP(c_Nat_OSuc, _1063302))))], (48711 ^ _777959) ^ [_1760196, _1760198] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1760196, _1760196), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1760196, _1760198)), c_Relation_OId(_1760196)) = c_Transitive__Closure_Ortrancl(_1760196, _1760198))], (46188 ^ _777959) ^ [_1700028, _1700030, _1700032, _1700034] : [hBOOL(hAPP(c_List_Olistsp(_1700028, _1700030), _1700032)), hBOOL(hAPP(c_List_Olistsp(_1700028, _1700034), _1700032)), -(hBOOL(hAPP(c_List_Olistsp(_1700028, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1700028, tc_HOL_Obool)), _1700030), _1700034)), _1700032)))], (42561 ^ _777959) ^ [_1620074, _1620076, _1620078, _1620080] : [-(c_Product__Type_Oapsnd(_1620074, _1620076, _1620078, _1620080) = c_Product__Type_Omap__pair(_1620078, _1620078, _1620074, _1620076, c_Fun_Oid(_1620078), _1620080))], (48887 ^ _777959) ^ [_1764741, _1764743] : [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), _1764741), _1764743)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1764741), _1764743)))], (37889 ^ _777959) ^ [_1503664, _1503666, _1503668] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1503664, _1503664)), _1503666), c_Relation_OId__on(_1503664, _1503668))), 37893 ^ _777959 : [(37896 ^ _777959) ^ [] : [-(_1503666 = hAPP(hAPP(c_Product__Type_OPair(_1503664, _1503664), 37892 ^ [_1503664, _1503666, _1503668]), 37892 ^ [_1503664, _1503666, _1503668]))], (37894 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1503664), 37892 ^ [_1503664, _1503666, _1503668]), _1503668)))]]], (43843 ^ _777959) ^ [_1649682, _1649684] : [-(_1649682 = c_List_Olist_ONil(_1649684)), -(hBOOL(hAPP(hAPP(c_member(_1649684), c_List_Olast(_1649684, _1649682)), hAPP(c_List_Oset(_1649684), _1649682))))], (43524 ^ _777959) ^ [_1642998, _1643000, _1643002] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642998)), hAPP(c_List_Orotate(_1642998, _1643000), _1643002)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642998)), _1643002))], (24466 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (47977 ^ _777959) ^ [_1743968, _1743970, _1743972] : [c_List_Olist__ex(_1743968, _1743970, _1743972), 47981 ^ _777959 : [(47984 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1743970, 47980 ^ [_1743968, _1743970, _1743972])))], (47982 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743968), 47980 ^ [_1743968, _1743970, _1743972]), hAPP(c_List_Oset(_1743968), _1743972))))]]], (38991 ^ _777959) ^ [_1528490, _1528492, _1528494, _1528496, _1528498, _1528500, _1528502, _1528504, _1528506, _1528508, _1528510] : [hAPP(_1528490, hAPP(_1528492, _1528494)) = hAPP(_1528496, hAPP(_1528498, _1528500)), -(hAPP(hAPP(c_Fun_Ocomp(_1528502, _1528504, _1528506, _1528490), _1528492), _1528494) = hAPP(hAPP(c_Fun_Ocomp(_1528508, _1528504, _1528510, _1528496), _1528498), _1528500))], (21994 ^ _777959) ^ [_1196187, _1196189, _1196191, _1196193] : [-(c_Hoare__Mirabelle_Otriple__valid(_1196187, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1196187), _1196189), hAPP(c_Com_Ocom_OBODY, _1196191)), _1196193)))], (7492 ^ _777959) ^ [_903753, _903755] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_903753, tc_HOL_Obool)), _903755)), -(hBOOL(hAPP(hAPP(c_member(_903753), _903755), c_Orderings_Obot__class_Obot(tc_fun(_903753, tc_HOL_Obool)))))], (29755 ^ _777959) ^ [_1339516, _1339518] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1339516, tc_HOL_Obool), tc_HOL_Obool)), _1339518), hAPP(c_Set_OPow(_1339516), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1339516, tc_HOL_Obool), _1339518)))))], (45370 ^ _777959) ^ [_1682159, _1682161] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1682159), _1682161) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1682159)), c_List_Oembed__list(_1682161))))], (25792 ^ _777959) ^ [_1267153, _1267155, _1267157, _1267159] : [class_Rings_Odivision__ring(_1267153), -(_1267155 = c_Groups_Ozero__class_Ozero(_1267153)), 25799 ^ _777959 : [(25806 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267153), _1267157), _1267155) = _1267159, -(_1267157 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267153), _1267159), _1267155))], (25800 ^ _777959) ^ [] : [_1267157 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267153), _1267159), _1267155), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1267153), _1267157), _1267155) = _1267159)]]], (46200 ^ _777959) ^ [_1700267, _1700269, _1700271] : [hBOOL(hAPP(c_List_Olistsp(_1700267, _1700269), _1700271)), 46203 ^ _777959 : [(46204 ^ _777959) ^ [_1700356] : [hBOOL(hAPP(hAPP(c_member(_1700267), _1700356), hAPP(c_List_Oset(_1700267), _1700271))), -(hBOOL(hAPP(_1700269, _1700356)))]]], (28490 ^ _777959) ^ [_1314892, _1314894, _1314896] : [class_Orderings_Oorder(_1314892), 28493 ^ _777959 : [(28500 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314892), _1314894), _1314896))), -(c_SetInterval_Oord__class_OatLeastAtMost(_1314892, _1314894, _1314896) = c_Orderings_Obot__class_Obot(tc_fun(_1314892, tc_HOL_Obool)))], (28494 ^ _777959) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_1314892, _1314894, _1314896) = c_Orderings_Obot__class_Obot(tc_fun(_1314892, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1314892), _1314894), _1314896))]]], (42417 ^ _777959) ^ [_1615593, _1615595, _1615597, _1615599] : [_1615593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1615595), _1615593), hAPP(hAPP(c_List_Olist_OCons(_1615595), _1615597), _1615599)) = c_List_Olist_ONil(_1615595))], (8668 ^ _777959) ^ [_927589, _927591, _927593, _927595] : [class_Orderings_Oorder(_927589), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927589), _927591), _927593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927589), _927595), _927591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927589), _927595), _927593)))], (13601 ^ _777959) ^ [_1027870, _1027872] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1027870, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1027870, tc_HOL_Obool))), _1027872) = c_Orderings_Otop__class_Otop(tc_fun(_1027870, tc_HOL_Obool)))], (39780 ^ _777959) ^ [_1546949, _1546951, _1546953] : [hBOOL(hAPP(c_List_Odistinct(_1546949), _1546951)), -(hBOOL(hAPP(c_List_Odistinct(_1546949), c_List_Oremove1(_1546949, _1546953, _1546951))))], (36139 ^ _777959) ^ [_1463254, _1463256] : [-(c_Divides_Odivmod__nat(_1463254, _1463256) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1463254), _1463256)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1463254, _1463256)))], (46383 ^ _777959) ^ [_1704491, _1704493, _1704495, _1704497, _1704499, _1704501, _1704503] : [c_List_Olist__all2(_1704491, _1704493, _1704495, _1704497, _1704499), c_List_Olist__all2(_1704491, _1704493, _1704495, _1704501, _1704503), -(c_List_Olist__all2(_1704491, _1704493, _1704495, hAPP(hAPP(c_List_Oappend(_1704491), _1704497), _1704501), hAPP(hAPP(c_List_Oappend(_1704493), _1704499), _1704503)))], (7498 ^ _777959) ^ [_903864, _903866] : [hBOOL(hAPP(hAPP(c_member(_903864), _903866), c_Orderings_Obot__class_Obot(tc_fun(_903864, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_903864, tc_HOL_Obool)), _903866)))], (14421 ^ _777959) ^ [_1048181, _1048183] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1048181, tc_HOL_Obool)), _1048183)), 14427 ^ _777959 : [(14430 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048181), 14426 ^ [_1048181, _1048183]))], (14428 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1048181, tc_HOL_Obool)), 14426 ^ [_1048181, _1048183]), _1048183)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048181), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1048181, tc_HOL_Obool), _1048183))))], (48002 ^ _777959) ^ [_1744425, _1744427, _1744429] : [c_List_Olist__ex(_1744425, _1744427, _1744429), -(c_List_Olist__ex(_1744425, _1744427, hAPP(c_List_Orev(_1744425), _1744429)))], (48869 ^ _777959) ^ [_1764091, _1764093, _1764095, _1764097] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1764091), tc_List_Olist(_1764091))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1764091), tc_List_Olist(_1764091)), _1764093), _1764095)), c_List_Olistrel1(_1764091, _1764097))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1764091), tc_List_Olist(_1764091))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1764091), tc_List_Olist(_1764091)), _1764093), _1764095)), c_List_Olistrel(_1764091, c_Transitive__Closure_Ortrancl(_1764091, _1764097)))))], (13079 ^ _777959) ^ [_1016292, _1016294, _1016296] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1016292, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016292, tc_HOL_Obool)), _1016294), _1016296)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1016292, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1016292, tc_HOL_Obool)), _1016294)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1016292, tc_HOL_Obool)), _1016296)))], (41201 ^ _777959) ^ [_1584288, _1584290] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1584288, tc_HOL_Obool), _1584290) = hAPP(c_Set_OCollect(_1584288), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1584288, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1584288), c_HOL_OAll(tc_fun(_1584288, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1584288, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1584288, tc_HOL_Obool), tc_HOL_Obool), _1584288), hAPP(c_COMBS(tc_fun(_1584288, 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(_1584288, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1584288, tc_HOL_Obool), tc_fun(tc_fun(_1584288, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1584288, tc_HOL_Obool))), _1584290)))), c_member(_1584288)))))], (16853 ^ _777959) ^ [_1100610, _1100612, _1100614, _1100616] : [class_Orderings_Olinorder(_1100610), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100610), _1100612), _1100614)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100610), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100610), _1100612), _1100616)), _1100614)))], (19069 ^ _777959) ^ [_1144505, _1144507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1144505)), _1144507)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1144505), _1144507)))], (5302 ^ _777959) ^ [_859121, _859123] : [_859123 = _859121, -(c_List_Odrop(_859123) = c_List_Odrop(_859121))], (5817 ^ _777959) ^ [_870163, _870165, _870167] : [-(hAPP(hAPP(c_Set_Oinsert(_870163), _870165), hAPP(hAPP(c_Set_Oinsert(_870163), _870165), _870167)) = hAPP(hAPP(c_Set_Oinsert(_870163), _870165), _870167))], (12660 ^ _777959) ^ [_1007736, _1007738] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1007736, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1007736, tc_HOL_Obool)), _1007738)) = _1007738)], (31048 ^ _777959) ^ [_1364504, _1364506, _1364508] : [class_Groups_Oordered__ab__group__add__abs(_1364504), -(hAPP(c_Groups_Oabs__class_Oabs(_1364504), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364504), hAPP(c_Groups_Oabs__class_Oabs(_1364504), _1364506)), hAPP(c_Groups_Oabs__class_Oabs(_1364504), _1364508))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1364504), hAPP(c_Groups_Oabs__class_Oabs(_1364504), _1364506)), hAPP(c_Groups_Oabs__class_Oabs(_1364504), _1364508)))], (11014 ^ _777959) ^ [_973773, _973775, _973777, _973779] : [-(hAPP(c_Map_Orestrict__map(_973773, _973775, hAPP(c_COMBK(tc_Option_Ooption(_973775), _973773), c_Option_Ooption_ONone(_973775)), _973777), _973779) = c_Option_Ooption_ONone(_973775))], (9052 ^ _777959) ^ [_933435, _933437, _933439] : [class_Orderings_Oorder(_933435), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933435), _933437), _933439)), -(_933437 = _933439), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933435), _933437), _933439)))], (13699 ^ _777959) ^ [_1030965] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1030965, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1030965), hAPP(c_COMBK(tc_HOL_Obool, _1030965), c_fFalse)))], (33997 ^ _777959) ^ [_1418322, _1418324, _1418326] : [class_Int_Onumber__ring(_1418322), 34000 ^ _777959 : [(34007 ^ _777959) ^ [] : [c_Int_Oiszero(_1418322, hAPP(c_Int_Onumber__class_Onumber__of(_1418322), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1418324), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1418326)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1418322), _1418324) = hAPP(c_Int_Onumber__class_Onumber__of(_1418322), _1418326))], (34001 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1418322), _1418324) = hAPP(c_Int_Onumber__class_Onumber__of(_1418322), _1418326), -(c_Int_Oiszero(_1418322, hAPP(c_Int_Onumber__class_Onumber__of(_1418322), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1418324), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1418326)))))]]], (46219 ^ _777959) ^ [_1700676, _1700678, _1700680, _1700682] : [hBOOL(hAPP(c_List_Olistsp(_1700676, _1700678), hAPP(hAPP(c_List_Oappend(_1700676), _1700680), _1700682))), 46222 ^ _777959 : [(46225 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1700676, _1700678), _1700682)))], (46223 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1700676, _1700678), _1700680)))]]], (6121 ^ _777959) ^ [_876033, _876035, _876037] : [class_Orderings_Oorder(_876033), 6124 ^ _777959 : [(6133 ^ _777959) ^ [] : [-(_876035 = _876037), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876033), _876035), _876037)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876033), _876037), _876035))], (6125 ^ _777959) ^ [] : [_876035 = _876037, 6128 ^ _777959 : [(6131 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876033), _876037), _876035)))], (6129 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876033), _876035), _876037)))]]]]], (8790 ^ _777959) ^ [_929605, _929607, _929609, _929611, _929613] : [c_Finite__Set_Ofun__left__comm__idem(_929605, _929607, _929609), -(c_Finite__Set_Ofun__left__comm__idem(_929611, _929607, hAPP(hAPP(c_COMBB(_929605, tc_fun(_929607, _929607), _929611), _929609), _929613)))], (46341 ^ _777959) ^ [_1703379, _1703381, _1703383, _1703385, _1703387, _1703389, _1703391] : [c_List_Olist__all2(_1703379, _1703381, _1703383, hAPP(hAPP(c_List_Olist_OCons(_1703379), _1703385), _1703387), hAPP(hAPP(c_List_Olist_OCons(_1703381), _1703389), _1703391)), 46344 ^ _777959 : [(46347 ^ _777959) ^ [] : [-(c_List_Olist__all2(_1703379, _1703381, _1703383, _1703387, _1703391))], (46345 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1703383, _1703385), _1703389)))]]], (22008 ^ _777959) ^ [_1196440, _1196442] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1196440)), -(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)), _1196440))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1196442))))) = 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)), _1196440))), 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, _1196442))))))], (24850 ^ _777959) ^ [_1249163, _1249165, _1249167, _1249169] : [class_Orderings_Oorder(_1249163), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1249163, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1249163, _1249165), _1249167)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1249163, _1249167), _1249169)) = c_Orderings_Obot__class_Obot(tc_fun(_1249163, tc_HOL_Obool)))], (6012 ^ _777959) ^ [_873973, _873975, _873977, _873979, _873981, _873983] : [_873973 = hAPP(_873975, _873977), hBOOL(hAPP(hAPP(c_member(_873979), _873977), _873981)), -(hBOOL(hAPP(hAPP(c_member(_873983), _873973), hAPP(c_Set_Oimage(_873979, _873983, _873975), _873981))))], (40361 ^ _777959) ^ [_1561293, _1561295, _1561297] : [-(hAPP(hAPP(c_List_Olist__update(_1561293, _1561295), _1561297), hAPP(hAPP(c_List_Onth(_1561293), _1561295), _1561297)) = _1561295)], (43873 ^ _777959) ^ [_1650182, _1650184, _1650186, _1650188] : [-(hAPP(hAPP(c_List_Oappend(_1650182), _1650184), hAPP(hAPP(c_List_Olist_OCons(_1650182), _1650186), c_List_Olist_ONil(_1650182))) = _1650188), -(_1650188 = c_List_Olist_ONil(_1650182)), c_List_Obutlast(_1650182, _1650188) = _1650184, c_List_Olast(_1650182, _1650188) = _1650186], (25168 ^ _777959) ^ [_1254875, _1254877, _1254879] : [class_Groups_Ocomm__monoid__add(_1254875), hAPP(_1254877, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1254875), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1254875), _1254877), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1254879)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1254875), _1254877), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1254879)))], (44947 ^ _777959) ^ [_1672145, _1672147, _1672149] : [-(hAPP(c_List_Ofilter(_1672145, _1672147), c_List_Oconcat(_1672145, _1672149)) = c_List_Oconcat(_1672145, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1672145), tc_List_Olist(_1672145)), c_List_Ofilter(_1672145, _1672147)), _1672149)))], (31973 ^ _777959) ^ [_1381611, _1381613, _1381615, _1381617, _1381619, _1381621] : [c_Com_Ocom_OLocal(_1381611, _1381613, _1381615) = c_Com_Ocom_OCall(_1381617, _1381619, _1381621)], (5669 ^ _777959) ^ [_867381, _867383, _867385, _867387] : [c_Hoare__Mirabelle_Ohoare__derivs(_867381, _867383, _867385), c_Hoare__Mirabelle_Ohoare__derivs(_867381, _867387, _867383), -(c_Hoare__Mirabelle_Ohoare__derivs(_867381, _867387, _867385))], (2814 ^ _777959) ^ [_819979, _819981, _819983, _819985] : [-(c_Hilbert__Choice_OEps(_819985, _819981) = c_Hilbert__Choice_OEps(_819983, _819979)), _819985 = _819983, _819981 = _819979], (14839 ^ _777959) ^ [_1057458, _1057460, _1057462] : [class_Lattices_Odistrib__lattice(_1057458), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057458), _1057460)), -(_1057460 = c_Orderings_Obot__class_Obot(tc_fun(_1057458, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1057458), _1057462)), -(_1057462 = c_Orderings_Obot__class_Obot(tc_fun(_1057458, tc_HOL_Obool))), 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tc_fun(_1057458, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1057458, tc_fun(_1057458, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1057458, tc_fun(tc_fun(_1057458, tc_HOL_Obool), tc_fun(_1057458, tc_HOL_Obool))), _1057458), hAPP(c_COMBB(tc_fun(_1057458, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1057458, tc_HOL_Obool), tc_fun(_1057458, tc_HOL_Obool)), _1057458), c_COMBS(_1057458, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1057458, tc_fun(_1057458, tc_HOL_Obool)), tc_fun(_1057458, tc_fun(_1057458, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1057458), hAPP(c_COMBB(tc_fun(_1057458, tc_HOL_Obool), tc_fun(_1057458, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1057458), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1057458), c_fconj))), hAPP(hAPP(c_COMBC(_1057458, tc_fun(_1057458, tc_fun(_1057458, _1057458)), tc_fun(_1057458, tc_fun(_1057458, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1057458, _1057458), tc_fun(_1057458, tc_HOL_Obool)), tc_fun(tc_fun(_1057458, tc_fun(_1057458, _1057458)), tc_fun(_1057458, tc_fun(_1057458, tc_HOL_Obool))), _1057458), c_COMBB(tc_fun(_1057458, _1057458), tc_fun(_1057458, tc_HOL_Obool), _1057458)), hAPP(hAPP(c_COMBB(tc_fun(_1057458, tc_HOL_Obool), tc_fun(tc_fun(_1057458, _1057458), tc_fun(_1057458, tc_HOL_Obool)), _1057458), c_COMBB(_1057458, tc_HOL_Obool, _1057458)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1057458)))))), hAPP(hAPP(c_COMBC(_1057458, tc_fun(_1057458, tc_HOL_Obool), tc_fun(_1057458, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1057458, tc_HOL_Obool), tc_fun(_1057458, tc_HOL_Obool)), _1057458), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1057458)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1057458), c_fconj), hAPP(hAPP(c_COMBC(_1057458, tc_fun(_1057458, tc_HOL_Obool), tc_HOL_Obool), c_member(_1057458)), _1057460)))), hAPP(hAPP(c_COMBC(_1057458, tc_fun(_1057458, tc_HOL_Obool), tc_HOL_Obool), c_member(_1057458)), _1057462))))))))], (15034 ^ _777959) ^ [_1063877, _1063879, _1063881] : [class_Lattices_Oab__semigroup__idem__mult(_1063877), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063877), _1063879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063877), _1063879), _1063881)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063877), _1063879), _1063881))], (14131 ^ _777959) ^ [_1040815, _1040817, _1040819] : [-(c_Map_Odom(_1040815, _1040817, hAPP(hAPP(c_COMBB(_1040817, tc_Option_Ooption(_1040817), _1040815), c_Option_Ooption_OSome(_1040817)), _1040819)) = c_Orderings_Otop__class_Otop(tc_fun(_1040815, tc_HOL_Obool)))], (10186 ^ _777959) ^ [_956490, _956492, _956494, _956496] : [class_Lattices_Olattice(_956490), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956490), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_956490), _956492), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956490), _956494), _956496))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956490), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_956490), _956492), _956494)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_956490), _956492), _956496)))))], (6157 ^ _777959) ^ [_876668, _876670, _876672, _876674] : [6158 ^ _777959 : [(6161 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_876668), _876670), _876674))], (6159 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_876668), _876670), _876672))]], -(hBOOL(hAPP(hAPP(c_member(_876668), _876670), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876668, tc_HOL_Obool)), _876672), _876674))))], (24179 ^ _777959) ^ [_1237584, _1237586, _1237588, _1237590, _1237592, _1237594] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237584), _1237586)), _1237588) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1237590), _1237592)), _1237594), 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), _1237590), _1237592)), _1237594))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1237594), _1237590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237588)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1237590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237590), _1237584)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1237586), _1237592)))], (43570 ^ _777959) ^ [_1643952, _1643954, _1643956] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1643952, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643954)), _1643956)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1643954, _1643952), _1643956) = _1643956)], (26544 ^ _777959) ^ [_1280729, _1280731, _1280733] : [class_Fields_Olinordered__field(_1280729), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280729), _1280731), c_Groups_Ozero__class_Ozero(_1280729))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1280729), c_Groups_Ozero__class_Ozero(_1280729)), _1280733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280729), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1280729), _1280731), _1280733)), c_Groups_Ozero__class_Ozero(_1280729))))], (48232 ^ _777959) ^ [] : [-(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))], (51100 ^ _777959) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (34715 ^ _777959) ^ [_1431014, _1431016, _1431018] : [class_Rings_Olinordered__idom(_1431014), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1431014), c_Groups_Ozero__class_Ozero(_1431014)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1431014), hAPP(hAPP(c_Power_Opower__class_Opower(_1431014), _1431016), 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(_1431014), _1431018), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (15276 ^ _777959) ^ [_1068883, _1068885] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068883), _1068885))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068883), hAPP(c_Nat_OSuc, _1068885))), -(_1068885 = _1068883)], (21107 ^ _777959) ^ [_1178971, _1178973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1178971), _1178973)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1178971), _1178973) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38930 ^ _777959) ^ [_1526450, _1526452, _1526454] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1526450, hAPP(hAPP(c_COMBC(_1526450, tc_fun(tc_prod(_1526450, _1526450), tc_HOL_Obool), tc_fun(_1526450, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526450, tc_fun(tc_fun(tc_prod(_1526450, _1526450), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526450, _1526450), tc_HOL_Obool), tc_fun(_1526450, tc_HOL_Obool)), _1526450), c_COMBC(_1526450, tc_fun(tc_prod(_1526450, _1526450), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526450, tc_prod(_1526450, _1526450)), tc_fun(_1526450, tc_fun(tc_fun(tc_prod(_1526450, _1526450), tc_HOL_Obool), tc_HOL_Obool)), _1526450), hAPP(c_COMBB(tc_prod(_1526450, _1526450), tc_fun(tc_fun(tc_prod(_1526450, _1526450), tc_HOL_Obool), tc_HOL_Obool), _1526450), c_member(tc_prod(_1526450, _1526450)))), c_Product__Type_OPair(_1526450, _1526450)))), _1526452)), _1526454)), -(hBOOL(hAPP(hAPP(c_member(_1526450), _1526454), c_Wellfounded_Oacc(_1526450, _1526452))))], (13887 ^ _777959) ^ [_1034927, _1034929, _1034931, _1034933] : [-(hBOOL(hAPP(hAPP(c_member(_1034927), hAPP(_1034929, _1034931)), hAPP(c_Set_Oimage(_1034933, _1034927, _1034929), c_Orderings_Otop__class_Otop(tc_fun(_1034933, tc_HOL_Obool))))))], (24075 ^ _777959) ^ [_1235674, _1235676, _1235678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235674)), _1235674 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1235676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1235674), _1235678)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1235676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1235678), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (27107 ^ _777959) ^ [_1291350, _1291352, _1291354] : [class_Orderings_Olinorder(_1291350), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1291350), _1291352), _1291354)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1291350, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1291350, _1291352, _1291354)), hAPP(hAPP(c_Set_Oinsert(_1291350), _1291354), c_Orderings_Obot__class_Obot(tc_fun(_1291350, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1291350, _1291352, _1291354))], (5380 ^ _777959) ^ [_860248, _860250, _860252, _860254] : [-(c_Product__Type_OPair(_860254, _860250) = c_Product__Type_OPair(_860252, _860248)), _860254 = _860252, _860250 = _860248], (22275 ^ _777959) ^ [_1201958, _1201960, _1201962, _1201964, _1201966] : [class_Groups_Oordered__comm__monoid__add(_1201958), hBOOL(hAPP(c_Finite__Set_Ofinite(_1201960), _1201962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1201960, tc_HOL_Obool)), _1201964), _1201962)), 22289 ^ _777959 : [(22292 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1201958), c_Groups_Ozero__class_Ozero(_1201958)), hAPP(_1201966, 22288 ^ [_1201958, _1201960, _1201962, _1201964, _1201966])))], (22290 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1201960), 22288 ^ [_1201958, _1201960, _1201962, _1201964, _1201966]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201960, tc_HOL_Obool)), _1201962), _1201964))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1201958), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1201960, _1201958), _1201966), _1201964)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1201960, _1201958), _1201966), _1201962))))], (30056 ^ _777959) ^ [_1346396, _1346398] : [c_Nat__Transfer_Ois__nat(_1346396), c_Nat__Transfer_Ois__nat(_1346398), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1346396, _1346398)))], (3310 ^ _777959) ^ [_827843, _827845, _827847, _827849, _827851, _827853] : [-(c_List_Oremove1(_827853, _827849, _827845) = c_List_Oremove1(_827851, _827847, _827843)), _827853 = _827851, _827849 = _827847, _827845 = _827843], (49036 ^ _777959) ^ [_1768595, _1768597, _1768599, _1768601] : [-(hAPP(c_Relation_Oconverse(_1768595, _1768597), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1768595, _1768597), tc_HOL_Obool)), _1768599), _1768601)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1768597, _1768595), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1768595, _1768597), _1768599)), hAPP(c_Relation_Oconverse(_1768595, _1768597), _1768601)))], (38975 ^ _777959) ^ [_1528092, _1528094, _1528096, _1528098, _1528100] : [c_Finite__Set_Ofun__left__comm(_1528092, _1528094, _1528096), -(hAPP(c_Fun_Ocomp(_1528094, _1528094, _1528094, hAPP(_1528096, _1528098)), hAPP(_1528096, _1528100)) = hAPP(c_Fun_Ocomp(_1528094, _1528094, _1528094, hAPP(_1528096, _1528100)), hAPP(_1528096, _1528098)))], (2710 ^ _777959) ^ [_818331, _818333, _818335, _818337, _818339, _818341] : [-(c_Com_Ocom_OCond(_818341, _818337, _818333) = c_Com_Ocom_OCond(_818339, _818335, _818331)), _818341 = _818339, _818337 = _818335, _818333 = _818331], (23064 ^ _777959) ^ [_1217740] : [-(c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY, _1217740)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47251 ^ _777959) ^ [_1725922, _1725924, _1725926, _1725928] : [47252 ^ _777959 : [(47253 ^ _777959) ^ [_1725997] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1725926, _1725922)), hAPP(hAPP(c_Product__Type_OPair(_1725926, _1725922), _1725997), _1725924)), _1725928))]], -(hBOOL(hAPP(hAPP(c_member(_1725922), _1725924), hAPP(c_Relation_ORange(_1725926, _1725922), _1725928))))], (47959 ^ _777959) ^ [_1743691, _1743693, _1743695, _1743697] : [c_List_Olist__ex(_1743691, _1743693, hAPP(hAPP(c_List_Olist_OCons(_1743691), _1743695), _1743697)), -(hBOOL(hAPP(_1743693, _1743695))), -(c_List_Olist__ex(_1743691, _1743693, _1743697))], (30191 ^ _777959) ^ [_1348847] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1348847), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29996 ^ _777959) ^ [_1345076, _1345078, _1345080, _1345082] : [class_Divides_Osemiring__div(_1345076), -(c_Divides_Odiv__class_Omod(_1345076, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345076), _1345078), _1345080), _1345082) = c_Divides_Odiv__class_Omod(_1345076, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345076), _1345078), c_Divides_Odiv__class_Omod(_1345076, _1345080, _1345082)), _1345082))], (13995 ^ _777959) ^ [_1037579, _1037581, _1037583] : [hBOOL(hAPP(_1037579, _1037581)), -(hAPP(c_Set_OCollect(_1037583), hAPP(hAPP(c_COMBS(_1037583, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1037583), c_fconj), hAPP(c_fequal, _1037581))), _1037579)) = hAPP(hAPP(c_Set_Oinsert(_1037583), _1037581), c_Orderings_Obot__class_Obot(tc_fun(_1037583, tc_HOL_Obool))))], (13951 ^ _777959) ^ [_1036572] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1036572, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1036572, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1036572, tc_HOL_Obool)))], (702 ^ _777959) ^ [_788714, _788716, _788718, _788720, _788722, _788724] : [-(c_List_Olist__ex(_788722, _788718, _788714)), c_List_Olist__ex(_788724, _788720, _788716), _788724 = _788722, _788720 = _788718, _788716 = _788714], (39376 ^ _777959) ^ [_1537449, _1537451, _1537453, _1537455, _1537457, _1537459, _1537461] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1537449, _1537451, _1537453), hAPP(c_Fun_Ocomp(_1537455, tc_fun(_1537451, _1537453), _1537449, _1537457), _1537459)), _1537461) = hAPP(hAPP(_1537457, hAPP(_1537459, hAPP(c_Product__Type_Ofst(_1537449, _1537451), _1537461))), hAPP(c_Product__Type_Osnd(_1537449, _1537451), _1537461)))], (37730 ^ _777959) ^ [_1499720, _1499722, _1499724, _1499726, _1499728] : [c_Equiv__Relations_Oequivp(_1499720, _1499722), hBOOL(hAPP(hAPP(_1499722, _1499724), _1499726)), hBOOL(hAPP(hAPP(_1499722, _1499726), _1499728)), -(hBOOL(hAPP(hAPP(_1499722, _1499724), _1499728)))], (19751 ^ _777959) ^ [_1155275, _1155277, _1155279, _1155281] : [class_Groups_Oordered__comm__monoid__add(_1155275), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155275), c_Groups_Ozero__class_Ozero(_1155275)), _1155277)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155275), _1155279), _1155281)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155275), _1155279), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155275), _1155281), _1155277))))], (50916 ^ _777959) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (11366 ^ _777959) ^ [_980556, _980558, _980560, _980562, _980564] : [_980556 = c_Option_Ooption_ONone(_980558), -(c_Map_Odom(_980560, _980558, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_980560, tc_Option_Ooption(_980558)), _980562), _980564), _980556)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980560, tc_HOL_Obool)), c_Map_Odom(_980560, _980558, _980562)), hAPP(hAPP(c_Set_Oinsert(_980560), _980564), c_Orderings_Obot__class_Obot(tc_fun(_980560, tc_HOL_Obool)))))], (25928 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19210 ^ _777959) ^ [_1146945, _1146947] : [class_Groups_Omonoid__add(_1146945), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146945), _1146947), c_Groups_Ozero__class_Ozero(_1146945)) = _1146947)], (8538 ^ _777959) ^ [_925511, _925513, _925515] : [class_Orderings_Opreorder(_925511), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925511), _925513), _925515)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_925511), _925515), _925513))], (6079 ^ _777959) ^ [_875274, _875276, _875278] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875274, tc_HOL_Obool)), _875276), _875278) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875274, tc_HOL_Obool)), _875278), _875276))], (37014 ^ _777959) ^ [_1482051] : [-(_1482051 = 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)), _1482051), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (44100 ^ _777959) ^ [_1655392, _1655394, _1655396, _1655398, _1655400] : [-(hAPP(hAPP(c_List_Omap(_1655392, _1655394), _1655396), hAPP(c_List_Ofilter(_1655392, _1655398), _1655400)) = c_List_Omap__filter(_1655392, _1655394, hAPP(hAPP(c_COMBC(_1655392, tc_Option_Ooption(_1655394), tc_Option_Ooption(_1655394)), hAPP(hAPP(c_COMBS(_1655392, tc_Option_Ooption(_1655394), tc_fun(tc_Option_Ooption(_1655394), tc_Option_Ooption(_1655394))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1655394), tc_fun(tc_Option_Ooption(_1655394), tc_Option_Ooption(_1655394))), _1655392), c_If(tc_Option_Ooption(_1655394))), _1655398)), hAPP(hAPP(c_COMBB(_1655394, tc_Option_Ooption(_1655394), _1655392), c_Option_Ooption_OSome(_1655394)), _1655396))), c_Option_Ooption_ONone(_1655394)), _1655400))], (40282 ^ _777959) ^ [_1559563, _1559565, _1559567, _1559569] : [-(hBOOL(hAPP(hAPP(c_member(_1559563), _1559565), hAPP(c_List_Oset(_1559563), _1559567)))), hBOOL(hAPP(hAPP(c_member(_1559563), _1559565), hAPP(c_List_Oset(_1559563), c_List_Osublist(_1559563, _1559567, _1559569))))], (3844 ^ _777959) ^ [_836152, _836154] : [_836154 = _836152, -(c_List_Odistinct(_836154) = c_List_Odistinct(_836152))], (44190 ^ _777959) ^ [_1657184, _1657186] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657184), _1657186))), -(c_List_Oupt(_1657184, _1657186) = c_List_Olist_ONil(tc_Nat_Onat))], (34225 ^ _777959) ^ [_1422359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1422359)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422359), c_Int_OPls)))], (38969 ^ _777959) ^ [_1527894, _1527896, _1527898, _1527900, _1527902, _1527904] : [-(hAPP(hAPP(c_List_Omap(_1527894, _1527896), _1527898), hAPP(hAPP(c_List_Omap(_1527900, _1527894), _1527902), _1527904)) = hAPP(hAPP(c_List_Omap(_1527900, _1527896), hAPP(c_Fun_Ocomp(_1527894, _1527896, _1527900, _1527898), _1527902)), _1527904))], (48683 ^ _777959) ^ [_1759445, _1759447, _1759449] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1759445, _1759445), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1759445, _1759445), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1759445, _1759447)), c_Transitive__Closure_Ortrancl(_1759445, _1759449))), c_Transitive__Closure_Ortrancl(_1759445, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1759445, _1759445), tc_HOL_Obool)), _1759447), _1759449)))))], (13287 ^ _777959) ^ [_1020859, _1020861, _1020863, _1020865, _1020867, _1020869] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1020859, tc_fun(_1020861, tc_HOL_Obool)), _1020863), _1020865), _1020867)), -(hBOOL(hAPP(hAPP(_1020865, _1020869), _1020867))), hBOOL(hAPP(hAPP(c_member(_1020859), _1020869), _1020863))], (30323 ^ _777959) ^ [_1351378, _1351380, _1351382, _1351384] : [_1351378 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1351380), _1351382)), _1351384), -(_1351380 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1351378, _1351380) = _1351384), 30330 ^ _777959 : [(30333 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1351384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1351384), _1351380))], (30331 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1351380)))]], 30338 ^ _777959 : [(30341 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1351380), _1351384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1351384), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (30339 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1351380))]]], (5520 ^ _777959) ^ [_862298, _862300, _862302, _862304] : [-(c_COMBK(_862304, _862300) = c_COMBK(_862302, _862298)), _862304 = _862302, _862300 = _862298], (11557 ^ _777959) ^ [_984538, _984540, _984542, _984544, _984546] : [-(_984538 = c_Orderings_Obot__class_Obot(tc_fun(_984540, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_984540, tc_fun(_984542, tc_HOL_Obool)), _984538), hAPP(hAPP(c_COMBB(tc_fun(_984542, tc_HOL_Obool), tc_fun(_984542, tc_HOL_Obool), _984540), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984542, tc_HOL_Obool)), _984544)), _984546)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984542, tc_HOL_Obool)), _984544), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_984540, tc_fun(_984542, tc_HOL_Obool)), _984538), _984546)))], (20335 ^ _777959) ^ [_1165867, _1165869, _1165871] : [class_Rings_Olinordered__semiring__strict(_1165867), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165867), c_Groups_Ozero__class_Ozero(_1165867)), _1165869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165867), _1165871), c_Groups_Ozero__class_Ozero(_1165867))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165867), _1165869), _1165871)), c_Groups_Ozero__class_Ozero(_1165867))))], (41165 ^ _777959) ^ [_1583493, _1583495, _1583497] : [-(c_Hoare__Mirabelle_Ohoare__valids(_1583493, _1583495, _1583497)), 41167 ^ _777959 : [(41168 ^ _777959) ^ [_1583639] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1583493)), _1583639), _1583495)), -(c_Hoare__Mirabelle_Otriple__valid(_1583493, 41166 ^ [_1583493, _1583495, _1583497], _1583639))], (41177 ^ _777959) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1583493, 41166 ^ [_1583493, _1583495, _1583497], 41173 ^ [_1583493, _1583495, _1583497])], (41175 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1583493)), 41173 ^ [_1583493, _1583495, _1583497]), _1583497)))]]], (13409 ^ _777959) ^ [_1023849, _1023851, _1023853, _1023855] : [-(_1023849 = c_Orderings_Obot__class_Obot(tc_fun(_1023851, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023851, tc_fun(_1023853, tc_HOL_Obool)), _1023849), hAPP(c_COMBK(tc_fun(_1023853, tc_HOL_Obool), _1023851), _1023855)) = _1023855)], (28478 ^ _777959) ^ [_1314725, _1314727] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1314725), hAPP(c_Nat_OSuc, _1314727)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1314725, _1314727))], (4094 ^ _777959) ^ [_839949, _839951, _839953, _839955] : [-(c_Relation_Oinv__image(_839955, _839951) = c_Relation_Oinv__image(_839953, _839949)), _839955 = _839953, _839951 = _839949], (43697 ^ _777959) ^ [_1646641, _1646643] : [class_Complete__Lattice_Ocomplete__lattice(_1646641), -(c_Complete__Lattice_OInf__class_OInf(_1646641, hAPP(c_List_Oset(_1646641), _1646643)) = hAPP(c_List_Ofoldl(_1646641, _1646641, c_Lattices_Osemilattice__inf__class_Oinf(_1646641), c_Orderings_Otop__class_Otop(_1646641)), _1646643))], (30637 ^ _777959) ^ [_1357027, _1357029, _1357031] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1357027), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1357029, _1357031)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1357027), _1357029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1357027), _1357031)))], (43976 ^ _777959) ^ [_1652349, _1652351, _1652353, _1652355] : [-(hBOOL(hAPP(_1652349, _1652351))), -(c_List_Oremove1(_1652353, _1652351, hAPP(c_List_Ofilter(_1652353, _1652349), _1652355)) = hAPP(c_List_Ofilter(_1652353, _1652349), _1652355))], (35287 ^ _777959) ^ [_1441342, _1441344] : [_1441342 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1441342, _1441344) = _1441344)], (32171 ^ _777959) ^ [_1385697, _1385699] : [class_Int_Onumber__ring(_1385697), -(hBOOL(hAPP(hAPP(c_member(_1385697), hAPP(c_Int_Onumber__class_Onumber__of(_1385697), _1385699)), c_Int_Oring__1__class_OInts(_1385697))))], (50514 ^ _777959) ^ [_1802925, _1802927, _1802929, _1802931, _1802933] : [-(c_List_Oreplicate(_1802925, _1802927, _1802929) = c_List_Oreplicate(_1802925, _1802931, _1802933)), _1802927 = _1802931, 50519 ^ _777959 : [(50522 ^ _777959) ^ [] : [_1802929 = _1802933], (50520 ^ _777959) ^ [] : [_1802927 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (20637 ^ _777959) ^ [_1171326, _1171328] : [class_Groups_Oordered__ab__group__add(_1171326), 20640 ^ _777959 : [(20647 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171326), c_Groups_Ozero__class_Ozero(_1171326)), _1171328)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171326), hAPP(c_Groups_Ouminus__class_Ouminus(_1171326), _1171328)), c_Groups_Ozero__class_Ozero(_1171326))))], (20641 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171326), hAPP(c_Groups_Ouminus__class_Ouminus(_1171326), _1171328)), c_Groups_Ozero__class_Ozero(_1171326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171326), c_Groups_Ozero__class_Ozero(_1171326)), _1171328)))]]], (51086 ^ _777959) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (50116 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (49700 ^ _777959) ^ [_1785914, _1785916, _1785918] : [-(c_Nitpick_Oof__frac(_1785916, _1785914, _1785918) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1785914), hAPP(c_Int_Oring__1__class_Oof__int(_1785914), hAPP(c_Nitpick_Onum(_1785916), _1785918))), hAPP(c_Int_Oring__1__class_Oof__int(_1785914), hAPP(c_Nitpick_Odenom(_1785916), _1785918)))), class_Rings_Oinverse(_1785914), class_Rings_Oring__1(_1785914)], (46750 ^ _777959) ^ [_1713079, _1713081, _1713083, _1713085, _1713087, _1713089, _1713091, _1713093] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1713079, _1713081)), hAPP(hAPP(c_Product__Type_OPair(_1713079, _1713081), _1713083), _1713085)), _1713087)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1713081, _1713089)), hAPP(hAPP(c_Product__Type_OPair(_1713081, _1713089), _1713085), _1713091)), _1713093)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1713079, _1713089)), hAPP(hAPP(c_Product__Type_OPair(_1713079, _1713089), _1713083), _1713091)), hAPP(hAPP(c_Relation_Orel__comp(_1713079, _1713081, _1713089), _1713087), _1713093))))], (4938 ^ _777959) ^ [_853345, _853347, _853349, _853351, _853353, _853355] : [-(c_New__DSequence_Opos__union(_853355, _853351, _853347) = c_New__DSequence_Opos__union(_853353, _853349, _853345)), _853355 = _853353, _853351 = _853349, _853347 = _853345], (3344 ^ _777959) ^ [_828370, _828372] : [_828372 = _828370, -(c_List_Oreturn__list(_828372) = c_List_Oreturn__list(_828370))], (16741 ^ _777959) ^ [_1098661, _1098663, _1098665] : [class_Orderings_Olinorder(_1098661), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098661), _1098663), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1098661), _1098663), _1098665))))], (17321 ^ _777959) ^ [_1109188, _1109190, _1109192] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1109188, tc_HOL_Obool)), _1109190), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1109188, tc_HOL_Obool), _1109192)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1109188, tc_HOL_Obool), tc_fun(_1109188, tc_HOL_Obool)), _1109192), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1109188, tc_HOL_Obool)), _1109190)))], (35061 ^ _777959) ^ [_1437808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1437808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1437808)))], (42565 ^ _777959) ^ [_1620160, _1620162] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1620160, _1620162, tc_prod(_1620160, _1620162)), c_Product__Type_OPair(_1620160, _1620162)) = c_Fun_Oid(tc_prod(_1620160, _1620162)))], (29186 ^ _777959) ^ [_1328138, _1328140] : [class_Orderings_Olinorder(_1328138), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328138, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1328138), _1328140), c_Orderings_Obot__class_Obot(tc_fun(_1328138, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1328138), _1328140)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1328138), _1328140))], (41761 ^ _777959) ^ [_1599406, _1599408, _1599410, _1599412, _1599414, _1599416, _1599418, _1599420] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599406, _1599408)), _1599410), hAPP(c_Set_Oimage(tc_prod(_1599412, _1599414), tc_prod(_1599406, _1599408), c_Product__Type_Omap__pair(_1599412, _1599406, _1599414, _1599408, _1599416, _1599418)), _1599420))), 41766 ^ _777959 : [(41769 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1599412, _1599414)), hAPP(hAPP(c_Product__Type_OPair(_1599412, _1599414), 41764 ^ [_1599406, _1599408, _1599410, _1599412, _1599414, _1599416, _1599418, _1599420]), 41765 ^ [_1599406, _1599408, _1599410, _1599412, _1599414, _1599416, _1599418, _1599420])), _1599420)))], (41767 ^ _777959) ^ [] : [-(_1599410 = hAPP(hAPP(c_Product__Type_OPair(_1599406, _1599408), hAPP(_1599416, 41764 ^ [_1599406, _1599408, _1599410, _1599412, _1599414, _1599416, _1599418, _1599420])), hAPP(_1599418, 41765 ^ [_1599406, _1599408, _1599410, _1599412, _1599414, _1599416, _1599418, _1599420])))]]], (42112 ^ _777959) ^ [_1607778, _1607780, _1607782] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1607778, _1607780), _1607782), hAPP(c_COMBK(tc_fun(_1607780, tc_HOL_Obool), _1607778), c_Orderings_Obot__class_Obot(tc_fun(_1607780, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1607778, _1607780), tc_HOL_Obool)))], (12696 ^ _777959) ^ [_1008347, _1008349, _1008351] : [class_Lattices_Oboolean__algebra(_1008347), 12699 ^ _777959 : [(12706 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008347), _1008351), _1008349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008347), hAPP(c_Groups_Ouminus__class_Ouminus(_1008347), _1008349)), hAPP(c_Groups_Ouminus__class_Ouminus(_1008347), _1008351))))], (12700 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008347), hAPP(c_Groups_Ouminus__class_Ouminus(_1008347), _1008349)), hAPP(c_Groups_Ouminus__class_Ouminus(_1008347), _1008351))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1008347), _1008351), _1008349)))]]], (7928 ^ _777959) ^ [_913008, _913010] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913008, tc_HOL_Obool)), _913010), c_Orderings_Obot__class_Obot(tc_fun(_913008, tc_HOL_Obool))) = _913010)], (51464 ^ _777959) ^ [] : [-(c_Hoare__Mirabelle_Ostate__not__singleton)], (51034 ^ _777959) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (1520 ^ _777959) ^ [_799683, _799685] : [-(class_Groups_Ocancel__semigroup__add(_799683)), _799685 = _799683, class_Groups_Ocancel__semigroup__add(_799685)], (41535 ^ _777959) ^ [_1592287, _1592289, _1592291, _1592293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592287)), _1592289)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1592287)), _1592291))), _1592289 = hAPP(hAPP(c_List_Olist_OCons(_1592287), _1592293), _1592291)], (50868 ^ _777959) ^ [] : [-(class_Nat_Osize(tc_Com_Ocom))], (41840 ^ _777959) ^ [_1601280, _1601282] : [-(c_List_Olists(_1601280, _1601282) = hAPP(c_Set_OCollect(tc_List_Olist(_1601280)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1601280), tc_fun(_1601280, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1601280, tc_HOL_Obool), tc_fun(tc_fun(_1601280, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1601280)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1601280, tc_HOL_Obool))), c_List_Oset(_1601280))), _1601282)))], (32597 ^ _777959) ^ [_1393558, _1393560, _1393562, _1393564] : [class_Fields_Olinordered__field__inverse__zero(_1393558), class_Int_Onumber(_1393558), 32604 ^ _777959 : [(32605 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393558), _1393560), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1393558), _1393562), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564)))), 32608 ^ _777959 : [(32615 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393558), c_Groups_Ozero__class_Ozero(_1393558)), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564)))), 32618 ^ _777959 : [(32625 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393558), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564)), c_Groups_Ozero__class_Ozero(_1393558)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393558), _1393560), c_Groups_Ozero__class_Ozero(_1393558))))], (32619 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393558), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564)), c_Groups_Ozero__class_Ozero(_1393558))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393558), _1393562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393558), _1393560), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564)))))]]], (32609 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393558), c_Groups_Ozero__class_Ozero(_1393558)), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393558), _1393560), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564))), _1393562)))]]], (32631 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393558), _1393560), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1393558), _1393562), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564))))), 32634 ^ _777959 : [(32637 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393558), _1393560), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564))), _1393562))], (32635 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393558), c_Groups_Ozero__class_Ozero(_1393558)), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564))))]], 32638 ^ _777959 : [(32641 ^ _777959) ^ [] : [32642 ^ _777959 : [(32645 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393558), _1393562), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1393558), _1393560), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564))))], (32643 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393558), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564)), c_Groups_Ozero__class_Ozero(_1393558))))]], 32646 ^ _777959 : [(32649 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1393558), _1393560), c_Groups_Ozero__class_Ozero(_1393558)))], (32647 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393558), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564)), c_Groups_Ozero__class_Ozero(_1393558)))]]], (32639 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393558), c_Groups_Ozero__class_Ozero(_1393558)), hAPP(c_Int_Onumber__class_Onumber__of(_1393558), _1393564)))]]]]], (35343 ^ _777959) ^ [_1442996, _1442998, _1443000, _1443002, _1443004, _1443006] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1442996, _1442998)), hAPP(hAPP(c_Product__Type_OPair(_1442996, _1442998), _1443004), _1443006)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool)), _1443000), _1443002))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1442996, tc_fun(_1442998, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1442996, tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_fun(_1442998, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1442998, tc_fun(tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_fun(_1442998, tc_HOL_Obool)), _1442996), c_COMBC(_1442998, tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1442998, tc_prod(_1442996, _1442998)), tc_fun(_1442998, tc_fun(tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_HOL_Obool)), _1442996), hAPP(c_COMBB(tc_prod(_1442996, _1442998), tc_fun(tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_HOL_Obool), _1442998), c_member(tc_prod(_1442996, _1442998)))), c_Product__Type_OPair(_1442996, _1442998)))), _1443000)), hAPP(hAPP(c_COMBC(_1442996, tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_fun(_1442998, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1442998, tc_fun(tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_fun(_1442998, tc_HOL_Obool)), _1442996), c_COMBC(_1442998, tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1442998, tc_prod(_1442996, _1442998)), tc_fun(_1442998, tc_fun(tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_HOL_Obool)), _1442996), hAPP(c_COMBB(tc_prod(_1442996, _1442998), tc_fun(tc_fun(tc_prod(_1442996, _1442998), tc_HOL_Obool), tc_HOL_Obool), _1442998), c_member(tc_prod(_1442996, _1442998)))), c_Product__Type_OPair(_1442996, _1442998)))), _1443002)), _1443004), _1443006)))], (39298 ^ _777959) ^ [_1535582, _1535584, _1535586, _1535588, _1535590, _1535592] : [c_Finite__Set_Ofolding(_1535582, _1535584, _1535586, _1535588), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535582), _1535590)), hBOOL(hAPP(hAPP(c_member(_1535582), _1535592), _1535590)), -(hAPP(_1535588, _1535590) = hAPP(c_Fun_Ocomp(_1535584, _1535584, _1535584, hAPP(_1535588, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1535582, tc_HOL_Obool)), _1535590), hAPP(hAPP(c_Set_Oinsert(_1535582), _1535592), c_Orderings_Obot__class_Obot(tc_fun(_1535582, tc_HOL_Obool)))))), hAPP(_1535586, _1535592)))], (14628 ^ _777959) ^ [_1052741, _1052743] : [-(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), _1052741)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1052743))))))], (3022 ^ _777959) ^ [_823213, _823215, _823217, _823219, _823221, _823223] : [-(c_Big__Operators_Olattice_OInf__fin(_823223, _823219, _823215) = c_Big__Operators_Olattice_OInf__fin(_823221, _823217, _823213)), _823223 = _823221, _823219 = _823217, _823215 = _823213], (4362 ^ _777959) ^ [_843993, _843995, _843997, _843999] : [-(c_Nitpick_Oinverse__frac(_843999, _843995) = c_Nitpick_Oinverse__frac(_843997, _843993)), _843999 = _843997, _843995 = _843993], (13050 ^ _777959) ^ [_1015520, _1015522] : [_1015522 = c_Orderings_Obot__class_Obot(tc_fun(_1015520, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015520, tc_HOL_Obool)), _1015522), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1015520, tc_HOL_Obool)), _1015522))))], (50874 ^ _777959) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (5308 ^ _777959) ^ [_859206, _859208] : [_859208 = _859206, -(c_Groups_Ominus__class_Ominus(_859208) = c_Groups_Ominus__class_Ominus(_859206))], (17075 ^ _777959) ^ [_1104578] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1104578) = c_Orderings_Oord__class_Omin(_1104578)), class_Lattices_Osemilattice__inf(_1104578), class_Orderings_Olinorder(_1104578)], (2204 ^ _777959) ^ [_810442, _810444, _810446, _810448, _810450, _810452] : [-(c_Hoare__Mirabelle_Otriple_Otriple__size(_810452, _810448, _810444) = c_Hoare__Mirabelle_Otriple_Otriple__size(_810450, _810446, _810442)), _810452 = _810450, _810448 = _810446, _810444 = _810442], (4014 ^ _777959) ^ [_838779, _838781] : [_838781 = _838779, -(c_Random_Orange(_838781) = c_Random_Orange(_838779))], (25838 ^ _777959) ^ [_1267817, _1267819, _1267821] : [class_Rings_Odivision__ring(_1267817), -(_1267819 = c_Groups_Ozero__class_Ozero(_1267817)), 25845 ^ _777959 : [(25852 ^ _777959) ^ [] : [_1267821 = _1267819, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267817), _1267821), _1267819) = c_Groups_Oone__class_Oone(_1267817))], (25846 ^ _777959) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1267817), _1267821), _1267819) = c_Groups_Oone__class_Oone(_1267817), -(_1267821 = _1267819)]]], (24285 ^ _777959) ^ [_1239514, _1239516] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1239514), _1239516)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239514)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1239516))))], (1340 ^ _777959) ^ [_797433, _797435] : [-(class_Lattices_Olattice(_797433)), _797435 = _797433, class_Lattices_Olattice(_797435)], (15010 ^ _777959) ^ [_1063427, _1063429, _1063431] : [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, _1063427)), _1063429)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1063427)), _1063431))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063429), _1063431)))], (31683 ^ _777959) ^ [_1376203, _1376205] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1376203), _1376205)), 31689 ^ _777959 : [(31692 ^ _777959) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31690 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1376203), 31688 ^ [_1376203, _1376205]), _1376205)))]], -(hAPP(c_Finite__Set_Ocard(_1376203), _1376205) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37300 ^ _777959) ^ [_1489570, _1489572, _1489574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1489570, _1489570), tc_HOL_Obool)), _1489572), _1489574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1489570, tc_HOL_Obool)), hAPP(c_Relation_OField(_1489570), _1489572)), hAPP(c_Relation_OField(_1489570), _1489574))))], (1290 ^ _777959) ^ [_796808, _796810] : [-(class_Lattices_Obounded__lattice__bot(_796808)), _796810 = _796808, class_Lattices_Obounded__lattice__bot(_796810)], (25732 ^ _777959) ^ [_1266083, _1266085] : [class_Rings_Odivision__ring(_1266083), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266083), c_Groups_Ozero__class_Ozero(_1266083)), _1266085) = c_Groups_Ozero__class_Ozero(_1266083))], (48214 ^ _777959) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (50668 ^ _777959) ^ [_1805767, _1805769, _1805771] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1805767), hAPP(c_COMBK(_1805767, tc_Nat_Onat), _1805769)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1805771)) = c_List_Oreplicate(_1805767, _1805771, _1805769))], (12524 ^ _777959) ^ [_1005779, _1005781, _1005783] : [-(hBOOL(hAPP(hAPP(c_member(_1005779), _1005781), _1005783))), -(hBOOL(hAPP(hAPP(c_member(_1005779), _1005781), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1005779, tc_HOL_Obool)), _1005783))))], (45451 ^ _777959) ^ [_1683863, _1683865, _1683867, _1683869, _1683871] : [-(c_List_OdropWhile(_1683863, _1683865, hAPP(hAPP(c_List_Omap(_1683867, _1683863), _1683869), _1683871)) = hAPP(hAPP(c_List_Omap(_1683867, _1683863), _1683869), c_List_OdropWhile(_1683867, hAPP(c_Fun_Ocomp(_1683863, tc_HOL_Obool, _1683867, _1683865), _1683869), _1683871)))], (43672 ^ _777959) ^ [_1646155, _1646157] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1646155), _1646157) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1646155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43678 ^ _777959 : [(43681 ^ _777959) ^ [] : [43677 ^ [_1646155, _1646157] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (43679 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43677 ^ [_1646155, _1646157]), hAPP(c_List_Oset(tc_Nat_Onat), _1646157))))]]], (21636 ^ _777959) ^ [_1188990, _1188992] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1188990)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1188992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1188990), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188990), _1188992))))], (42349 ^ _777959) ^ [_1613637, _1613639, _1613641, _1613643] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1613637), _1613639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1613637, _1613637), tc_HOL_Obool)), _1613641), hAPP(hAPP(c_Product__Type_OSigma(_1613637, _1613637), _1613639), hAPP(c_COMBK(tc_fun(_1613637, tc_HOL_Obool), _1613637), _1613639)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1613637, tc_HOL_Obool)), _1613643), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1613637), _1613639), _1613641))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1613637), _1613643)))], (43925 ^ _777959) ^ [_1651157, _1651159, _1651161, _1651163] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651157)), _1651159))), c_List_Ofoldr(tc_List_Olist(_1651161), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1651161)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1651161))), _1651163, 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(_1651157)), _1651159)), c_List_Ofoldr(tc_List_Olist(_1651161), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1651161)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1651161), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1651161)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1651161)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1651161), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1651161)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1651161), tc_List_Olist(_1651161), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1651161)))), _1651163), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (9734 ^ _777959) ^ [_946806, _946808, _946810] : [class_Lattices_Osemilattice__inf(_946806), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946806), _946808), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946806), _946808), _946810)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946806), _946808), _946810))], (14928 ^ _777959) ^ [_1061245, _1061247, _1061249] : [class_Groups_Olinordered__ab__semigroup__add(_1061245), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061245), _1061247)), -(_1061247 = c_Orderings_Obot__class_Obot(tc_fun(_1061245, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061245), _1061249), c_Big__Operators_Olinorder__class_OMin(_1061245, _1061247)) = c_Big__Operators_Olinorder__class_OMin(_1061245, hAPP(c_Set_OCollect(_1061245), hAPP(hAPP(c_COMBB(tc_fun(_1061245, tc_HOL_Obool), tc_HOL_Obool, _1061245), c_HOL_OEx(_1061245)), hAPP(hAPP(c_COMBC(_1061245, tc_fun(_1061245, tc_HOL_Obool), tc_fun(_1061245, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061245, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1061245, tc_HOL_Obool), tc_fun(_1061245, tc_HOL_Obool)), _1061245), c_COMBS(_1061245, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061245, tc_HOL_Obool), tc_fun(_1061245, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1061245), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1061245), c_fconj)), hAPP(hAPP(c_COMBC(_1061245, tc_fun(_1061245, _1061245), tc_fun(_1061245, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061245, tc_HOL_Obool), tc_fun(tc_fun(_1061245, _1061245), tc_fun(_1061245, tc_HOL_Obool)), _1061245), c_COMBB(_1061245, tc_HOL_Obool, _1061245)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1061245), _1061249))))), hAPP(hAPP(c_COMBC(_1061245, tc_fun(_1061245, tc_HOL_Obool), tc_HOL_Obool), c_member(_1061245)), _1061247))))))], (13653 ^ _777959) ^ [_1029349, _1029351, _1029353, _1029355, _1029357, _1029359] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029349, tc_fun(_1029351, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1029353, _1029349, _1029355), _1029357)), _1029359) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029353, tc_fun(_1029351, tc_HOL_Obool)), _1029357), hAPP(hAPP(c_COMBB(_1029349, tc_fun(_1029351, tc_HOL_Obool), _1029353), _1029359), _1029355)))], (40805 ^ _777959) ^ [_1571325, _1571327, _1571329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1571325)), _1571327)), _1571329)), -(hAPP(hAPP(c_List_Otake(_1571325), _1571329), _1571327) = _1571327)], (9660 ^ _777959) ^ [_945121, _945123, _945125, _945127] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945121, tc_HOL_Obool)), _945123), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945121, tc_HOL_Obool)), _945125), _945127)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945121, tc_HOL_Obool)), _945125), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945121, tc_HOL_Obool)), _945123), _945127)))], (28976 ^ _777959) ^ [_1324105, _1324107, _1324109] : [class_Orderings_Oord(_1324105), 28979 ^ _777959 : [(28986 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324105), _1324107), _1324109)), -(hBOOL(hAPP(hAPP(c_member(_1324105), _1324107), hAPP(c_SetInterval_Oord__class_OatMost(_1324105), _1324109))))], (28980 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1324105), _1324107), hAPP(c_SetInterval_Oord__class_OatMost(_1324105), _1324109))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324105), _1324107), _1324109)))]]], (36626 ^ _777959) ^ [_1472757, _1472759, _1472761, _1472763] : [hAPP(c_Product__Type_Ofst(_1472757, _1472759), _1472761) = hAPP(c_Product__Type_Ofst(_1472757, _1472759), _1472763), hAPP(c_Product__Type_Osnd(_1472757, _1472759), _1472761) = hAPP(c_Product__Type_Osnd(_1472757, _1472759), _1472763), -(_1472761 = _1472763)], (41131 ^ _777959) ^ [_1582725, _1582727, _1582729] : [41133 ^ _777959 : [(41136 ^ _777959) ^ [] : [c_Hoare__Mirabelle_Otriple__valid(_1582725, hAPP(c_Nat_OSuc, _1582729), 41132 ^ [_1582725, _1582727, _1582729])], (41134 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1582725)), 41132 ^ [_1582725, _1582727, _1582729]), _1582727)))]], 41137 ^ _777959 : [(41138 ^ _777959) ^ [_1582898] : [hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(_1582725)), _1582898), _1582727)), -(c_Hoare__Mirabelle_Otriple__valid(_1582725, _1582729, _1582898))]]], (42028 ^ _777959) ^ [_1606160, _1606162, _1606164] : [-(hAPP(hAPP(c_List_Omap(_1606160, _1606162), _1606164), c_List_Olist_ONil(_1606160)) = c_List_Olist_ONil(_1606162))], (48234 ^ _777959) ^ [_1748919, _1748921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1748919)), hAPP(c_Code__Numeral_Oof__nat, _1748921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1748919), _1748921)))], (30046 ^ _777959) ^ [_1346193, _1346195, _1346197] : [class_Divides_Osemiring__div(_1346193), -(c_Divides_Odiv__class_Omod(_1346193, c_Divides_Odiv__class_Omod(_1346193, _1346195, _1346197), _1346197) = c_Divides_Odiv__class_Omod(_1346193, _1346195, _1346197))], (42477 ^ _777959) ^ [_1617104, _1617106, _1617108, _1617110, _1617112, _1617114] : [-(hAPP(c_List_Olist_Olist__case(_1617104, _1617106, _1617108, _1617110), hAPP(hAPP(c_List_Olist_OCons(_1617106), _1617112), _1617114)) = hAPP(hAPP(_1617110, _1617112), _1617114))], (23291 ^ _777959) ^ [_1221851, _1221853] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221851) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221853), -(_1221851 = _1221853)], (11855 ^ _777959) ^ [_992978, _992980, _992982, _992984, _992986] : [class_Complete__Lattice_Ocomplete__lattice(_992978), class_Orderings_Olinorder(_992978), 11862 ^ _777959 : [(11872 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992978), _992980), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992982, _992978), _992984), _992986)))), 11873 ^ _777959 : [(11874 ^ _777959) ^ [_993326] : [hBOOL(hAPP(hAPP(c_member(_992982), _993326), _992984)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992978), _992980), hAPP(_992986, _993326)))]]], (11863 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992978), _992980), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992982, _992978), _992984), _992986))), 11867 ^ _777959 : [(11870 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992978), _992980), hAPP(_992986, 11866 ^ [_992978, _992980, _992982, _992984, _992986]))))], (11868 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_992982), 11866 ^ [_992978, _992980, _992982, _992984, _992986]), _992984)))]]]]], (37271 ^ _777959) ^ [_1488917, _1488919, _1488921, _1488923] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1488917), _1488923)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1488921), _1488919))), -(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), _1488917), _1488919)), 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), _1488921), _1488923)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (23885 ^ _777959) ^ [_1232081, _1232083, _1232085] : [class_Rings_Olinordered__semidom(_1232081), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232081), c_Groups_Oone__class_Oone(_1232081)), _1232083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1232081), c_Groups_Oone__class_Oone(_1232081)), hAPP(hAPP(c_Power_Opower__class_Opower(_1232081), _1232083), hAPP(c_Nat_OSuc, _1232085)))))], (37308 ^ _777959) ^ [_1489782, _1489784] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1489782, _1489782)), _1489784)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1489782), hAPP(c_Relation_OField(_1489782), _1489784))))], (13632 ^ _777959) ^ [_1028751, _1028753, _1028755, _1028757, _1028759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1028751, tc_HOL_Obool)), _1028753), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1028755, tc_fun(_1028751, tc_HOL_Obool)), _1028757), _1028759))), 13635 ^ _777959 : [(13636 ^ _777959) ^ [_1028884] : [hBOOL(hAPP(hAPP(c_member(_1028755), _1028884), _1028757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1028751, tc_HOL_Obool)), _1028753), hAPP(_1028759, _1028884))))]]], (25484 ^ _777959) ^ [_1261101, _1261103, _1261105] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1261101)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1261101), _1261103)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1261101), _1261105)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1261103), _1261105))], (47481 ^ _777959) ^ [_1732020, _1732022] : [c_Wellfounded_OwfP(_1732020, hAPP(hAPP(c_COMBC(_1732020, tc_fun(tc_prod(_1732020, _1732020), tc_HOL_Obool), tc_fun(_1732020, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1732020, tc_fun(tc_fun(tc_prod(_1732020, _1732020), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1732020, _1732020), tc_HOL_Obool), tc_fun(_1732020, tc_HOL_Obool)), _1732020), c_COMBC(_1732020, tc_fun(tc_prod(_1732020, _1732020), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1732020, tc_prod(_1732020, _1732020)), tc_fun(_1732020, tc_fun(tc_fun(tc_prod(_1732020, _1732020), tc_HOL_Obool), tc_HOL_Obool)), _1732020), hAPP(c_COMBB(tc_prod(_1732020, _1732020), tc_fun(tc_fun(tc_prod(_1732020, _1732020), tc_HOL_Obool), tc_HOL_Obool), _1732020), c_member(tc_prod(_1732020, _1732020)))), c_Product__Type_OPair(_1732020, _1732020)))), _1732022)), -(c_Wellfounded_Owf(_1732020, _1732022))], (39794 ^ _777959) ^ [_1547214, _1547216, _1547218] : [-(hBOOL(hAPP(hAPP(c_member(_1547214), _1547216), hAPP(c_List_Oset(_1547214), _1547218)))), -(c_List_Oremove1(_1547214, _1547216, _1547218) = _1547218)], (46934 ^ _777959) ^ [_1719066, _1719068, _1719070] : [c_Wellfounded_Owf(_1719066, _1719068), hBOOL(hAPP(hAPP(c_member(tc_prod(_1719066, _1719066)), hAPP(hAPP(c_Product__Type_OPair(_1719066, _1719066), _1719070), _1719070)), _1719068))], (51354 ^ _777959) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (5679 ^ _777959) ^ [_867524, _867526, _867528, _867530] : [c_Hoare__Mirabelle_Ohoare__derivs(_867524, _867526, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_867524)), _867528), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867524), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_867524, _867526, _867530), -(c_Hoare__Mirabelle_Ohoare__derivs(_867524, _867526, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_867524)), _867528), _867530)))], (33889 ^ _777959) ^ [_1416363] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1416363))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416363)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (38973 ^ _777959) ^ [_1528030, _1528032, _1528034, _1528036, _1528038, _1528040] : [-(hAPP(c_Set_Ovimage(_1528030, _1528032, hAPP(c_Fun_Ocomp(_1528034, _1528032, _1528030, _1528036), _1528038)), _1528040) = hAPP(c_Set_Ovimage(_1528030, _1528034, _1528038), hAPP(c_Set_Ovimage(_1528034, _1528032, _1528036), _1528040)))], (9698 ^ _777959) ^ [_945984, _945986, _945988, _945990] : [class_Lattices_Osemilattice__inf(_945984), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945984), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945984), _945986), _945988)), _945990) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945984), _945986), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945984), _945988), _945990)))], (10886 ^ _777959) ^ [_971374, _971376, _971378, _971380] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_971374), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971374), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971374), _971376), _971378)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_971374), _971380), _971378))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_971374), _971376), _971380)))], (16503 ^ _777959) ^ [_1094042, _1094044, _1094046, _1094048] : [class_Orderings_Olinorder(_1094042), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094042), _1094044), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094042), _1094046), _1094048)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094042), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094042), _1094044), _1094046)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094042), _1094044), _1094048)))], (32873 ^ _777959) ^ [_1398900, _1398902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1398900), _1398902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398900)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398902))))], (10166 ^ _777959) ^ [_955880, _955882, _955884, _955886, _955888] : [hBOOL(hAPP(hAPP(c_member(_955880), _955882), _955884)), -(hAPP(c_Map_Orestrict__map(_955880, _955886, _955888, _955884), _955882) = hAPP(_955888, _955882))], (3816 ^ _777959) ^ [_835710, _835712, _835714, _835716, _835718, _835720] : [-(c_Predicate_ORangeP(_835720, _835716, _835712) = c_Predicate_ORangeP(_835718, _835714, _835710)), _835720 = _835718, _835716 = _835714, _835712 = _835710], (33207 ^ _777959) ^ [_1404788, _1404790] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1404788), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404790)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404788)) = 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), _1404790), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1404788)))), 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)))], (44467 ^ _777959) ^ [_1661754, _1661756, _1661758] : [class_Orderings_Olinorder(_1661754), 44470 ^ _777959 : [(44489 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1661754, hAPP(hAPP(c_List_Oappend(_1661754), _1661756), _1661758))), c_List_Olinorder__class_Osorted(_1661754, _1661756), c_List_Olinorder__class_Osorted(_1661754, _1661758), 44499 ^ _777959 : [(44505 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1661754), 44498 ^ [_1661754, _1661756, _1661758]), 44501 ^ [_1661754, _1661756, _1661758]))], (44503 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1661754), 44501 ^ [_1661754, _1661756, _1661758]), hAPP(c_List_Oset(_1661754), _1661758))))], (44500 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1661754), 44498 ^ [_1661754, _1661756, _1661758]), hAPP(c_List_Oset(_1661754), _1661756))))]]], (44471 ^ _777959) ^ [] : [c_List_Olinorder__class_Osorted(_1661754, hAPP(hAPP(c_List_Oappend(_1661754), _1661756), _1661758)), 44474 ^ _777959 : [(44479 ^ _777959) ^ [_1661990] : [hBOOL(hAPP(hAPP(c_member(_1661754), _1661990), hAPP(c_List_Oset(_1661754), _1661756))), 44482 ^ _777959 : [(44483 ^ _777959) ^ [_1662100] : [hBOOL(hAPP(hAPP(c_member(_1661754), _1662100), hAPP(c_List_Oset(_1661754), _1661758))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1661754), _1661990), _1662100)))]]], (44477 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1661754, _1661758))], (44475 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1661754, _1661756))]]]]], (29771 ^ _777959) ^ [_1340047, _1340049] : [-(hAPP(c_Set_OPow(_1340047), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1340047, tc_HOL_Obool)), _1340049)) = hAPP(c_Set_OCollect(tc_fun(_1340047, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1340047, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1340047, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1340047, tc_HOL_Obool), tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1340047, tc_HOL_Obool)), c_COMBS(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1340047, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1340047, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1340047, tc_HOL_Obool), tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_fun(_1340047, tc_HOL_Obool)), tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_fun(_1340047, tc_HOL_Obool)), tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1340047, tc_HOL_Obool)), c_COMBB(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1340047, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1340047, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1340047, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1340047, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1340047, tc_HOL_Obool)), _1340049)), c_Set_OPow(_1340047))))))], (34357 ^ _777959) ^ [_1424707, _1424709] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1424707)), c_Int_OBit1(_1424709))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1424707), _1424709)))], (21131 ^ _777959) ^ [_1179291, _1179293, _1179295] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1179291), _1179293)), 21134 ^ _777959 : [(21135 ^ _777959) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1179291, tc_Nat_Onat), _1179295), _1179293) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 21138 ^ _777959 : [(21139 ^ _777959) ^ [_1179453] : [hBOOL(hAPP(hAPP(c_member(_1179291), _1179453), _1179293)), -(hAPP(_1179295, _1179453) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (21145 ^ _777959) ^ [] : [21147 ^ _777959 : [(21150 ^ _777959) ^ [] : [hAPP(_1179295, 21146 ^ [_1179291, _1179293, _1179295]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (21148 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1179291), 21146 ^ [_1179291, _1179293, _1179295]), _1179293)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1179291, tc_Nat_Onat), _1179295), _1179293) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (29896 ^ _777959) ^ [_1343138, _1343140] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1343138, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1343140)) = 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), _1343138), _1343140)))], (20937 ^ _777959) ^ [_1176071, _1176073] : [20938 ^ _777959 : [(20941 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176073))], (20939 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176071))]], -(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), _1176071), _1176073))))], (39886 ^ _777959) ^ [_1549872, _1549874, _1549876, _1549878, _1549880, _1549882, _1549884, _1549886] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549872)), _1549874) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549876)), _1549878), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549872)), _1549880) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1549876)), _1549878), -(hBOOL(hAPP(hAPP(c_member(_1549876), _1549882), hAPP(c_List_Oset(_1549876), _1549878)))), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1549876, tc_Option_Ooption(_1549872)), hAPP(c_Map_Omap__of(_1549876, _1549872), hAPP(hAPP(c_List_Ozip(_1549876, _1549872), _1549878), _1549874))), _1549882), hAPP(c_Option_Ooption_OSome(_1549872), _1549884)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1549876, tc_Option_Ooption(_1549872)), hAPP(c_Map_Omap__of(_1549876, _1549872), hAPP(hAPP(c_List_Ozip(_1549876, _1549872), _1549878), _1549880))), _1549882), hAPP(c_Option_Ooption_OSome(_1549872), _1549886)), -(hAPP(c_Map_Omap__of(_1549876, _1549872), hAPP(hAPP(c_List_Ozip(_1549876, _1549872), _1549878), _1549874)) = hAPP(c_Map_Omap__of(_1549876, _1549872), hAPP(hAPP(c_List_Ozip(_1549876, _1549872), _1549878), _1549880)))], (5797 ^ _777959) ^ [_869843, _869845, _869847, _869849] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_869843), _869845), _869847), _869849)), -(_869845 = _869849), -(hBOOL(hAPP(_869847, _869849)))], (40759 ^ _777959) ^ [_1570081, _1570083, _1570085] : [-(c_Hilbert__Choice_OEps(tc_prod(_1570081, _1570083), hAPP(c_Product__Type_Oprod_Oprod__case(_1570081, _1570083, tc_HOL_Obool), _1570085)) = c_Hilbert__Choice_OEps(tc_prod(_1570081, _1570083), hAPP(hAPP(c_COMBS(tc_prod(_1570081, _1570083), _1570083, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1570081, tc_fun(_1570083, tc_HOL_Obool), tc_prod(_1570081, _1570083)), _1570085), c_Product__Type_Ofst(_1570081, _1570083))), c_Product__Type_Osnd(_1570081, _1570083))))], (6879 ^ _777959) ^ [_890335, _890337, _890339, _890341] : [c_Hoare__Mirabelle_Ohoare__derivs(_890335, _890337, _890339), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_890335), tc_HOL_Obool)), _890337), _890341)), -(c_Hoare__Mirabelle_Ohoare__derivs(_890335, _890341, _890339))], (12165 ^ _777959) ^ [_998769, _998771, _998773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998769), _998771)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998769), _998773))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _998771), _998773)))], (35215 ^ _777959) ^ [_1440049] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1440049)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1440049)))], (23433 ^ _777959) ^ [_1224168, _1224170, _1224172] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224168), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224170), _1224172)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224170), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224168), _1224172)))], (15966 ^ _777959) ^ [_1082192, _1082194] : [class_Orderings_Olinorder(_1082192), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082192), _1082194)), -(_1082194 = c_Orderings_Obot__class_Obot(tc_fun(_1082192, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1082192), c_Big__Operators_Olinorder__class_OMax(_1082192, _1082194)), _1082194)))], (40528 ^ _777959) ^ [_1564710, _1564712] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1564710), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1564712))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1564712), _1564710)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1564712))))], (31012 ^ _777959) ^ [_1363832, _1363834] : [class_Groups_Oordered__ab__group__add__abs(_1363832), -(hAPP(c_Groups_Oabs__class_Oabs(_1363832), hAPP(c_Groups_Oabs__class_Oabs(_1363832), _1363834)) = hAPP(c_Groups_Oabs__class_Oabs(_1363832), _1363834))], (23671 ^ _777959) ^ [_1228290, _1228292, _1228294, _1228296] : [class_Rings_Olinordered__semidom(_1228290), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228290), _1228292), _1228294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228290), c_Groups_Ozero__class_Ozero(_1228290)), _1228292)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1228290), hAPP(hAPP(c_Power_Opower__class_Opower(_1228290), _1228292), _1228296)), hAPP(hAPP(c_Power_Opower__class_Opower(_1228290), _1228294), _1228296))))], (40061 ^ _777959) ^ [_1553955, _1553957, _1553959] : [hBOOL(hAPP(hAPP(c_member(_1553955), _1553957), hAPP(c_List_Oset(_1553955), _1553959))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553955)), c_List_Oremove1(_1553955, _1553957, _1553959)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553955)), _1553959)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (16419 ^ _777959) ^ [_1092266, _1092268, _1092270] : [class_Orderings_Olinorder(_1092266), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092266), _1092268), _1092270) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092266), _1092270), _1092268))], (37116 ^ _777959) ^ [_1483822, _1483824, _1483826, _1483828] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1483822), _1483828) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1483826), _1483824), -(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), _1483822), _1483824)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1483826), _1483828))), c_Int_Ointrel)))], (45718 ^ _777959) ^ [_1690150, _1690152, _1690154, _1690156] : [class_Orderings_Olinorder(_1690150), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690152)), c_List_Olinorder__class_Osort__key(_1690152, _1690150, _1690154, _1690156)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690152)), _1690156))], (7594 ^ _777959) ^ [_905702, _905704, _905706, _905708, _905710] : [c_Finite__Set_Ofolding__one__idem(_905702, _905704, _905706), hBOOL(hAPP(c_Finite__Set_Ofinite(_905702), _905708)), -(_905708 = c_Orderings_Obot__class_Obot(tc_fun(_905702, tc_HOL_Obool))), -(hAPP(_905706, hAPP(hAPP(c_Set_Oinsert(_905702), _905710), _905708)) = hAPP(hAPP(_905704, _905710), hAPP(_905706, _905708)))], (43945 ^ _777959) ^ [_1651766, _1651768, _1651770] : [hAPP(c_List_Ofilter(_1651766, _1651768), _1651770) = _1651770, 43948 ^ _777959 : [(43949 ^ _777959) ^ [_1651857] : [hBOOL(hAPP(hAPP(c_member(_1651766), _1651857), hAPP(c_List_Oset(_1651766), _1651770))), -(hBOOL(hAPP(_1651768, _1651857)))]]], (16833 ^ _777959) ^ [_1100270, _1100272, _1100274] : [class_Orderings_Olinorder(_1100270), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100270), _1100272), _1100274)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100270), _1100272), _1100274) = _1100272)], (39500 ^ _777959) ^ [_1540384, _1540386, _1540388, _1540390, _1540392] : [c_Hoare__Mirabelle_Ohoare__derivs(_1540384, _1540386, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1540384)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1540384), c_Hoare__Mirabelle_Opeek__and(_1540384, _1540388, _1540390)), _1540392), _1540388)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1540384), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_1540384, _1540386, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_1540384)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1540384), _1540388), c_Com_Ocom_OWhile(_1540390, _1540392)), c_Hoare__Mirabelle_Opeek__and(_1540384, _1540388, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Com_Ostate, c_fNot), _1540390)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_1540384), tc_HOL_Obool)))))], (21626 ^ _777959) ^ [_1188831, _1188833] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1188831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1188833)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1188831), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1188833), _1188831))))], (4114 ^ _777959) ^ [_840247, _840249, _840251, _840253] : [-(c_Relation_ODomain(_840253, _840249) = c_Relation_ODomain(_840251, _840247)), _840253 = _840251, _840249 = _840247], (38542 ^ _777959) ^ [_1517333, _1517335, _1517337, _1517339, _1517341] : [c_Fun_Oinj__on(_1517333, _1517335, _1517337, _1517339), hBOOL(hAPP(hAPP(c_member(_1517333), _1517341), _1517339)), -(hAPP(c_Fun_Othe__inv__into(_1517333, _1517335, _1517339, _1517337), hAPP(_1517337, _1517341)) = _1517341)], (21196 ^ _777959) ^ [_1180799, _1180801, _1180803] : [class_Groups_Oordered__comm__monoid__add(_1180799), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180799), c_Groups_Ozero__class_Ozero(_1180799)), _1180801)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1180799), c_Groups_Ozero__class_Ozero(_1180799)), _1180803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1180799), c_Groups_Ozero__class_Ozero(_1180799)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1180799), _1180801), _1180803))))], (36285 ^ _777959) ^ [_1465926, _1465928, _1465930, _1465932] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1465926, _1465928), _1465930)), hBOOL(hAPP(hAPP(_1465928, _1465932), _1465930)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1465926, _1465928), _1465932)))], (33297 ^ _777959) ^ [_1406128, _1406130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1406128)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1406130)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406128)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1406130), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1406128))))], (51116 ^ _777959) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (10126 ^ _777959) ^ [_954791, _954793, _954795, _954797] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954791, tc_HOL_Obool)), _954793), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954791, tc_HOL_Obool)), _954795), _954797)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954791, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954791, tc_HOL_Obool)), _954793), _954795)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954791, tc_HOL_Obool)), _954793), _954797)))], (19594 ^ _777959) ^ [_1152684] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152684) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49060 ^ _777959) ^ [_1769293, _1769295] : [c_Wellfounded_Owf(_1769293, hAPP(c_Relation_Oconverse(_1769293, _1769293), _1769295)), -(c_Wellfounded_Owf(_1769293, hAPP(c_Relation_Oconverse(_1769293, _1769293), c_Transitive__Closure_Otrancl(_1769293, _1769295))))], (17843 ^ _777959) ^ [_1119022, _1119024, _1119026] : [class_Orderings_Olinorder(_1119022), hBOOL(hAPP(c_Finite__Set_Ofinite(_1119022), _1119024)), hBOOL(hAPP(hAPP(c_member(_1119022), _1119026), _1119024)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1119022), _1119026), c_Big__Operators_Olattice_OSup__fin(_1119022, c_Orderings_Oord__class_Omax(_1119022), _1119024)) = c_Big__Operators_Olattice_OSup__fin(_1119022, c_Orderings_Oord__class_Omax(_1119022), _1119024))], (47872 ^ _777959) ^ [_1741606, _1741608, _1741610, _1741612] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1741606, tc_HOL_Obool), tc_fun(_1741606, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1741606, tc_HOL_Obool), tc_fun(_1741606, tc_HOL_Obool)), _1741608), _1741610)), c_Wellfounded_Omax__ext(_1741606, _1741612))), 47875 ^ _777959 : [(47878 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1741606), _1741610)))], (47880 ^ _777959) ^ [] : [_1741610 = c_Orderings_Obot__class_Obot(tc_fun(_1741606, tc_HOL_Obool))], (47882 ^ _777959) ^ [_1741900] : [hBOOL(hAPP(hAPP(c_member(_1741606), _1741900), _1741608)), 47886 ^ _777959 : [(47889 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1741606, _1741606)), hAPP(hAPP(c_Product__Type_OPair(_1741606, _1741606), _1741900), 47885 ^ [_1741606, _1741608, _1741610, _1741612, _1741900])), _1741612)))], (47887 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1741606), 47885 ^ [_1741606, _1741608, _1741610, _1741612, _1741900]), _1741610)))]]], (47876 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1741606), _1741608)))]]], (41777 ^ _777959) ^ [_1599882, _1599884, _1599886] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1599882)), _1599884), c_Wellfounded_Oacc(tc_List_Olist(_1599882), c_List_Olistrel1(_1599882, _1599886)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1599882)), _1599884), c_List_Olists(_1599882, c_Wellfounded_Oacc(_1599882, _1599886)))))], (3392 ^ _777959) ^ [_829080, _829082, _829084, _829086] : [-(c_Enum_Oenum__the(_829086, _829082) = c_Enum_Oenum__the(_829084, _829080)), _829086 = _829084, _829082 = _829080], (38742 ^ _777959) ^ [_1521526, _1521528, _1521530, _1521532, _1521534] : [-(hAPP(c_Set_Ovimage(_1521526, _1521528, _1521530), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521528, tc_HOL_Obool)), _1521532), _1521534)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1521526, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1521526, _1521528, _1521530), _1521532)), hAPP(c_Set_Ovimage(_1521526, _1521528, _1521530), _1521534)))], (43470 ^ _777959) ^ [_1642190, _1642192, _1642194] : [-(_1642190 = c_List_Olist_ONil(_1642192)), -(hAPP(c_List_Ohd(_1642192), hAPP(hAPP(c_List_Oappend(_1642192), _1642190), _1642194)) = hAPP(c_List_Ohd(_1642192), _1642190))], (37464 ^ _777959) ^ [_1493504, _1493506, _1493508, _1493510, _1493512] : [c_Equiv__Relations_Oequiv(_1493504, _1493506, _1493508), hBOOL(hAPP(hAPP(c_member(tc_prod(_1493504, _1493504)), hAPP(hAPP(c_Product__Type_OPair(_1493504, _1493504), _1493510), _1493512)), _1493508)), -(hAPP(c_Relation_OImage(_1493504, _1493504, _1493508), hAPP(hAPP(c_Set_Oinsert(_1493504), _1493510), c_Orderings_Obot__class_Obot(tc_fun(_1493504, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1493504, _1493504, _1493508), hAPP(hAPP(c_Set_Oinsert(_1493504), _1493512), c_Orderings_Obot__class_Obot(tc_fun(_1493504, tc_HOL_Obool)))))], (33657 ^ _777959) ^ [_1411805, _1411807] : [class_Int_Onumber__ring(_1411805), class_Rings_Olinordered__idom(_1411805), 33664 ^ _777959 : [(33671 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1411807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411805), c_Groups_Oone__class_Oone(_1411805)), hAPP(c_Int_Onumber__class_Onumber__of(_1411805), _1411807))))], (33665 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1411805), c_Groups_Oone__class_Oone(_1411805)), hAPP(c_Int_Onumber__class_Onumber__of(_1411805), _1411807))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1411807)))]]], (1390 ^ _777959) ^ [_798058, _798060] : [-(class_Finite__Set_Ofinite(_798058)), _798060 = _798058, class_Finite__Set_Ofinite(_798060)], (38736 ^ _777959) ^ [_1521385, _1521387, _1521389, _1521391] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521385, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1521387, _1521385, _1521389), hAPP(c_Set_Ovimage(_1521387, _1521385, _1521389), _1521391))), _1521391)))], (19664 ^ _777959) ^ [_1153723] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1153723), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1153723)], (49034 ^ _777959) ^ [_1768503, _1768505, _1768507, _1768509, _1768511] : [-(hAPP(c_Relation_Oconverse(_1768503, _1768505), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1768507, tc_fun(tc_prod(_1768503, _1768505), tc_HOL_Obool)), _1768509), _1768511)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1768507, tc_fun(tc_prod(_1768505, _1768503), tc_HOL_Obool)), _1768509), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1768503, _1768505), tc_HOL_Obool), tc_fun(tc_prod(_1768505, _1768503), tc_HOL_Obool), _1768507), c_Relation_Oconverse(_1768503, _1768505)), _1768511)))], (28480 ^ _777959) ^ [_1314763, _1314765] : [c_Nat__Transfer_Ois__nat(_1314763), c_Nat__Transfer_Ois__nat(_1314765), -(c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(_1314763, _1314765)))], (22667 ^ _777959) ^ [_1210425, _1210427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210425)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210427)))), 22670 ^ _777959 : [(22673 ^ _777959) ^ [] : [-(_1210427 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22671 ^ _777959) ^ [] : [-(_1210425 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (34997 ^ _777959) ^ [_1436774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1436774)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436774), c_Int_OMin)))], (33737 ^ _777959) ^ [_1413043, _1413045] : [class_Int_Onumber__ring(_1413043), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1413043), hAPP(c_Int_Onumber__class_Onumber__of(_1413043), _1413045)), c_Groups_Oone__class_Oone(_1413043)) = hAPP(c_Int_Onumber__class_Onumber__of(_1413043), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1413045), c_Int_OBit1(c_Int_OPls))))], (14061 ^ _777959) ^ [_1039229, _1039231, _1039233, _1039235, _1039237] : [-(hBOOL(hAPP(hAPP(c_member(_1039229), _1039231), c_Map_Odom(_1039229, _1039233, _1039235)))), -(hAPP(c_Map_Omap__add(_1039229, _1039233, _1039237, _1039235), _1039231) = hAPP(_1039237, _1039231))], (14163 ^ _777959) ^ [_1041434, _1041436, _1041438, _1041440] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041434), _1041436)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1041438), hAPP(c_Set_Oimage(_1041434, _1041438, _1041440), _1041436))), hAPP(c_Finite__Set_Ocard(_1041434), _1041436))))], (33037 ^ _777959) ^ [_1401909] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401909))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401909) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50440 ^ _777959) ^ [_1801028, _1801030, _1801032, _1801034, _1801036] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1801028, _1801030, _1801032), _1801034), _1801036)), -(hBOOL(hAPP(hAPP(_1801032, _1801036), _1801034)))], (2268 ^ _777959) ^ [_811486, _811488, _811490, _811492, _811494, _811496] : [-(c_Power_Opower_Opower(_811496, _811492, _811488) = c_Power_Opower_Opower(_811494, _811490, _811486)), _811496 = _811494, _811492 = _811490, _811488 = _811486], (24223 ^ _777959) ^ [_1238439, _1238441, _1238443] : [class_Rings_Osemiring__1(_1238439), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1238439, _1238441, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1238443) = _1238443)], (13709 ^ _777959) ^ [_1031217, _1031219, _1031221] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1031217), hAPP(c_Set_OCollect(_1031217), hAPP(hAPP(c_COMBS(_1031217, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1031217), c_fdisj), _1031219)), _1031221))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1031217), hAPP(c_Set_OCollect(_1031217), _1031219))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1031217), hAPP(c_Set_OCollect(_1031217), _1031221)))], (43221 ^ _777959) ^ [_1636057, _1636059, _1636061, _1636063] : [-(hAPP(c_List_Orotate1(_1636059), hAPP(hAPP(c_List_Olist_OCons(_1636059), _1636061), _1636063)) = hAPP(hAPP(c_List_Oappend(_1636059), _1636063), hAPP(hAPP(c_List_Olist_OCons(_1636059), _1636061), c_List_Olist_ONil(_1636059))))], (2014 ^ _777959) ^ [_807227, _807229, _807231, _807233, _807235, _807237] : [-(c_SetInterval_Oord_OgreaterThan(_807237, _807233, _807229) = c_SetInterval_Oord_OgreaterThan(_807235, _807231, _807227)), _807237 = _807235, _807233 = _807231, _807229 = _807227], (36552 ^ _777959) ^ [_1471308, _1471310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1471308), 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)), _1471310)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1471308, _1471310) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1471308, _1471310)))], (32933 ^ _777959) ^ [_1400038, _1400040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1400038)), c_Int_OBit1(_1400040))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400038), _1400040)))], (21802 ^ _777959) ^ [_1192032, _1192034, _1192036, _1192038, _1192040] : [class_Groups_Ocomm__monoid__mult(_1192032), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192034), _1192036)), -(hBOOL(hAPP(hAPP(c_member(_1192034), _1192038), _1192036))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1192034, _1192032), _1192040), hAPP(hAPP(c_Set_Oinsert(_1192034), _1192038), _1192036)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1192032), hAPP(_1192040, _1192038)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1192034, _1192032), _1192040), _1192036)))], (40858 ^ _777959) ^ [_1572684, _1572686, _1572688, _1572690] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1572684), tc_List_Olist(_1572684))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1572684), tc_List_Olist(_1572684)), _1572686), _1572688)), c_List_Olexord(_1572684, _1572690)))), 40859 ^ _777959 : [(40866 ^ _777959) ^ [_1572991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1572991), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572684)), _1572686)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572684)), _1572688)))), hAPP(hAPP(c_List_Otake(_1572684), _1572991), _1572686) = hAPP(hAPP(c_List_Otake(_1572684), _1572991), _1572688), hBOOL(hAPP(hAPP(c_member(tc_prod(_1572684, _1572684)), hAPP(hAPP(c_Product__Type_OPair(_1572684, _1572684), hAPP(hAPP(c_List_Onth(_1572684), _1572686), _1572991)), hAPP(hAPP(c_List_Onth(_1572684), _1572688), _1572991))), _1572690))], (40860 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572684)), _1572686)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572684)), _1572688))), hAPP(hAPP(c_List_Otake(_1572684), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1572684)), _1572686)), _1572688) = _1572686]]], (46810 ^ _777959) ^ [_1714905, _1714907, _1714909, _1714911, _1714913, _1714915, _1714917] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1714905, _1714907, _1714909), _1714911), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1714913, tc_fun(tc_prod(_1714907, _1714909), tc_HOL_Obool)), _1714915), _1714917)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1714913, tc_fun(tc_prod(_1714905, _1714909), tc_HOL_Obool)), _1714915), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1714907, _1714909), tc_HOL_Obool), tc_fun(tc_prod(_1714905, _1714909), tc_HOL_Obool), _1714913), hAPP(c_Relation_Orel__comp(_1714905, _1714907, _1714909), _1714911)), _1714917)))], (7968 ^ _777959) ^ [_913839, _913841, _913843] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913839, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913839, tc_HOL_Obool)), _913841), _913843)), _913841)))], (15799 ^ _777959) ^ [_1078428, _1078430] : [class_Groups_Olinordered__ab__group__add(_1078428), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078428), _1078430)), -(_1078430 = c_Orderings_Obot__class_Obot(tc_fun(_1078428, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1078428), c_Big__Operators_Olinorder__class_OMin(_1078428, _1078430)) = c_Big__Operators_Olinorder__class_OMax(_1078428, hAPP(c_Set_Oimage(_1078428, _1078428, c_Groups_Ouminus__class_Ouminus(_1078428)), _1078430)))], (6617 ^ _777959) ^ [_885097, _885099, _885101] : [_885101 = hAPP(c_Option_Ooption_OSome(_885097), _885099), -(hBOOL(hAPP(hAPP(c_member(_885097), _885099), c_Option_Oset(_885097, _885101))))], (47210 ^ _777959) ^ [_1724975, _1724977, _1724979, _1724981, _1724983] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1724975, _1724977)), hAPP(hAPP(c_Product__Type_OPair(_1724975, _1724977), _1724979), _1724981)), _1724983)), -(hBOOL(hAPP(hAPP(c_member(_1724977), _1724981), hAPP(c_Relation_ORange(_1724975, _1724977), _1724983))))], (11058 ^ _777959) ^ [_974584, _974586, _974588, _974590, _974592] : [-(hBOOL(hAPP(hAPP(c_member(_974584), _974586), _974588))), -(hAPP(c_Map_Orestrict__map(_974584, _974590, _974592, _974588), _974586) = c_Option_Ooption_ONone(_974590))], (50502 ^ _777959) ^ [_1802789, _1802791, _1802793, _1802795, _1802797] : [c_List_Oreplicate(_1802789, _1802791, _1802793) = c_List_Oreplicate(_1802789, _1802795, _1802797), 50505 ^ _777959 : [(50508 ^ _777959) ^ [] : [-(_1802791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1802793 = _1802797)], (50506 ^ _777959) ^ [] : [-(_1802791 = _1802795)]]], (3122 ^ _777959) ^ [_824773, _824775, _824777, _824779, _824781, _824783, _824785, _824787, _824789, _824791] : [-(c_List_Olinorder__class_Oinsort__insert__key(_824791, _824787, _824783, _824779, _824775) = c_List_Olinorder__class_Oinsort__insert__key(_824789, _824785, _824781, _824777, _824773)), _824791 = _824789, _824787 = _824785, _824783 = _824781, _824779 = _824777, _824775 = _824773], (21600 ^ _777959) ^ [_1188382, _1188384] : [21601 ^ _777959 : [(21604 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1188382), _1188384)))], (21602 ^ _777959) ^ [] : [_1188384 = c_Orderings_Obot__class_Obot(tc_fun(_1188382, tc_HOL_Obool))]], -(hAPP(c_Finite__Set_Ocard(_1188382), _1188384) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (40427 ^ _777959) ^ [_1562676, _1562678, _1562680, _1562682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1562676), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562678)), _1562680))), 40430 ^ _777959 : [(40437 ^ _777959) ^ [] : [hAPP(hAPP(c_List_Onth(_1562678), _1562680), _1562676) = _1562682, -(hAPP(hAPP(c_List_Olist__update(_1562678, _1562680), _1562676), _1562682) = _1562680)], (40431 ^ _777959) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1562678, _1562680), _1562676), _1562682) = _1562680, -(hAPP(hAPP(c_List_Onth(_1562678), _1562680), _1562676) = _1562682)]]], (44326 ^ _777959) ^ [_1659392, _1659394] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1659392, _1659394)))], (50880 ^ _777959) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (33109 ^ _777959) ^ [_1403126, _1403128, _1403130] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403126))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403126)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403128)), _1403130)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403128)), _1403130))], (5789 ^ _777959) ^ [_869650, _869652, _869654, _869656] : [_869656 = c_Orderings_Obot__class_Obot(tc_fun(_869650, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_869650, _869652, _869654), _869656) = c_Orderings_Obot__class_Obot(tc_fun(_869652, tc_HOL_Obool)))], (44583 ^ _777959) ^ [_1664062, _1664064, _1664066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1664062), _1664064)), _1664066)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1664062, _1664066)), _1664064) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1664062), _1664064))], (28636 ^ _777959) ^ [_1317431, _1317433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1317431), hAPP(c_Nat_OSuc, _1317433))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1317431, hAPP(c_Nat_OSuc, _1317433)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1317433)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1317431, _1317433)))], (34243 ^ _777959) ^ [_1422650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1422650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1422650))))], (46566 ^ _777959) ^ [_1708327, _1708329, _1708331, _1708333, _1708335] : [46568 ^ _777959 : [(46571 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1708327, _1708329, tc_HOL_Obool), _1708335), 46567 ^ [_1708327, _1708329, _1708331, _1708333, _1708335]))], (46569 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1708327, _1708329)), 46567 ^ [_1708327, _1708329, _1708331, _1708333, _1708335]), hAPP(c_List_Oset(tc_prod(_1708327, _1708329)), hAPP(hAPP(c_List_Ozip(_1708327, _1708329), _1708331), _1708333)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708327)), _1708331) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708329)), _1708333), -(c_List_Olist__all2(_1708327, _1708329, _1708335, _1708331, _1708333))], (17539 ^ _777959) ^ [_1113109, _1113111, _1113113, _1113115, _1113117, _1113119, _1113121] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1113109, _1113111, _1113113, _1113115, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1113109, tc_HOL_Obool)), _1113117), hAPP(hAPP(c_Set_Oinsert(_1113109), _1113119), c_Orderings_Obot__class_Obot(tc_fun(_1113109, tc_HOL_Obool))))), _1113121)), hBOOL(hAPP(hAPP(c_member(_1113109), _1113119), _1113117)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1113109, _1113111, _1113113, _1113115, _1113117), hAPP(hAPP(_1113113, _1113119), _1113121))))], (48549 ^ _777959) ^ [_1756127, _1756129] : [-(c_Transitive__Closure_Otrancl(_1756127, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1756127, _1756127), tc_HOL_Obool)), _1756129), c_Relation_OId(_1756127))) = c_Transitive__Closure_Ortrancl(_1756127, _1756129))], (31929 ^ _777959) ^ [_1380779, _1380781] : [class_Int_Onumber__ring(_1380779), 31932 ^ _777959 : [(31939 ^ _777959) ^ [] : [-(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), _1380781)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1380779), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1380781)) = c_Groups_Ozero__class_Ozero(_1380779))], (31933 ^ _777959) ^ [] : [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), _1380781))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1380779), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1380781)) = hAPP(c_Int_Onumber__class_Onumber__of(_1380779), _1380781))]]], (2740 ^ _777959) ^ [_818786, _818788, _818790, _818792, _818794, _818796] : [-(c_Hoare__Mirabelle_Opeek__and(_818796, _818792, _818788) = c_Hoare__Mirabelle_Opeek__and(_818794, _818790, _818786)), _818796 = _818794, _818792 = _818790, _818788 = _818786], (36990 ^ _777959) ^ [_1481571, _1481573, _1481575, _1481577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1481571), _1481573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1481575), _1481577)), -(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), _1481571), _1481575)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1481573), _1481577))), c_FunDef_Opair__leq)))], (8280 ^ _777959) ^ [_920930, _920932, _920934, _920936, _920938, _920940] : [-(hBOOL(hAPP(hAPP(c_member(_920930), _920932), _920934))), -(hAPP(c_Set_Oimage(_920930, _920936, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_920930, _920936), _920938), _920932), _920940)), _920934) = hAPP(c_Set_Oimage(_920930, _920936, _920938), _920934))], (30205 ^ _777959) ^ [_1349153, _1349155, _1349157] : [class_Divides_Osemiring__div(_1349153), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349153), _1349155), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1349153), _1349157), _1349155))), c_Divides_Odiv__class_Omod(_1349153, _1349157, _1349155)) = _1349157)], (7064 ^ _777959) ^ [_895808, _895810, _895812] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895808, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_895808, tc_fun(_895808, tc_HOL_Obool), tc_HOL_Obool), c_member(_895808)), _895810)), hAPP(hAPP(c_COMBC(_895808, tc_fun(_895808, tc_HOL_Obool), tc_HOL_Obool), c_member(_895808)), _895812))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_895808, tc_HOL_Obool)), _895810), _895812)))], (35021 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (29818 ^ _777959) ^ [_1341560, _1341562, _1341564] : [class_Fields_Olinordered__field__inverse__zero(_1341560), 29824 ^ _777959 : [(29829 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341560), 29823 ^ [_1341560, _1341562, _1341564]), _1341562)), _1341564))], (29827 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341560), 29823 ^ [_1341560, _1341562, _1341564]), c_Groups_Oone__class_Oone(_1341560))))], (29825 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341560), c_Groups_Ozero__class_Ozero(_1341560)), 29823 ^ [_1341560, _1341562, _1341564])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341560), _1341562), _1341564)))], (48124 ^ _777959) ^ [_1746922, _1746924, _1746926] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1746922), _1746924))), -(c_Random_Ominus__shift(_1746926, _1746922, _1746924) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1746922), _1746924))], (49673 ^ _777959) ^ [_1785081, _1785083, _1785085, _1785087] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785081, _1785083)), _1785085), hAPP(c_Relation_Oconverse(_1785083, _1785081), _1785087))), 49678 ^ _777959 : [(49681 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785083, _1785081)), hAPP(hAPP(c_Product__Type_OPair(_1785083, _1785081), 49676 ^ [_1785081, _1785083, _1785085, _1785087]), 49677 ^ [_1785081, _1785083, _1785085, _1785087])), _1785087)))], (49679 ^ _777959) ^ [] : [-(_1785085 = hAPP(hAPP(c_Product__Type_OPair(_1785081, _1785083), 49677 ^ [_1785081, _1785083, _1785085, _1785087]), 49676 ^ [_1785081, _1785083, _1785085, _1785087]))]]], (6704 ^ _777959) ^ [_886850, _886852] : [6705 ^ _777959 : [(6706 ^ _777959) ^ [_886903] : [hBOOL(hAPP(hAPP(c_member(_886850), _886903), _886852))]], _886852 = c_Orderings_Obot__class_Obot(tc_fun(_886850, tc_HOL_Obool))], (42752 ^ _777959) ^ [_1624789, _1624791, _1624793, _1624795] : [-(hAPP(hAPP(c_List_Oappend(_1624789), hAPP(hAPP(c_List_Olist_OCons(_1624789), _1624791), _1624793)), _1624795) = hAPP(hAPP(c_List_Olist_OCons(_1624789), _1624791), hAPP(hAPP(c_List_Oappend(_1624789), _1624793), _1624795)))], (35828 ^ _777959) ^ [_1457501, _1457503, _1457505, _1457507, _1457509, _1457511, _1457513, _1457515] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1457501, _1457503, _1457505), _1457507), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1457509, _1457511, tc_prod(_1457501, _1457503)), _1457513), _1457515)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1457509, _1457511, _1457505), hAPP(hAPP(c_COMBB(tc_fun(_1457511, tc_prod(_1457501, _1457503)), tc_fun(_1457511, _1457505), _1457509), hAPP(c_COMBB(tc_prod(_1457501, _1457503), _1457505, _1457511), hAPP(c_Product__Type_Oprod_Oprod__case(_1457501, _1457503, _1457505), _1457507))), _1457513)), _1457515))], (22902 ^ _777959) ^ [_1214726, _1214728, _1214730] : [class_Rings_Olinordered__semidom(_1214726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1214728), _1214730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214726), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1214726), _1214728)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1214726), _1214730))))], (47015 ^ _777959) ^ [_1720601] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1720601)))], (31332 ^ _777959) ^ [_1369834, _1369836, _1369838] : [class_Groups_Oordered__ab__group__add__abs(_1369834), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369834), hAPP(c_Groups_Oabs__class_Oabs(_1369834), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1369834), _1369836), _1369838))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1369834), hAPP(c_Groups_Oabs__class_Oabs(_1369834), _1369836)), hAPP(c_Groups_Oabs__class_Oabs(_1369834), _1369838)))))], (45266 ^ _777959) ^ [_1680303, _1680305] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680303)), c_List_Oremdups(_1680303, _1680305))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680303)), _1680305))))], (11575 ^ _777959) ^ [_985022, _985024, _985026, _985028, _985030] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985022, tc_fun(_985024, tc_HOL_Obool)), _985026), _985028), _985030)), 11579 ^ _777959 : [(11582 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_985028, 11578 ^ [_985022, _985024, _985026, _985028, _985030]), _985030)))], (11580 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_985022), 11578 ^ [_985022, _985024, _985026, _985028, _985030]), _985026)))]]], (22709 ^ _777959) ^ [_1211091] : [_1211091 = 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), _1211091)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (42987 ^ _777959) ^ [_1629814, _1629816, _1629818, _1629820] : [-(hAPP(hAPP(c_List_Onth(_1629814), hAPP(hAPP(c_List_Oappend(_1629814), _1629816), _1629818)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629814)), _1629816)), _1629820)) = hAPP(hAPP(c_List_Onth(_1629814), _1629818), _1629820))], (24532 ^ _777959) ^ [_1243814, _1243816] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243814)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1243816)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1243814), _1243816))], (27323 ^ _777959) ^ [_1295000, _1295002, _1295004, _1295006] : [class_Orderings_Olinorder(_1295000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295000), _1295002), _1295004)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1295000), _1295004), _1295006)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1295000, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1295000, _1295002, _1295004)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1295000, _1295004, _1295006)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1295000, _1295002, _1295006))], (10458 ^ _777959) ^ [_962790, _962792, _962794, _962796, _962798] : [c_Finite__Set_Ofolding__one(_962790, _962792, _962794), hBOOL(hAPP(c_Finite__Set_Ofinite(_962790), _962796)), -(_962796 = c_Orderings_Obot__class_Obot(tc_fun(_962790, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_962790), _962798)), -(_962798 = c_Orderings_Obot__class_Obot(tc_fun(_962790, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962790, tc_HOL_Obool)), _962796), _962798) = c_Orderings_Obot__class_Obot(tc_fun(_962790, tc_HOL_Obool)), -(hAPP(_962794, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962790, tc_HOL_Obool)), _962796), _962798)) = hAPP(hAPP(_962792, hAPP(_962794, _962796)), hAPP(_962794, _962798)))], (45614 ^ _777959) ^ [_1688231, _1688233, _1688235, _1688237] : [-(hAPP(c_List_Oset(tc_prod(_1688231, _1688233)), c_Enum_Oproduct(_1688231, _1688233, _1688235, _1688237)) = hAPP(hAPP(c_Product__Type_OSigma(_1688231, _1688233), hAPP(c_List_Oset(_1688231), _1688235)), hAPP(c_COMBK(tc_fun(_1688233, tc_HOL_Obool), _1688231), hAPP(c_List_Oset(_1688233), _1688237))))], (14881 ^ _777959) ^ [_1059404, _1059406, _1059408, _1059410] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1059404), hAPP(c_Set_OCollect(_1059404), _1059406))), 14884 ^ _777959 : [(14885 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1059408), hAPP(c_Set_OCollect(_1059408), hAPP(hAPP(c_COMBB(tc_fun(_1059404, tc_HOL_Obool), tc_HOL_Obool, _1059408), c_HOL_OEx(_1059404)), hAPP(hAPP(c_COMBB(tc_fun(_1059404, tc_HOL_Obool), tc_fun(_1059404, tc_HOL_Obool), _1059408), hAPP(c_COMBS(_1059404, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1059404), c_fconj), _1059406))), _1059410))))), 14888 ^ _777959 : [(14889 ^ _777959) ^ [_1059687] : [hBOOL(hAPP(_1059406, _1059687)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1059408), hAPP(c_Set_OCollect(_1059408), hAPP(hAPP(c_COMBC(_1059408, _1059404, tc_HOL_Obool), _1059410), _1059687)))))]]], (14895 ^ _777959) ^ [] : [14897 ^ _777959 : [(14900 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1059408), hAPP(c_Set_OCollect(_1059408), hAPP(hAPP(c_COMBC(_1059408, _1059404, tc_HOL_Obool), _1059410), 14896 ^ [_1059404, _1059406, _1059408, _1059410]))))], (14898 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1059406, 14896 ^ [_1059404, _1059406, _1059408, _1059410])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1059408), hAPP(c_Set_OCollect(_1059408), hAPP(hAPP(c_COMBB(tc_fun(_1059404, tc_HOL_Obool), tc_HOL_Obool, _1059408), c_HOL_OEx(_1059404)), hAPP(hAPP(c_COMBB(tc_fun(_1059404, tc_HOL_Obool), tc_fun(_1059404, tc_HOL_Obool), _1059408), hAPP(c_COMBS(_1059404, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1059404), c_fconj), _1059406))), _1059410))))))]]], (29705 ^ _777959) ^ [_1338367, _1338369] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1338367, tc_HOL_Obool)), _1338369), hAPP(c_Set_OPow(_1338367), _1338369))))], (35305 ^ _777959) ^ [_1441785, _1441787] : [-(_1441785 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1441787, _1441785), c_Divides_Odivmod__int(_1441787, _1441785))))], (7760 ^ _777959) ^ [_909694, _909696, _909698, _909700, _909702] : [c_Finite__Set_Ofolding__one(_909694, _909696, _909698), hBOOL(hAPP(c_Finite__Set_Ofinite(_909694), _909700)), hBOOL(hAPP(hAPP(c_member(_909694), _909702), _909700)), 7771 ^ _777959 : [(7778 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909694, tc_HOL_Obool)), _909700), hAPP(hAPP(c_Set_Oinsert(_909694), _909702), c_Orderings_Obot__class_Obot(tc_fun(_909694, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_909694, tc_HOL_Obool))), -(hAPP(_909698, _909700) = hAPP(hAPP(_909696, _909702), hAPP(_909698, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909694, tc_HOL_Obool)), _909700), hAPP(hAPP(c_Set_Oinsert(_909694), _909702), c_Orderings_Obot__class_Obot(tc_fun(_909694, tc_HOL_Obool)))))))], (7772 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_909694, tc_HOL_Obool)), _909700), hAPP(hAPP(c_Set_Oinsert(_909694), _909702), c_Orderings_Obot__class_Obot(tc_fun(_909694, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_909694, tc_HOL_Obool)), -(hAPP(_909698, _909700) = _909702)]]], (34477 ^ _777959) ^ [_1426949] : [-(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)))), _1426949) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1426949)))], (5410 ^ _777959) ^ [_860695, _860697, _860699, _860701, _860703, _860705] : [-(c_List_Oreplicate(_860705, _860701, _860697) = c_List_Oreplicate(_860703, _860699, _860695)), _860705 = _860703, _860701 = _860699, _860697 = _860695], (47282 ^ _777959) ^ [_1727211, _1727213, _1727215, _1727217, _1727219] : [hBOOL(hAPP(hAPP(_1727211, _1727213), _1727215)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1727217, _1727219, _1727211), _1727215)))], (4854 ^ _777959) ^ [_851955, _851957, _851959, _851961, _851963, _851965] : [-(c_Lazy__Sequence_Obind(_851965, _851961, _851957) = c_Lazy__Sequence_Obind(_851963, _851959, _851955)), _851965 = _851963, _851961 = _851959, _851957 = _851955], (24352 ^ _777959) ^ [_1240663] : [hBOOL(hAPP(_1240663, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 24353 ^ [_1240663]))), 24356 ^ _777959 : [(24357 ^ _777959) ^ [_1240763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240763)), -(hBOOL(hAPP(_1240663, _1240763)))]]], (35693 ^ _777959) ^ [_1454583, _1454585, _1454587, _1454589, _1454591] : [hBOOL(hAPP(hAPP(_1454583, _1454585), _1454587)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1454589, _1454591, tc_HOL_Obool), _1454583), hAPP(hAPP(c_Product__Type_OPair(_1454589, _1454591), _1454585), _1454587))))], (6889 ^ _777959) ^ [_890518, _890520, _890522, _890524] : [hAPP(c_Com_Ocom_OBODY, _890518) = c_Com_Ocom_OCall(_890520, _890522, _890524)], (25516 ^ _777959) ^ [_1261645, _1261647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1261645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1261647), _1261645))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1261647), _1261645) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1261647), _1261645)), _1261645)))], (43021 ^ _777959) ^ [_1630729, _1630731, _1630733, _1630735, _1630737, _1630739] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1630729), tc_List_Olist(_1630729))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1630729), tc_List_Olist(_1630729)), hAPP(hAPP(c_List_Oappend(_1630729), _1630731), _1630737)), hAPP(hAPP(c_List_Oappend(_1630729), _1630733), _1630739))), c_List_Olistrel1(_1630729, _1630735)))), 43022 ^ _777959 : [(43029 ^ _777959) ^ [] : [_1630731 = _1630733, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1630729), tc_List_Olist(_1630729))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1630729), tc_List_Olist(_1630729)), _1630737), _1630739)), c_List_Olistrel1(_1630729, _1630735)))], (43023 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1630729), tc_List_Olist(_1630729))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1630729), tc_List_Olist(_1630729)), _1630731), _1630733)), c_List_Olistrel1(_1630729, _1630735))), _1630737 = _1630739]]], (50019 ^ _777959) ^ [_1792297, _1792299] : [-(c_FunDef_Ois__measure(_1792297, _1792299))], (1040 ^ _777959) ^ [_793683, _793685] : [-(class_Groups_Olinordered__ab__group__add(_793683)), _793685 = _793683, class_Groups_Olinordered__ab__group__add(_793685)], (44551 ^ _777959) ^ [_1663368, _1663370, _1663372, _1663374, _1663376, _1663378] : [class_Orderings_Olinorder(_1663368), c_List_Olinorder__class_Osorted(_1663368, hAPP(hAPP(c_List_Omap(_1663370, _1663368), _1663372), _1663374)), hBOOL(hAPP(_1663376, _1663378)), -(hAPP(c_List_Ofilter(_1663370, _1663376), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1663370, _1663368, _1663372), _1663378), _1663374)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1663370, _1663368, _1663372), _1663378), hAPP(c_List_Ofilter(_1663370, _1663376), _1663374)))], (50238 ^ _777959) ^ [_1796232, _1796234, _1796236, _1796238, _1796240] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1796232, _1796234, _1796236, _1796238, _1796240) = hAPP(c_Option_Ooption_Ooption__case(_1796232, tc_prod(_1796234, tc_Lazy__Sequence_Olazy__sequence(_1796234)), _1796236, hAPP(c_Product__Type_Oprod_Oprod__case(_1796234, tc_Lazy__Sequence_Olazy__sequence(_1796234), _1796232), _1796238)), hAPP(c_Lazy__Sequence_Oyield(_1796234), _1796240)))], (45018 ^ _777959) ^ [_1674172, _1674174, _1674176] : [c_List_Oconcat(_1674172, _1674174) = c_List_Oconcat(_1674172, _1674176), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1674172))), _1674174) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1674172))), _1674176), 45028 ^ _777959 : [(45031 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1674172), tc_List_Olist(_1674172), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1674172), tc_fun(tc_List_Olist(_1674172), tc_Nat_Onat), tc_fun(tc_List_Olist(_1674172), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1674172), tc_Nat_Onat), tc_fun(tc_List_Olist(_1674172), tc_HOL_Obool)), tc_List_Olist(_1674172)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1674172))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1674172)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1674172))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1674172)))), 45027 ^ [_1674172, _1674174, _1674176]))], (45029 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1674172), tc_List_Olist(_1674172))), 45027 ^ [_1674172, _1674174, _1674176]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1674172), tc_List_Olist(_1674172))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1674172), tc_List_Olist(_1674172)), _1674174), _1674176)))))]], -(_1674174 = _1674176)], (41555 ^ _777959) ^ [_1592689, _1592691, _1592693, _1592695] : [-(hAPP(hAPP(c_List_Onth(_1592689), hAPP(hAPP(c_List_Olist_OCons(_1592689), _1592691), _1592693)), _1592695) = c_Nat_Onat_Onat__case(_1592689, _1592691, hAPP(c_List_Onth(_1592689), _1592693), _1592695))], (30677 ^ _777959) ^ [_1357709] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1357709, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29120 ^ _777959) ^ [_1326775, _1326777, _1326779, _1326781] : [class_Orderings_Olinorder(_1326775), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326775, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1326775, _1326777, _1326779)), hAPP(c_SetInterval_Oord__class_OatLeast(_1326775), _1326781)) = c_SetInterval_Oord__class_OatLeastAtMost(_1326775, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1326775), _1326777), _1326781), _1326779))], (38052 ^ _777959) ^ [_1506929, _1506931, _1506933, _1506935] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1506929), hAPP(c_Set_Oimage(_1506931, _1506929, _1506933), _1506935))), c_Fun_Oinj__on(_1506931, _1506929, _1506933, _1506935), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1506931), _1506935)))], (24385 ^ _777959) ^ [] : [-(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))))], (9018 ^ _777959) ^ [_933007, _933009, _933011] : [class_Orderings_Olinorder(_933007), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933007), _933009), _933011)), 9025 ^ _777959 : [(9032 ^ _777959) ^ [] : [_933009 = _933011, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933007), _933009), _933011))], (9026 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933007), _933009), _933011))), -(_933009 = _933011)]]], (28398 ^ _777959) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)))], (41719 ^ _777959) ^ [_1597956, _1597958, _1597960, _1597962, _1597964, _1597966, _1597968] : [-(hAPP(c_Product__Type_Osnd(_1597956, _1597958), hAPP(c_Product__Type_Omap__pair(_1597960, _1597956, _1597962, _1597958, _1597964, _1597966), _1597968)) = hAPP(_1597966, hAPP(c_Product__Type_Osnd(_1597960, _1597962), _1597968)))], (38340 ^ _777959) ^ [_1512689] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1512689)), c_Int_OInteg)))], (23549 ^ _777959) ^ [_1226162, _1226164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226162), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1226164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226162), _1226164)))], (48677 ^ _777959) ^ [_1759296, _1759298, _1759300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1759296, _1759296), tc_HOL_Obool)), _1759298), c_Transitive__Closure_Ortrancl(_1759296, _1759300))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1759296, _1759296), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1759296, _1759298)), c_Transitive__Closure_Ortrancl(_1759296, _1759300))))], (5592 ^ _777959) ^ [_863416, _863418, _863420, _863422, _863424, _863426] : [-(c_Map_Odom(_863426, _863422, _863418) = c_Map_Odom(_863424, _863420, _863416)), _863426 = _863424, _863422 = _863420, _863418 = _863416], (13536 ^ _777959) ^ [_1026331, _1026333] : [-(hBOOL(hAPP(_1026333, 13537 ^ [_1026331, _1026333]))), -(hAPP(c_Set_OCollect(_1026331), _1026333) = c_Orderings_Obot__class_Obot(tc_fun(_1026331, tc_HOL_Obool)))], (34419 ^ _777959) ^ [_1426002, _1426004] : [class_Int_Onumber__ring(_1426002), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1426002), _1426004), hAPP(c_Int_Onumber__class_Onumber__of(_1426002), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426002), _1426004), _1426004))], (10284 ^ _777959) ^ [_958935, _958937, _958939, _958941] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_958935), _958937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958935, tc_HOL_Obool)), _958937), _958939)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_958935, tc_Nat_Onat), _958941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958935, tc_HOL_Obool)), _958939), _958937)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_958935, tc_Nat_Onat), _958941), _958939)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_958935, tc_Nat_Onat), _958941), _958937)))], (12884 ^ _777959) ^ [_1011809, _1011811] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1011809), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1011809, tc_HOL_Obool), _1011811))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1011809, tc_HOL_Obool)), _1011811)))], (13451 ^ _777959) ^ [_1024697] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1024697), c_Orderings_Otop__class_Otop(tc_fun(_1024697, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1024697)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1024697), tc_HOL_Obool)))))], (31010 ^ _777959) ^ [_1363800] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1363800)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1363800))], (19108 ^ _777959) ^ [_1145231] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1145231)))], (51322 ^ _777959) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (3724 ^ _777959) ^ [_834286, _834288, _834290, _834292] : [-(c_Complete__Lattice_OInf__class_OInf(_834292, _834288) = c_Complete__Lattice_OInf__class_OInf(_834290, _834286)), _834292 = _834290, _834288 = _834286], (16933 ^ _777959) ^ [_1101997, _1101999, _1102001, _1102003] : [class_Orderings_Olinorder(_1101997), 16936 ^ _777959 : [(16937 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101997), _1101999), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1101997), _1102001), _1102003))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101997), _1101999), _1102001))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101997), _1101999), _1102003)))], (16947 ^ _777959) ^ [] : [16948 ^ _777959 : [(16951 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101997), _1101999), _1102003))], (16949 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101997), _1101999), _1102001))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101997), _1101999), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1101997), _1102001), _1102003))))]]], (45582 ^ _777959) ^ [_1687340, _1687342, _1687344] : [-(hAPP(c_List_Oset(tc_List_Olist(_1687340)), c_Enum_On__lists(_1687340, _1687342, _1687344)) = hAPP(c_Set_OCollect(tc_List_Olist(_1687340)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1687340), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1687340)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687340), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1687340)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1687340)))), _1687342))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1687340), tc_fun(_1687340, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1687340, tc_HOL_Obool), tc_fun(tc_fun(_1687340, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1687340)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1687340, tc_HOL_Obool))), c_List_Oset(_1687340))), hAPP(c_List_Oset(_1687340), _1687344)))))], (29524 ^ _777959) ^ [_1334682, _1334684, _1334686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334682)), 29530 ^ _777959 : [(29533 ^ _777959) ^ [] : [hBOOL(hAPP(_1334684, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 29529 ^ [_1334682, _1334684, _1334686]), _1334682)))], (29531 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1334684, 29529 ^ [_1334682, _1334684, _1334686])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334686)), 29538 ^ _777959 : [(29539 ^ _777959) ^ [_1334971] : [hBOOL(hAPP(_1334684, _1334971)), -(hBOOL(hAPP(_1334684, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1334971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1334686), _1334682)))))]]], (19418 ^ _777959) ^ [_1150050, _1150052] : [class_Groups_Ogroup__add(_1150050), 19421 ^ _777959 : [(19428 ^ _777959) ^ [] : [_1150052 = c_Groups_Ozero__class_Ozero(_1150050), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1150050), _1150052) = c_Groups_Ozero__class_Ozero(_1150050))], (19422 ^ _777959) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1150050), _1150052) = c_Groups_Ozero__class_Ozero(_1150050), -(_1150052 = c_Groups_Ozero__class_Ozero(_1150050))]]], (49084 ^ _777959) ^ [_1769951, _1769953, _1769955] : [hAPP(hAPP(c_Relation_Orel__comp(_1769951, _1769951, _1769951), hAPP(c_Relation_Oconverse(_1769951, _1769951), _1769953)), _1769953) = _1769953, hAPP(c_Relation_ODomain(_1769951, _1769951), _1769953) = _1769955, -(c_Equiv__Relations_Oequiv(_1769951, _1769955, _1769953))], (38746 ^ _777959) ^ [_1521684, _1521686, _1521688, _1521690, _1521692] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521684, tc_HOL_Obool)), _1521686), _1521688)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1521690, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1521690, _1521684, _1521692), _1521686)), hAPP(c_Set_Ovimage(_1521690, _1521684, _1521692), _1521688))))], (51026 ^ _777959) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (15352 ^ _777959) ^ [_1070042, _1070044] : [class_Groups_Ocomm__monoid__mult(_1070042), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070042), _1070044), c_Groups_Oone__class_Oone(_1070042)) = _1070044)], (48362 ^ _777959) ^ [_1751138, _1751140] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1751138), _1751140) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1751138)), hAPP(c_Code__Numeral_Onat__of, _1751140))))], (3526 ^ _777959) ^ [_831137, _831139, _831141, _831143] : [-(c_List_Oremdups(_831143, _831139) = c_List_Oremdups(_831141, _831137)), _831143 = _831141, _831139 = _831137], (50021 ^ _777959) ^ [_1792322, _1792324] : [-(c_FunDef_Ois__measure(_1792322, _1792324))], (11212 ^ _777959) ^ [_977551, _977553, _977555, _977557, _977559] : [class_Groups_Ocomm__monoid__add(_977551), hBOOL(hAPP(c_Finite__Set_Ofinite(_977553), _977555)), hBOOL(hAPP(c_Finite__Set_Ofinite(_977553), _977557)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977551), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977553, _977551), _977559), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977553, tc_HOL_Obool)), _977555), _977557))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977553, _977551), _977559), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977553, tc_HOL_Obool)), _977555), _977557))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977551), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977553, _977551), _977559), _977555)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977553, _977551), _977559), _977557)))], (33233 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (15444 ^ _777959) ^ [_1071636, _1071638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1071636)), hAPP(c_Nat_OSuc, _1071638))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071636), _1071638)))], (34549 ^ _777959) ^ [_1428234, _1428236] : [class_Fields_Olinordered__field__inverse__zero(_1428234), class_Int_Onumber__ring(_1428234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428234), c_Groups_Ozero__class_Ozero(_1428234)), _1428236)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1428234), c_Groups_Ozero__class_Ozero(_1428234)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1428234), _1428236), hAPP(c_Int_Onumber__class_Onumber__of(_1428234), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (38392 ^ _777959) ^ [_1513911, _1513913, _1513915, _1513917, _1513919] : [c_Fun_Oinj__on(_1513911, _1513913, _1513915, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1513911, tc_HOL_Obool)), _1513917), _1513919)), 38395 ^ _777959 : [(38400 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1513913, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1513911, _1513913, _1513915), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1513911, tc_HOL_Obool)), _1513917), _1513919))), hAPP(c_Set_Oimage(_1513911, _1513913, _1513915), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1513911, tc_HOL_Obool)), _1513919), _1513917))) = c_Orderings_Obot__class_Obot(tc_fun(_1513913, tc_HOL_Obool)))], (38398 ^ _777959) ^ [] : [-(c_Fun_Oinj__on(_1513911, _1513913, _1513915, _1513919))], (38396 ^ _777959) ^ [] : [-(c_Fun_Oinj__on(_1513911, _1513913, _1513915, _1513917))]]], (20909 ^ _777959) ^ [_1175679, _1175681] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1175679), _1175681)), 20910 ^ _777959 : [(20917 ^ _777959) ^ [] : [_1175679 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1175681 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20911 ^ _777959) ^ [] : [_1175679 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175681 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (44398 ^ _777959) ^ [_1660477, _1660479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1660477), _1660479)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1660477, _1660479)) = _1660477)], (6425 ^ _777959) ^ [_881695, _881697, _881699, _881701] : [hBOOL(hAPP(hAPP(c_member(_881695), _881697), _881699)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881695, tc_HOL_Obool)), _881699), _881701)), -(hBOOL(hAPP(hAPP(c_member(_881695), _881697), _881701)))], (45290 ^ _777959) ^ [_1680709, _1680711] : [_1680711 = c_List_Olist_ONil(_1680709), -(c_List_Olist_ONil(_1680709) = c_List_Oremdups(_1680709, _1680711))], (44875 ^ _777959) ^ [_1670550, _1670552, _1670554] : [_1670552 = hAPP(c_List_Orev(_1670550), _1670554), -(hAPP(c_List_Orev(_1670550), _1670552) = _1670554)], (31582 ^ _777959) ^ [_1374343, _1374345, _1374347] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1374343, _1374345, _1374347))), 31585 ^ _777959 : [(31588 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1374347)))], (31586 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1374345)))]]], (6549 ^ _777959) ^ [_883811, _883813, _883815, _883817, _883819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883811, tc_HOL_Obool)), _883813), _883815)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883811, tc_HOL_Obool)), _883817), _883819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883811, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_883811, tc_HOL_Obool)), _883813), _883817)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_883811, tc_HOL_Obool)), _883815), _883819))))], (33959 ^ _777959) ^ [_1417774] : [class_Rings_Osemiring__1(_1417774), -(c_Int_Oiszero(_1417774, c_Groups_Ozero__class_Ozero(_1417774)))], (12171 ^ _777959) ^ [_998888, _998890, _998892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _998890), _998892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998888), _998890)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998888), _998892))))], (41517 ^ _777959) ^ [_1591818, _1591820, _1591822, _1591824, _1591826, _1591828] : [-(hAPP(hAPP(c_List_Ozip(_1591818, _1591820), hAPP(hAPP(c_List_Olist_OCons(_1591818), _1591822), _1591824)), hAPP(hAPP(c_List_Olist_OCons(_1591820), _1591826), _1591828)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1591818, _1591820)), hAPP(hAPP(c_Product__Type_OPair(_1591818, _1591820), _1591822), _1591826)), hAPP(hAPP(c_List_Ozip(_1591818, _1591820), _1591824), _1591828)))], (39828 ^ _777959) ^ [_1547872, _1547874, _1547876, _1547878, _1547880, _1547882, _1547884, _1547886] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1547872, _1547874), _1547876), _1547878), hAPP(hAPP(c_List_Ozip(_1547872, _1547874), hAPP(hAPP(c_List_Omap(_1547880, _1547872), _1547882), _1547884)), _1547886)) = hAPP(hAPP(c_List_Omap(tc_prod(_1547880, _1547874), _1547876), hAPP(c_Product__Type_Oprod_Oprod__case(_1547880, _1547874, _1547876), hAPP(hAPP(c_COMBB(tc_fun(_1547874, tc_prod(_1547872, _1547874)), tc_fun(_1547874, _1547876), _1547880), hAPP(c_COMBB(tc_prod(_1547872, _1547874), _1547876, _1547874), _1547878)), hAPP(hAPP(c_COMBB(_1547872, tc_fun(_1547874, tc_prod(_1547872, _1547874)), _1547880), c_Product__Type_OPair(_1547872, _1547874)), _1547882)))), hAPP(hAPP(c_List_Ozip(_1547880, _1547874), _1547884), _1547886)))], (37375 ^ _777959) ^ [_1491525, _1491527, _1491529, _1491531] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1491525, _1491525)), hAPP(hAPP(c_Product__Type_OPair(_1491525, _1491525), _1491527), _1491529)), c_Relation_OId__on(_1491525, _1491531))), 37378 ^ _777959 : [(37381 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1491525), _1491527), _1491531)))], (37379 ^ _777959) ^ [] : [-(_1491527 = _1491529)]]], (48419 ^ _777959) ^ [_1752147, _1752149, _1752151] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1752147, _1752147)), _1752149), _1752151)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1752147, _1752147)), _1752149), c_Transitive__Closure_Otrancl(_1752147, _1752151))))], (49985 ^ _777959) ^ [_1791645, _1791647, _1791649, _1791651] : [class_Rings_Olinordered__semidom(_1791645), 49991 ^ _777959 : [(49994 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1791645), c_Groups_Ozero__class_Ozero(_1791645)), hAPP(_1791651, 49990 ^ [_1791645, _1791647, _1791649, _1791651])))], (49992 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791647), 49990 ^ [_1791645, _1791647, _1791649, _1791651]), _1791649)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1791645), c_Groups_Ozero__class_Ozero(_1791645)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1791647, _1791645), _1791651), _1791649))))], (30066 ^ _777959) ^ [_1346527, _1346529, _1346531, _1346533] : [class_Divides_Oring__div(_1346527), -(c_Divides_Odiv__class_Omod(_1346527, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346527), _1346529), _1346531), _1346533) = c_Divides_Odiv__class_Omod(_1346527, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346527), _1346529), c_Divides_Odiv__class_Omod(_1346527, _1346531, _1346533)), _1346533))], (34991 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (1660 ^ _777959) ^ [_801433, _801435] : [-(class_Rings_Ozero__neq__one(_801433)), _801435 = _801433, class_Rings_Ozero__neq__one(_801435)], (45481 ^ _777959) ^ [_1684521, _1684523, _1684525] : [-(c_List_OdropWhile(_1684521, _1684523, _1684525) = hAPP(hAPP(c_List_Odrop(_1684521), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684521)), c_List_OtakeWhile(_1684521, _1684523, _1684525))), _1684525))], (2360 ^ _777959) ^ [_812856, _812858, _812860, _812862, _812864, _812866] : [-(c_Com_Ocom_OCall(_812866, _812862, _812858) = c_Com_Ocom_OCall(_812864, _812860, _812856)), _812866 = _812864, _812862 = _812860, _812858 = _812856], (1830 ^ _777959) ^ [_803558, _803560] : [-(class_Nat_Osize(_803558)), _803560 = _803558, class_Nat_Osize(_803560)], (9244 ^ _777959) ^ [_936781, _936783, _936785, _936787, _936789, _936791, _936793] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_936781, tc_Option_Ooption(_936783)), _936785), _936787), hAPP(c_Option_Ooption_OSome(_936783), _936789)), _936791) = hAPP(c_Option_Ooption_OSome(_936783), _936793)), 9245 ^ _777959 : [(9252 ^ _777959) ^ [] : [-(_936791 = _936787), hAPP(_936785, _936791) = hAPP(c_Option_Ooption_OSome(_936783), _936793)], (9246 ^ _777959) ^ [] : [_936791 = _936787, _936789 = _936793]]], (15751 ^ _777959) ^ [_1077611, _1077613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077611), hAPP(c_Nat_OSuc, _1077613))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1077611), _1077613)))], (19634 ^ _777959) ^ [_1153272, _1153274, _1153276] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1153272), _1153274) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1153276), _1153274), -(_1153272 = _1153276), -(_1153274 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5902 ^ _777959) ^ [_871716, _871718, _871720, _871722, _871724] : [c_Hoare__Mirabelle_Ohoare__derivs(_871716, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871716)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871716), _871718), hAPP(c_Com_Ocom_OBODY, _871720)), _871722)), _871724), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871716)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871716), _871718), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _871720))), _871722)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871716), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_871716, _871724, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871716)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871716), _871718), hAPP(c_Com_Ocom_OBODY, _871720)), _871722)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871716), tc_HOL_Obool)))))], (44428 ^ _777959) ^ [_1660992, _1660994] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1660992), _1660994) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1660992, _1660994)))], (26084 ^ _777959) ^ [_1272604, _1272606, _1272608] : [class_Fields_Ofield__inverse__zero(_1272604), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272604), hAPP(c_Groups_Ouminus__class_Ouminus(_1272604), _1272606)), hAPP(c_Groups_Ouminus__class_Ouminus(_1272604), _1272608)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272604), _1272606), _1272608))], (3478 ^ _777959) ^ [_830435, _830437] : [_830437 = _830435, -(c_Enum_Oenum__class_Oenum__ex(_830437) = c_Enum_Oenum__class_Oenum__ex(_830435))], (7426 ^ _777959) ^ [_902518, _902520, _902522] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_902518), hAPP(hAPP(c_Set_Oinsert(_902518), _902520), _902522))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_902518), _902522)))], (34771 ^ _777959) ^ [_1432072, _1432074, _1432076] : [class_Int_Onumber__ring(_1432072), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1432072), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432072), _1432074), _1432076)), 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(_1432072), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432072), hAPP(hAPP(c_Power_Opower__class_Opower(_1432072), _1432074), 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(_1432072), _1432076), 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(_1432072), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432072), hAPP(c_Int_Onumber__class_Onumber__of(_1432072), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1432074)), _1432076)))], (39874 ^ _777959) ^ [_1549523, _1549525, _1549527, _1549529, _1549531, _1549533] : [-(hAPP(hAPP(c_List_Ozip(_1549523, _1549525), _1549527), hAPP(hAPP(c_List_Omap(_1549529, _1549525), _1549531), _1549533)) = hAPP(hAPP(c_List_Omap(tc_prod(_1549523, _1549529), tc_prod(_1549523, _1549525)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549523, _1549529, tc_prod(_1549523, _1549525)), hAPP(hAPP(c_COMBC(_1549523, tc_fun(_1549529, _1549525), tc_fun(_1549529, tc_prod(_1549523, _1549525))), hAPP(hAPP(c_COMBB(tc_fun(_1549525, tc_prod(_1549523, _1549525)), tc_fun(tc_fun(_1549529, _1549525), tc_fun(_1549529, tc_prod(_1549523, _1549525))), _1549523), c_COMBB(_1549525, tc_prod(_1549523, _1549525), _1549529)), c_Product__Type_OPair(_1549523, _1549525))), _1549531))), hAPP(hAPP(c_List_Ozip(_1549523, _1549529), _1549527), _1549533)))], (28386 ^ _777959) ^ [_1313182, _1313184] : [c_Nat__Transfer_Ois__nat(_1313182), c_Nat__Transfer_Ois__nat(_1313184), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1313182), _1313184)))], (51108 ^ _777959) ^ [] : [-(class_HOL_Oequal(tc_Nat_Onat))], (43941 ^ _777959) ^ [_1651603, _1651605, _1651607, _1651609, _1651611] : [-(hAPP(c_List_Ofilter(_1651603, _1651605), hAPP(hAPP(c_List_Omap(_1651607, _1651603), _1651609), _1651611)) = hAPP(hAPP(c_List_Omap(_1651607, _1651603), _1651609), hAPP(c_List_Ofilter(_1651607, hAPP(c_Fun_Ocomp(_1651603, tc_HOL_Obool, _1651607, _1651605), _1651609)), _1651611)))], (46950 ^ _777959) ^ [_1719398, _1719400, _1719402, _1719404] : [c_Wellfounded_Owf(_1719398, _1719400), hBOOL(hAPP(hAPP(c_member(tc_prod(_1719398, _1719398)), hAPP(hAPP(c_Product__Type_OPair(_1719398, _1719398), _1719402), _1719404)), _1719400)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1719398, _1719398)), hAPP(hAPP(c_Product__Type_OPair(_1719398, _1719398), _1719404), _1719402)), _1719400))], (34051 ^ _777959) ^ [_1419279, _1419281] : [-(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), _1419279)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1419281)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1419279))) = 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), _1419281)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1419279)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35283 ^ _777959) ^ [_1441159] : [-(c_Int_Oint__ge__less__than2(_1441159) = 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), _1441159)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (23775 ^ _777959) ^ [_1230042, _1230044, _1230046] : [class_Groups_Omonoid__mult(_1230042), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1230042), _1230044), hAPP(c_Nat_OSuc, _1230046)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1230042), hAPP(hAPP(c_Power_Opower__class_Opower(_1230042), _1230044), _1230046)), _1230044))], (768 ^ _777959) ^ [_789781, _789783, _789785, _789787] : [-(c_Relation_Oirrefl(_789785, _789781)), c_Relation_Oirrefl(_789787, _789783), _789787 = _789785, _789783 = _789781], (19112 ^ _777959) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27173 ^ _777959) ^ [_1292680, _1292682] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1292680, _1292682))))], (24472 ^ _777959) ^ [_1242754, _1242756, _1242758, _1242760] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1242754, _1242756, _1242758), _1242760), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1242756)], (31640 ^ _777959) ^ [_1375367, _1375369, _1375371, _1375373, _1375375] : [c_Com_Ocom_OSemi(_1375367, _1375369) = c_Com_Ocom_OCond(_1375371, _1375373, _1375375)], (33901 ^ _777959) ^ [_1416506, _1416508] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416506)), hAPP(c_Nat_OSuc, _1416508)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1416506))), 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, _1416508))), 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)), _1416508)))))], (4498 ^ _777959) ^ [_846009, _846011] : [_846011 = _846009, -(c_Nat_Osemiring__1__class_Oof__nat(_846011) = c_Nat_Osemiring__1__class_Oof__nat(_846009))], (11120 ^ _777959) ^ [_975754] : [-(c_Option_Oset(_975754, c_Option_Ooption_ONone(_975754)) = c_Orderings_Obot__class_Obot(tc_fun(_975754, tc_HOL_Obool)))], (21364 ^ _777959) ^ [_1183939, _1183941, _1183943, _1183945, _1183947] : [class_Rings_Olinordered__semiring__strict(_1183939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183939), _1183941), _1183943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183939), _1183945), _1183947)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183939), c_Groups_Ozero__class_Ozero(_1183939)), _1183941)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183939), c_Groups_Ozero__class_Ozero(_1183939)), _1183945)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183939), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183939), _1183941), _1183945)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183939), _1183943), _1183947))))], (47719 ^ _777959) ^ [_1737558, _1737560, _1737562, _1737564] : [47721 ^ _777959 : [(47724 ^ _777959) ^ [] : [hBOOL(hAPP(_1737562, 47720 ^ [_1737558, _1737560, _1737562, _1737564]))], (47722 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1737558), 47720 ^ [_1737558, _1737560, _1737562, _1737564]), hAPP(c_List_Oset(_1737558), _1737560))))]], -(c_List_OtakeWhile(_1737558, _1737562, hAPP(hAPP(c_List_Oappend(_1737558), _1737560), _1737564)) = hAPP(hAPP(c_List_Oappend(_1737558), _1737560), c_List_OtakeWhile(_1737558, _1737562, _1737564)))], (21069 ^ _777959) ^ [_1178279, _1178281, _1178283] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1178279), _1178281)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1178283), _1178281)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1178281)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1178279), _1178283))], (1280 ^ _777959) ^ [_796683, _796685] : [-(class_Lattices_Obounded__lattice__top(_796683)), _796685 = _796683, class_Lattices_Obounded__lattice__top(_796685)], (14988 ^ _777959) ^ [_1063002, _1063004] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1063002), _1063004)), -(_1063004 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1063002, 14992 ^ [_1063002, _1063004]), 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)), 14991 ^ [_1063002, _1063004]))))], (30641 ^ _777959) ^ [_1357133, _1357135] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1357133), _1357135) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1357133, _1357135)), _1357135))], (3516 ^ _777959) ^ [_830988, _830990, _830992, _830994] : [-(c_List_Olist__update(_830994, _830990) = c_List_Olist__update(_830992, _830988)), _830994 = _830992, _830990 = _830988], (43207 ^ _777959) ^ [_1635836, _1635838] : [hAPP(c_List_Orotate1(_1635836), _1635838) = c_List_Olist_ONil(_1635836), -(_1635838 = c_List_Olist_ONil(_1635836))], (36562 ^ _777959) ^ [_1471471, _1471473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1471471)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1471473)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1471471, _1471473) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1471471, _1471473)))], (28768 ^ _777959) ^ [_1319925, _1319927, _1319929] : [class_Orderings_Oorder(_1319925), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319925, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1319925, _1319927, _1319929)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1319925), _1319929)) = c_Orderings_Obot__class_Obot(tc_fun(_1319925, tc_HOL_Obool)))], (49122 ^ _777959) ^ [_1770816, _1770818, _1770820] : [c_Relation_Ototal__on(_1770816, _1770818, _1770820), -(c_Relation_Ototal__on(_1770816, _1770818, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1770816, _1770816), tc_HOL_Obool)), _1770820), c_Relation_OId(_1770816))))], (12828 ^ _777959) ^ [_1010686, _1010688, _1010690] : [class_Groups_Ogroup__add(_1010686), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010686), hAPP(c_Groups_Ouminus__class_Ouminus(_1010686), _1010688)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010686), _1010688), _1010690)) = _1010690)], (13783 ^ _777959) ^ [_1032867, _1032869] : [class_Lattices_Obounded__lattice__top(_1032867), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1032867), c_Orderings_Otop__class_Otop(_1032867)), _1032869) = _1032869)], (3164 ^ _777959) ^ [_825468, _825470, _825472, _825474, _825476, _825478] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_825478, _825474, _825470) = c_SetInterval_Oord__class_OgreaterThanAtMost(_825476, _825472, _825468)), _825478 = _825476, _825474 = _825472, _825470 = _825468], (15833 ^ _777959) ^ [_1079017, _1079019, _1079021, _1079023, _1079025, _1079027, _1079029] : [c_Map_Omap__comp(_1079017, _1079019, _1079021, _1079023, _1079025, _1079027) = hAPP(c_Option_Ooption_OSome(_1079019), _1079029), 15837 ^ _777959 : [(15840 ^ _777959) ^ [] : [-(hAPP(_1079023, 15836 ^ [_1079017, _1079019, _1079021, _1079023, _1079025, _1079027, _1079029]) = hAPP(c_Option_Ooption_OSome(_1079019), _1079029))], (15838 ^ _777959) ^ [] : [-(hAPP(_1079025, _1079027) = hAPP(c_Option_Ooption_OSome(_1079017), 15836 ^ [_1079017, _1079019, _1079021, _1079023, _1079025, _1079027, _1079029]))]]], (34127 ^ _777959) ^ [_1420739, _1420741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1420739)), c_Int_OBit0(_1420741))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420739), _1420741)))], (10020 ^ _777959) ^ [_952325, _952327, _952329, _952331] : [hBOOL(hAPP(hAPP(c_member(_952325), _952327), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952325, tc_HOL_Obool)), _952329), _952331))), -(hBOOL(hAPP(hAPP(c_member(_952325), _952327), _952331)))], (26802 ^ _777959) ^ [_1285566, _1285568, _1285570, _1285572] : [class_Fields_Olinordered__field(_1285566), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285566), _1285568), _1285570)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285566), _1285572), c_Groups_Ozero__class_Ozero(_1285566))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285566), c_Groups_Ozero__class_Ozero(_1285566)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1285566), _1285568), _1285570))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285566), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285566), _1285572), _1285568)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1285566), _1285572), _1285570))))], (25052 ^ _777959) ^ [_1252473, _1252475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252473)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1252475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1252473), _1252475)), _1252473)))], (34177 ^ _777959) ^ [_1421521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1421521))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1421521)))], (20581 ^ _777959) ^ [_1170402] : [class_Rings_Olinordered__semidom(_1170402), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170402), c_Groups_Oone__class_Oone(_1170402)), c_Groups_Ozero__class_Ozero(_1170402)))], (8228 ^ _777959) ^ [_919814, _919816, _919818, _919820, _919822, _919824, _919826, _919828] : [c_Finite__Set_Ofolding__image__simple__idem(_919814, _919816, _919818, _919820, _919822, _919824), hBOOL(hAPP(c_Finite__Set_Ofinite(_919816), _919826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_919816, tc_HOL_Obool)), _919828), _919826)), -(hAPP(hAPP(_919818, hAPP(_919824, _919828)), hAPP(_919824, _919826)) = hAPP(_919824, _919826))], (27768 ^ _777959) ^ [_1302598, _1302600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1302598)), 27771 ^ _777959 : [(27778 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1302598), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1302600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1302598)), _1302600)))], (27772 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1302598)), _1302600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1302598), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1302600))))]]], (16191 ^ _777959) ^ [_1086969, _1086971, _1086973, _1086975, _1086977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1086969), _1086971)), 16194 ^ _777959 : [(16201 ^ _777959) ^ [] : [_1086975 = 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), _1086971), _1086969)), _1086973)), _1086977), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086969), _1086973)), _1086975) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086971), _1086973)), _1086977))], (16195 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086969), _1086973)), _1086975) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086971), _1086973)), _1086977), -(_1086975 = 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), _1086971), _1086969)), _1086973)), _1086977))]]], (10040 ^ _777959) ^ [_952775, _952777, _952779, _952781] : [-(hBOOL(hAPP(hAPP(c_member(_952775), _952777), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952775, tc_HOL_Obool)), _952779), _952781)))), hBOOL(hAPP(hAPP(c_member(_952775), _952777), _952779)), hBOOL(hAPP(hAPP(c_member(_952775), _952777), _952781))], (9066 ^ _777959) ^ [_933609, _933611, _933613] : [class_Orderings_Oorder(_933609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933609), _933611), _933613)), -(_933613 = _933611), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933609), _933611), _933613)))], (30020 ^ _777959) ^ [_1345632, _1345634, _1345636, _1345638] : [class_Divides_Osemiring__div(_1345632), -(c_Divides_Odiv__class_Omod(_1345632, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345632), _1345634), _1345636), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345632), _1345638), _1345636)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345632), c_Divides_Odiv__class_Omod(_1345632, _1345634, _1345638)), _1345636))], (50542 ^ _777959) ^ [_1803331, _1803333, _1803335, _1803337] : [50544 ^ _777959 : [(50547 ^ _777959) ^ [] : [hBOOL(hAPP(_1803337, 50543 ^ [_1803331, _1803333, _1803335, _1803337]))], (50545 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1803331), 50543 ^ [_1803331, _1803333, _1803335, _1803337]), hAPP(c_List_Oset(_1803331), c_List_Oreplicate(_1803331, _1803333, _1803335)))))]], -(hBOOL(hAPP(_1803337, _1803335))), -(_1803333 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27533 ^ _777959) ^ [_1298449, _1298451] : [_1298449 = hAPP(c_Int_Onat, _1298451), 27536 ^ _777959 : [(27543 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298451))), -(_1298449 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27537 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298451)), -(_1298451 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1298449))]]], (32987 ^ _777959) ^ [_1400955] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400955)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1400955))], (44545 ^ _777959) ^ [_1663257, _1663259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663257), _1663259)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1663257, _1663259)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1663259), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (50172 ^ _777959) ^ [_1794847, _1794849] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1794847), _1794849)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1794847)), c_Int_OBit1(_1794849))))], (15922 ^ _777959) ^ [_1081340, _1081342, _1081344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1081340), _1081342)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1081342), _1081340))), _1081344) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1081342)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1081340), _1081344)))], (50126 ^ _777959) ^ [_1794055] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1794055), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1794055)), c_Int_OMin)))], (46800 ^ _777959) ^ [_1714632, _1714634, _1714636, _1714638] : [hAPP(hAPP(c_Relation_Orel__comp(_1714632, _1714632, _1714632), _1714634), _1714636) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1714632, _1714632), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1714632, _1714632, _1714632), _1714634), _1714638) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1714632, _1714632), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1714632, _1714632, _1714632), _1714634), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1714632, _1714632), tc_HOL_Obool)), _1714636), _1714638)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1714632, _1714632), tc_HOL_Obool)))], (41097 ^ _777959) ^ [_1581436, _1581438, _1581440] : [c_Relation_Orefl__on(_1581436, _1581438, _1581440), 41100 ^ _777959 : [(41107 ^ _777959) ^ [_1581920] : [hBOOL(hAPP(hAPP(c_member(_1581436), _1581920), _1581438)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1581436, _1581436)), hAPP(hAPP(c_Product__Type_OPair(_1581436, _1581436), _1581920), _1581920)), _1581440)))], (41101 ^ _777959) ^ [_1581647] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1581436, _1581436)), _1581647), _1581440)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1581436, _1581436, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1581436, tc_fun(_1581436, tc_HOL_Obool), tc_fun(_1581436, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1581436, tc_HOL_Obool), tc_fun(_1581436, tc_HOL_Obool)), _1581436), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1581436)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1581436), c_fconj), hAPP(hAPP(c_COMBC(_1581436, tc_fun(_1581436, tc_HOL_Obool), tc_HOL_Obool), c_member(_1581436)), _1581438)))), hAPP(hAPP(c_COMBC(_1581436, tc_fun(_1581436, tc_HOL_Obool), tc_HOL_Obool), c_member(_1581436)), _1581438))), _1581647)))]]], (48304 ^ _777959) ^ [] : [-(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))], (40168 ^ _777959) ^ [_1556749, _1556751, _1556753] : [class_Orderings_Olinorder(_1556749), -(c_List_Oremove1(_1556749, _1556751, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1556749, _1556749, c_COMBI(_1556749)), _1556751), _1556753)) = _1556753)], (22956 ^ _777959) ^ [_1215710, _1215712, _1215714, _1215716] : [class_Rings_Osemiring__1(_1215710), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215710), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1215712, tc_Nat_Onat), _1215714), _1215716)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1215712, _1215710), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1215710, _1215712), c_Nat_Osemiring__1__class_Oof__nat(_1215710)), _1215714)), _1215716))], (8074 ^ _777959) ^ [_916062, _916064, _916066] : [-(hAPP(hAPP(c_Set_Oinsert(_916062), _916064), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916062, tc_HOL_Obool)), _916066), hAPP(hAPP(c_Set_Oinsert(_916062), _916064), c_Orderings_Obot__class_Obot(tc_fun(_916062, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_916062), _916064), _916066))], (44290 ^ _777959) ^ [_1658859, _1658861, _1658863] : [class_Orderings_Olinorder(_1658859), c_List_Olinorder__class_Osorted(_1658859, _1658861), -(c_List_Olinorder__class_Osorted(_1658859, hAPP(hAPP(c_List_Otake(_1658859), _1658863), _1658861)))], (7902 ^ _777959) ^ [_912434, _912436, _912438, _912440] : [hBOOL(hAPP(hAPP(c_member(_912434), _912436), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912434, tc_HOL_Obool)), _912438), _912440))), -(hBOOL(hAPP(hAPP(c_member(_912434), _912436), _912438)))], (43592 ^ _777959) ^ [_1644362, _1644364, _1644366] : [-(hAPP(c_List_Orotate(_1644362, _1644364), _1644366) = hAPP(hAPP(c_List_Oappend(_1644362), hAPP(hAPP(c_List_Odrop(_1644362), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1644364, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644362)), _1644366))), _1644366)), hAPP(hAPP(c_List_Otake(_1644362), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1644364, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644362)), _1644366))), _1644366)))], (19737 ^ _777959) ^ [_1155020, _1155022, _1155024] : [class_Groups_Oordered__comm__monoid__add(_1155020), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155020), _1155022), c_Groups_Ozero__class_Ozero(_1155020))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155020), _1155024), c_Groups_Ozero__class_Ozero(_1155020))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155020), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155020), _1155022), _1155024)), c_Groups_Ozero__class_Ozero(_1155020))))], (47232 ^ _777959) ^ [_1725488, _1725490] : [-(hAPP(c_Relation_ORange(_1725488, _1725488), c_Relation_OId__on(_1725488, _1725490)) = _1725490)], (25372 ^ _777959) ^ [_1258802, _1258804] : [25380 ^ _777959 : [(25383 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1258804, 25379 ^ [_1258802, _1258804])))], (25381 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 25379 ^ [_1258802, _1258804]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258802))))]], 25373 ^ _777959 : [(25374 ^ _777959) ^ [_1258870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1258870), _1258802)), hBOOL(hAPP(_1258804, _1258870))]]], (7052 ^ _777959) ^ [_895386, _895388, _895390, _895392] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895386, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_895386, tc_fun(_895386, tc_HOL_Obool), tc_HOL_Obool), c_member(_895386)), _895388)), hAPP(hAPP(c_COMBC(_895386, tc_fun(_895386, tc_HOL_Obool), tc_HOL_Obool), c_member(_895386)), _895390)), _895392)), -(hBOOL(hAPP(hAPP(c_member(_895386), _895392), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895386, tc_HOL_Obool)), _895388), _895390))))], (15162 ^ _777959) ^ [_1066842, _1066844, _1066846, _1066848, _1066850] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1066842), 15165 ^ _777959 : [(15166 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066842), _1066844), _1066848)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066842), _1066846), _1066850)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066842), _1066844), _1066850)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066842), _1066846), _1066848)), -(_1066844 = _1066846), -(_1066848 = _1066850)], (15176 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066842), _1066844), _1066848)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066842), _1066846), _1066850)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066842), _1066844), _1066850)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066842), _1066846), _1066848))), 15179 ^ _777959 : [(15182 ^ _777959) ^ [] : [_1066848 = _1066850], (15180 ^ _777959) ^ [] : [_1066844 = _1066846]]]]], (42230 ^ _777959) ^ [_1610518, _1610520] : [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(_1610518)), _1610520))), _1610520 = c_List_Olist_ONil(_1610518)], (14169 ^ _777959) ^ [_1041567, _1041569, _1041571, _1041573, _1041575] : [class_Complete__Lattice_Ocomplete__lattice(_1041567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1041569, tc_HOL_Obool)), _1041571), _1041573)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1041567), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1041569, _1041567), _1041573), _1041575)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1041569, _1041567), _1041571), _1041575))))], (34351 ^ _777959) ^ [_1424585, _1424587] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1424585), _1424587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1424585)), c_Int_OBit0(_1424587))))], (5689 ^ _777959) ^ [_867721, _867723, _867725, _867727] : [c_Hoare__Mirabelle_Ohoare__derivs(_867721, _867723, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_867721)), _867725), _867727)), 5692 ^ _777959 : [(5695 ^ _777959) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_867721, _867723, _867727))], (5693 ^ _777959) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_867721, _867723, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_867721)), _867725), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867721), tc_HOL_Obool)))))]]], (15739 ^ _777959) ^ [_1077392, _1077394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077392)), _1077394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077392), _1077394)))], (16657 ^ _777959) ^ [_1097238, _1097240, _1097242] : [class_Orderings_Olinorder(_1097238), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097238), _1097240), _1097242)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1097238), _1097242), _1097240) = _1097242)], (13415 ^ _777959) ^ [_1023917, _1023919, _1023921, _1023923, _1023925, _1023927] : [class_Complete__Lattice_Ocomplete__lattice(_1023917), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023919, tc_fun(_1023921, _1023917)), _1023923), _1023925), _1023927) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023919, _1023917), _1023923), hAPP(hAPP(c_COMBC(_1023919, _1023921, _1023917), _1023925), _1023927)))], (23345 ^ _777959) ^ [] : [-(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))], (3596 ^ _777959) ^ [_832258, _832260, _832262, _832264] : [-(c_List_Olenlex(_832264, _832260) = c_List_Olenlex(_832262, _832258)), _832264 = _832262, _832260 = _832258], (5918 ^ _777959) ^ [_872278, _872280] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), _872278), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), _872280)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _872280)), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), _872280)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _872278, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), _872280)))], (38302 ^ _777959) ^ [_1511825, _1511827, _1511829, _1511831, _1511833, _1511835] : [c_Fun_Oinj__on(_1511825, _1511827, _1511829, _1511831), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1511825, tc_HOL_Obool)), _1511833), _1511831)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1511825, tc_HOL_Obool)), _1511835), _1511831)), -(hAPP(c_Set_Oimage(_1511825, _1511827, _1511829), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1511825, tc_HOL_Obool)), _1511833), _1511835)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1511827, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1511825, _1511827, _1511829), _1511833)), hAPP(c_Set_Oimage(_1511825, _1511827, _1511829), _1511835)))], (30976 ^ _777959) ^ [_1363105, _1363107, _1363109, _1363111] : [class_Groups_Oordered__ab__group__add__abs(_1363105), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1363105), c_Groups_Ozero__class_Ozero(_1363105)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1363107, _1363105), hAPP(hAPP(c_COMBB(_1363105, _1363105, _1363107), c_Groups_Oabs__class_Oabs(_1363105)), _1363109)), _1363111))))], (21948 ^ _777959) ^ [_1195182, _1195184, _1195186, _1195188, _1195190] : [class_Groups_Ocomm__monoid__add(_1195182), hBOOL(hAPP(c_Finite__Set_Ofinite(_1195184), _1195186)), 21955 ^ _777959 : [(21962 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1195184), _1195188), _1195186))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1195184, _1195182), hAPP(hAPP(c_COMBC(_1195184, _1195182, _1195182), hAPP(hAPP(c_COMBS(_1195184, _1195182, tc_fun(_1195182, _1195182)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1195182, tc_fun(_1195182, _1195182)), _1195184), c_If(_1195182)), hAPP(hAPP(c_COMBC(_1195184, _1195184, tc_HOL_Obool), c_fequal), _1195188))), _1195190)), c_Groups_Ozero__class_Ozero(_1195182))), _1195186) = c_Groups_Ozero__class_Ozero(_1195182))], (21956 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1195184), _1195188), _1195186)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1195184, _1195182), hAPP(hAPP(c_COMBC(_1195184, _1195182, _1195182), hAPP(hAPP(c_COMBS(_1195184, _1195182, tc_fun(_1195182, _1195182)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1195182, tc_fun(_1195182, _1195182)), _1195184), c_If(_1195182)), hAPP(hAPP(c_COMBC(_1195184, _1195184, tc_HOL_Obool), c_fequal), _1195188))), _1195190)), c_Groups_Ozero__class_Ozero(_1195182))), _1195186) = hAPP(_1195190, _1195188))]]], (51142 ^ _777959) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (42539 ^ _777959) ^ [_1619644, _1619646] : [-(hAPP(c_Set_Ovimage(_1619644, _1619644, c_Fun_Oid(_1619644)), _1619646) = _1619646)], (4424 ^ _777959) ^ [_844916, _844918] : [_844918 = _844916, -(c_Nitpick_ORep__Frac(_844918) = c_Nitpick_ORep__Frac(_844916))], (6907 ^ _777959) ^ [_890921, _890923, _890925] : [hBOOL(hAPP(hAPP(c_member(_890921), _890923), hAPP(hAPP(c_Set_Oinsert(_890921), _890925), c_Orderings_Obot__class_Obot(tc_fun(_890921, tc_HOL_Obool))))), -(_890923 = _890925)], (40777 ^ _777959) ^ [_1570640, _1570642, _1570644, _1570646] : [-(hAPP(hAPP(c_List_Otake(_1570640), _1570642), hAPP(hAPP(c_List_Otake(_1570640), _1570644), _1570646)) = hAPP(hAPP(c_List_Otake(_1570640), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1570642), _1570644)), _1570646))], (37198 ^ _777959) ^ [_1486844, _1486846, _1486848, _1486850, _1486852] : [hBOOL(hAPP(hAPP(c_member(_1486844), _1486846), hAPP(c_Relation_OImage(_1486848, _1486844, _1486850), _1486852))), 37202 ^ _777959 : [(37205 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486848, _1486844)), hAPP(hAPP(c_Product__Type_OPair(_1486848, _1486844), 37201 ^ [_1486844, _1486846, _1486848, _1486850, _1486852]), _1486846)), _1486850)))], (37203 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1486848), 37201 ^ [_1486844, _1486846, _1486848, _1486850, _1486852]), _1486852)))]]], (23130 ^ _777959) ^ [_1218795, _1218797, _1218799, _1218801] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1218795, _1218797)), c_Sum__Type_OPlus(_1218795, _1218797, _1218799, _1218801))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1218795), _1218799)))], (50336 ^ _777959) ^ [_1798784, _1798786] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1798784), _1798786))), -(c_Lazy__Sequence_Osmall__lazy_H(_1798784, _1798786) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1798786), c_Lazy__Sequence_Osmall__lazy_H(_1798784, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1798786), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (29484 ^ _777959) ^ [_1333866, _1333868, _1333870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333866)), 29487 ^ _777959 : [(29488 ^ _777959) ^ [_1334000] : [29490 ^ _777959 : [(29496 ^ _777959) ^ [] : [-(_1334000 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 29492 ^ [_1333866, _1333868, _1333870, _1334000]), 29489 ^ [_1333866, _1333868, _1333870, _1334000]))], (29494 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29492 ^ [_1333866, _1333868, _1333870, _1334000]), _1333868)))], (29491 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29489 ^ [_1333866, _1333868, _1333870, _1334000]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1333866))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334000), _1333870)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1334000), _1333866)), _1333870)))]]], (11391 ^ _777959) ^ [_981199, _981201, _981203] : [class_Lattices_Olattice(_981199), hBOOL(hAPP(c_Finite__Set_Ofinite(_981199), _981201)), -(hBOOL(hAPP(hAPP(c_member(_981199), _981203), _981201))), -(_981201 = c_Orderings_Obot__class_Obot(tc_fun(_981199, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_981199, hAPP(hAPP(c_Set_Oinsert(_981199), _981203), _981201)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981199), _981203), c_Big__Operators_Olattice__class_OInf__fin(_981199, _981201)))], (17315 ^ _777959) ^ [_1109024, _1109026, _1109028, _1109030] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1109024, tc_fun(_1109026, tc_HOL_Obool)), _1109028), _1109030) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1109026, tc_HOL_Obool), hAPP(c_Set_Oimage(_1109024, tc_fun(_1109026, tc_HOL_Obool), _1109030), _1109028)))], (33511 ^ _777959) ^ [_1409458] : [-(c_Int_Osucc(_1409458) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1409458), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (49292 ^ _777959) ^ [_1774771, _1774773, _1774775, _1774777] : [-(hAPP(_1774771, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1774773, _1774773), _1774775), _1774771), _1774777)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1774773, _1774773), _1774775), _1774771), hAPP(_1774771, _1774777)))], (11784 ^ _777959) ^ [_991190, _991192, _991194, _991196, _991198] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_991190, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991192, tc_fun(_991190, tc_HOL_Obool)), _991194), _991196)), _991198) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991192, tc_fun(_991190, tc_HOL_Obool)), _991194), hAPP(hAPP(c_COMBC(_991192, tc_fun(_991190, tc_HOL_Obool), tc_fun(_991190, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_991190, tc_HOL_Obool), tc_fun(tc_fun(_991190, tc_HOL_Obool), tc_fun(_991190, tc_HOL_Obool)), _991192), c_Groups_Ominus__class_Ominus(tc_fun(_991190, tc_HOL_Obool))), _991196)), _991198)))], (50612 ^ _777959) ^ [_1804674, _1804676, _1804678] : [c_List_Oreplicate(_1804674, _1804676, _1804678) = c_List_Olist_ONil(_1804674), -(_1804676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8106 ^ _777959) ^ [_917037, _917039, _917041, _917043] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917037, tc_HOL_Obool)), _917039), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917037, tc_HOL_Obool)), _917041), _917043))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_917037, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_917037, tc_HOL_Obool)), _917039), _917041)), _917043)))], (30271 ^ _777959) ^ [_1350452, _1350454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1350452)), -(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, _1350454, _1350452))))], (32123 ^ _777959) ^ [_1384631, _1384633, _1384635] : [class_Int_Onumber__ring(_1384631), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384631), hAPP(c_Int_Onumber__class_Onumber__of(_1384631), _1384633)), hAPP(c_Int_Onumber__class_Onumber__of(_1384631), _1384635)) = hAPP(c_Int_Onumber__class_Onumber__of(_1384631), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1384633), _1384635)))], (39657 ^ _777959) ^ [_1544376, _1544378] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1544376, _1544378) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1544376), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1544378)))], (34563 ^ _777959) ^ [_1428475, _1428477] : [class_Rings_Olinordered__idom(_1428475), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1428475), c_Groups_Ozero__class_Ozero(_1428475)), hAPP(hAPP(c_Power_Opower__class_Opower(_1428475), _1428477), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35225 ^ _777959) ^ [] : [-(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))], (2380 ^ _777959) ^ [_813162, _813164, _813166, _813168, _813170, _813172] : [-(c_Com_Ocom_OLocal(_813172, _813168, _813164) = c_Com_Ocom_OLocal(_813170, _813166, _813162)), _813172 = _813170, _813168 = _813166, _813164 = _813162], (31360 ^ _777959) ^ [_1370486, _1370488] : [class_Groups_Oabs__if(_1370486), 31363 ^ _777959 : [(31370 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1370486), _1370488), c_Groups_Ozero__class_Ozero(_1370486)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1370486), _1370488) = _1370488)], (31364 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1370486), _1370488), c_Groups_Ozero__class_Ozero(_1370486))), -(hAPP(c_Groups_Oabs__class_Oabs(_1370486), _1370488) = hAPP(c_Groups_Ouminus__class_Ouminus(_1370486), _1370488))]]], (13619 ^ _777959) ^ [_1028311, _1028313, _1028315, _1028317, _1028319] : [13621 ^ _777959 : [(13624 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1028311), _1028313), hAPP(_1028319, 13620 ^ [_1028311, _1028313, _1028315, _1028317, _1028319])))], (13622 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1028315), 13620 ^ [_1028311, _1028313, _1028315, _1028317, _1028319]), _1028317)))]], -(hBOOL(hAPP(hAPP(c_member(_1028311), _1028313), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1028315, tc_fun(_1028311, tc_HOL_Obool)), _1028317), _1028319))))], (9680 ^ _777959) ^ [_945561, _945563, _945565, _945567, _945569] : [class_Lattices_Olattice(_945561), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945563, _945561)), _945565), _945567), _945569) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945561), hAPP(_945565, _945569)), hAPP(_945567, _945569)))], (30748 ^ _777959) ^ [_1358868, _1358870, _1358872] : [-(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), _1358868), _1358870)), _1358872)), _1358870) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1358872), _1358870))], (37162 ^ _777959) ^ [_1485476, _1485478, _1485480, _1485482] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1485476, _1485478), _1485480), _1485482) = hAPP(c_Set_OCollect(tc_prod(_1485478, _1485478)), hAPP(c_Product__Type_Oprod_Oprod__case(_1485478, _1485478, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1485478, tc_fun(tc_prod(_1485476, _1485476), tc_HOL_Obool), tc_fun(_1485478, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485478, tc_fun(tc_fun(tc_prod(_1485476, _1485476), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1485476, _1485476), tc_HOL_Obool), tc_fun(_1485478, tc_HOL_Obool)), _1485478), c_COMBC(_1485478, tc_fun(tc_prod(_1485476, _1485476), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1485478, tc_prod(_1485476, _1485476)), tc_fun(_1485478, tc_fun(tc_fun(tc_prod(_1485476, _1485476), tc_HOL_Obool), tc_HOL_Obool)), _1485478), hAPP(c_COMBB(tc_prod(_1485476, _1485476), tc_fun(tc_fun(tc_prod(_1485476, _1485476), tc_HOL_Obool), tc_HOL_Obool), _1485478), c_member(tc_prod(_1485476, _1485476)))), hAPP(hAPP(c_COMBC(_1485478, tc_fun(_1485478, _1485476), tc_fun(_1485478, tc_prod(_1485476, _1485476))), hAPP(hAPP(c_COMBB(tc_fun(_1485476, tc_prod(_1485476, _1485476)), tc_fun(tc_fun(_1485478, _1485476), tc_fun(_1485478, tc_prod(_1485476, _1485476))), _1485478), c_COMBB(_1485476, tc_prod(_1485476, _1485476), _1485478)), hAPP(hAPP(c_COMBB(_1485476, tc_fun(_1485476, tc_prod(_1485476, _1485476)), _1485478), c_Product__Type_OPair(_1485476, _1485476)), _1485482))), _1485482)))), _1485480))))], (42092 ^ _777959) ^ [_1607367] : [-(hAPP(c_List_Oset(_1607367), c_List_Olist_ONil(_1607367)) = c_Orderings_Obot__class_Obot(tc_fun(_1607367, tc_HOL_Obool)))], (38778 ^ _777959) ^ [_1522496, _1522498, _1522500, _1522502, _1522504] : [hBOOL(hAPP(hAPP(c_member(_1522496), hAPP(_1522498, _1522500)), _1522502)), -(hBOOL(hAPP(hAPP(c_member(_1522504), _1522500), hAPP(c_Set_Ovimage(_1522504, _1522496, _1522498), _1522502))))], (15230 ^ _777959) ^ [_1068165, _1068167] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068165), hAPP(c_Nat_OSuc, _1068167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068165), _1068167))), -(_1068165 = _1068167)], (16769 ^ _777959) ^ [_1099117, _1099119, _1099121, _1099123] : [class_Orderings_Olinorder(_1099117), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099117), _1099119), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099117), _1099121), _1099123))), 16776 ^ _777959 : [(16779 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099117), _1099119), _1099123)))], (16777 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099117), _1099119), _1099121)))]]], (46928 ^ _777959) ^ [_1718959, _1718961, _1718963] : [c_Wellfounded_Owf(_1718959, _1718961), -(c_Wellfounded_Owf(_1718959, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1718959, _1718959), tc_HOL_Obool)), _1718961), _1718963)))], (24291 ^ _777959) ^ [_1239619, _1239621] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239619)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1239621))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1239619), _1239621)))], (7228 ^ _777959) ^ [_899074, _899076, _899078] : [_899076 = _899078, -(hAPP(hAPP(c_COMBC(_899074, tc_fun(_899074, tc_HOL_Obool), tc_HOL_Obool), c_member(_899074)), _899076) = hAPP(hAPP(c_COMBC(_899074, tc_fun(_899074, tc_HOL_Obool), tc_HOL_Obool), c_member(_899074)), _899078))], (27672 ^ _777959) ^ [_1300675, _1300677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300675)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1300675), _1300677)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1300675)), hAPP(c_Int_Onat, _1300677)))], (33137 ^ _777959) ^ [_1403686] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403686)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403686)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403686))], (34601 ^ _777959) ^ [_1429154, _1429156] : [class_Rings_Olinordered__idom(_1429154), 34604 ^ _777959 : [(34611 ^ _777959) ^ [] : [-(_1429156 = c_Groups_Ozero__class_Ozero(_1429154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429154), c_Groups_Ozero__class_Ozero(_1429154)), hAPP(hAPP(c_Power_Opower__class_Opower(_1429154), _1429156), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (34605 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1429154), c_Groups_Ozero__class_Ozero(_1429154)), hAPP(hAPP(c_Power_Opower__class_Opower(_1429154), _1429156), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1429156 = c_Groups_Ozero__class_Ozero(_1429154)]]], (29910 ^ _777959) ^ [_1343383, _1343385] : [class_Divides_Osemiring__div(_1343383), -(c_Divides_Odiv__class_Omod(_1343383, _1343385, c_Groups_Ozero__class_Ozero(_1343383)) = _1343385)], (13044 ^ _777959) ^ [_1015401, _1015403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015401, tc_HOL_Obool)), _1015403), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1015401, tc_HOL_Obool)), _1015403))), -(_1015403 = c_Orderings_Obot__class_Obot(tc_fun(_1015401, tc_HOL_Obool)))], (7872 ^ _777959) ^ [_911755, _911757, _911759] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911755, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911755, tc_HOL_Obool)), _911757), _911759)), _911759) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911755, tc_HOL_Obool)), _911757), _911759))], (44569 ^ _777959) ^ [_1663744] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1663744) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1663744)))], (29504 ^ _777959) ^ [_1334274, _1334276, _1334278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1334274)), 29507 ^ _777959 : [(29508 ^ _777959) ^ [_1334408] : [29510 ^ _777959 : [(29516 ^ _777959) ^ [] : [-(_1334408 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 29512 ^ [_1334274, _1334276, _1334278, _1334408]), 29509 ^ [_1334274, _1334276, _1334278, _1334408]))], (29514 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29512 ^ [_1334274, _1334276, _1334278, _1334408]), _1334276)))], (29511 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29509 ^ [_1334274, _1334276, _1334278, _1334408]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1334274))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334278), _1334408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1334278), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1334408), _1334274))))]]], (2768 ^ _777959) ^ [_819228, _819230, _819232, _819234, _819236, _819238, _819240, _819242] : [-(c_Map_Orestrict__map(_819242, _819238, _819234, _819230) = c_Map_Orestrict__map(_819240, _819236, _819232, _819228)), _819242 = _819240, _819238 = _819236, _819234 = _819232, _819230 = _819228], (5240 ^ _777959) ^ [_858158, _858160] : [_858160 = _858158, -(c_List_Otl(_858160) = c_List_Otl(_858158))], (44567 ^ _777959) ^ [_1663706, _1663708] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1663706, _1663708) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1663706, hAPP(c_Nat_OSuc, _1663708))))], (30295 ^ _777959) ^ [_1350808, _1350810] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350808, _1350810) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350808, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1350810)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350808, _1350810)), _1350810))], (8358 ^ _777959) ^ [_922714, _922716, _922718, _922720, _922722] : [-(hAPP(c_Option_Ooption_Ooption__case(_922714, _922716, _922718, _922720), hAPP(c_Option_Ooption_OSome(_922716), _922722)) = hAPP(_922720, _922722))], (5928 ^ _777959) ^ [_872463, _872465, _872467] : [hAPP(c_Option_Ooption_OSome(_872463), _872465) = hAPP(c_Option_Ooption_OSome(_872463), _872467), -(_872465 = _872467)], (31042 ^ _777959) ^ [_1364365, _1364367, _1364369] : [class_Rings_Olinordered__idom(_1364365), -(hAPP(c_Groups_Oabs__class_Oabs(_1364365), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364365), _1364367), _1364369)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364365), hAPP(c_Groups_Oabs__class_Oabs(_1364365), _1364367)), hAPP(c_Groups_Oabs__class_Oabs(_1364365), _1364369)))], (14023 ^ _777959) ^ [_1038265, _1038267, _1038269, _1038271] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038265, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038267, tc_fun(_1038265, tc_HOL_Obool)), _1038269), _1038271)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1038267, tc_fun(_1038265, tc_HOL_Obool)), _1038269), hAPP(hAPP(c_COMBB(tc_fun(_1038265, tc_HOL_Obool), tc_fun(_1038265, tc_HOL_Obool), _1038267), c_Groups_Ouminus__class_Ouminus(tc_fun(_1038265, tc_HOL_Obool))), _1038271)))], (48431 ^ _777959) ^ [_1752409, _1752411] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1752409, _1752409)), c_Transitive__Closure_Otrancl(_1752409, _1752411))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1752409, _1752409)), _1752411)))], (30742 ^ _777959) ^ [_1358769, _1358771] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1358769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1358771, _1358769)), _1358769)))], (14758 ^ _777959) ^ [_1055387, _1055389, _1055391, _1055393, _1055395, _1055397] : [-(hBOOL(hAPP(hAPP(c_member(_1055387), _1055389), c_SetInterval_Oord_OatLeastLessThan(_1055387, _1055391, _1055393, _1055395, _1055397)))), hBOOL(hAPP(hAPP(_1055391, _1055395), _1055389)), hBOOL(hAPP(hAPP(_1055393, _1055389), _1055397))], (45666 ^ _777959) ^ [_1689272] : [class_Enum_Oenum(_1689272), -(c_Enum_Oenum__class_Oenum(tc_Option_Ooption(_1689272)) = hAPP(hAPP(c_List_Olist_OCons(tc_Option_Ooption(_1689272)), c_Option_Ooption_ONone(_1689272)), hAPP(hAPP(c_List_Omap(_1689272, tc_Option_Ooption(_1689272)), c_Option_Ooption_OSome(_1689272)), c_Enum_Oenum__class_Oenum(_1689272))))], (3356 ^ _777959) ^ [_828540, _828542, _828544, _828546, _828548, _828550] : [-(c_List_Opartition(_828550, _828546, _828542) = c_List_Opartition(_828548, _828544, _828540)), _828550 = _828548, _828546 = _828544, _828542 = _828540], (13475 ^ _777959) ^ [_1025149, _1025151] : [-(hAPP(c_Set_OCollect(_1025149), _1025151) = _1025151)], (49290 ^ _777959) ^ [_1774708, _1774710, _1774712, _1774714] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1774708, _1774710), tc_fun(_1774708, _1774710)), _1774712), c_Fun_Ocomp(_1774710, _1774710, _1774708, _1774714)) = c_Fun_Ocomp(_1774710, _1774710, _1774708, hAPP(hAPP(c_Nat_Ocompow(_1774710, _1774710), _1774712), _1774714)))], (43262 ^ _777959) ^ [_1637045, _1637047, _1637049, _1637051, _1637053] : [-(hAPP(hAPP(c_List_Odrop(_1637045), _1637047), hAPP(hAPP(c_List_Omap(_1637049, _1637045), _1637051), _1637053)) = hAPP(hAPP(c_List_Omap(_1637049, _1637045), _1637051), hAPP(hAPP(c_List_Odrop(_1637049), _1637047), _1637053)))], (6483 ^ _777959) ^ [_882700, _882702, _882704] : [class_Orderings_Oorder(_882700), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882700), _882702), _882704)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_882700), _882704), _882702)), -(_882702 = _882704)], (45694 ^ _777959) ^ [_1689760] : [class_Enum_Oenum(_1689760), -(hAPP(c_List_Oset(_1689760), c_Enum_Oenum__class_Oenum(_1689760)) = c_Orderings_Otop__class_Otop(tc_fun(_1689760, tc_HOL_Obool)))], (16863 ^ _777959) ^ [_1100789, _1100791, _1100793, _1100795] : [class_Orderings_Olinorder(_1100789), 16866 ^ _777959 : [(16875 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), _1100791), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100789), _1100793), _1100795)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), _1100791), _1100793)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), _1100791), _1100795))], (16867 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), _1100791), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1100789), _1100793), _1100795))), 16870 ^ _777959 : [(16873 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), _1100791), _1100795)))], (16871 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1100789), _1100791), _1100793)))]]]]], (44098 ^ _777959) ^ [_1655331, _1655333] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1655331))), c_List_Otranspose(_1655331, _1655333)) = c_List_Ofoldr(tc_List_Olist(_1655331), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1655331)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1655331))), _1655333, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48360 ^ _777959) ^ [_1751092, _1751094] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1751092), _1751094) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1751092)), hAPP(c_Code__Numeral_Onat__of, _1751094))))], (9642 ^ _777959) ^ [_944737, _944739, _944741] : [9643 ^ _777959 : [(9646 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_944737), _944741))], (9644 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_944737), _944739))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_944737), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944737, tc_HOL_Obool)), _944739), _944741))))], (33617 ^ _777959) ^ [_1411092] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1411092))) = 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)))), _1411092))], (41892 ^ _777959) ^ [_1602903, _1602905, _1602907, _1602909, _1602911, _1602913] : [class_Groups_Ocomm__monoid__mult(_1602903), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1602905, _1602903), hAPP(hAPP(c_COMBC(_1602905, tc_fun(_1602907, tc_HOL_Obool), _1602903), hAPP(hAPP(c_COMBB(tc_fun(_1602907, _1602903), tc_fun(tc_fun(_1602907, tc_HOL_Obool), _1602903), _1602905), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1602907, _1602903)), _1602909)), _1602911)), _1602913) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1602905, _1602907), _1602903), hAPP(c_Product__Type_Oprod_Oprod__case(_1602905, _1602907, _1602903), _1602909)), hAPP(hAPP(c_Product__Type_OSigma(_1602905, _1602907), _1602913), hAPP(c_COMBK(tc_fun(_1602907, tc_HOL_Obool), _1602905), _1602911))))], (50906 ^ _777959) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (28868 ^ _777959) ^ [_1322079, _1322081, _1322083] : [28870 ^ _777959 : [(28873 ^ _777959) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1322083, 28869 ^ [_1322079, _1322081, _1322083]))], (28871 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1322079), 28869 ^ [_1322079, _1322081, _1322083]), _1322081)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1322079, tc_Int_Oint), _1322083), _1322081) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1322079, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1322079), c_Int_Onat), _1322083)), _1322081)))], (28784 ^ _777959) ^ [_1320277, _1320279, _1320281, _1320283] : [class_Groups_Ocomm__monoid__add(_1320277), 28787 ^ _777959 : [(28794 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1320279)), _1320281))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1320277), _1320283), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1320281, hAPP(c_Nat_OSuc, _1320279))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320277), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1320277), _1320283), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1320281, _1320279))), hAPP(_1320283, hAPP(c_Nat_OSuc, _1320279))))], (28788 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1320279)), _1320281)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1320277), _1320283), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1320281, hAPP(c_Nat_OSuc, _1320279))) = c_Groups_Ozero__class_Ozero(_1320277))]]], (45061 ^ _777959) ^ [_1675436, _1675438, _1675440] : [class_Orderings_Olinorder(_1675436), c_List_Olinorder__class_Osorted(_1675436, hAPP(c_List_Orev(_1675436), _1675438)), 45068 ^ _777959 : [(45075 ^ _777959) ^ [] : [-(_1675438 = c_List_Olist_ONil(_1675436)), -(c_List_Ofoldr(_1675436, _1675436, c_Orderings_Oord__class_Omax(_1675436), _1675438, _1675440) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1675436), hAPP(hAPP(c_List_Onth(_1675436), _1675438), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1675440))], (45069 ^ _777959) ^ [] : [_1675438 = c_List_Olist_ONil(_1675436), -(c_List_Ofoldr(_1675436, _1675436, c_Orderings_Oord__class_Omax(_1675436), _1675438, _1675440) = _1675440)]]], (42429 ^ _777959) ^ [_1615793, _1615795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1615793)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1615795))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1615793), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1615795)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1615793)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1615793)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1615795))))], (48437 ^ _777959) ^ [_1752516, _1752518] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1752516, _1752516)), _1752518)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1752516, _1752516)), c_Transitive__Closure_Otrancl(_1752516, _1752518))))], (10731 ^ _777959) ^ [_968425, _968427, _968429, _968431] : [class_Groups_Ocancel__semigroup__add(_968425), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968425), _968427), _968429) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968425), _968427), _968431), -(_968429 = _968431)], (42525 ^ _777959) ^ [_1619423, _1619425] : [-(hAPP(c_Fun_Oid(_1619423), _1619425) = _1619425)], (47633 ^ _777959) ^ [_1735391, _1735393, _1735395] : [c_Wellfounded_OwfP(_1735391, hAPP(_1735393, 47634 ^ [_1735391, _1735393, _1735395])), 47641 ^ _777959 : [(47644 ^ _777959) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1735391, tc_HOL_Obool)), c_Predicate_ODomainP(_1735391, _1735391, hAPP(_1735393, 47639 ^ [_1735391, _1735393, _1735395]))), c_Predicate_ORangeP(_1735391, _1735391, hAPP(_1735393, 47640 ^ [_1735391, _1735393, _1735395]))) = c_Orderings_Obot__class_Obot(tc_fun(_1735391, tc_HOL_Obool))], (47642 ^ _777959) ^ [] : [hAPP(_1735393, 47639 ^ [_1735391, _1735393, _1735395]) = hAPP(_1735393, 47640 ^ [_1735391, _1735393, _1735395])]], -(c_Wellfounded_OwfP(_1735391, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1735395, tc_fun(_1735391, tc_fun(_1735391, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1735395, tc_HOL_Obool))), _1735393)))], (51300 ^ _777959) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (30716 ^ _777959) ^ [_1358294, _1358296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1358294), _1358296)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1358294, _1358296) = _1358294)], (8154 ^ _777959) ^ [_918144, _918146, _918148, _918150] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918144, tc_HOL_Obool)), _918146), hAPP(hAPP(c_Set_Oinsert(_918144), _918148), _918150))), 8157 ^ _777959 : [(8164 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_918144), _918148), _918146))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918144, tc_HOL_Obool)), _918146), _918150)))], (8158 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_918144), _918148), _918146)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_918144, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918144, tc_HOL_Obool)), _918146), hAPP(hAPP(c_Set_Oinsert(_918144), _918148), c_Orderings_Obot__class_Obot(tc_fun(_918144, tc_HOL_Obool))))), _918150)))]]], (42318 ^ _777959) ^ [_1612667, _1612669, _1612671] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612667), tc_List_Olist(_1612667))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612667), tc_List_Olist(_1612667)), c_List_Olist_ONil(_1612667)), _1612669)), c_List_Olex(_1612667, _1612671)))], (8100 ^ _777959) ^ [_916876, _916878, _916880, _916882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916876, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916876, tc_HOL_Obool)), _916878), _916880)), _916882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916876, tc_HOL_Obool)), _916878), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916876, tc_HOL_Obool)), _916880), _916882))))], (22731 ^ _777959) ^ [_1211420] : [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, _1211420)))))], (40991 ^ _777959) ^ [_1578433, _1578435, _1578437] : [hBOOL(hAPP(c_Predicate_OPowp(_1578433, _1578435), _1578437)), 40994 ^ _777959 : [(40995 ^ _777959) ^ [_1578517] : [hBOOL(hAPP(hAPP(c_member(_1578433), _1578517), _1578437)), -(hBOOL(hAPP(_1578435, _1578517)))]]], (47828 ^ _777959) ^ [_1740444, _1740446, _1740448, _1740450, _1740452, _1740454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1740444, tc_HOL_Obool)), _1740446), _1740448)), 47834 ^ _777959 : [(47837 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1740450, tc_HOL_Obool)), hAPP(_1740452, 47833 ^ [_1740444, _1740446, _1740448, _1740450, _1740452, _1740454])), hAPP(_1740454, 47833 ^ [_1740444, _1740446, _1740448, _1740450, _1740452, _1740454])))], (47835 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1740444), 47833 ^ [_1740444, _1740446, _1740448, _1740450, _1740452, _1740454]), _1740446)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1740444, _1740450), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1740444, _1740450), _1740446), _1740452)), hAPP(hAPP(c_Product__Type_OSigma(_1740444, _1740450), _1740448), _1740454))))], (30054 ^ _777959) ^ [_1346345, _1346347, _1346349] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1346345), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1346347, _1346349)), _1346349) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1346345), _1346347), _1346349))], (44404 ^ _777959) ^ [_1660576, _1660578, _1660580] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1660576), c_List_Oupt(_1660578, _1660580)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1660578), _1660576), _1660580))], (6147 ^ _777959) ^ [_876514, _876516, _876518, _876520] : [hBOOL(hAPP(hAPP(c_member(_876514), _876516), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_876514, tc_HOL_Obool)), _876518), _876520))), -(hBOOL(hAPP(hAPP(c_member(_876514), _876516), _876518))), -(hBOOL(hAPP(hAPP(c_member(_876514), _876516), _876520)))], (23617 ^ _777959) ^ [_1227216, _1227218] : [23618 ^ _777959 : [(23621 ^ _777959) ^ [] : [_1227218 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (23619 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227216))]], -(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), _1227216), _1227218))))], (47336 ^ _777959) ^ [_1728488, _1728490, _1728492] : [_1728492 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1728488, _1728490), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1728488, _1728490), _1728492) = c_Orderings_Obot__class_Obot(tc_fun(_1728488, tc_HOL_Obool)))], (12662 ^ _777959) ^ [_1007777, _1007779, _1007781] : [class_Lattices_Oboolean__algebra(_1007777), 12665 ^ _777959 : [(12672 ^ _777959) ^ [] : [_1007779 = _1007781, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1007777), _1007779) = hAPP(c_Groups_Ouminus__class_Ouminus(_1007777), _1007781))], (12666 ^ _777959) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1007777), _1007779) = hAPP(c_Groups_Ouminus__class_Ouminus(_1007777), _1007781), -(_1007779 = _1007781)]]], (50938 ^ _777959) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (51042 ^ _777959) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (33357 ^ _777959) ^ [_1407025, _1407027] : [class_Int_Onumber__ring(_1407025), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1407025), _1407027), hAPP(c_Int_Onumber__class_Onumber__of(_1407025), c_Int_OBit1(c_Int_OPls))) = _1407027)], (50968 ^ _777959) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (25972 ^ _777959) ^ [_1270347, _1270349, _1270351] : [class_Fields_Ofield(_1270347), -(_1270349 = c_Groups_Oone__class_Oone(_1270347)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1270347), hAPP(c_Power_Opower__class_Opower(_1270347), _1270349)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1270351)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270347), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270347), hAPP(hAPP(c_Power_Opower__class_Opower(_1270347), _1270349), _1270351)), c_Groups_Oone__class_Oone(_1270347))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1270347), _1270349), c_Groups_Oone__class_Oone(_1270347))))], (28854 ^ _777959) ^ [_1321814, _1321816, _1321818, _1321820] : [class_Orderings_Olinorder(_1321814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321814), _1321816), _1321818)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321814), _1321818), _1321820)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321814, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1321814, _1321816, _1321818)), c_SetInterval_Oord__class_OatLeastAtMost(_1321814, _1321818, _1321820)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1321814, _1321816, _1321820))], (1200 ^ _777959) ^ [_795683, _795685] : [-(class_Groups_Osgn__if(_795683)), _795685 = _795683, class_Groups_Osgn__if(_795685)], (45236 ^ _777959) ^ [_1679680, _1679682] : [-(_1679680 = c_List_Olist_ONil(_1679682)), hBOOL(hAPP(c_List_Odistinct(_1679682), _1679680)), -(c_List_OtakeWhile(_1679682, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1679682), c_fNot), hAPP(hAPP(c_COMBC(_1679682, _1679682, tc_HOL_Obool), c_fequal), c_List_Olast(_1679682, _1679680))), _1679680) = c_List_Obutlast(_1679682, _1679680))], (16381 ^ _777959) ^ [_1091581, _1091583, _1091585, _1091587] : [hBOOL(hAPP(hAPP(c_member(_1091581), _1091583), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1091581, tc_HOL_Obool), _1091585))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1091581, tc_HOL_Obool)), _1091587), _1091585)), -(hBOOL(hAPP(hAPP(c_member(_1091581), _1091583), _1091587)))], (21780 ^ _777959) ^ [_1191620, _1191622, _1191624] : [21781 ^ _777959 : [(21784 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1191622), _1191624))], (21782 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1191620)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1191620), _1191622)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1191620), _1191624))))], (13573 ^ _777959) ^ [_1027260, _1027262, _1027264, _1027266, _1027268] : [-(_1027260 = c_Orderings_Obot__class_Obot(tc_fun(_1027262, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1027262, tc_fun(_1027264, tc_HOL_Obool)), _1027260), hAPP(hAPP(c_COMBC(_1027262, tc_fun(_1027264, tc_HOL_Obool), tc_fun(_1027264, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1027264, tc_HOL_Obool), tc_fun(tc_fun(_1027264, tc_HOL_Obool), tc_fun(_1027264, tc_HOL_Obool)), _1027262), c_Groups_Ominus__class_Ominus(tc_fun(_1027264, tc_HOL_Obool))), _1027266)), _1027268)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1027264, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1027262, tc_fun(_1027264, tc_HOL_Obool)), _1027260), _1027266)), _1027268))], (46451 ^ _777959) ^ [_1705846, _1705848, _1705850, _1705852] : [c_List_Olist__all2(_1705846, _1705848, _1705850, _1705852, c_List_Olist_ONil(_1705848)), -(_1705852 = c_List_Olist_ONil(_1705846))], (51124 ^ _777959) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (38888 ^ _777959) ^ [_1525066, _1525068, _1525070, _1525072, _1525074, _1525076] : [hBOOL(hAPP(hAPP(c_member(_1525066), _1525068), _1525070)), 38891 ^ _777959 : [(38898 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1525066), _1525072), _1525070))), -(hAPP(c_Set_Ovimage(_1525074, _1525066, hAPP(hAPP(c_COMBC(_1525074, _1525066, _1525066), hAPP(hAPP(c_COMBC(_1525074, _1525066, tc_fun(_1525066, _1525066)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525066, tc_fun(_1525066, _1525066)), _1525074), c_If(_1525066)), hAPP(hAPP(c_COMBC(_1525074, tc_fun(_1525074, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525074)), _1525076))), _1525068)), _1525072)), _1525070) = _1525076)], (38892 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1525066), _1525072), _1525070)), -(hAPP(c_Set_Ovimage(_1525074, _1525066, hAPP(hAPP(c_COMBC(_1525074, _1525066, _1525066), hAPP(hAPP(c_COMBC(_1525074, _1525066, tc_fun(_1525066, _1525066)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1525066, tc_fun(_1525066, _1525066)), _1525074), c_If(_1525066)), hAPP(hAPP(c_COMBC(_1525074, tc_fun(_1525074, tc_HOL_Obool), tc_HOL_Obool), c_member(_1525074)), _1525076))), _1525068)), _1525072)), _1525070) = c_Orderings_Otop__class_Otop(tc_fun(_1525074, tc_HOL_Obool)))]]], (50296 ^ _777959) ^ [_1797557, _1797559, _1797561, _1797563, _1797565] : [-(hAPP(c_New__DSequence_Oneg__bind(_1797557, _1797559, _1797561, _1797563), _1797565) = c_Lazy__Sequence_Ohb__bind(_1797557, _1797559, hAPP(_1797561, _1797565), hAPP(hAPP(c_COMBC(_1797557, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1797559))), _1797563), _1797565)))], (33177 ^ _777959) ^ [_1404313, _1404315] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404313))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404313)), _1404315) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1404315))], (8616 ^ _777959) ^ [_926721, _926723, _926725, _926727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926721, tc_HOL_Obool)), _926723), _926725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926721, tc_HOL_Obool)), _926725), _926727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_926721, tc_HOL_Obool)), _926723), _926727)))], (41659 ^ _777959) ^ [_1595254, _1595256, _1595258, _1595260, _1595262, _1595264] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595254, _1595254)), hAPP(hAPP(c_Product__Type_OPair(_1595254, _1595254), _1595256), _1595258)), _1595260)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595254), tc_List_Olist(_1595254))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595254), tc_List_Olist(_1595254)), _1595262), _1595264)), c_List_Olistrel(_1595254, _1595260))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595254), tc_List_Olist(_1595254))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595254), tc_List_Olist(_1595254)), hAPP(hAPP(c_List_Olist_OCons(_1595254), _1595256), _1595262)), hAPP(hAPP(c_List_Olist_OCons(_1595254), _1595258), _1595264))), c_List_Olistrel(_1595254, _1595260))))], (25696 ^ _777959) ^ [_1265299, _1265301, _1265303] : [class_Rings_Odivision__ring(_1265299), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1265299), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265299), _1265301), _1265303)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265299), hAPP(c_Groups_Ouminus__class_Ouminus(_1265299), _1265301)), _1265303))], (7166 ^ _777959) ^ [_897797, _897799, _897801, _897803] : [class_Lattices_Osemilattice__sup(_897797), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897797), _897799), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897797), _897801), _897803)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897797), _897801), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897797), _897799), _897803)))], (31184 ^ _777959) ^ [_1367029, _1367031, _1367033] : [class_Groups_Oordered__ab__group__add__abs(_1367029), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1367029), hAPP(c_Groups_Oabs__class_Oabs(_1367029), _1367031)), hAPP(c_Groups_Oabs__class_Oabs(_1367029), _1367033))), hAPP(c_Groups_Oabs__class_Oabs(_1367029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1367029), _1367031), _1367033)))))], (47263 ^ _777959) ^ [_1726338, _1726340, _1726342, _1726344] : [hBOOL(hAPP(c_Predicate_ORangeP(_1726338, _1726340, hAPP(hAPP(c_COMBC(_1726338, tc_fun(tc_prod(_1726338, _1726340), tc_HOL_Obool), tc_fun(_1726340, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1726340, tc_fun(tc_fun(tc_prod(_1726338, _1726340), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1726338, _1726340), tc_HOL_Obool), tc_fun(_1726340, tc_HOL_Obool)), _1726338), c_COMBC(_1726340, tc_fun(tc_prod(_1726338, _1726340), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1726340, tc_prod(_1726338, _1726340)), tc_fun(_1726340, tc_fun(tc_fun(tc_prod(_1726338, _1726340), tc_HOL_Obool), tc_HOL_Obool)), _1726338), hAPP(c_COMBB(tc_prod(_1726338, _1726340), tc_fun(tc_fun(tc_prod(_1726338, _1726340), tc_HOL_Obool), tc_HOL_Obool), _1726340), c_member(tc_prod(_1726338, _1726340)))), c_Product__Type_OPair(_1726338, _1726340)))), _1726342)), _1726344)), -(hBOOL(hAPP(hAPP(c_member(_1726340), _1726344), hAPP(c_Relation_ORange(_1726338, _1726340), _1726342))))], (50892 ^ _777959) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (46525 ^ _777959) ^ [_1707369, _1707371, _1707373, _1707375, _1707377] : [-(c_List_Olist__all2(_1707369, _1707371, _1707373, _1707375, _1707377)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707369)), _1707375) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707371)), _1707377), 46531 ^ _777959 : [(46534 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1707373, hAPP(hAPP(c_List_Onth(_1707369), _1707375), 46530 ^ [_1707369, _1707371, _1707373, _1707375, _1707377])), hAPP(hAPP(c_List_Onth(_1707371), _1707377), 46530 ^ [_1707369, _1707371, _1707373, _1707375, _1707377])))], (46532 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46530 ^ [_1707369, _1707371, _1707373, _1707375, _1707377]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707369)), _1707375))))]]], (20853 ^ _777959) ^ [_1174833, _1174835] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174833), hAPP(c_Nat_OSuc, _1174835)))), 20854 ^ _777959 : [(20857 ^ _777959) ^ [_1174921] : [_1174833 = hAPP(c_Nat_OSuc, _1174921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174921), _1174835))], (20855 ^ _777959) ^ [] : [_1174833 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (38704 ^ _777959) ^ [_1520770, _1520772, _1520774, _1520776, _1520778] : [c_Fun_Oinj__on(_1520770, _1520772, _1520774, c_Orderings_Otop__class_Otop(tc_fun(_1520770, tc_HOL_Obool))), 38707 ^ _777959 : [(38714 ^ _777959) ^ [] : [_1520776 = _1520778, -(hAPP(hAPP(c_List_Omap(_1520770, _1520772), _1520774), _1520776) = hAPP(hAPP(c_List_Omap(_1520770, _1520772), _1520774), _1520778))], (38708 ^ _777959) ^ [] : [hAPP(hAPP(c_List_Omap(_1520770, _1520772), _1520774), _1520776) = hAPP(hAPP(c_List_Omap(_1520770, _1520772), _1520774), _1520778), -(_1520776 = _1520778)]]], (24478 ^ _777959) ^ [_1242880, _1242882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1242880), _1242882)), -(c_Nat__Transfer_Otsub(_1242882, _1242880) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1242882), _1242880))], (15084 ^ _777959) ^ [_1064851, _1064853, _1064855] : [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, _1064851)), _1064853)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1064851)), _1064855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1064853), _1064855)))], (37674 ^ _777959) ^ [_1498482, _1498484] : [c_Equiv__Relations_Oequivp(_1498482, hAPP(hAPP(c_COMBC(_1498482, tc_fun(tc_prod(_1498482, _1498482), tc_HOL_Obool), tc_fun(_1498482, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498482, tc_fun(tc_fun(tc_prod(_1498482, _1498482), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1498482, _1498482), tc_HOL_Obool), tc_fun(_1498482, tc_HOL_Obool)), _1498482), c_COMBC(_1498482, tc_fun(tc_prod(_1498482, _1498482), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1498482, tc_prod(_1498482, _1498482)), tc_fun(_1498482, tc_fun(tc_fun(tc_prod(_1498482, _1498482), tc_HOL_Obool), tc_HOL_Obool)), _1498482), hAPP(c_COMBB(tc_prod(_1498482, _1498482), tc_fun(tc_fun(tc_prod(_1498482, _1498482), tc_HOL_Obool), tc_HOL_Obool), _1498482), c_member(tc_prod(_1498482, _1498482)))), c_Product__Type_OPair(_1498482, _1498482)))), _1498484)), -(c_Equiv__Relations_Oequiv(_1498482, c_Orderings_Otop__class_Otop(tc_fun(_1498482, tc_HOL_Obool)), _1498484))], (13659 ^ _777959) ^ [_1029738, _1029740, _1029742, _1029744, _1029746] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029738, tc_HOL_Obool)), _1029740), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029742, tc_fun(_1029738, tc_HOL_Obool)), _1029744), _1029746)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029742, tc_fun(_1029738, tc_HOL_Obool)), _1029744), hAPP(hAPP(c_COMBB(tc_fun(_1029738, tc_HOL_Obool), tc_fun(_1029738, tc_HOL_Obool), _1029742), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029738, tc_HOL_Obool)), _1029740)), _1029746)))], (2674 ^ _777959) ^ [_817729, _817731, _817733, _817735, _817737, _817739, _817741, _817743] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_817743, _817739, _817735, _817731) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_817741, _817737, _817733, _817729)), _817743 = _817741, _817739 = _817737, _817735 = _817733, _817731 = _817729], (42413 ^ _777959) ^ [_1615414, _1615416, _1615418, _1615420, _1615422, _1615424] : [-(hAPP(c_Set_Ovimage(_1615414, tc_prod(_1615416, _1615418), _1615420), hAPP(hAPP(c_Product__Type_OSigma(_1615416, _1615418), _1615422), hAPP(c_COMBK(tc_fun(_1615418, tc_HOL_Obool), _1615416), _1615424))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1615414, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1615414, _1615416, hAPP(c_Fun_Ocomp(tc_prod(_1615416, _1615418), _1615416, _1615414, c_Product__Type_Ofst(_1615416, _1615418)), _1615420)), _1615422)), hAPP(c_Set_Ovimage(_1615414, _1615418, hAPP(c_Fun_Ocomp(tc_prod(_1615416, _1615418), _1615418, _1615414, c_Product__Type_Osnd(_1615416, _1615418)), _1615420)), _1615424)))], (42541 ^ _777959) ^ [_1619678, _1619680, _1619682, _1619684, _1619686, _1619688, _1619690] : [hAPP(c_Fun_Ocomp(_1619678, _1619680, _1619682, _1619684), _1619686) = hAPP(c_Fun_Ocomp(_1619680, _1619680, _1619682, c_Fun_Oid(_1619680)), _1619688), -(hAPP(_1619684, hAPP(_1619686, _1619690)) = hAPP(_1619688, _1619690))], (45264 ^ _777959) ^ [_1680271, _1680273] : [-(hBOOL(hAPP(c_List_Odistinct(_1680271), c_List_Oremdups(_1680271, _1680273))))], (50246 ^ _777959) ^ [_1796422, _1796424, _1796426, _1796428] : [-(c_New__Random__Sequence_Opos__empty(_1796422, _1796424, _1796426, _1796428) = c_New__DSequence_Opos__empty(_1796422))], (42871 ^ _777959) ^ [_1627715, _1627717, _1627719] : [class_Groups_Omonoid__add(_1627715), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1627715), hAPP(hAPP(c_List_Oappend(_1627715), _1627717), _1627719)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1627715), hAPP(c_List_Omonoid__add__class_Olistsum(_1627715), _1627717)), hAPP(c_List_Omonoid__add__class_Olistsum(_1627715), _1627719)))], (20795 ^ _777959) ^ [_1174007, _1174009, _1174011, _1174013] : [class_Groups_Ocomm__monoid__add(_1174007), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1174009), _1174011))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1174009, _1174007), _1174013), _1174011) = c_Groups_Ozero__class_Ozero(_1174007))], (28960 ^ _777959) ^ [_1323837, _1323839, _1323841] : [class_Orderings_Oord(_1323837), 28963 ^ _777959 : [(28970 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323837), _1323841), _1323839)), -(hBOOL(hAPP(hAPP(c_member(_1323837), _1323839), hAPP(c_SetInterval_Oord__class_OatLeast(_1323837), _1323841))))], (28964 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1323837), _1323839), hAPP(c_SetInterval_Oord__class_OatLeast(_1323837), _1323841))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323837), _1323841), _1323839)))]]], (17183 ^ _777959) ^ [_1106455, _1106457] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1106455), _1106457)), _1106457) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1106455), _1106457))], (4276 ^ _777959) ^ [_842692, _842694, _842696, _842698, _842700, _842702] : [-(c_Relation_Orel__comp(_842702, _842698, _842694) = c_Relation_Orel__comp(_842700, _842696, _842692)), _842702 = _842700, _842698 = _842696, _842694 = _842692], (37026 ^ _777959) ^ [_1482233, _1482235, _1482237, _1482239] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1482233), _1482235)), 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)), _1482237), _1482233)), 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)), _1482239), _1482235)), 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)), _1482237), _1482239)), _1482235)), c_FunDef_Omax__weak)))], (29707 ^ _777959) ^ [_1338407, _1338409] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1338407, tc_HOL_Obool), hAPP(c_Set_OPow(_1338407), _1338409)) = _1338409)], (44002 ^ _777959) ^ [_1652786, _1652788] : [-(hAPP(c_List_Ofilter(_1652786, _1652788), c_List_Olist_ONil(_1652786)) = c_List_Olist_ONil(_1652786))], (13889 ^ _777959) ^ [_1034978, _1034980, _1034982, _1034984, _1034986] : [hBOOL(hAPP(hAPP(c_member(_1034978), _1034980), _1034982)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1034984, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1034978, tc_fun(_1034984, tc_HOL_Obool)), _1034982), _1034986)), hAPP(_1034986, _1034980))))], (9972 ^ _777959) ^ [_951273, _951275] : [class_Lattices_Obounded__lattice__bot(_951273), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951273), _951275), c_Orderings_Obot__class_Obot(_951273)) = c_Orderings_Obot__class_Obot(_951273))], (16697 ^ _777959) ^ [_1097918, _1097920, _1097922, _1097924] : [class_Orderings_Olinorder(_1097918), 16700 ^ _777959 : [(16709 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097918), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1097918), _1097920), _1097922)), _1097924))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097918), _1097920), _1097924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097918), _1097922), _1097924))], (16701 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097918), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1097918), _1097920), _1097922)), _1097924)), 16704 ^ _777959 : [(16707 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097918), _1097922), _1097924)))], (16705 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097918), _1097920), _1097924)))]]]]], (51338 ^ _777959) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (20563 ^ _777959) ^ [_1170064, _1170066, _1170068, _1170070, _1170072, _1170074] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1170064), -(_1170066 = c_Groups_Ozero__class_Ozero(_1170064)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170064), _1170068), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170064), _1170066), _1170072)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170064), _1170070), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1170064), _1170066), _1170074)), _1170068 = _1170070, -(_1170072 = _1170074)], (50930 ^ _777959) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (42435 ^ _777959) ^ [_1615952, _1615954] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1615952)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1615954)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1615952), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1615954)) = c_List_Olist_ONil(tc_Int_Oint))], (36276 ^ _777959) ^ [_1465740, _1465742, _1465744] : [36278 ^ _777959 : [(36281 ^ _777959) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1465740, _1465742), 36277 ^ [_1465740, _1465742, _1465744]))], (36279 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1465742, 36277 ^ [_1465740, _1465742, _1465744]), _1465744)))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1465740, _1465742), _1465744)))], (3578 ^ _777959) ^ [_831957, _831959, _831961, _831963, _831965, _831967, _831969, _831971] : [-(c_Wellfounded_Olex__prod(_831971, _831967, _831963, _831959) = c_Wellfounded_Olex__prod(_831969, _831965, _831961, _831957)), _831971 = _831969, _831967 = _831965, _831963 = _831961, _831959 = _831957], (41308 ^ _777959) ^ [_1586900, _1586902, _1586904, _1586906] : [41311 ^ _777959 : [(41316 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586900, _1586900)), hAPP(hAPP(c_Product__Type_OPair(_1586900, _1586900), 41310 ^ [_1586900, _1586902, _1586904, _1586906]), 41309 ^ [_1586900, _1586902, _1586904, _1586906])), _1586902))], (41314 ^ _777959) ^ [] : [41309 ^ [_1586900, _1586902, _1586904, _1586906] = 41310 ^ [_1586900, _1586902, _1586904, _1586906]], (41312 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586900, _1586900)), hAPP(hAPP(c_Product__Type_OPair(_1586900, _1586900), 41309 ^ [_1586900, _1586902, _1586904, _1586906]), 41310 ^ [_1586900, _1586902, _1586904, _1586906])), _1586902))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1586900), tc_List_Olist(_1586900))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1586900), tc_List_Olist(_1586900)), _1586904), _1586906)), c_List_Olexord(_1586900, _1586902)))), -(_1586904 = _1586906), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1586900), tc_List_Olist(_1586900))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1586900), tc_List_Olist(_1586900)), _1586906), _1586904)), c_List_Olexord(_1586900, _1586902))))], (28293 ^ _777959) ^ [_1311352, _1311354] : [c_Nat__Transfer_Onat__set(_1311352), c_Nat__Transfer_Onat__set(_1311354), 28300 ^ _777959 : [(28307 ^ _777959) ^ [] : [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), _1311352)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311354))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1311352), _1311354)))], (28301 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1311352), _1311354)), -(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), _1311352)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311354))))]]], (34665 ^ _777959) ^ [] : [-(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))))], (8864 ^ _777959) ^ [_930722, _930724, _930726] : [class_Orderings_Oorder(_930722), 8867 ^ _777959 : [(8876 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930722), _930724), _930726))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930722), _930724), _930726)), -(_930724 = _930726)], (8868 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930722), _930724), _930726)), 8871 ^ _777959 : [(8874 ^ _777959) ^ [] : [_930724 = _930726], (8872 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930722), _930724), _930726)))]]]]], (43476 ^ _777959) ^ [_1642244, _1642246] : [-(_1642244 = c_List_Olist_ONil(_1642246)), -(hBOOL(hAPP(hAPP(c_member(_1642246), hAPP(c_List_Ohd(_1642246), _1642244)), hAPP(c_List_Oset(_1642246), _1642244))))], (278 ^ _777959) ^ [_782242, _782244, _782246, _782248] : [-(c_Equiv__Relations_Oequivp(_782246, _782242)), c_Equiv__Relations_Oequivp(_782248, _782244), _782248 = _782246, _782244 = _782242], (37314 ^ _777959) ^ [_1489891, _1489893] : [-(c_Relation_OId__on(_1489891, _1489893) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1489891, tc_fun(tc_prod(_1489891, _1489891), tc_HOL_Obool)), _1489893), hAPP(hAPP(c_COMBC(_1489891, tc_fun(tc_prod(_1489891, _1489891), tc_HOL_Obool), tc_fun(tc_prod(_1489891, _1489891), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1489891, _1489891), tc_fun(tc_fun(tc_prod(_1489891, _1489891), tc_HOL_Obool), tc_fun(tc_prod(_1489891, _1489891), tc_HOL_Obool)), _1489891), c_Set_Oinsert(tc_prod(_1489891, _1489891))), hAPP(hAPP(c_COMBS(_1489891, _1489891, tc_prod(_1489891, _1489891)), c_Product__Type_OPair(_1489891, _1489891)), c_COMBI(_1489891)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1489891, _1489891), tc_HOL_Obool)))))], (45534 ^ _777959) ^ [_1685915, _1685917, _1685919, _1685921] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1685915)), _1685917), hAPP(c_List_Oset(tc_List_Olist(_1685915)), c_Enum_On__lists(_1685915, _1685919, _1685921)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685915)), _1685917) = _1685919)], (7306 ^ _777959) ^ [_900458, _900460, _900462, _900464] : [class_Lattices_Osemilattice__sup(_900458), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900458), _900460), _900462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900458), _900460), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_900458), _900464), _900462))))], (42762 ^ _777959) ^ [_1625062, _1625064, _1625066, _1625068] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1625062)), hAPP(hAPP(c_List_Oappend(_1625062), _1625064), _1625066)), c_List_Olists(_1625062, _1625068)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1625062)), _1625064), c_List_Olists(_1625062, _1625068))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1625062)), _1625066), c_List_Olists(_1625062, _1625068)))], (34363 ^ _777959) ^ [_1424808, _1424810] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1424808), _1424810)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1424808)), c_Int_OBit1(_1424810))))], (38402 ^ _777959) ^ [_1514178, _1514180, _1514182, _1514184, _1514186] : [-(c_Fun_Oinj__on(_1514178, _1514180, _1514182, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1514178, tc_HOL_Obool)), _1514184), _1514186))), c_Fun_Oinj__on(_1514178, _1514180, _1514182, _1514184), c_Fun_Oinj__on(_1514178, _1514180, _1514182, _1514186), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1514180, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1514178, _1514180, _1514182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1514178, tc_HOL_Obool)), _1514184), _1514186))), hAPP(c_Set_Oimage(_1514178, _1514180, _1514182), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1514178, tc_HOL_Obool)), _1514186), _1514184))) = c_Orderings_Obot__class_Obot(tc_fun(_1514180, tc_HOL_Obool))], (4570 ^ _777959) ^ [_847239, _847241] : [_847241 = _847239, -(c_HOL_Oequal__class_Oequal(_847241) = c_HOL_Oequal__class_Oequal(_847239))], (26744 ^ _777959) ^ [_1284445, _1284447, _1284449, _1284451] : [class_Fields_Olinordered__field(_1284445), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284445), _1284447), c_Groups_Ozero__class_Ozero(_1284445))), 26751 ^ _777959 : [(26758 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284445), _1284451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284445), _1284449), _1284447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284445), _1284449), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1284445), _1284451), _1284447))))], (26752 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284445), _1284449), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1284445), _1284451), _1284447))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1284445), _1284451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1284445), _1284449), _1284447))))]]], (34045 ^ _777959) ^ [_1419132, _1419134] : [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), _1419132))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1419134)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1419132))) = 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), _1419134), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1419132)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (16159 ^ _777959) ^ [_1086157] : [-(hAPP(c_Nat_OSuc, _1086157) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1086157), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (40411 ^ _777959) ^ [_1562380, _1562382, _1562384, _1562386, _1562388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1562380), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1562382)), _1562384))), 40414 ^ _777959 : [(40421 ^ _777959) ^ [] : [-(_1562380 = _1562386), -(hAPP(hAPP(c_List_Onth(_1562382), hAPP(hAPP(c_List_Olist__update(_1562382, _1562384), _1562380), _1562388)), _1562386) = hAPP(hAPP(c_List_Onth(_1562382), _1562384), _1562386))], (40415 ^ _777959) ^ [] : [_1562380 = _1562386, -(hAPP(hAPP(c_List_Onth(_1562382), hAPP(hAPP(c_List_Olist__update(_1562382, _1562384), _1562380), _1562388)), _1562386) = _1562388)]]], (11012 ^ _777959) ^ [_973713, _973715, _973717, _973719] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_973713, tc_Option_Ooption(_973715)), hAPP(c_COMBK(tc_Option_Ooption(_973715), _973713), c_Option_Ooption_ONone(_973715))), _973717), c_Option_Ooption_ONone(_973715)), _973719) = c_Option_Ooption_ONone(_973715))], (35840 ^ _777959) ^ [_1457852, _1457854, _1457856, _1457858] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1457852, _1457854, _1457856), hAPP(hAPP(c_COMBB(tc_fun(_1457854, tc_prod(_1457852, _1457854)), tc_fun(_1457854, _1457856), _1457852), hAPP(c_COMBB(tc_prod(_1457852, _1457854), _1457856, _1457854), _1457858)), c_Product__Type_OPair(_1457852, _1457854))) = _1457858)], (50086 ^ _777959) ^ [_1793405, _1793407] : [class_HOL_Oequal(_1793405), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1793405), _1793407), _1793407)))], (49548 ^ _777959) ^ [_1781860, _1781862, _1781864] : [-(hBOOL(hAPP(hAPP(c_member(_1781860), _1781862), hAPP(c_List_Oset(_1781860), _1781864)))), 49549 ^ _777959 : [(49550 ^ _777959) ^ [_1781949] : [49551 ^ _777959 : [(49552 ^ _777959) ^ [_1782022] : [_1781864 = hAPP(hAPP(c_List_Oappend(_1781860), _1781949), hAPP(hAPP(c_List_Olist_OCons(_1781860), _1781862), _1782022))]], -(hBOOL(hAPP(hAPP(c_member(_1781860), _1781862), hAPP(c_List_Oset(_1781860), _1781949))))]]], (20453 ^ _777959) ^ [_1168047, _1168049, _1168051, _1168053] : [class_Rings_Olinordered__semiring__strict(_1168047), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168047), _1168049), _1168051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168047), c_Groups_Ozero__class_Ozero(_1168047)), _1168053)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168047), _1168053), _1168049)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168047), _1168053), _1168051))))], (43789 ^ _777959) ^ [_1648986, _1648988, _1648990] : [_1648986 = c_List_Olist_ONil(_1648988), -(c_List_Olast(_1648988, hAPP(hAPP(c_List_Olist_OCons(_1648988), _1648990), _1648986)) = _1648990)], (6737 ^ _777959) ^ [_887416, _887418, _887420] : [-(hBOOL(hAPP(hAPP(c_member(_887416), _887418), hAPP(hAPP(c_Set_Oinsert(_887416), _887418), _887420))))], (23082 ^ _777959) ^ [_1218056, _1218058] : [-(_1218056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1218058), _1218056) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1218058), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1218058), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1218056), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (16401 ^ _777959) ^ [_1091975, _1091977] : [class_Orderings_Olinorder(_1091975), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1091975), _1091977), _1091977) = _1091977)], (14271 ^ _777959) ^ [_1043974, _1043976, _1043978, _1043980, _1043982] : [class_Complete__Lattice_Ocomplete__lattice(_1043974), hBOOL(hAPP(hAPP(c_member(_1043976), _1043978), _1043980)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1043974), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1043976, _1043974), _1043980), _1043982)), hAPP(_1043982, _1043978))))], (24888 ^ _777959) ^ [_1249888, _1249890, _1249892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1249888), 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)), _1249890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249890), _1249892)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1249888), _1249890)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1249888), _1249892))))], (34231 ^ _777959) ^ [_1422454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422454), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1422454)), c_Int_OPls)))], (33231 ^ _777959) ^ [_1405178] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1405178) = _1405178)], (48940 ^ _777959) ^ [_1766115] : [-(hAPP(c_Relation_Oconverse(_1766115, _1766115), c_Relation_OId(_1766115)) = c_Relation_OId(_1766115))], (34885 ^ _777959) ^ [_1434530, _1434532] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1434530)), -(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)))), _1434532))), 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)))), _1434530)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1434532), _1434530))], (51218 ^ _777959) ^ [_1812231, _1812233] : [-(class_Finite__Set_Ofinite(tc_prod(_1812231, _1812233))), class_Finite__Set_Ofinite(_1812231), class_Finite__Set_Ofinite(_1812233)], (29052 ^ _777959) ^ [_1325436, _1325438] : [class_Orderings_Olinorder(_1325436), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1325436, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1325436), _1325438)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1325436), _1325438))], (49558 ^ _777959) ^ [_1782161, _1782163, _1782165] : [hBOOL(hAPP(hAPP(c_member(_1782161), _1782163), hAPP(c_List_Oset(_1782161), _1782165))), -(_1782165 = hAPP(hAPP(c_List_Oappend(_1782161), 49561 ^ [_1782161, _1782163, _1782165]), hAPP(hAPP(c_List_Olist_OCons(_1782161), _1782163), 49562 ^ [_1782161, _1782163, _1782165])))], (23315 ^ _777959) ^ [_1222230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1222230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222230)))], (38206 ^ _777959) ^ [_1509862, _1509864, _1509866] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1509862), _1509864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509862, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1509862, _1509862, _1509866), _1509864)), _1509864)), 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[hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1600417)), hAPP(hAPP(c_List_Olist_OCons(_1600417), _1600419), _1600421)), c_List_Olists(_1600417, _1600423))), 41806 ^ _777959 : [(41809 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1600417)), _1600421), c_List_Olists(_1600417, _1600423))))], (41807 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1600417), _1600419), _1600423)))]]], (4444 ^ _777959) ^ [_845222, _845224, _845226, _845228] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_845228, _845224) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_845226, _845222)), _845228 = _845226, _845224 = _845222], (50166 ^ _777959) ^ [_1794746, _1794748] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1794746)), c_Int_OBit1(_1794748))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1794746), _1794748)))], (40570 ^ _777959) ^ [_1565868, _1565870, _1565872] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1565868), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1565870))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1565870), _1565868), _1565872)) = 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), _1565870)), _1565872)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1565870), _1565868)))], (21566 ^ _777959) ^ [_1187774, _1187776, _1187778] : [class_Rings_Olinordered__idom(_1187774), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187774), c_Groups_Ozero__class_Ozero(_1187774)), _1187776)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187774), c_Groups_Ozero__class_Ozero(_1187774)), _1187778)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187774), _1187778), c_Groups_Oone__class_Oone(_1187774))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187774), _1187776), _1187778)), _1187776)))], (28756 ^ _777959) ^ [_1319671, _1319673, _1319675, _1319677] : [class_Orderings_Oorder(_1319671), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319671, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1319671, _1319673, _1319675)), c_SetInterval_Oord__class_OatLeastAtMost(_1319671, _1319675, _1319677)) = c_Orderings_Obot__class_Obot(tc_fun(_1319671, tc_HOL_Obool)))], (29062 ^ _777959) ^ [] : [-(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)))], (46261 ^ _777959) ^ [_1701506, _1701508, _1701510] : [hBOOL(hAPP(c_List_Olistsp(_1701506, hAPP(hAPP(c_COMBC(_1701506, tc_fun(_1701506, tc_HOL_Obool), tc_HOL_Obool), c_member(_1701506)), _1701508)), _1701510)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1701506)), _1701510), c_List_Olists(_1701506, _1701508))))], (2954 ^ _777959) ^ [_822167, _822169, _822171, _822173, _822175, _822177, _822179, _822181] : [-(c_Nat_Onat_Onat__case(_822181, _822177, _822173, _822169) = c_Nat_Onat_Onat__case(_822179, _822175, _822171, _822167)), _822181 = _822179, _822177 = _822175, _822173 = _822171, _822169 = _822167], (12030 ^ _777959) ^ [_996273, _996275, _996277] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996273), _996275)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996275), _996277)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996273), _996277)))], (45712 ^ _777959) ^ [_1690055, _1690057, _1690059] : [class_Orderings_Olinorder(_1690055), -(c_List_Olinorder__class_Osort__key(_1690057, _1690055, _1690059, c_List_Olist_ONil(_1690057)) = c_List_Olist_ONil(_1690057))], (13387 ^ _777959) ^ [_1023141] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1023141, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1023141, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1023141, tc_HOL_Obool)))], (35511 ^ _777959) ^ [_1451010, _1451012] : [-(c_Divides_Odivmod__int(_1451010, _1451012) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1451010), _1451012)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1451010, _1451012)))], (47324 ^ _777959) ^ [_1728210, _1728212, _1728214, _1728216, _1728218] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1728210, _1728212)), hAPP(hAPP(c_Product__Type_OPair(_1728210, _1728212), _1728214), _1728216)), _1728218)), -(hBOOL(hAPP(hAPP(c_member(_1728210), _1728214), hAPP(c_Relation_ODomain(_1728210, _1728212), _1728218))))], (9122 ^ _777959) ^ [_934482, _934484, _934486, _934488] : [class_Orderings_Oorder(_934482), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934482), _934484), _934486)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934482), _934488), _934484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934482), _934488), _934486)))], (47385 ^ _777959) ^ [_1729756, _1729758, _1729760] : [-(hAPP(c_Relation_ODomain(_1729756, _1729758), hAPP(c_Set_OCollect(tc_prod(_1729756, _1729758)), hAPP(c_Product__Type_Oprod_Oprod__case(_1729756, _1729758, tc_HOL_Obool), _1729760))) = hAPP(c_Set_OCollect(_1729756), hAPP(hAPP(c_COMBB(tc_fun(_1729758, tc_HOL_Obool), tc_HOL_Obool, _1729756), c_HOL_OEx(_1729758)), _1729760)))], (5196 ^ _777959) ^ [_857482, _857484] : [_857484 = _857482, -(c_Lattices_Osemilattice__inf__class_Oinf(_857484) = c_Lattices_Osemilattice__inf__class_Oinf(_857482))], (12754 ^ _777959) ^ [_1009375, _1009377, _1009379] : [class_Groups_Oordered__ab__group__add(_1009375), 12757 ^ _777959 : [(12764 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009375), _1009379), _1009377)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009375), hAPP(c_Groups_Ouminus__class_Ouminus(_1009375), _1009377)), hAPP(c_Groups_Ouminus__class_Ouminus(_1009375), _1009379))))], (12758 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009375), hAPP(c_Groups_Ouminus__class_Ouminus(_1009375), _1009377)), hAPP(c_Groups_Ouminus__class_Ouminus(_1009375), _1009379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009375), _1009379), _1009377)))]]], (41701 ^ _777959) ^ [_1597348, _1597350, _1597352, _1597354, _1597356] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597348), tc_List_Olist(_1597348))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597348), tc_List_Olist(_1597348)), _1597350), hAPP(hAPP(c_List_Olist_OCons(_1597348), _1597352), _1597354))), c_List_Olistrel(_1597348, _1597356))), 41706 ^ _777959 : [(41711 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1597348), tc_List_Olist(_1597348))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1597348), tc_List_Olist(_1597348)), 41705 ^ [_1597348, _1597350, _1597352, _1597354, _1597356]), _1597354)), c_List_Olistrel(_1597348, _1597356))))], (41709 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597348, _1597348)), hAPP(hAPP(c_Product__Type_OPair(_1597348, _1597348), 41704 ^ [_1597348, _1597350, _1597352, _1597354, _1597356]), _1597352)), _1597356)))], (41707 ^ _777959) ^ [] : [-(_1597350 = hAPP(hAPP(c_List_Olist_OCons(_1597348), 41704 ^ [_1597348, _1597350, _1597352, _1597354, _1597356]), 41705 ^ [_1597348, _1597350, _1597352, _1597354, _1597356]))]]], (16569 ^ _777959) ^ [_1095619, _1095621, _1095623] : [class_Groups_Olinordered__ab__group__add(_1095619), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1095619), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095619), _1095621), _1095623)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095619), hAPP(c_Groups_Ouminus__class_Ouminus(_1095619), _1095621)), hAPP(c_Groups_Ouminus__class_Ouminus(_1095619), _1095623)))], (41890 ^ _777959) ^ [_1602820, _1602822, _1602824, _1602826, _1602828] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1602820, _1602822), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602820, tc_HOL_Obool)), _1602824), _1602826)), _1602828) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1602820, _1602822), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1602820, _1602822), _1602824), _1602828)), hAPP(hAPP(c_Product__Type_OSigma(_1602820, _1602822), _1602826), _1602828)))], (13181 ^ _777959) ^ [_1018439, _1018441, _1018443] : [class_Rings_Ocomm__ring__1(_1018439), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1018439), _1018441), _1018443) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1018439), _1018441), hAPP(c_Groups_Ouminus__class_Ouminus(_1018439), _1018443)))], (22559 ^ _777959) ^ [_1207953, _1207955, _1207957, _1207959] : [class_Rings_Ocomm__semiring__1(_1207953), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207953), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207953), c_Groups_Oone__class_Oone(_1207953)), c_Groups_Oone__class_Oone(_1207953))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207953), hAPP(hAPP(c_COMBB(_1207953, _1207953, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1207953), _1207955)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1207953, _1207953), hAPP(hAPP(c_COMBB(_1207953, tc_fun(_1207953, _1207953), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1207953)), c_Nat_Osemiring__1__class_Oof__nat(_1207953))), _1207957))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1207959))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207953), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1207953), _1207959)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207953), _1207955), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1207953), _1207955), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1207953), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1207953), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1207959), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1207957)))))], (39994 ^ _777959) ^ [_1552340, _1552342, _1552344, _1552346, _1552348] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1552340)), _1552342) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1552344)), _1552346), 39997 ^ _777959 : [(40006 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1552340, _1552344), _1552342), _1552346) = _1552348), hAPP(hAPP(c_List_Omap(tc_prod(_1552340, _1552344), _1552340), c_Product__Type_Ofst(_1552340, _1552344)), _1552348) = _1552342, hAPP(hAPP(c_List_Omap(tc_prod(_1552340, _1552344), _1552344), c_Product__Type_Osnd(_1552340, _1552344)), _1552348) = _1552346], (39998 ^ _777959) ^ [] : [hAPP(hAPP(c_List_Ozip(_1552340, _1552344), _1552342), _1552346) = _1552348, 40001 ^ _777959 : [(40004 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1552340, _1552344), _1552344), c_Product__Type_Osnd(_1552340, _1552344)), _1552348) = _1552346)], (40002 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1552340, _1552344), _1552340), c_Product__Type_Ofst(_1552340, _1552344)), _1552348) = _1552342)]]]]], (25688 ^ _777959) ^ [_1265109, _1265111] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1265109, _1265111))))], (46832 ^ _777959) ^ [_1716548, _1716550, _1716552, _1716554, _1716556, _1716558, _1716560] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1716548, _1716552)), hAPP(hAPP(c_Product__Type_OPair(_1716548, _1716552), _1716558), _1716560)), hAPP(hAPP(c_Relation_Orel__comp(_1716548, _1716550, _1716552), _1716554), _1716556))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1716548, _1716550, _1716552, hAPP(hAPP(c_COMBC(_1716548, tc_fun(tc_prod(_1716548, _1716550), tc_HOL_Obool), tc_fun(_1716550, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1716550, tc_fun(tc_fun(tc_prod(_1716548, _1716550), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1716548, _1716550), tc_HOL_Obool), tc_fun(_1716550, tc_HOL_Obool)), _1716548), c_COMBC(_1716550, tc_fun(tc_prod(_1716548, _1716550), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1716550, tc_prod(_1716548, _1716550)), tc_fun(_1716550, tc_fun(tc_fun(tc_prod(_1716548, _1716550), tc_HOL_Obool), tc_HOL_Obool)), _1716548), hAPP(c_COMBB(tc_prod(_1716548, _1716550), tc_fun(tc_fun(tc_prod(_1716548, _1716550), tc_HOL_Obool), tc_HOL_Obool), _1716550), c_member(tc_prod(_1716548, _1716550)))), c_Product__Type_OPair(_1716548, _1716550)))), _1716554), hAPP(hAPP(c_COMBC(_1716550, tc_fun(tc_prod(_1716550, _1716552), tc_HOL_Obool), tc_fun(_1716552, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1716552, tc_fun(tc_fun(tc_prod(_1716550, _1716552), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1716550, _1716552), tc_HOL_Obool), tc_fun(_1716552, tc_HOL_Obool)), _1716550), c_COMBC(_1716552, tc_fun(tc_prod(_1716550, _1716552), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1716552, tc_prod(_1716550, _1716552)), tc_fun(_1716552, tc_fun(tc_fun(tc_prod(_1716550, _1716552), tc_HOL_Obool), tc_HOL_Obool)), _1716550), hAPP(c_COMBB(tc_prod(_1716550, _1716552), tc_fun(tc_fun(tc_prod(_1716550, _1716552), tc_HOL_Obool), tc_HOL_Obool), _1716552), c_member(tc_prod(_1716550, _1716552)))), c_Product__Type_OPair(_1716550, _1716552)))), _1716556)), _1716558), _1716560)))], (1380 ^ _777959) ^ [_797933, _797935] : [-(class_Lazy__Sequence_Osmall__lazy(_797933)), _797935 = _797933, class_Lazy__Sequence_Osmall__lazy(_797935)], (12564 ^ _777959) ^ [_1006394, _1006396] : [-(_1006394 = _1006396), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006394), _1006396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006396), _1006394)))], (45332 ^ _777959) ^ [_1681411, _1681413] : [c_List_Oremdups(_1681411, _1681413) = _1681413, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681411)), c_List_Oremdups(_1681411, _1681413)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681411)), _1681413))], (44521 ^ _777959) ^ [_1662843, _1662845, _1662847, _1662849] : [c_List_Oupt(_1662843, _1662845) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1662847), _1662849), 44524 ^ _777959 : [(44529 ^ _777959) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1662843), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1662845) = _1662849)], (44527 ^ _777959) ^ [] : [-(_1662843 = _1662847)], (44525 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1662843), _1662845)))]]], (17142 ^ _777959) ^ [_1105750, _1105752, _1105754] : [class_Complete__Lattice_Ocomplete__lattice(_1105750), class_Orderings_Olinorder(_1105750), 17149 ^ _777959 : [(17159 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105750), c_Complete__Lattice_OInf__class_OInf(_1105750, _1105752)), _1105754))), 17160 ^ _777959 : [(17161 ^ _777959) ^ [_1106056] : [hBOOL(hAPP(hAPP(c_member(_1105750), _1106056), _1105752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105750), _1106056), _1105754))]]], (17150 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105750), c_Complete__Lattice_OInf__class_OInf(_1105750, _1105752)), _1105754)), 17154 ^ _777959 : [(17157 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1105750), 17153 ^ [_1105750, _1105752, _1105754]), _1105754)))], (17155 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1105750), 17153 ^ [_1105750, _1105752, _1105754]), _1105752)))]]]]], (43626 ^ _777959) ^ [_1645175, _1645177, _1645179, _1645181] : [class_Groups_Osemigroup__add(_1645175), -(hAPP(c_List_Ofoldl(_1645175, _1645175, c_Groups_Oplus__class_Oplus(_1645175), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1645175), _1645177), _1645179)), _1645181) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1645175), _1645177), hAPP(c_List_Ofoldl(_1645175, _1645175, c_Groups_Oplus__class_Oplus(_1645175), _1645179), _1645181)))], (23799 ^ _777959) ^ [_1230520, _1230522, _1230524, _1230526] : [class_Rings_Olinordered__semidom(_1230520), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230520), hAPP(hAPP(c_Power_Opower__class_Opower(_1230520), _1230522), _1230524)), hAPP(hAPP(c_Power_Opower__class_Opower(_1230520), _1230526), _1230524))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230520), c_Groups_Ozero__class_Ozero(_1230520)), _1230526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1230520), _1230522), _1230526)))], (624 ^ _777959) ^ [_787565, _787567, _787569, _787571] : [-(c_Nitpick_Owf_H(_787569, _787565)), c_Nitpick_Owf_H(_787571, _787567), _787571 = _787569, _787567 = _787565], (18510 ^ _777959) ^ [_1133595, _1133597, _1133599, _1133601, _1133603] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1133595, _1133597, hAPP(hAPP(c_Set_Oinsert(_1133595), _1133599), _1133601)), _1133603))), 18511 ^ _777959 : [(18512 ^ _777959) ^ [_1133699, _1133701] : [hAPP(hAPP(c_Set_Oinsert(_1133595), _1133599), _1133601) = hAPP(hAPP(c_Set_Oinsert(_1133595), _1133701), _1133699), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1133595, _1133595, _1133597, _1133701, _1133699), _1133603)), -(hBOOL(hAPP(hAPP(c_member(_1133595), _1133701), _1133699)))]]], (33973 ^ _777959) ^ [_1417963, _1417965, _1417967, _1417969] : [-(hAPP(c_Nat_Onat_Onat__rec(_1417963, _1417965, _1417967), hAPP(c_Nat_OSuc, _1417969)) = hAPP(hAPP(_1417967, _1417969), hAPP(c_Nat_Onat_Onat__rec(_1417963, _1417965, _1417967), _1417969)))], (7970 ^ _777959) ^ [_913887, _913889, _913891, _913893] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913887, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913887, tc_HOL_Obool)), _913889), _913891)), _913893) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913887, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913887, tc_HOL_Obool)), _913889), _913893)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913887, tc_HOL_Obool)), _913891), _913893)))], (20743 ^ _777959) ^ [_1173113, _1173115] : [class_Groups_Oab__group__add(_1173113), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173113), hAPP(c_Groups_Ouminus__class_Ouminus(_1173113), _1173115)), _1173115) = c_Groups_Ozero__class_Ozero(_1173113))], (5908 ^ _777959) ^ [_871981, _871983, _871985, _871987, _871989] : [c_Hoare__Mirabelle_Ohoare__derivs(_871981, _871983, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871981)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871981), _871985), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _871987))), _871989)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871981), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_871981, _871983, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_871981)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_871981), _871985), hAPP(c_Com_Ocom_OBODY, _871987)), _871989)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_871981), tc_HOL_Obool)))))], (7378 ^ _777959) ^ [_901728, _901730, _901732, _901734] : [class_Lattices_Osemilattice__sup(_901728), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901728), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901728), _901730), _901732)), _901734)), 7385 ^ _777959 : [(7388 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901728), _901732), _901734)))], (7386 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901728), _901730), _901734)))]]], (14129 ^ _777959) ^ [_1040734, _1040736, _1040738, _1040740, _1040742, _1040744] : [-(c_Map_Omap__add(_1040734, _1040736, _1040738, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1040734, tc_Option_Ooption(_1040736)), _1040740), _1040742), hAPP(c_Option_Ooption_OSome(_1040736), _1040744))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1040734, tc_Option_Ooption(_1040736)), c_Map_Omap__add(_1040734, _1040736, _1040738, _1040740)), _1040742), hAPP(c_Option_Ooption_OSome(_1040736), _1040744)))], (15524 ^ _777959) ^ [_1073116, _1073118, _1073120] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073116), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1073118), _1073120)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073116), _1073118)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073116), _1073120)))], (13585 ^ _777959) ^ [_1027570, _1027572, _1027574, _1027576, _1027578] : [-(_1027570 = c_Orderings_Obot__class_Obot(tc_fun(_1027572, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1027574, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1027572, tc_fun(_1027574, tc_HOL_Obool)), _1027570), _1027576)), _1027578) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1027572, tc_fun(_1027574, tc_HOL_Obool)), _1027570), hAPP(hAPP(c_COMBC(_1027572, tc_fun(_1027574, tc_HOL_Obool), tc_fun(_1027574, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1027574, tc_HOL_Obool), tc_fun(tc_fun(_1027574, tc_HOL_Obool), tc_fun(_1027574, tc_HOL_Obool)), _1027572), c_Groups_Ominus__class_Ominus(tc_fun(_1027574, tc_HOL_Obool))), _1027576)), _1027578)))], (23365 ^ _777959) ^ [_1223049, _1223051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1223049)), 23368 ^ _777959 : [(23377 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223049), _1223051) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1223049 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1223051 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (23369 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223049), _1223051) = c_Groups_Oone__class_Oone(tc_Int_Oint), 23372 ^ _777959 : [(23375 ^ _777959) ^ [] : [-(_1223051 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (23373 ^ _777959) ^ [] : [-(_1223049 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (47240 ^ _777959) ^ [_1725635, _1725637, _1725639] : [-(hAPP(c_Relation_ORange(_1725635, _1725637), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1725635, _1725637), tc_HOL_Obool), _1725639)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1725635, _1725637), tc_HOL_Obool), tc_fun(_1725637, tc_HOL_Obool)), _1725639), c_Relation_ORange(_1725635, _1725637)))], (28658 ^ _777959) ^ [_1317822, _1317824, _1317826, _1317828] : [class_Orderings_Olinorder(_1317822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317822), _1317824), _1317826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1317822), _1317826), _1317828)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1317822, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1317822, _1317824), _1317826)), c_SetInterval_Oord__class_OatLeastAtMost(_1317822, _1317826, _1317828)) = c_SetInterval_Oord__class_OatLeastAtMost(_1317822, _1317824, _1317828))], (36307 ^ _777959) ^ [_1466283, _1466285, _1466287] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1466283, _1466285), _1466287)), -(c_Divides_Odivmod__nat(_1466283, _1466285) = _1466287)], (21548 ^ _777959) ^ [_1187451, _1187453, _1187455] : [class_Rings_Olinordered__idom(_1187451), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187451), c_Groups_Ozero__class_Ozero(_1187451)), _1187453)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187451), c_Groups_Ozero__class_Ozero(_1187451)), _1187455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187451), _1187455), c_Groups_Oone__class_Oone(_1187451))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1187451), _1187455), _1187453)), _1187453)))], (40381 ^ _777959) ^ [_1561719, _1561721, _1561723, _1561725, _1561727, _1561729] : [-(hAPP(hAPP(c_List_Omap(_1561719, _1561721), _1561723), hAPP(hAPP(c_List_Olist__update(_1561719, _1561725), _1561727), _1561729)) = hAPP(hAPP(c_List_Olist__update(_1561721, hAPP(hAPP(c_List_Omap(_1561719, _1561721), _1561723), _1561725)), _1561727), hAPP(_1561723, _1561729)))], (18951 ^ _777959) ^ [_1141800, _1141802, _1141804] : [class_Lattices_Oab__semigroup__idem__mult(_1141800), hAPP(_1141802, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141800), 18956 ^ [_1141800, _1141802, _1141804]), 18957 ^ [_1141800, _1141802, _1141804])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141800), hAPP(_1141802, 18956 ^ [_1141800, _1141802, _1141804])), hAPP(_1141802, 18957 ^ [_1141800, _1141802, _1141804])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1141800), _1141804)), -(_1141804 = c_Orderings_Obot__class_Obot(tc_fun(_1141800, tc_HOL_Obool))), -(hAPP(_1141802, hAPP(c_Finite__Set_Ofold1(_1141800, c_Groups_Otimes__class_Otimes(_1141800)), _1141804)) = hAPP(c_Finite__Set_Ofold1(_1141800, c_Groups_Otimes__class_Otimes(_1141800)), hAPP(c_Set_Oimage(_1141800, _1141800, _1141802), _1141804)))], (8362 ^ _777959) ^ [_922806, _922808, _922810] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_922806), _922808)), hBOOL(hAPP(_922810, c_Orderings_Obot__class_Obot(tc_fun(_922806, tc_HOL_Obool)))), 8373 ^ _777959 : [(8376 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_922806), 8371 ^ [_922806, _922808, _922810]), 8372 ^ [_922806, _922808, _922810]))], (8378 ^ _777959) ^ [] : [-(hBOOL(hAPP(_922810, 8372 ^ [_922806, _922808, _922810])))], (8380 ^ _777959) ^ [] : [hBOOL(hAPP(_922810, hAPP(hAPP(c_Set_Oinsert(_922806), 8371 ^ [_922806, _922808, _922810]), 8372 ^ [_922806, _922808, _922810])))], (8374 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_922806), 8372 ^ [_922806, _922808, _922810])))]], -(hBOOL(hAPP(_922810, _922808)))], (878 ^ _777959) ^ [_791368, _791370, _791372, _791374, _791376, _791378] : [-(c_Nitpick_Oless__eq__frac(_791376, _791372, _791368)), c_Nitpick_Oless__eq__frac(_791378, _791374, _791370), _791378 = _791376, _791374 = _791372, _791370 = _791368], (4460 ^ _777959) ^ [_845456, _845458] : [_845458 = _845456, -(c_Finite__Set_Ofinite(_845458) = c_Finite__Set_Ofinite(_845456))], (34689 ^ _777959) ^ [_1430473, _1430475, _1430477] : [class_Rings_Ocomm__semiring__1(_1430473), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1430473), _1430475), 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)))), _1430477)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1430473), hAPP(hAPP(c_Power_Opower__class_Opower(_1430473), _1430475), _1430477)), hAPP(hAPP(c_Power_Opower__class_Opower(_1430473), _1430475), _1430477)))], (16437 ^ _777959) ^ [_1092593, _1092595, _1092597] : [class_Orderings_Olinorder(_1092593), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092593), _1092595), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1092593), _1092595), _1092597)) = _1092595)], (20840 ^ _777959) ^ [_1174653, _1174655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174653), hAPP(c_Nat_OSuc, _1174655))), -(_1174653 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20848 ^ _777959 : [(20851 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20847 ^ [_1174653, _1174655]), _1174655)))], (20849 ^ _777959) ^ [] : [-(_1174653 = hAPP(c_Nat_OSuc, 20847 ^ [_1174653, _1174655]))]]], (42567 ^ _777959) ^ [_1620203, _1620205, _1620207, _1620209] : [class_Groups_Ocomm__monoid__add(_1620203), c_Fun_Oinj__on(_1620205, _1620203, _1620207, _1620209), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1620205, _1620203), _1620207), _1620209) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1620203, _1620203), c_Fun_Oid(_1620203)), hAPP(c_Set_Oimage(_1620205, _1620203, _1620207), _1620209)))], (2860 ^ _777959) ^ [_820668, _820670] : [_820670 = _820668, -(c_Equiv__Relations_Oquotient(_820670) = c_Equiv__Relations_Oquotient(_820668))], (2972 ^ _777959) ^ [_822468, _822470, _822472, _822474] : [-(c_Finite__Set_Ofold1(_822474, _822470) = c_Finite__Set_Ofold1(_822472, _822468)), _822474 = _822472, _822470 = _822468], (15370 ^ _777959) ^ [_1070327, _1070329] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070327), hAPP(c_Nat_OSuc, _1070329)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070327), _1070329)))], (35003 ^ _777959) ^ [_1436869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436869), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1436869)), c_Int_OMin)))], (50100 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23507 ^ _777959) ^ [_1225418, _1225420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225418), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225420), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225418), _1225420))), -(_1225418 = _1225420)], (10396 ^ _777959) ^ [_961460, _961462, _961464, _961466] : [class_Lattices_Osemilattice__sup(_961460), hBOOL(hAPP(c_Finite__Set_Ofinite(_961460), _961462)), hBOOL(hAPP(hAPP(c_member(_961460), _961464), _961462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961460), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_961460), _961464), _961466)), hAPP(hAPP(c_Finite__Set_Ofold(_961460, _961460, c_Lattices_Osemilattice__sup__class_Osup(_961460)), _961466), _961462))))], (11385 ^ _777959) ^ [_981011, _981013, _981015, _981017] : [11386 ^ _777959 : [(11387 ^ _777959) ^ [_981100] : [_981015 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_981011, tc_Option_Ooption(_981013)), hAPP(c_COMBK(tc_Option_Ooption(_981013), _981011), c_Option_Ooption_ONone(_981013))), _981017), hAPP(c_Option_Ooption_OSome(_981013), _981100))]], -(c_Map_Odom(_981011, _981013, _981015) = hAPP(hAPP(c_Set_Oinsert(_981011), _981017), c_Orderings_Obot__class_Obot(tc_fun(_981011, tc_HOL_Obool))))], (26038 ^ _777959) ^ [_1271648, _1271650, _1271652, _1271654] : [class_Fields_Olinordered__field(_1271648), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271648), _1271650), c_Groups_Ozero__class_Ozero(_1271648))), 26045 ^ _777959 : [(26052 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271648), _1271654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1271648), _1271652), _1271650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271648), _1271652), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271648), _1271654), _1271650))))], (26046 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271648), _1271652), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271648), _1271654), _1271650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271648), _1271654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1271648), _1271652), _1271650))))]]], (21858 ^ _777959) ^ [_1193116, _1193118, _1193120, _1193122, _1193124] : [class_Groups_Ocomm__monoid__mult(_1193116), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193118), _1193120)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193118), _1193122)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193116), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1193118, _1193116), _1193124), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1193118, tc_HOL_Obool)), _1193120), _1193122))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1193118, _1193116), _1193124), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1193118, tc_HOL_Obool)), _1193120), _1193122))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1193116), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1193118, _1193116), _1193124), _1193120)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1193118, _1193116), _1193124), _1193122)))], (41978 ^ _777959) ^ [_1605205, _1605207, _1605209, _1605211, _1605213] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1605205, _1605207), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1605205, tc_HOL_Obool)), _1605209), _1605211)), _1605213) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1605205, _1605207), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1605205, _1605207), _1605209), _1605213)), hAPP(hAPP(c_Product__Type_OSigma(_1605205, _1605207), _1605211), _1605213)))], (14790 ^ _777959) ^ [_1055895, _1055897, _1055899, _1055901, _1055903, _1055905] : [-(hBOOL(hAPP(hAPP(c_member(_1055895), _1055897), c_SetInterval_Oord_OgreaterThanAtMost(_1055895, _1055899, _1055901, _1055903, _1055905)))), hBOOL(hAPP(hAPP(_1055901, _1055903), _1055897)), hBOOL(hAPP(hAPP(_1055899, _1055897), _1055905))], (39659 ^ _777959) ^ [_1544429] : [c_List_Onat__list(_1544429), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1544429)))], (4958 ^ _777959) ^ [_853651, _853653] : [_853653 = _853651, -(c_Lazy__Sequence_Osingle(_853653) = c_Lazy__Sequence_Osingle(_853651))], (19374 ^ _777959) ^ [_1149419, _1149421, _1149423] : [class_Groups_Ogroup__add(_1149419), 19377 ^ _777959 : [(19384 ^ _777959) ^ [] : [_1149421 = _1149423, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149419), _1149421), _1149423) = c_Groups_Ozero__class_Ozero(_1149419))], (19378 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149419), _1149421), _1149423) = c_Groups_Ozero__class_Ozero(_1149419), -(_1149421 = _1149423)]]], (6048 ^ _777959) ^ [_874682, _874684] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_874682, tc_HOL_Obool)), _874684), _874684) = _874684)], (7958 ^ _777959) ^ [_913594, _913596, _913598, _913600, _913602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913594, tc_HOL_Obool)), _913596), _913598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913594, tc_HOL_Obool)), _913600), _913602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_913594, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913594, tc_HOL_Obool)), _913596), _913602)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913594, tc_HOL_Obool)), _913598), _913600))))], (45416 ^ _777959) ^ [_1683191, _1683193, _1683195, _1683197] : [-(hBOOL(hAPP(_1683191, _1683193))), -(c_List_OdropWhile(_1683195, _1683191, hAPP(hAPP(c_List_Olist_OCons(_1683195), _1683193), _1683197)) = hAPP(hAPP(c_List_Olist_OCons(_1683195), _1683193), _1683197))], (9380 ^ _777959) ^ [_939116, _939118] : [class_Lattices_Olattice(_939116), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939116), _939118), _939118) = _939118)], (24423 ^ _777959) ^ [_1241892, _1241894] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241892)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241894)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1241892), _1241894)))], (41936 ^ _777959) ^ [_1603949, _1603951] : [-(hAPP(hAPP(c_List_Otake(_1603949), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1603951) = c_List_Olist_ONil(_1603949))], (50494 ^ _777959) ^ [_1802595, _1802597, _1802599, _1802601] : [-(c_List_Oreplicate(_1802595, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1802597), _1802599), _1802601) = hAPP(hAPP(c_List_Oappend(_1802595), c_List_Oreplicate(_1802595, _1802597, _1802601)), c_List_Oreplicate(_1802595, _1802599, _1802601)))], (16179 ^ _777959) ^ [_1086609, _1086611, _1086613, _1086615, _1086617] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1086609), _1086611)), -(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), _1086611), _1086613)), _1086615)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086609), _1086613)), _1086617)) = 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), _1086611), _1086609)), _1086613)), _1086615)), _1086617))], (32835 ^ _777959) ^ [_1398122] : [-(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), _1398122)) = 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), _1398122))))], (22194 ^ _777959) ^ [_1200402, _1200404] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1200402), _1200404)), -(hAPP(c_Finite__Set_Ocard(_1200402), _1200404) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1200402, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1200402), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1200404))], (24492 ^ _777959) ^ [_1243062] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(_1243062)), c_Option_Ooption_ONone(_1243062)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50358 ^ _777959) ^ [_1799102] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1799102) = c_Lazy__Sequence_Osmall__lazy_H(_1799102, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1799102)))], (23088 ^ _777959) ^ [_1218118, _1218120] : [class_Rings_Olinordered__semidom(_1218118), 23091 ^ _777959 : [(23098 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218118), c_Groups_Ozero__class_Ozero(_1218118)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1218118), _1218120))))], (23092 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1218118), c_Groups_Ozero__class_Ozero(_1218118)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1218118), _1218120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1218120)))]]], (13663 ^ _777959) ^ [_1029918, _1029920, _1029922, _1029924, _1029926] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029918, tc_fun(_1029920, tc_HOL_Obool)), _1029922), hAPP(hAPP(c_COMBC(_1029918, tc_fun(_1029920, tc_HOL_Obool), tc_fun(_1029920, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1029920, tc_HOL_Obool), tc_fun(tc_fun(_1029920, tc_HOL_Obool), tc_fun(_1029920, tc_HOL_Obool)), _1029918), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029920, tc_HOL_Obool))), _1029924)), _1029926)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1029920, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029918, tc_fun(_1029920, tc_HOL_Obool)), _1029922), _1029924)), _1029926))], (40083 ^ _777959) ^ [_1554391, _1554393, _1554395] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1554391), _1554393)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1554391)), hAPP(c_Set_OCollect(tc_List_Olist(_1554391)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1554391), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1554391)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1554391), tc_fun(_1554391, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1554391, tc_HOL_Obool), tc_fun(tc_fun(_1554391, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1554391)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1554391, tc_HOL_Obool))), c_List_Oset(_1554391))), _1554393))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1554391), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1554391)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1554391)))), _1554395))))))], (37094 ^ _777959) ^ [] : [-(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)))], (29338 ^ _777959) ^ [_1331073, _1331075, _1331077] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1331073)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1331075), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1331077)), 29348 ^ _777959 : [(29354 ^ _777959) ^ [] : [-(_1331075 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 29350 ^ [_1331073, _1331075, _1331077]), 29347 ^ [_1331073, _1331075, _1331077]))], (29352 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29350 ^ [_1331073, _1331075, _1331077]), _1331077)))], (29349 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29347 ^ [_1331073, _1331075, _1331077]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1331073))))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1331075), _1331073) = _1331075)], (39824 ^ _777959) ^ [_1547755, _1547757, _1547759] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1547755, tc_HOL_Obool)), hAPP(c_List_Oset(_1547755), c_List_Oremove1(_1547755, _1547757, _1547759))), hAPP(c_List_Oset(_1547755), _1547759))))], (51272 ^ _777959) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (44857 ^ _777959) ^ [_1670241, _1670243, _1670245] : [hAPP(c_List_Orev(_1670241), _1670243) = hAPP(c_List_Orev(_1670241), _1670245), -(_1670243 = _1670245)], (10300 ^ _777959) ^ [_959327, _959329, _959331, _959333] : [class_Lattices_Osemilattice__sup(_959327), hBOOL(hAPP(c_Finite__Set_Ofinite(_959327), _959329)), -(hAPP(hAPP(c_Finite__Set_Ofold(_959327, _959327, c_Lattices_Osemilattice__sup__class_Osup(_959327)), _959331), hAPP(hAPP(c_Set_Oinsert(_959327), _959333), _959329)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_959327), _959333), hAPP(hAPP(c_Finite__Set_Ofold(_959327, _959327, c_Lattices_Osemilattice__sup__class_Osup(_959327)), _959331), _959329)))], (13109 ^ _777959) ^ [_1017084, _1017086] : [class_Complete__Lattice_Ocomplete__lattice(_1017084), -(c_Complete__Lattice_OSup__class_OSup(_1017084, hAPP(hAPP(c_Set_Oinsert(_1017084), _1017086), c_Orderings_Obot__class_Obot(tc_fun(_1017084, tc_HOL_Obool)))) = _1017086)], (19684 ^ _777959) ^ [_1154085, _1154087, _1154089, _1154091] : [class_Groups_Ocomm__monoid__mult(_1154085), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1154087), _1154089))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1154087, _1154085), _1154091), _1154089) = c_Groups_Oone__class_Oone(_1154085))], (39055 ^ _777959) ^ [_1530136, _1530138, _1530140, _1530142, _1530144, _1530146] : [c_Fun_Oinj__on(_1530136, _1530138, _1530140, _1530142), 39058 ^ _777959 : [(39065 ^ _777959) ^ [] : [c_Fun_Oinj__on(_1530136, _1530144, hAPP(c_Fun_Ocomp(_1530138, _1530144, _1530136, _1530146), _1530140), _1530142), -(c_Fun_Oinj__on(_1530138, _1530144, _1530146, hAPP(c_Set_Oimage(_1530136, _1530138, _1530140), _1530142)))], (39059 ^ _777959) ^ [] : [c_Fun_Oinj__on(_1530138, _1530144, _1530146, hAPP(c_Set_Oimage(_1530136, _1530138, _1530140), _1530142)), -(c_Fun_Oinj__on(_1530136, _1530144, hAPP(c_Fun_Ocomp(_1530138, _1530144, _1530136, _1530146), _1530140), _1530142))]]], (50326 ^ _777959) ^ [_1798590, _1798592, _1798594] : [-(hAPP(c_New__DSequence_Oneg__single(_1798590, _1798592), _1798594) = c_Lazy__Sequence_Ohb__single(_1798590, _1798592))], (32895 ^ _777959) ^ [_1399323, _1399325] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399323)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399325)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1399323), _1399325)))], (48533 ^ _777959) ^ [_1755737, _1755739] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1755737, _1755737)), hAPP(hAPP(c_Product__Type_OPair(_1755737, _1755737), _1755739), _1755739)), c_Relation_OId(_1755737))))], (43614 ^ _777959) ^ [_1644925, _1644927, _1644929] : [class_Groups_Oab__semigroup__add(_1644925), -(c_List_Ofoldr(_1644925, _1644925, c_Groups_Oplus__class_Oplus(_1644925), _1644927, _1644929) = hAPP(c_List_Ofoldl(_1644925, _1644925, c_Groups_Oplus__class_Oplus(_1644925), _1644929), _1644927))], (50598 ^ _777959) ^ [_1804427, _1804429] : [-(c_List_Oreplicate(_1804427, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1804429) = c_List_Olist_ONil(_1804427))], (51028 ^ _777959) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (38738 ^ _777959) ^ [_1521438, _1521440, _1521442] : [-(hAPP(c_Set_Ovimage(_1521438, _1521440, _1521442), c_Orderings_Otop__class_Otop(tc_fun(_1521440, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1521438, tc_HOL_Obool)))], (4164 ^ _777959) ^ [_841000, _841002] : [_841002 = _841000, -(c_Orderings_Otop__class_Otop(_841002) = c_Orderings_Otop__class_Otop(_841000))], (10136 ^ _777959) ^ [_955200, _955202, _955204, _955206] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_955200, tc_HOL_Obool)), _955202), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_955200, tc_HOL_Obool)), _955204), _955206)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_955200, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_955200, tc_HOL_Obool)), _955202), _955204)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_955200, tc_HOL_Obool)), _955202), _955206)))], (28944 ^ _777959) ^ [_1323585] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1323585) = 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), _1323585))))], (20495 ^ _777959) ^ [_1168854, _1168856, _1168858, _1168860] : [class_Rings_Olinordered__ring__strict(_1168854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168854), _1168856), _1168858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168854), _1168860), c_Groups_Ozero__class_Ozero(_1168854))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1168854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168854), _1168860), _1168858)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168854), _1168860), _1168856))))], (30138 ^ _777959) ^ [_1347985, _1347987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1347985)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1347985, _1347987)), _1347985)))], (31270 ^ _777959) ^ [_1368626, _1368628, _1368630] : [class_Fields_Olinordered__field(_1368626), -(_1368628 = c_Groups_Ozero__class_Ozero(_1368626)), -(hAPP(c_Groups_Oabs__class_Oabs(_1368626), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1368626), _1368630), _1368628)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1368626), hAPP(c_Groups_Oabs__class_Oabs(_1368626), _1368630)), hAPP(c_Groups_Oabs__class_Oabs(_1368626), _1368628)))], (8578 ^ _777959) ^ [_926123, _926125, _926127] : [class_Orderings_Oorder(_926123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926123), _926125), _926127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926123), _926127), _926125))], (11290 ^ _777959) ^ [_978911, _978913] : [class_Lattices_Olattice(_978911), hBOOL(hAPP(c_Finite__Set_Ofinite(_978911), _978913)), -(_978913 = c_Orderings_Obot__class_Obot(tc_fun(_978911, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_978911), c_Big__Operators_Olattice__class_OInf__fin(_978911, _978913)), c_Big__Operators_Olattice__class_OSup__fin(_978911, _978913))))], (43801 ^ _777959) ^ [_1649137, _1649139, _1649141] : [-(_1649137 = c_List_Olist_ONil(_1649139)), -(c_List_Olast(_1649139, hAPP(hAPP(c_List_Olist_OCons(_1649139), _1649141), _1649137)) = c_List_Olast(_1649139, _1649137))], (25772 ^ _777959) ^ [_1266825, _1266827, _1266829, _1266831] : [class_Rings_Odivision__ring(_1266825), -(_1266827 = c_Groups_Ozero__class_Ozero(_1266825)), 25779 ^ _777959 : [(25786 ^ _777959) ^ [] : [_1266829 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266825), _1266831), _1266827), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266825), _1266829), _1266827) = _1266831)], (25780 ^ _777959) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266825), _1266829), _1266827) = _1266831, -(_1266829 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1266825), _1266831), _1266827))]]], (10368 ^ _777959) ^ [_960766, _960768, _960770, _960772] : [hBOOL(hAPP(hAPP(c_member(_960766), _960768), _960770)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_960766, tc_Nat_Onat), _960772), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960766, tc_HOL_Obool)), _960770), hAPP(hAPP(c_Set_Oinsert(_960766), _960768), c_Orderings_Obot__class_Obot(tc_fun(_960766, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_960766, tc_Nat_Onat), _960772), _960770)), hAPP(_960772, _960768)))], (27856 ^ _777959) ^ [_1304091, _1304093, _1304095] : [class_Orderings_Olinorder(_1304091), 27859 ^ _777959 : [(27866 ^ _777959) ^ [] : [_1304093 = _1304095, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_1304091), _1304093) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1304091), _1304095))], (27860 ^ _777959) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_1304091), _1304093) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1304091), _1304095), -(_1304093 = _1304095)]]], (19334 ^ _777959) ^ [_1148790, _1148792] : [class_Rings_Ocomm__semiring__1(_1148790), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148790), _1148792), c_Groups_Ozero__class_Ozero(_1148790)) = c_Groups_Ozero__class_Ozero(_1148790))], (44819 ^ _777959) ^ [_1669496, _1669498] : [_1669498 = c_List_Olist_ONil(_1669496), -(c_List_Olist_ONil(_1669496) = hAPP(c_List_Orev(_1669496), _1669498))], (27363 ^ _777959) ^ [_1295708, _1295710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1295708)), hAPP(c_Int_Onat, _1295710))), 27366 ^ _777959 : [(27369 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1295708), _1295710)))], (27367 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1295710)))]]], (44753 ^ _777959) ^ [_1667807, _1667809] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1667807)), c_List_Otranspose__rel(_1667807)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1667807)), c_List_Olist_ONil(_1667807)), _1667809))), -(c_List_Otranspose(_1667807, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1667807)), c_List_Olist_ONil(_1667807)), _1667809)) = c_List_Otranspose(_1667807, _1667809))], (41725 ^ _777959) ^ [_1598117, _1598119, _1598121, _1598123, _1598125, _1598127] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1598117, _1598119), _1598119, tc_prod(_1598121, _1598123), c_Product__Type_Osnd(_1598117, _1598119)), c_Product__Type_Omap__pair(_1598121, _1598117, _1598123, _1598119, _1598125, _1598127)) = hAPP(c_Fun_Ocomp(_1598123, _1598119, tc_prod(_1598121, _1598123), _1598127), c_Product__Type_Osnd(_1598121, _1598123)))], (30283 ^ _777959) ^ [_1350647, _1350649] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350647, _1350649) = 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), _1350647), _1350649) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1350649), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350647, _1350649)))], (18570 ^ _777959) ^ [_1134943, _1134945] : [class_Lattices_Olattice(_1134943), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134943), _1134945)), -(c_Big__Operators_Olattice__class_OSup__fin(_1134943, _1134945) = hAPP(c_Finite__Set_Ofold1(_1134943, c_Lattices_Osemilattice__sup__class_Osup(_1134943)), _1134945))], (30108 ^ _777959) ^ [_1347430, _1347432, _1347434] : [class_Divides_Osemiring__div(_1347430), -(c_Divides_Odiv__class_Omod(_1347430, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347430), _1347432), _1347434), _1347432) = c_Groups_Ozero__class_Ozero(_1347430))], (41970 ^ _777959) ^ [_1604796, _1604798, _1604800] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1604796, _1604798), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1604796, _1604798), c_Orderings_Otop__class_Otop(tc_fun(_1604796, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1604798, tc_HOL_Obool), _1604796), _1604800))) = hAPP(hAPP(c_Product__Type_OSigma(_1604796, _1604798), c_Orderings_Otop__class_Otop(tc_fun(_1604796, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1604798, tc_HOL_Obool), _1604796), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1604798, tc_HOL_Obool)), _1604800))))], (33697 ^ _777959) ^ [_1412424, _1412426] : [class_Int_Onumber__ring(_1412424), class_Rings_Olinordered__idom(_1412424), 33704 ^ _777959 : [(33711 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1412426), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412424), hAPP(c_Int_Onumber__class_Onumber__of(_1412424), _1412426)), c_Groups_Oone__class_Oone(_1412424))))], (33705 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412424), hAPP(c_Int_Onumber__class_Onumber__of(_1412424), _1412426)), c_Groups_Oone__class_Oone(_1412424))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1412426), c_Int_OBit1(c_Int_OPls))))]]], (15566 ^ _777959) ^ [_1073766] : [class_Groups_Oab__semigroup__mult(_1073766), -(c_Finite__Set_Ofun__left__comm(_1073766, _1073766, c_Groups_Otimes__class_Otimes(_1073766)))], (35167 ^ _777959) ^ [_1439411] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1439411, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (44352 ^ _777959) ^ [_1659839, _1659841] : [class_Orderings_Olinorder(_1659839), -(_1659841 = c_List_Olist_ONil(_1659839)), c_List_Olinorder__class_Osorted(_1659839, _1659841), -(c_List_Olinorder__class_Osorted(_1659839, c_List_Obutlast(_1659839, _1659841)))], (7350 ^ _777959) ^ [_901208, _901210, _901212, _901214] : [class_Lattices_Osemilattice__sup(_901208), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901208), _901210), _901212)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901208), _901214), _901212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901208), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901208), _901210), _901214)), _901212)))], (33253 ^ _777959) ^ [_1405456, _1405458] : [class_Int_Onumber__ring(_1405456), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1405456), hAPP(c_Int_Onumber__class_Onumber__of(_1405456), c_Int_OPls)), _1405458) = _1405458)], (47891 ^ _777959) ^ [_1742112, _1742114, _1742116, _1742118] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1742112, tc_HOL_Obool), tc_fun(_1742112, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1742112, tc_HOL_Obool), tc_fun(_1742112, tc_HOL_Obool)), _1742114), _1742116)), c_Wellfounded_Omax__ext(_1742112, _1742118)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1742112), _1742114)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1742112), _1742116)), -(_1742116 = c_Orderings_Obot__class_Obot(tc_fun(_1742112, tc_HOL_Obool))), 47905 ^ _777959 : [(47908 ^ _777959) ^ [_1742517] : [hBOOL(hAPP(hAPP(c_member(_1742112), _1742517), _1742116)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1742112, _1742112)), hAPP(hAPP(c_Product__Type_OPair(_1742112, _1742112), 47904 ^ [_1742112, _1742114, _1742116, _1742118]), _1742517)), _1742118))], (47906 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1742112), 47904 ^ [_1742112, _1742114, _1742116, _1742118]), _1742114)))]]], (32159 ^ _777959) ^ [_1385475, _1385477] : [class_Int_Onumber__ring(_1385475), -(hAPP(c_Int_Onumber__class_Onumber__of(_1385475), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385477)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1385475), hAPP(c_Int_Onumber__class_Onumber__of(_1385475), _1385477)))], (37758 ^ _777959) ^ [_1500200, _1500202, _1500204, _1500206, _1500208, _1500210, _1500212, _1500214, _1500216, _1500218] : [c_Equiv__Relations_Ocongruent2(_1500200, _1500202, _1500204, _1500206, _1500208, _1500210), hBOOL(hAPP(hAPP(c_member(tc_prod(_1500200, _1500200)), hAPP(hAPP(c_Product__Type_OPair(_1500200, _1500200), _1500212), _1500214)), _1500206)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1500202, _1500202)), hAPP(hAPP(c_Product__Type_OPair(_1500202, _1500202), _1500216), _1500218)), _1500208)), -(hAPP(hAPP(_1500210, _1500212), _1500216) = hAPP(hAPP(_1500210, _1500214), _1500218))], (38504 ^ _777959) ^ [_1516636, _1516638] : [-(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)), _1516636), _1516638))], (25738 ^ _777959) ^ [_1266182, _1266184, _1266186, _1266188, _1266190] : [class_Fields_Ofield(_1266182), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1266182), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1266184, _1266182), _1266186), _1266188)), _1266190) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1266184, _1266182), hAPP(hAPP(c_COMBC(_1266184, _1266182, _1266182), hAPP(hAPP(c_COMBB(_1266182, tc_fun(_1266182, _1266182), _1266184), c_Rings_Oinverse__class_Odivide(_1266182)), _1266186)), _1266190)), _1266188))], (43998 ^ _777959) ^ [_1652681, _1652683, _1652685] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652681)), hAPP(c_List_Ofilter(_1652681, _1652683), _1652685))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652681)), _1652685))))], (50555 ^ _777959) ^ [_1803538, _1803540, _1803542, _1803544] : [50556 ^ _777959 : [(50559 ^ _777959) ^ [] : [_1803540 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (50557 ^ _777959) ^ [] : [hBOOL(hAPP(_1803544, _1803542))]], 50560 ^ _777959 : [(50561 ^ _777959) ^ [_1803663] : [hBOOL(hAPP(hAPP(c_member(_1803538), _1803663), hAPP(c_List_Oset(_1803538), c_List_Oreplicate(_1803538, _1803540, _1803542)))), -(hBOOL(hAPP(_1803544, _1803663)))]]], (47597 ^ _777959) ^ [_1734548, _1734550, _1734552, _1734554] : [hAPP(c_List_Oset(_1734548), hAPP(hAPP(c_List_Omap(tc_prod(_1734548, _1734550), _1734548), c_Product__Type_Ofst(_1734548, _1734550)), _1734552)) = hAPP(c_List_Oset(_1734548), hAPP(hAPP(c_List_Omap(tc_prod(_1734548, _1734550), _1734548), c_Product__Type_Ofst(_1734548, _1734550)), _1734554)), 47603 ^ _777959 : [(47606 ^ _777959) ^ [] : [hAPP(hAPP(c_Map_Omap__of(_1734548, _1734550), _1734552), 47602 ^ [_1734548, _1734550, _1734552, _1734554]) = hAPP(hAPP(c_Map_Omap__of(_1734548, _1734550), _1734554), 47602 ^ [_1734548, _1734550, _1734552, _1734554])], (47604 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1734548), 47602 ^ [_1734548, _1734550, _1734552, _1734554]), hAPP(c_List_Oset(_1734548), hAPP(hAPP(c_List_Omap(tc_prod(_1734548, _1734550), _1734548), c_Product__Type_Ofst(_1734548, _1734550)), _1734552)))))]], -(hAPP(c_Map_Omap__of(_1734548, _1734550), _1734552) = hAPP(c_Map_Omap__of(_1734548, _1734550), _1734554))], (48162 ^ _777959) ^ [_1747478, _1747480] : [-(c_Random_Oselect__weight(_1747478, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1747478), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1747478, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1747478, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1747478)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1747480)) = c_Random_Oselect__weight(_1747478, _1747480))], (43857 ^ _777959) ^ [_1649910, _1649912] : [-(_1649910 = c_List_Olist_ONil(_1649912)), -(hAPP(hAPP(c_List_Oappend(_1649912), c_List_Obutlast(_1649912, _1649910)), hAPP(hAPP(c_List_Olist_OCons(_1649912), c_List_Olast(_1649912, _1649910)), c_List_Olist_ONil(_1649912))) = _1649910)], (36894 ^ _777959) ^ [_1478315, _1478317, _1478319, _1478321, _1478323, _1478325, _1478327, _1478329] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1478315, _1478317), tc_prod(_1478315, _1478317))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1478315, _1478317), tc_prod(_1478315, _1478317)), hAPP(hAPP(c_Product__Type_OPair(_1478315, _1478317), _1478319), _1478321)), hAPP(hAPP(c_Product__Type_OPair(_1478315, _1478317), _1478323), _1478325))), c_Wellfounded_Olex__prod(_1478315, _1478317, _1478327, _1478329))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1478315, _1478315)), hAPP(hAPP(c_Product__Type_OPair(_1478315, _1478315), _1478319), _1478323)), _1478327))), 36901 ^ _777959 : [(36904 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1478317, _1478317)), hAPP(hAPP(c_Product__Type_OPair(_1478317, _1478317), _1478321), _1478325)), _1478329)))], (36902 ^ _777959) ^ [] : [-(_1478319 = _1478323)]]], (14587 ^ _777959) ^ [_1051981] : [14589 ^ _777959 : [(14592 ^ _777959) ^ [_1052091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 14588 ^ [_1051981, _1052091]), _1052091))], (14590 ^ _777959) ^ [_1052057] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 14588 ^ [_1051981, _1052057]), _1051981)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1051981)))], (8950 ^ _777959) ^ [_931953, _931955, _931957] : [class_Orderings_Olinorder(_931953), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931953), _931955), _931957))), 8957 ^ _777959 : [(8964 ^ _777959) ^ [] : [_931955 = _931957, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931953), _931955), _931957)))], (8958 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931953), _931955), _931957)), -(_931955 = _931957)]]], (4990 ^ _777959) ^ [_854119, _854121, _854123, _854125] : [-(c_Wellfounded_Oaccp(_854125, _854121) = c_Wellfounded_Oaccp(_854123, _854119)), _854125 = _854123, _854121 = _854119], (49943 ^ _777959) ^ [_1790679, _1790681] : [c_List_Olist__ex1(_1790679, _1790681, c_List_Olist_ONil(_1790679))], (48731 ^ _777959) ^ [_1760658, _1760660] : [-(hAPP(c_Relation_ODomain(_1760658, _1760658), c_Transitive__Closure_Ortrancl(_1760658, _1760660)) = c_Orderings_Otop__class_Otop(tc_fun(_1760658, tc_HOL_Obool)))], (42296 ^ _777959) ^ [_1611916, _1611918, _1611920] : [-(hAPP(hAPP(c_List_Otake(_1611916), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1611916), _1611918), _1611920)) = hAPP(hAPP(c_List_Olist_OCons(_1611916), _1611918), c_List_Olist_ONil(_1611916)))], (16111 ^ _777959) ^ [_1084904, _1084906, _1084908, _1084910, _1084912] : [class_Groups_Ocomm__monoid__mult(_1084904), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084906), _1084908)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084906), _1084910)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084904), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084904, _1084906, c_Groups_Otimes__class_Otimes(_1084904)), _1084912), c_Groups_Oone__class_Oone(_1084904)), _1084908)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084904, _1084906, c_Groups_Otimes__class_Otimes(_1084904)), _1084912), c_Groups_Oone__class_Oone(_1084904)), _1084910)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084904), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084904, _1084906, c_Groups_Otimes__class_Otimes(_1084904)), _1084912), c_Groups_Oone__class_Oone(_1084904)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1084906, tc_HOL_Obool)), _1084908), _1084910))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084904, _1084906, c_Groups_Otimes__class_Otimes(_1084904)), _1084912), c_Groups_Oone__class_Oone(_1084904)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1084906, tc_HOL_Obool)), _1084908), _1084910))))], (39179 ^ _777959) ^ [_1532687, _1532689, _1532691, _1532693, _1532695, _1532697, _1532699] : [-(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1532687), tc_Option_Ooption(_1532689), _1532691, hAPP(c_Option_Omap(_1532687, _1532689), _1532693)), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1532691, tc_Option_Ooption(_1532687)), _1532695), _1532697), hAPP(c_Option_Ooption_OSome(_1532687), _1532699))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1532691, tc_Option_Ooption(_1532689)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1532687), tc_Option_Ooption(_1532689), _1532691, hAPP(c_Option_Omap(_1532687, _1532689), _1532693)), _1532695)), _1532697), hAPP(c_Option_Ooption_OSome(_1532689), hAPP(_1532693, _1532699))))], (38876 ^ _777959) ^ [_1524731, _1524733, _1524735, _1524737] : [-(hAPP(c_Set_Ovimage(_1524731, _1524733, _1524735), _1524737) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524733, tc_fun(_1524731, tc_HOL_Obool)), _1524737), hAPP(hAPP(c_COMBB(tc_fun(_1524733, tc_HOL_Obool), tc_fun(_1524731, tc_HOL_Obool), _1524733), c_Set_Ovimage(_1524731, _1524733, _1524735)), hAPP(hAPP(c_COMBC(_1524733, tc_fun(_1524733, tc_HOL_Obool), tc_fun(_1524733, tc_HOL_Obool)), c_Set_Oinsert(_1524733)), c_Orderings_Obot__class_Obot(tc_fun(_1524733, tc_HOL_Obool))))))], (14978 ^ _777959) ^ [_1062758, _1062760, _1062762] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1062758), _1062760)), hBOOL(hAPP(hAPP(c_member(_1062758), _1062762), _1062760)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1062758), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1062758, tc_HOL_Obool)), _1062760), hAPP(hAPP(c_Set_Oinsert(_1062758), _1062762), c_Orderings_Obot__class_Obot(tc_fun(_1062758, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1062758), _1062760))], (43634 ^ _777959) ^ [_1645428, _1645430, _1645432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1645428), _1645430)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1645428), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1645430), _1645432))))], (16997 ^ _777959) ^ [_1103084, _1103086, _1103088, _1103090] : [class_Orderings_Olinorder(_1103084), 17000 ^ _777959 : [(17009 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103084), _1103086), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1103084), _1103088), _1103090)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103084), _1103086), _1103088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103084), _1103086), _1103090))], (17001 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103084), _1103086), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1103084), _1103088), _1103090))), 17004 ^ _777959 : [(17007 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103084), _1103086), _1103090)))], (17005 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1103084), _1103086), _1103088)))]]]]], (51382 ^ _777959) ^ [] : [hBOOL(c_fFalse)], (31947 ^ _777959) ^ [_1381099, _1381101, _1381103, _1381105, _1381107] : [c_Com_Ocom_OWhile(_1381099, _1381101) = c_Com_Ocom_OLocal(_1381103, _1381105, _1381107)], (12161 ^ _777959) ^ [_998667, _998669] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998667), _998669)), _998667))], (24211 ^ _777959) ^ [_1238215, _1238217] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1238215)), -(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), _1238215), _1238217))))], (34487 ^ _777959) ^ [_1427113, _1427115] : [class_Rings_Oring__1(_1427113), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427113), hAPP(c_Groups_Ouminus__class_Ouminus(_1427113), _1427115)), 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(_1427113), _1427115), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (19616 ^ _777959) ^ [_1152999, _1153001, _1153003] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152999), _1153001) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152999), _1153003), -(_1153001 = _1153003), -(_1152999 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9656 ^ _777959) ^ [_944991, _944993, _944995, _944997] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944991, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944991, tc_HOL_Obool)), _944993), _944995)), _944997) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944991, tc_HOL_Obool)), _944993), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944991, tc_HOL_Obool)), _944995), _944997)))], (49128 ^ _777959) ^ [_1770933] : [-(c_Relation_Osingle__valued(_1770933, _1770933, c_Relation_OId(_1770933)))], (22493 ^ _777959) ^ [_1206704] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1206704)) = _1206704)], (42148 ^ _777959) ^ [_1608557, _1608559] : [-(_1608557 = c_List_Olist_ONil(_1608559)), hBOOL(hAPP(c_List_Odistinct(_1608559), _1608557)), -(hBOOL(hAPP(c_List_Odistinct(_1608559), c_List_Obutlast(_1608559, _1608557))))], (34967 ^ _777959) ^ [_1436378] : [c_Int_OMin = c_Int_OBit1(_1436378), -(c_Int_OMin = _1436378)], (15416 ^ _777959) ^ [_1071162, _1071164, _1071166] : [class_Rings_Oring(_1071162), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1071162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071162), _1071164), _1071166)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1071162), _1071164), hAPP(c_Groups_Ouminus__class_Ouminus(_1071162), _1071166)))], (47149 ^ _777959) ^ [_1723654, _1723656, _1723658, _1723660] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1723654), _1723656)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1723654), _1723658)), -(_1723658 = c_Orderings_Obot__class_Obot(tc_fun(_1723654, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1723654, tc_HOL_Obool), tc_fun(_1723654, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1723654, tc_HOL_Obool), tc_fun(_1723654, tc_HOL_Obool)), _1723656), _1723658)), c_Wellfounded_Omax__ext(_1723654, _1723660)))), 47163 ^ _777959 : [(47166 ^ _777959) ^ [_1724059] : [hBOOL(hAPP(hAPP(c_member(_1723654), _1724059), _1723658)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1723654, _1723654)), hAPP(hAPP(c_Product__Type_OPair(_1723654, _1723654), 47162 ^ [_1723654, _1723656, _1723658, _1723660]), _1724059)), _1723660))], (47164 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1723654), 47162 ^ [_1723654, _1723656, _1723658, _1723660]), _1723656)))]]], (6838 ^ _777959) ^ [_889465, _889467, _889469, _889471, _889473] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889465, tc_HOL_Obool)), _889467), hAPP(c_Set_Oimage(_889469, _889465, _889471), _889473))), 6842 ^ _777959 : [(6845 ^ _777959) ^ [] : [-(_889467 = hAPP(c_Set_Oimage(_889469, _889465, _889471), 6841 ^ [_889465, _889467, _889469, _889471, _889473]))], (6843 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889469, tc_HOL_Obool)), 6841 ^ [_889465, _889467, _889469, _889471, _889473]), _889473)))]]], (1400 ^ _777959) ^ [_798183, _798185] : [-(class_Smallcheck_Osmall(_798183)), _798185 = _798183, class_Smallcheck_Osmall(_798185)], (25426 ^ _777959) ^ [_1260067, _1260069, _1260071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1260067), _1260069)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260067), _1260071)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260069), _1260071))))], (22800 ^ _777959) ^ [_1212823, _1212825, _1212827] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1212823, tc_Nat_Onat), _1212825), _1212827)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1212823, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1212823), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212825)), _1212827))], (6040 ^ _777959) ^ [_874511, _874513] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874511, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_874511, tc_HOL_Obool))), _874513)))], (1130 ^ _777959) ^ [_794808, _794810] : [-(class_Groups_Oab__group__add(_794808)), _794810 = _794808, class_Groups_Oab__group__add(_794810)], (21043 ^ _777959) ^ [_1177780, _1177782, _1177784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177780), _1177782)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1177780), _1177784))), 21046 ^ _777959 : [(21049 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1177782), _1177784)))], (21047 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1177780)))]]], (39826 ^ _777959) ^ [_1547806, _1547808, _1547810] : [-(hAPP(hAPP(c_List_Ozip(_1547806, _1547808), hAPP(hAPP(c_List_Omap(tc_prod(_1547806, _1547808), _1547806), c_Product__Type_Ofst(_1547806, _1547808)), _1547810)), hAPP(hAPP(c_List_Omap(tc_prod(_1547806, _1547808), _1547808), c_Product__Type_Osnd(_1547806, _1547808)), _1547810)) = _1547810)], (45471 ^ _777959) ^ [_1684307, _1684309, _1684311, _1684313, _1684315] : [-(c_List_OdropWhile(_1684307, _1684309, _1684311) = hAPP(hAPP(c_List_Olist_OCons(_1684307), _1684313), _1684315)), _1684311 = hAPP(hAPP(c_List_Oappend(_1684307), c_List_OtakeWhile(_1684307, _1684309, _1684311)), hAPP(hAPP(c_List_Olist_OCons(_1684307), _1684313), _1684315)), -(hBOOL(hAPP(_1684309, _1684313)))], (35751 ^ _777959) ^ [_1455821, _1455823, _1455825, _1455827, _1455829, _1455831] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1455821, tc_fun(_1455823, tc_HOL_Obool))), _1455825), _1455827), _1455829), _1455831)), -(hBOOL(hAPP(hAPP(_1455827, _1455829), _1455831)))], (16030 ^ _777959) ^ [_1083319, _1083321, _1083323, _1083325, _1083327, _1083329] : [class_Groups_Oab__semigroup__mult(_1083319), hBOOL(hAPP(c_Finite__Set_Ofinite(_1083321), _1083323)), -(hBOOL(hAPP(hAPP(c_member(_1083321), _1083325), _1083323))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1083319, _1083321, c_Groups_Otimes__class_Otimes(_1083319)), _1083327), _1083329), hAPP(hAPP(c_Set_Oinsert(_1083321), _1083325), _1083323)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083319), hAPP(_1083327, _1083325)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1083319, _1083321, c_Groups_Otimes__class_Otimes(_1083319)), _1083327), _1083329), _1083323)))], (43745 ^ _777959) ^ [_1647713, _1647715, _1647717, _1647719] : [class_Complete__Lattice_Ocomplete__lattice(_1647713), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1647715, _1647713), hAPP(c_List_Oset(_1647715), _1647717)), _1647719) = hAPP(c_List_Ofoldl(_1647713, _1647715, hAPP(c_COMBC(_1647715, _1647713, _1647713), hAPP(hAPP(c_COMBB(_1647713, tc_fun(_1647713, _1647713), _1647715), c_Lattices_Osemilattice__inf__class_Oinf(_1647713)), _1647719)), c_Orderings_Otop__class_Otop(_1647713)), _1647717))], (34283 ^ _777959) ^ [_1423390, _1423392] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1423390))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1423392))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1423390)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1423392)))], (13026 ^ _777959) ^ [_1014989, _1014991, _1014993] : [class_Lattices_Oboolean__algebra(_1014989), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014989), _1014991), _1014993) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1014989), _1014991), hAPP(c_Groups_Ouminus__class_Ouminus(_1014989), _1014993)))], (20377 ^ _777959) ^ [_1166632, _1166634, _1166636] : [class_Rings_Olinordered__semiring__strict(_1166632), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166632), c_Groups_Ozero__class_Ozero(_1166632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166632), _1166634), _1166636))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166632), c_Groups_Ozero__class_Ozero(_1166632)), _1166636)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166632), c_Groups_Ozero__class_Ozero(_1166632)), _1166634)))], (37172 ^ 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hAPP(hAPP(c_Power_Opower__class_Opower(_1429378), _1429380), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1429378)))], (15512 ^ _777959) ^ [_1072862, _1072864, _1072866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072862), _1072864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072862), _1072866)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072864), _1072866))))], (32977 ^ _777959) ^ [_1400788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1400788), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1400788)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (9996 ^ _777959) ^ [_951689, _951691, _951693, _951695] : [class_Lattices_Odistrib__lattice(_951689), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951689), _951691), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_951689), _951693), _951695)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_951689), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951689), _951691), _951693)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_951689), _951691), _951695)))], (39215 ^ _777959) ^ [_1533538, _1533540, _1533542, _1533544] : [hBOOL(hAPP(hAPP(c_member(_1533538), _1533540), c_Wellfounded_Oacc(_1533538, _1533542))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1533538, _1533538)), hAPP(hAPP(c_Product__Type_OPair(_1533538, _1533538), _1533544), _1533540)), _1533542)), -(hBOOL(hAPP(hAPP(c_member(_1533538), _1533544), c_Wellfounded_Oacc(_1533538, _1533542))))], (48519 ^ _777959) ^ [_1755136, _1755138, _1755140, _1755142] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1755136, _1755136)), hAPP(hAPP(c_Product__Type_OPair(_1755136, _1755136), _1755140), _1755142)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1755136, _1755136), tc_HOL_Obool)), _1755138), c_Relation_OId(_1755136)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1755136, tc_fun(_1755136, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1755136, tc_fun(tc_prod(_1755136, _1755136), tc_HOL_Obool), tc_fun(_1755136, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1755136, tc_fun(tc_fun(tc_prod(_1755136, _1755136), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1755136, _1755136), tc_HOL_Obool), tc_fun(_1755136, tc_HOL_Obool)), _1755136), c_COMBC(_1755136, tc_fun(tc_prod(_1755136, _1755136), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1755136, tc_prod(_1755136, _1755136)), tc_fun(_1755136, tc_fun(tc_fun(tc_prod(_1755136, _1755136), tc_HOL_Obool), tc_HOL_Obool)), _1755136), hAPP(c_COMBB(tc_prod(_1755136, _1755136), tc_fun(tc_fun(tc_prod(_1755136, _1755136), tc_HOL_Obool), tc_HOL_Obool), _1755136), c_member(tc_prod(_1755136, _1755136)))), c_Product__Type_OPair(_1755136, _1755136)))), _1755138)), c_fequal), _1755140), _1755142)))], (11240 ^ _777959) ^ [_978120, _978122, _978124] : [class_Lattices_Olattice(_978120), hBOOL(hAPP(c_Finite__Set_Ofinite(_978120), _978122)), -(_978124 = c_Orderings_Obot__class_Obot(tc_fun(_978120, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_978120, tc_HOL_Obool)), _978124), _978122)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978120), c_Big__Operators_Olattice__class_OInf__fin(_978120, _978124)), c_Big__Operators_Olattice__class_OInf__fin(_978120, _978122)) = c_Big__Operators_Olattice__class_OInf__fin(_978120, _978122))], (3282 ^ _777959) ^ [_827393, _827395, _827397, _827399, _827401, _827403, _827405, _827407] : [-(c_Map_Omap__add(_827407, _827403, _827399, _827395) = c_Map_Omap__add(_827405, _827401, _827397, _827393)), _827407 = _827405, _827403 = _827401, _827399 = _827397, _827395 = _827393], (44949 ^ _777959) ^ [_1672221, _1672223, _1672225, _1672227] : [hAPP(c_List_Orev(_1672221), _1672223) = hAPP(hAPP(c_List_Olist_OCons(_1672221), _1672225), _1672227), -(_1672223 = hAPP(hAPP(c_List_Oappend(_1672221), hAPP(c_List_Orev(_1672221), _1672227)), hAPP(hAPP(c_List_Olist_OCons(_1672221), _1672225), c_List_Olist_ONil(_1672221))))], (44965 ^ _777959) ^ [_1672641, _1672643] : [-(hAPP(c_List_Oset(_1672641), c_List_Oconcat(_1672641, _1672643)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1672641), tc_fun(_1672641, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1672641)), _1672643)), c_List_Oset(_1672641)))], (5638 ^ _777959) ^ [_864101, _864103] : [_864103 = _864101, -(tc_Hoare__Mirabelle_Otriple(_864103) = tc_Hoare__Mirabelle_Otriple(_864101))], (4466 ^ _777959) ^ [_845541, _845543] : [_845543 = _845541, -(c_Groups_Oabs__class_Oabs(_845543) = c_Groups_Oabs__class_Oabs(_845541))], (3112 ^ _777959) ^ [_824624, _824626, _824628, _824630] : [-(c_List_Oupto(_824630, _824626) = c_List_Oupto(_824628, _824624)), _824630 = _824628, _824626 = _824624], (31392 ^ _777959) ^ [_1371012, _1371014, _1371016] : [class_Fields_Olinordered__field__inverse__zero(_1371012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1371012), c_Groups_Ozero__class_Ozero(_1371012)), _1371014)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1371012), hAPP(c_Groups_Oabs__class_Oabs(_1371012), _1371016)), _1371014) = hAPP(c_Groups_Oabs__class_Oabs(_1371012), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1371012), _1371016), _1371014)))], (50214 ^ _777959) ^ [_1795613] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1795613), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1795613)), c_Int_OPls)))], (44901 ^ _777959) ^ [_1671118, _1671120, _1671122, _1671124, _1671126] : [-(hAPP(c_List_Ofoldl(_1671118, _1671120, _1671122, _1671124), _1671126) = c_List_Ofoldr(_1671120, _1671118, hAPP(c_COMBC(_1671118, _1671120, _1671118), _1671122), hAPP(c_List_Orev(_1671120), _1671126), _1671124))], (11978 ^ _777959) ^ [_995473, _995475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995473), _995475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995473), _995475)))], (51306 ^ _777959) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (51350 ^ _777959) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (20815 ^ _777959) ^ [_1174267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1174267)), -(_1174267 = hAPP(c_Nat_OSuc, 20818 ^ [_1174267]))], (13665 ^ _777959) ^ [_1030027, _1030029, _1030031, _1030033, _1030035] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030027, tc_fun(_1030029, tc_HOL_Obool)), _1030031), hAPP(hAPP(c_COMBB(tc_fun(_1030029, tc_HOL_Obool), tc_fun(_1030029, tc_HOL_Obool), _1030027), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1030029, tc_HOL_Obool)), _1030033)), _1030035)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1030029, tc_HOL_Obool)), _1030033), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030027, tc_fun(_1030029, tc_HOL_Obool)), _1030031), _1030035)))], (11968 ^ _777959) ^ [_995361, _995363] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995361), _995363)), -(_995361 = _995363), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995361), _995363)))], (34847 ^ _777959) ^ [_1433769, _1433771, _1433773] : [class_Rings_Olinordered__idom(_1433769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433769), _1433771), c_Groups_Ozero__class_Ozero(_1433769))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1433769), hAPP(hAPP(c_Power_Opower__class_Opower(_1433769), _1433771), 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)))), _1433773)))), c_Groups_Ozero__class_Ozero(_1433769))))], (8000 ^ _777959) ^ [_914553, _914555, _914557, _914559, _914561] : [c_Com_Ocom_OWhile(_914553, _914555) = c_Com_Ocom_OCall(_914557, _914559, _914561)], (27992 ^ _777959) ^ [_1306124, _1306126, _1306128] : [class_Rings_Oring__1(_1306124), -(hAPP(c_Int_Oring__1__class_Oof__int(_1306124), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1306126), _1306128)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1306124), hAPP(c_Int_Oring__1__class_Oof__int(_1306124), _1306126)), hAPP(c_Int_Oring__1__class_Oof__int(_1306124), _1306128)))], (31248 ^ _777959) ^ [_1368248, _1368250, _1368252] : [class_Rings_Olinordered__idom(_1368248), 31251 ^ _777959 : [(31260 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368248), hAPP(c_Groups_Oabs__class_Oabs(_1368248), _1368250)), _1368252))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368248), _1368250), _1368252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368248), hAPP(c_Groups_Ouminus__class_Ouminus(_1368248), _1368250)), _1368252))], (31252 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368248), hAPP(c_Groups_Oabs__class_Oabs(_1368248), _1368250)), _1368252)), 31255 ^ _777959 : [(31258 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368248), hAPP(c_Groups_Ouminus__class_Ouminus(_1368248), _1368250)), _1368252)))], (31256 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1368248), _1368250), _1368252)))]]]]], (50594 ^ _777959) ^ [_1804328, _1804330, _1804332, _1804334] : [-(hAPP(hAPP(c_List_Oappend(_1804328), c_List_Oreplicate(_1804328, _1804330, _1804332)), c_List_Oreplicate(_1804328, _1804334, _1804332)) = hAPP(hAPP(c_List_Oappend(_1804328), c_List_Oreplicate(_1804328, _1804334, _1804332)), c_List_Oreplicate(_1804328, _1804330, _1804332)))], (36924 ^ _777959) ^ [_1479222, _1479224, _1479226, _1479228, _1479230, _1479232] : [-(hAPP(c_Product__Type_Oapfst(_1479222, _1479224, _1479226, _1479228), hAPP(hAPP(c_Product__Type_OPair(_1479222, _1479226), _1479230), _1479232)) = hAPP(hAPP(c_Product__Type_OPair(_1479224, _1479226), hAPP(_1479228, _1479230)), _1479232))], (3324 ^ _777959) ^ [_828064, _828066] : [_828066 = _828064, -(c_Finite__Set_Ocard(_828066) = c_Finite__Set_Ocard(_828064))], (33619 ^ _777959) ^ [_1411136, _1411138] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1411136), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411136)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411138)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1411138))], (45364 ^ _777959) ^ [_1682008, _1682010, _1682012, _1682014, _1682016] : [c_Finite__Set_Ofun__left__comm(_1682008, _1682010, _1682012), -(hAPP(hAPP(c_Finite__Set_Ofold(_1682008, _1682010, _1682012), _1682014), hAPP(c_List_Oset(_1682008), _1682016)) = hAPP(c_List_Ofoldl(_1682010, _1682008, hAPP(c_COMBC(_1682008, _1682010, _1682010), _1682012), _1682014), c_List_Oremdups(_1682008, _1682016)))], (27549 ^ _777959) ^ [_1298641, _1298643] : [-(_1298641 = hAPP(c_Int_Onat, _1298643)), 27552 ^ _777959 : [(27555 ^ _777959) ^ [] : [_1298643 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1298641)], (27553 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298643)))]], 27556 ^ _777959 : [(27559 ^ _777959) ^ [] : [_1298641 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27557 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298643))]]], (42132 ^ _777959) ^ [_1608238, _1608240, _1608242, _1608244] : [class_Orderings_Olinorder(_1608238), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1608240, _1608238, _1608242), _1608244), c_List_Olist_ONil(_1608240)) = hAPP(hAPP(c_List_Olist_OCons(_1608240), _1608244), c_List_Olist_ONil(_1608240)))], (51286 ^ _777959) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (39924 ^ _777959) ^ [_1550921, _1550923, _1550925, _1550927] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550921)), hAPP(hAPP(c_List_Omap(_1550923, _1550921), _1550925), _1550927)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550923)), _1550927))], (27846 ^ _777959) ^ [_1303956, _1303958] : [c_Nat__Transfer_Onat__set(_1303956), c_Nat__Transfer_Onat__set(_1303958), -(c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1303956), _1303958)))], (28141 ^ _777959) ^ [_1308825, _1308827] : [c_Nat__Transfer_Onat__set(_1308825), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1308827), _1308825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1308827)))], (41089 ^ _777959) ^ [_1581215, _1581217, _1581219, _1581221, _1581223] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1581215), tc_List_Olist(_1581215))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1581215), tc_List_Olist(_1581215)), _1581217), _1581219)), hAPP(c_List_Olexn(_1581215, _1581221), _1581223))), 41092 ^ _777959 : [(41095 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1581215)), _1581219) = _1581223)], (41093 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1581215)), _1581217) = _1581223)]]], (40481 ^ _777959) ^ [_1563751, _1563753, _1563755] : [class_Orderings_Olinorder(_1563751), -(hBOOL(hAPP(hAPP(c_member(_1563751), _1563753), hAPP(c_List_Oset(_1563751), _1563755)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1563751, _1563751, c_COMBI(_1563751), _1563753, _1563755) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1563751, _1563751, c_COMBI(_1563751)), _1563753), _1563755))], (42551 ^ _777959) ^ [_1619893, _1619895] : [-(hAPP(c_Set_Oimage(_1619893, _1619893, c_Fun_Oid(_1619893)), _1619895) = _1619895)], (2108 ^ _777959) ^ [_808828, _808830, _808832, _808834, _808836, _808838] : [-(c_Smallcheck_Oorelse(_808838, _808834, _808830) = c_Smallcheck_Oorelse(_808836, _808832, _808828)), _808838 = _808836, _808834 = _808832, _808830 = _808828], (9360 ^ _777959) ^ [_938803, _938805, _938807, _938809, _938811] : [class_Groups_Oab__group__add(_938803), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_938803), _938805), _938807) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_938803), _938809), _938811), 9367 ^ _777959 : [(9374 ^ _777959) ^ [] : [_938809 = _938811, -(_938805 = _938807)], (9368 ^ _777959) ^ [] : [_938805 = _938807, -(_938809 = _938811)]]], (30738 ^ _777959) ^ [_1358644, _1358646] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1358644), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1358646)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1358644, _1358646)))], (23329 ^ _777959) ^ [_1222427] : [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)), _1222427)), _1222427) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (22002 ^ _777959) ^ [_1196310, _1196312] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1196310)), 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)), _1196310))), 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, _1196312))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (15114 ^ _777959) ^ [_1065514, _1065516, _1065518, _1065520] : [class_Rings_Ocomm__semiring__1(_1065514), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065514), _1065516), _1065518)), _1065520) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065514), _1065516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065514), _1065518), _1065520)))], (14714 ^ _777959) ^ [_1054511, _1054513, _1054515, _1054517, _1054519] : [hBOOL(hAPP(hAPP(c_member(_1054511), _1054513), c_SetInterval_Oord_OatLeastAtMost(_1054511, _1054515, _1054517, _1054519))), 14717 ^ _777959 : [(14720 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1054515, _1054513), _1054519)))], (14718 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1054515, _1054517), _1054513)))]]], (45424 ^ _777959) ^ [_1683323, _1683325, _1683327] : [c_List_OdropWhile(_1683323, _1683325, _1683327) = c_List_Olist_ONil(_1683323), 45427 ^ _777959 : [(45428 ^ _777959) ^ [_1683414] : [hBOOL(hAPP(hAPP(c_member(_1683323), _1683414), hAPP(c_List_Oset(_1683323), _1683327))), -(hBOOL(hAPP(_1683325, _1683414)))]]], (48425 ^ _777959) ^ [_1752272] : [-(c_Transitive__Closure_Otrancl(_1752272, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1752272, _1752272), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1752272, _1752272), tc_HOL_Obool)))], (29634 ^ _777959) ^ [_1336910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1336910)), 29638 ^ _777959 : [(29641 ^ _777959) ^ [] : [-(_1336910 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 29637 ^ [_1336910]))], (29639 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 29637 ^ [_1336910])))]]], (34281 ^ _777959) ^ [_1423347, _1423349] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1423347)), c_Int_OBit0(_1423349)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1423347), _1423349)))], (28606 ^ _777959) ^ [_1316787, _1316789, _1316791, _1316793] : [class_Groups_Ocomm__monoid__add(_1316787), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1316787), _1316789), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1316791), hAPP(c_Nat_OSuc, _1316793))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1316787), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1316787, tc_Nat_Onat), _1316789), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1316791, _1316793)))], (31338 ^ _777959) ^ [_1369987, _1369989, _1369991, _1369993, _1369995] : [class_Groups_Oordered__ab__group__add__abs(_1369987), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1369987), hAPP(c_Groups_Oabs__class_Oabs(_1369987), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1369987), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1369987), _1369989), _1369991)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1369987), _1369993), _1369995)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1369987), hAPP(c_Groups_Oabs__class_Oabs(_1369987), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1369987), _1369989), _1369993))), hAPP(c_Groups_Oabs__class_Oabs(_1369987), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1369987), _1369991), _1369995))))))], (42529 ^ _777959) ^ [_1619488] : [-(hAPP(c_Option_Omap(_1619488, _1619488), c_COMBI(_1619488)) = c_Fun_Oid(tc_Option_Ooption(_1619488)))], (27455 ^ _777959) ^ [_1297120, _1297122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1297120), hAPP(c_Int_Onat, _1297122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1297120)), _1297122)))], (11720 ^ _777959) ^ [_988807, _988809, _988811, _988813] : [11722 ^ _777959 : [(11725 ^ _777959) ^ [] : [hAPP(_988813, 11721 ^ [_988807, _988809, _988811, _988813]) = c_Orderings_Obot__class_Obot(tc_fun(_988807, tc_HOL_Obool))], (11723 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_988809), 11721 ^ [_988807, _988809, _988811, _988813]), _988811)))]], -(c_Orderings_Obot__class_Obot(tc_fun(_988807, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_988809, tc_fun(_988807, tc_HOL_Obool)), _988811), _988813))], (15120 ^ _777959) ^ [_1065657, _1065659, _1065661, _1065663] : [class_Rings_Ocomm__semiring__1(_1065657), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065657), _1065659), _1065661)), _1065663) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065657), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065657), _1065659), _1065663)), _1065661))], (8004 ^ _777959) ^ [_914643, _914645] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OWhile(_914643, _914645)], (40507 ^ _777959) ^ [_1564319, _1564321, _1564323, _1564325, _1564327, _1564329] : [-(c_Map_Omap__add(_1564319, _1564321, _1564323, c_Map_Omap__upds(_1564319, _1564321, _1564325, _1564327, _1564329)) = c_Map_Omap__upds(_1564319, _1564321, c_Map_Omap__add(_1564319, _1564321, _1564323, _1564325), _1564327, _1564329))], (48966 ^ _777959) ^ [_1766999, _1767001, _1767003, _1767005, _1767007] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1766999, _1767001)), hAPP(hAPP(c_Product__Type_OPair(_1766999, _1767001), _1767003), _1767005)), hAPP(c_Relation_Oconverse(_1767001, _1766999), _1767007))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1767001, _1766999)), hAPP(hAPP(c_Product__Type_OPair(_1767001, _1766999), _1767005), _1767003)), _1767007)))], (25434 ^ _777959) ^ [_1260226, _1260228, _1260230] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260226), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1260228), _1260230)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260226), _1260228)), _1260230))], (45604 ^ _777959) ^ [_1688054, _1688056, _1688058, _1688060] : [hBOOL(hAPP(c_List_Odistinct(_1688054), _1688056)), hBOOL(hAPP(c_List_Odistinct(_1688058), _1688060)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1688054, _1688058)), c_Enum_Oproduct(_1688054, _1688058, _1688056, _1688060))))], (11594 ^ _777959) ^ [_985434, _985436, _985438, _985440, _985442, _985444] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985434, tc_fun(_985436, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985438, tc_fun(_985434, tc_HOL_Obool)), _985440), _985442)), _985444) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985438, tc_fun(_985436, tc_HOL_Obool)), _985440), hAPP(hAPP(c_COMBC(_985438, tc_fun(_985434, tc_fun(_985436, tc_HOL_Obool)), tc_fun(_985436, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_985434, tc_HOL_Obool), tc_fun(tc_fun(_985434, tc_fun(_985436, tc_HOL_Obool)), tc_fun(_985436, tc_HOL_Obool)), _985438), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985434, tc_fun(_985436, tc_HOL_Obool))), _985442)), _985444)))], (45043 ^ _777959) ^ [_1675099, _1675101, _1675103, _1675105] : [class_Orderings_Olinorder(_1675099), c_List_Olinorder__class_Osorted(_1675099, hAPP(c_List_Orev(_1675099), _1675101)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1675103), _1675105)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1675105), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1675099)), _1675101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1675099), hAPP(hAPP(c_List_Onth(_1675099), _1675101), _1675105)), hAPP(hAPP(c_List_Onth(_1675099), _1675101), _1675103))))], (4522 ^ _777959) ^ [_846349, _846351, _846353, _846355, _846357, _846359, _846361, _846363, _846365, _846367, _846369, _846371, _846373, _846375] : [-(c_New__Random__Sequence_Opos__decr__bind(_846375, _846371, _846367, _846363, _846359, _846355, _846351) = c_New__Random__Sequence_Opos__decr__bind(_846373, _846369, _846365, _846361, _846357, _846353, _846349)), _846375 = _846373, _846371 = _846369, _846367 = _846365, _846363 = _846361, _846359 = _846357, _846355 = _846353, _846351 = _846349], (3484 ^ _777959) ^ [_830520, _830522] : [_830522 = _830520, -(c_Enum_Oenum__class_Oenum__all(_830522) = c_Enum_Oenum__class_Oenum__all(_830520))], (32939 ^ _777959) ^ [_1400139, _1400141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400139), _1400141)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1400139)), c_Int_OBit1(_1400141))))], (50894 ^ _777959) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (12457 ^ _777959) ^ [_1004254, _1004256, _1004258, _1004260, _1004262] : [hBOOL(hAPP(hAPP(c_member(_1004254), _1004256), c_Map_Oran(_1004258, _1004254, c_Map_Orestrict__map(_1004258, _1004254, _1004260, _1004262)))), 12461 ^ _777959 : [(12464 ^ _777959) ^ [] : [-(hAPP(_1004260, 12460 ^ [_1004254, _1004256, _1004258, _1004260, _1004262]) = hAPP(c_Option_Ooption_OSome(_1004254), _1004256))], (12462 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1004258), 12460 ^ [_1004254, _1004256, _1004258, _1004260, _1004262]), _1004262)))]]], (31030 ^ _777959) ^ [_1364147] : [class_Rings_Olinordered__idom(_1364147), -(hAPP(c_Groups_Oabs__class_Oabs(_1364147), c_Groups_Oone__class_Oone(_1364147)) = c_Groups_Oone__class_Oone(_1364147))], (42925 ^ _777959) ^ [_1628721, _1628723, _1628725] : [_1628721 = hAPP(hAPP(c_List_Oappend(_1628723), _1628725), _1628721), -(_1628725 = c_List_Olist_ONil(_1628723))], (4812 ^ _777959) ^ [_851268, _851270, _851272, _851274, _851276, _851278, _851280, _851282] : [-(c_New__Random__Sequence_Oneg__bind(_851282, _851278, _851274, _851270) = c_New__Random__Sequence_Oneg__bind(_851280, _851276, _851272, _851268)), _851282 = _851280, _851278 = _851276, _851274 = _851272, _851270 = _851268], (48061 ^ _777959) ^ [_1745767, _1745769, _1745771, _1745773, _1745775] : [_1745767 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1745769, _1745771, _1745767, _1745773), _1745775) = hAPP(c_Product__Type_OPair(_1745769, _1745771), _1745775))], (18787 ^ _777959) ^ [_1138726, _1138728, _1138730] : [class_Orderings_Olinorder(_1138726), hBOOL(hAPP(c_Finite__Set_Ofinite(_1138726), _1138728)), -(_1138728 = c_Orderings_Obot__class_Obot(tc_fun(_1138726, tc_HOL_Obool))), 18798 ^ _777959 : [(18799 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138726), _1138730), hAPP(c_Finite__Set_Ofold1(_1138726, c_Orderings_Oord__class_Omin(_1138726)), _1138728))), 18802 ^ _777959 : [(18803 ^ _777959) ^ [_1139019] : [hBOOL(hAPP(hAPP(c_member(_1138726), _1139019), _1138728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138726), _1138730), _1139019)))]]], (18809 ^ _777959) ^ [] : [18811 ^ _777959 : [(18814 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138726), _1138730), 18810 ^ [_1138726, _1138728, _1138730]))], (18812 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1138726), 18810 ^ [_1138726, _1138728, _1138730]), _1138728)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138726), _1138730), hAPP(c_Finite__Set_Ofold1(_1138726, c_Orderings_Oord__class_Omin(_1138726)), _1138728))))]]], (3226 ^ _777959) ^ [_826469, _826471] : [_826471 = _826469, -(c_List_Otranspose__rel(_826471) = c_List_Otranspose__rel(_826469))], (16467 ^ _777959) ^ [_1093186, _1093188, _1093190] : [class_Orderings_Olinorder(_1093186), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093186), _1093188), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093186), _1093188), _1093190)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093186), _1093188), _1093190))], (46445 ^ _777959) ^ [_1705728, _1705730, _1705732, _1705734] : [_1705734 = c_List_Olist_ONil(_1705730), -(c_List_Olist__all2(_1705728, _1705730, _1705732, c_List_Olist_ONil(_1705728), _1705734))], (31082 ^ _777959) ^ [_1365115, _1365117, _1365119] : [class_Groups_Oordered__ab__group__add__abs(_1365115), -(hAPP(c_Groups_Oabs__class_Oabs(_1365115), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1365115), _1365117), _1365119)) = hAPP(c_Groups_Oabs__class_Oabs(_1365115), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1365115), _1365119), _1365117)))], (39530 ^ _777959) ^ [_1541126, _1541128, _1541130] : [hBOOL(hAPP(c_List_Odistinct(_1541126), hAPP(hAPP(c_List_Omap(tc_prod(_1541126, _1541128), _1541126), c_Product__Type_Ofst(_1541126, _1541128)), _1541130))), -(hAPP(c_List_Oset(tc_prod(_1541126, _1541128)), _1541130) = hAPP(c_Set_OCollect(tc_prod(_1541126, _1541128)), hAPP(c_Product__Type_Oprod_Oprod__case(_1541126, _1541128, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1541126, tc_fun(_1541128, tc_Option_Ooption(_1541128)), tc_fun(_1541128, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1541128), tc_HOL_Obool), tc_fun(tc_fun(_1541128, tc_Option_Ooption(_1541128)), tc_fun(_1541128, tc_HOL_Obool)), _1541126), c_COMBB(tc_Option_Ooption(_1541128), tc_HOL_Obool, _1541128)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1541128), tc_fun(tc_Option_Ooption(_1541128), tc_HOL_Obool), _1541126), c_fequal), hAPP(c_Map_Omap__of(_1541126, _1541128), _1541130)))), c_Option_Ooption_OSome(_1541128)))))], (39735 ^ _777959) ^ [_1545883, _1545885, _1545887] : [hBOOL(hAPP(c_List_Odistinct(_1545883), _1545885)), -(hAPP(c_List_Oset(_1545883), c_List_Oremove1(_1545883, _1545887, _1545885)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1545883, tc_HOL_Obool)), hAPP(c_List_Oset(_1545883), _1545885)), hAPP(hAPP(c_Set_Oinsert(_1545883), _1545887), c_Orderings_Obot__class_Obot(tc_fun(_1545883, tc_HOL_Obool)))))], (51060 ^ _777959) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (45688 ^ _777959) ^ [_1689663] : [class_Enum_Oenum(_1689663), -(c_Orderings_Otop__class_Otop(tc_fun(_1689663, tc_HOL_Obool)) = hAPP(c_List_Oset(_1689663), c_Enum_Oenum__class_Oenum(_1689663)))], (47475 ^ _777959) ^ [_1731920, _1731922] : [c_Wellfounded_Owf(_1731920, _1731922), -(c_Wellfounded_OwfP(_1731920, c_FunDef_Oin__rel(_1731920, _1731920, _1731922)))], (30730 ^ _777959) ^ [_1358487, _1358489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1358487), _1358489)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1358489, _1358487) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1358489), _1358487), _1358487))], (45586 ^ _777959) ^ [_1687544, _1687546] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1687544))), c_Enum_Osublists(_1687544, _1687546)) = 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(_1687544)), _1687546)))], (45596 ^ _777959) ^ [_1687772, _1687774, _1687776] : [-(c_Enum_Osublists(_1687772, hAPP(hAPP(c_List_Olist_OCons(_1687772), _1687774), _1687776)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1687772)), tc_List_Olist(tc_List_Olist(_1687772))), c_Enum_Osublists(_1687772, _1687776)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1687772)), tc_List_Olist(tc_List_Olist(_1687772)), tc_List_Olist(tc_List_Olist(_1687772))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1687772)), tc_fun(tc_List_Olist(tc_List_Olist(_1687772)), tc_List_Olist(tc_List_Olist(_1687772))), tc_List_Olist(tc_List_Olist(_1687772))), c_List_Oappend(tc_List_Olist(_1687772))), hAPP(c_List_Omap(tc_List_Olist(_1687772), tc_List_Olist(_1687772)), hAPP(c_List_Olist_OCons(_1687772), _1687774)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1687772))))))], (50400 ^ _777959) ^ [_1800136, _1800138] : [c_Wellfounded_Oacyclic(_1800136, hAPP(c_Set_OCollect(tc_prod(_1800136, _1800136)), hAPP(c_Product__Type_Oprod_Oprod__case(_1800136, _1800136, tc_HOL_Obool), _1800138))), -(c_Wellfounded_Oacyclic(_1800136, hAPP(c_Set_OCollect(tc_prod(_1800136, _1800136)), hAPP(c_Product__Type_Oprod_Oprod__case(_1800136, _1800136, tc_HOL_Obool), c_Predicate_Oconversep(_1800136, _1800136, _1800138)))))], (7200 ^ _777959) ^ [_898534, _898536, _898538, _898540] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898534, tc_HOL_Obool)), _898536), _898538)), hBOOL(hAPP(_898536, _898540)), -(hBOOL(hAPP(_898538, _898540)))], (18037 ^ _777959) ^ [_1122442, _1122444, _1122446] : [class_Orderings_Olinorder(_1122442), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122442), _1122444)), -(hBOOL(hAPP(hAPP(c_member(_1122442), _1122446), _1122444))), -(_1122444 = c_Orderings_Obot__class_Obot(tc_fun(_1122442, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1122442, c_Orderings_Oord__class_Omin(_1122442), hAPP(hAPP(c_Set_Oinsert(_1122442), _1122446), _1122444)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1122442), _1122446), c_Big__Operators_Olattice_OInf__fin(_1122442, c_Orderings_Oord__class_Omin(_1122442), _1122444)))], (28892 ^ _777959) ^ [_1322686] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1322686))))], (35707 ^ _777959) ^ [_1454901, _1454903, _1454905, _1454907, _1454909, _1454911, _1454913] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1454901, _1454903, tc_fun(_1454905, tc_HOL_Obool)), _1454907), hAPP(hAPP(c_Product__Type_OPair(_1454901, _1454903), _1454909), _1454911)), _1454913)), -(hBOOL(hAPP(hAPP(hAPP(_1454907, _1454909), _1454911), _1454913)))], (12425 ^ _777959) ^ [_1003629, _1003631, _1003633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003629), _1003631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003629), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003631), _1003633))))], (42068 ^ _777959) ^ [_1606952, _1606954] : [hAPP(c_List_Oset(_1606952), _1606954) = c_Orderings_Obot__class_Obot(tc_fun(_1606952, tc_HOL_Obool)), -(_1606954 = c_List_Olist_ONil(_1606952))], (1610 ^ _777959) ^ [_800808, _800810] : [-(class_Rings_Ocomm__semiring__1(_800808)), _800810 = _800808, class_Rings_Ocomm__semiring__1(_800810)], (18986 ^ _777959) ^ [_1142541, _1142543, _1142545, _1142547, _1142549, _1142551, _1142553] : [c_Finite__Set_Ofun__left__comm(_1142541, _1142543, _1142545), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1142541, _1142543, _1142545, _1142547, hAPP(hAPP(c_Set_Oinsert(_1142541), _1142549), _1142551)), _1142553)), -(hBOOL(hAPP(hAPP(c_member(_1142541), _1142549), _1142551))), 18998 ^ _777959 : [(19001 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1142541, _1142543, _1142545, _1142547, _1142551), 18997 ^ [_1142541, _1142543, _1142545, _1142547, _1142549, _1142551, _1142553])))], (18999 ^ _777959) ^ [] : [-(_1142553 = hAPP(hAPP(_1142545, _1142549), 18997 ^ [_1142541, _1142543, _1142545, _1142547, _1142549, _1142551, _1142553]))]]], (13008 ^ _777959) ^ [_1014660, _1014662, _1014664] : [class_Groups_Ogroup__add(_1014660), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014660), _1014662), hAPP(c_Groups_Ouminus__class_Ouminus(_1014660), _1014664)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014660), _1014662), _1014664))], (7640 ^ _777959) ^ [_906784, _906786, _906788] : [c_Com_Ocom_OCall(_906784, _906786, _906788) = c_Com_Ocom_OSKIP], (43119 ^ _777959) ^ [_1633398, _1633400, _1633402, _1633404, _1633406, _1633408] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633398), tc_List_Olist(_1633398))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633398), tc_List_Olist(_1633398)), hAPP(hAPP(c_List_Oappend(_1633398), _1633400), hAPP(hAPP(c_List_Olist_OCons(_1633398), _1633402), c_List_Olist_ONil(_1633398)))), hAPP(hAPP(c_List_Oappend(_1633398), _1633404), hAPP(hAPP(c_List_Olist_OCons(_1633398), _1633406), c_List_Olist_ONil(_1633398))))), c_List_Olistrel1(_1633398, _1633408))), 43124 ^ _777959 : [(43127 ^ _777959) ^ [] : [-(_1633402 = _1633406)], (43125 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633398), tc_List_Olist(_1633398))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633398), tc_List_Olist(_1633398)), _1633400), _1633404)), c_List_Olistrel1(_1633398, _1633408))))]], 43128 ^ _777959 : [(43131 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1633398, _1633398)), hAPP(hAPP(c_Product__Type_OPair(_1633398, _1633398), _1633402), _1633406)), _1633408)))], (43129 ^ _777959) ^ [] : [-(_1633400 = _1633404)]]], (14127 ^ _777959) ^ [_1040677, _1040679, _1040681, _1040683] : [-(c_Map_Odom(_1040677, _1040679, c_Map_Omap__add(_1040677, _1040679, _1040681, _1040683)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040677, tc_HOL_Obool)), c_Map_Odom(_1040677, _1040679, _1040683)), c_Map_Odom(_1040677, _1040679, _1040681)))], (10602 ^ _777959) ^ [_965803, _965805, _965807, _965809, _965811, _965813] : [c_Finite__Set_Ofun__left__comm(_965803, _965805, _965807), hBOOL(hAPP(c_Finite__Set_Ofinite(_965803), _965809)), -(hBOOL(hAPP(hAPP(c_member(_965803), _965811), _965809))), -(hAPP(hAPP(c_Finite__Set_Ofold(_965803, _965805, _965807), _965813), hAPP(hAPP(c_Set_Oinsert(_965803), _965811), _965809)) = hAPP(hAPP(_965807, _965811), hAPP(hAPP(c_Finite__Set_Ofold(_965803, _965805, _965807), _965813), _965809)))], (19660 ^ _777959) ^ [_1153668] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1153668), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7754 ^ _777959) ^ [_909529, _909531] : [-(c_HOL_OThe(_909529, hAPP(hAPP(c_COMBC(_909529, _909529, tc_HOL_Obool), c_fequal), _909531)) = _909531)], (26908 ^ _777959) ^ [_1287487, _1287489, _1287491] : [class_Fields_Olinordered__field(_1287487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287487), _1287489), _1287491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287487), _1287489), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1287487), _1287489), _1287491)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1287487), c_Groups_Oone__class_Oone(_1287487)), c_Groups_Oone__class_Oone(_1287487))))))], (34139 ^ _777959) ^ [_1420959] : [c_Int_OBit0(_1420959) = c_Int_OPls, -(_1420959 = c_Int_OPls)], (48028 ^ _777959) ^ [_1744836, _1744838, _1744840, _1744842, _1744844, _1744846, _1744848, _1744850] : [class_Groups_Ocomm__monoid__add(_1744836), c_Fun_Oinj__on(_1744838, _1744840, _1744842, _1744844), _1744846 = hAPP(c_Set_Oimage(_1744838, _1744840, _1744842), _1744844), 48042 ^ _777959 : [(48045 ^ _777959) ^ [] : [hAPP(_1744848, 48041 ^ [_1744836, _1744838, _1744840, _1744842, _1744844, _1744846, _1744848, _1744850]) = hAPP(_1744850, hAPP(_1744842, 48041 ^ [_1744836, _1744838, _1744840, _1744842, _1744844, _1744846, _1744848, _1744850]))], (48043 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1744838), 48041 ^ [_1744836, _1744838, _1744840, _1744842, _1744844, _1744846, _1744848, _1744850]), _1744844)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1744840, _1744836), _1744850), _1744846) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1744838, _1744836), _1744848), _1744844))], (31967 ^ _777959) ^ [_1381438, _1381440, _1381442] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OLocal(_1381438, _1381440, _1381442)], (9716 ^ _777959) ^ [_946413, _946415, _946417, _946419] : [class_Lattices_Osemilattice__inf(_946413), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946413), _946415), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946413), _946417), _946419)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946413), _946417), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946413), _946415), _946419)))], (5833 ^ _777959) ^ [_870469, _870471, _870473] : [class_Orderings_Obot(_870469), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_870471, _870469)), _870473) = c_Orderings_Obot__class_Obot(_870469))], (6187 ^ _777959) ^ [_877346, _877348, _877350, _877352] : [6201 ^ _777959 : [(6204 ^ _777959) ^ [] : [-(hBOOL(hAPP(_877352, 6200 ^ [_877346, _877348, _877350, _877352])))], (6202 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877346), 6200 ^ [_877346, _877348, _877350, _877352]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_877346, tc_HOL_Obool)), _877348), _877350))))]], 6188 ^ _777959 : [(6195 ^ _777959) ^ [_877555] : [hBOOL(hAPP(hAPP(c_member(_877346), _877555), _877350)), hBOOL(hAPP(_877352, _877555))], (6189 ^ _777959) ^ [_877459] : [hBOOL(hAPP(hAPP(c_member(_877346), _877459), _877348)), hBOOL(hAPP(_877352, _877459))]]], (27491 ^ _777959) ^ [_1297769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1297769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1297769))))], (6935 ^ _777959) ^ [_891482, _891484, _891486, _891488, _891490, _891492] : [c_Hoare__Mirabelle_Ohoare__derivs(_891482, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_891482), tc_HOL_Obool)), _891484), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_891482), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_891482, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891482)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_891482, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891482))), hAPP(hAPP(c_COMBB(tc_fun(_891482, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_891482, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891482))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_891482)), _891486)), c_Com_Ocom_OBODY)), _891488)), _891490)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_891482), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_891482, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891482)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_891482, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891482))), hAPP(hAPP(c_COMBB(tc_fun(_891482, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_891482, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_891482))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_891482)), _891486)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _891488)), _891490)), hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), _891492), _891490)), -(c_Hoare__Mirabelle_Ohoare__derivs(_891482, _891484, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_891482)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_891482), hAPP(_891486, _891492)), hAPP(c_Com_Ocom_OBODY, _891492)), hAPP(_891488, _891492))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_891482), tc_HOL_Obool)))))], (30173 ^ _777959) ^ [_1348557, _1348559] : [30174 ^ _777959 : [(30175 ^ _777959) ^ [_1348606] : [_1348557 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1348559), _1348606)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1348557, _1348559) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (51090 ^ _777959) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (45149 ^ _777959) ^ [_1678021, _1678023, _1678025] : [c_List_OtakeWhile(_1678021, _1678023, _1678025) = _1678025, 45152 ^ _777959 : [(45153 ^ _777959) ^ [_1678108] : [hBOOL(hAPP(hAPP(c_member(_1678021), _1678108), hAPP(c_List_Oset(_1678021), _1678025))), -(hBOOL(hAPP(_1678023, _1678108)))]]], (10687 ^ _777959) ^ [_967617, _967619, _967621, _967623, _967625, _967627] : [c_Finite__Set_Ofun__left__comm(_967617, _967619, _967621), -(hAPP(hAPP(_967621, _967623), hAPP(hAPP(_967621, _967625), _967627)) = hAPP(hAPP(_967621, _967625), hAPP(hAPP(_967621, _967623), _967627)))], (45168 ^ _777959) ^ [_1678405, _1678407, _1678409] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678405)), c_List_OtakeWhile(_1678405, _1678407, _1678409))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678405)), _1678409))))], (23769 ^ _777959) ^ [_1229911, _1229913, _1229915] : [class_Power_Opower(_1229911), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1229911), _1229913), hAPP(c_Nat_OSuc, _1229915)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1229911), _1229913), hAPP(hAPP(c_Power_Opower__class_Opower(_1229911), _1229913), _1229915)))], (22200 ^ _777959) ^ [_1200529, _1200531] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1200529), _1200531))), -(hAPP(c_Finite__Set_Ocard(_1200529), _1200531) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (33749 ^ _777959) ^ [_1413291, _1413293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1413291)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1413293)), _1413291) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1413293), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1413291), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (47259 ^ _777959) ^ [_1726153, _1726155, _1726157, _1726159] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1726153, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1726155, _1726153), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1726155, _1726153), tc_HOL_Obool)), _1726157), _1726159))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1726153, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1726155, _1726153), _1726157)), hAPP(c_Relation_ORange(_1726155, _1726153), _1726159)))))], (50394 ^ _777959) ^ [_1799995, _1799997] : [c_Wellfounded_Oacyclic(_1799995, hAPP(c_Set_OCollect(tc_prod(_1799995, _1799995)), hAPP(c_Product__Type_Oprod_Oprod__case(_1799995, _1799995, tc_HOL_Obool), c_Predicate_Oconversep(_1799995, _1799995, _1799997)))), -(c_Wellfounded_Oacyclic(_1799995, hAPP(c_Set_OCollect(tc_prod(_1799995, _1799995)), hAPP(c_Product__Type_Oprod_Oprod__case(_1799995, _1799995, tc_HOL_Obool), _1799997))))], (50252 ^ _777959) ^ [_1796626, _1796628, _1796630, _1796632] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1796626, _1796628), c_Lazy__Sequence_Olazy__sequence_OInsert(_1796626, _1796630, _1796632)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1796628, _1796630)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1796626, _1796628), _1796632))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38094 ^ _777959) ^ [_1507667, _1507669, _1507671, _1507673, _1507675] : [c_Fun_Oinj__on(_1507667, _1507669, _1507671, c_Orderings_Otop__class_Otop(tc_fun(_1507667, tc_HOL_Obool))), 38097 ^ _777959 : [(38104 ^ _777959) ^ [] : [_1507673 = _1507675, -(hAPP(_1507671, _1507673) = hAPP(_1507671, _1507675))], (38098 ^ _777959) ^ [] : [hAPP(_1507671, _1507673) = hAPP(_1507671, _1507675), -(_1507673 = _1507675)]]], (21156 ^ _777959) ^ [_1179751, _1179753, _1179755, _1179757, _1179759] : [class_Groups_Ocomm__monoid__mult(_1179751), hBOOL(hAPP(c_Finite__Set_Ofinite(_1179753), _1179755)), 21163 ^ _777959 : [(21170 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1179753), _1179757), _1179755))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1179753, _1179751), hAPP(hAPP(c_COMBC(_1179753, _1179751, _1179751), hAPP(hAPP(c_COMBS(_1179753, _1179751, tc_fun(_1179751, _1179751)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1179751, tc_fun(_1179751, _1179751)), _1179753), c_If(_1179751)), hAPP(c_fequal, _1179757))), _1179759)), c_Groups_Oone__class_Oone(_1179751))), _1179755) = c_Groups_Oone__class_Oone(_1179751))], (21164 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1179753), _1179757), _1179755)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1179753, _1179751), hAPP(hAPP(c_COMBC(_1179753, _1179751, _1179751), hAPP(hAPP(c_COMBS(_1179753, _1179751, tc_fun(_1179751, _1179751)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1179751, tc_fun(_1179751, _1179751)), _1179753), c_If(_1179751)), hAPP(c_fequal, _1179757))), _1179759)), c_Groups_Oone__class_Oone(_1179751))), _1179755) = hAPP(_1179759, _1179757))]]], (45730 ^ _777959) ^ [_1690392, _1690394, _1690396, _1690398] : [class_Orderings_Olinorder(_1690392), -(c_List_Olinorder__class_Osorted(_1690392, hAPP(hAPP(c_List_Omap(_1690394, _1690392), _1690396), c_List_Olinorder__class_Osort__key(_1690394, _1690392, _1690396, _1690398))))], (10985 ^ _777959) ^ [_973205, _973207] : [_973205 = c_Option_Ooption_ONone(_973207), 10988 ^ _777959 : [(10989 ^ _777959) ^ [_973277] : [_973205 = hAPP(c_Option_Ooption_OSome(_973207), _973277)]]], (1320 ^ _777959) ^ [_797183, _797185] : [-(class_Lattices_Odistrib__lattice(_797183)), _797185 = _797183, class_Lattices_Odistrib__lattice(_797185)], (15346 ^ _777959) ^ [_1069947, _1069949] : [class_Groups_Omonoid__mult(_1069947), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069947), _1069949), c_Groups_Oone__class_Oone(_1069947)) = _1069949)], (27267 ^ _777959) ^ [_1294133, _1294135] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1294133), _1294135) = 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)), _1294133)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1294135))))], (1270 ^ _777959) ^ [_796558, _796560] : [-(class_Complete__Lattice_Ocomplete__lattice(_796558)), _796560 = _796558, class_Complete__Lattice_Ocomplete__lattice(_796560)], (9094 ^ _777959) ^ [_934016, _934018, _934020, _934022] : [class_Orderings_Oorder(_934016), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934016), _934018), _934020)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_934016), _934022), _934018)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_934016), _934022), _934020)))], (36940 ^ _777959) ^ [_1479669, _1479671, _1479673, _1479675, _1479677, _1479679, _1479681] : [-(hAPP(c_Product__Type_Oapsnd(_1479669, _1479671, _1479673, _1479675), hAPP(c_Product__Type_Oapfst(_1479677, _1479673, _1479669, _1479679), _1479681)) = hAPP(c_Product__Type_Oapfst(_1479677, _1479673, _1479671, _1479679), hAPP(c_Product__Type_Oapsnd(_1479669, _1479671, _1479677, _1479675), _1479681)))], (15002 ^ _777959) ^ [_1063269] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063269), hAPP(c_Nat_OSuc, _1063269))))], (36403 ^ _777959) ^ [_1467997, _1467999, _1468001] : [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), _1467997), _1467999))), -(hBOOL(hAPP(hAPP(_1468001, _1467997), _1467999))), 36410 ^ _777959 : [(36413 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1468001, 36408 ^ [_1467997, _1467999, _1468001]), 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)))), 36409 ^ [_1467997, _1467999, _1468001])))), -(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), 36408 ^ [_1467997, _1467999, _1468001]), 36409 ^ [_1467997, _1467999, _1468001])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 36409 ^ [_1467997, _1467999, _1468001]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36423 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1468001, 36408 ^ [_1467997, _1467999, _1468001]), 36409 ^ [_1467997, _1467999, _1468001]))], (36411 ^ _777959) ^ [] : [-(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), 36408 ^ [_1467997, _1467999, _1468001]), 36409 ^ [_1467997, _1467999, _1468001]))))]]], (9814 ^ _777959) ^ [_948500, _948502, _948504] : [class_Lattices_Osemilattice__inf(_948500), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948500), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_948500), _948502), _948504)), _948504)))], (10628 ^ _777959) ^ [_966341, _966343, _966345, _966347, _966349] : [class_Groups_Ocomm__monoid__add(_966341), class_Groups_Oordered__cancel__ab__semigroup__add(_966341), hBOOL(hAPP(c_Finite__Set_Ofinite(_966343), _966345)), -(_966345 = c_Orderings_Obot__class_Obot(tc_fun(_966343, tc_HOL_Obool))), 10646 ^ _777959 : [(10649 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966341), hAPP(_966347, 10645 ^ [_966341, _966343, _966345, _966347, _966349])), hAPP(_966349, 10645 ^ [_966341, _966343, _966345, _966347, _966349])))], (10647 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_966343), 10645 ^ [_966341, _966343, _966345, _966347, _966349]), _966345)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_966341), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966343, _966341), _966347), _966345)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_966343, _966341), _966349), _966345))))], (50466 ^ _777959) ^ [_1801527] : [-(c_Predicate_Oconversep(_1801527, _1801527, c_fequal) = c_fequal)], (29743 ^ _777959) ^ [_1339300, _1339302] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1339300, tc_HOL_Obool)), hAPP(c_Set_OPow(_1339300), _1339302))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1339300), _1339302)))], (11100 ^ _777959) ^ [_975442, _975444, _975446, _975448, _975450] : [-(hBOOL(hAPP(hAPP(c_member(_975442), _975444), _975446))), -(hAPP(c_Map_Orestrict__map(_975442, _975448, _975450, _975446), _975444) = c_Option_Ooption_ONone(_975448))], (33061 ^ _777959) ^ [_1402328, _1402330] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402328) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402330), 33064 ^ _777959 : [(33071 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402328)))), 33074 ^ _777959 : [(33081 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402330)))), -(_1402328 = _1402330)], (33075 ^ _777959) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402330))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402328) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (33065 ^ _777959) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402330)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (7932 ^ _777959) ^ [_913095, _913097, _913099] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_913095), _913097)), 7935 ^ _777959 : [(7942 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_913095), _913099)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_913095), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913095, tc_HOL_Obool)), _913099), _913097))))], (7936 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_913095), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913095, tc_HOL_Obool)), _913099), _913097))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_913095), _913099)))]]], (48567 ^ _777959) ^ [_1756535, _1756537, _1756539, _1756541] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1756535, _1756535)), hAPP(hAPP(c_Product__Type_OPair(_1756535, _1756535), _1756537), _1756539)), c_Transitive__Closure_Ortrancl(_1756535, _1756541)))), 48568 ^ _777959 : [(48571 ^ _777959) ^ [] : [-(_1756537 = _1756539), hBOOL(hAPP(hAPP(c_member(tc_prod(_1756535, _1756535)), hAPP(hAPP(c_Product__Type_OPair(_1756535, _1756535), _1756537), _1756539)), c_Transitive__Closure_Otrancl(_1756535, _1756541)))], (48569 ^ _777959) ^ [] : [_1756537 = _1756539]]], (27942 ^ _777959) ^ [_1305326, _1305328] : [class_Int_Oring__char__0(_1305326), 27945 ^ _777959 : [(27952 ^ _777959) ^ [] : [_1305328 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1305326), _1305328) = c_Groups_Ozero__class_Ozero(_1305326))], (27946 ^ _777959) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1305326), _1305328) = c_Groups_Ozero__class_Ozero(_1305326), -(_1305328 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (27425 ^ _777959) ^ [_1296708, _1296710] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1296708) = _1296710, 27428 ^ _777959 : [(27431 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1296710)))], (27429 ^ _777959) ^ [] : [-(_1296708 = hAPP(c_Int_Onat, _1296710))]]], (36333 ^ _777959) ^ [_1466775, _1466777] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1466775, _1466777), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1466775), _1466777)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1466775, _1466777)))))], (40709 ^ _777959) ^ [_1568948, _1568950] : [-(c_Hilbert__Choice_OEps(_1568948, hAPP(hAPP(c_COMBC(_1568948, _1568948, tc_HOL_Obool), c_fequal), _1568950)) = _1568950)], (14906 ^ _777959) ^ [_1060146, _1060148, _1060150] : [class_Lattices_Odistrib__lattice(_1060146), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060146), _1060148)), -(_1060148 = c_Orderings_Obot__class_Obot(tc_fun(_1060146, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060146), _1060150)), -(_1060150 = c_Orderings_Obot__class_Obot(tc_fun(_1060146, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1060146), c_Big__Operators_Olattice__class_OInf__fin(_1060146, _1060148)), c_Big__Operators_Olattice__class_OInf__fin(_1060146, _1060150)) = c_Big__Operators_Olattice__class_OInf__fin(_1060146, hAPP(c_Set_OCollect(_1060146), hAPP(hAPP(c_COMBB(tc_fun(_1060146, tc_HOL_Obool), tc_HOL_Obool, _1060146), c_HOL_OEx(_1060146)), 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c_COMBS(_1060146, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1060146, tc_fun(_1060146, tc_HOL_Obool)), tc_fun(_1060146, tc_fun(_1060146, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1060146), hAPP(c_COMBB(tc_fun(_1060146, tc_HOL_Obool), tc_fun(_1060146, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1060146), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1060146), c_fconj))), hAPP(hAPP(c_COMBC(_1060146, tc_fun(_1060146, tc_fun(_1060146, _1060146)), tc_fun(_1060146, tc_fun(_1060146, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1060146, _1060146), tc_fun(_1060146, tc_HOL_Obool)), tc_fun(tc_fun(_1060146, tc_fun(_1060146, _1060146)), tc_fun(_1060146, tc_fun(_1060146, tc_HOL_Obool))), _1060146), c_COMBB(tc_fun(_1060146, _1060146), tc_fun(_1060146, tc_HOL_Obool), _1060146)), hAPP(hAPP(c_COMBB(tc_fun(_1060146, tc_HOL_Obool), tc_fun(tc_fun(_1060146, _1060146), tc_fun(_1060146, tc_HOL_Obool)), _1060146), c_COMBB(_1060146, tc_HOL_Obool, _1060146)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1060146)))))), hAPP(hAPP(c_COMBC(_1060146, tc_fun(_1060146, tc_HOL_Obool), tc_fun(_1060146, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1060146, tc_HOL_Obool), tc_fun(_1060146, tc_HOL_Obool)), _1060146), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1060146)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1060146), c_fconj), hAPP(hAPP(c_COMBC(_1060146, tc_fun(_1060146, tc_HOL_Obool), tc_HOL_Obool), c_member(_1060146)), _1060148)))), hAPP(hAPP(c_COMBC(_1060146, tc_fun(_1060146, tc_HOL_Obool), tc_HOL_Obool), c_member(_1060146)), _1060150))))))))], (50310 ^ _777959) ^ [_1798288, _1798290, _1798292] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1798288, _1798290), _1798292) = c_Lazy__Sequence_Oproduct(_1798288, _1798290, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1798288, _1798292), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1798290, _1798292))), class_Lazy__Sequence_Osmall__lazy(_1798288), class_Lazy__Sequence_Osmall__lazy(_1798290)], (24133 ^ _777959) ^ [_1236763, _1236765, _1236767] : [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), _1236763), _1236765)), _1236767))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236767), _1236763)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236763)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236765)))], (44963 ^ _777959) ^ [_1672588, _1672590] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672588)), c_List_Oconcat(_1672588, _1672590)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1672588), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1672588))), _1672590)))], (2664 ^ _777959) ^ [_817580, _817582, _817584, _817586] : [-(c_FunDef_Orp__inv__image(_817586, _817582) = c_FunDef_Orp__inv__image(_817584, _817580)), _817586 = _817584, _817582 = _817580], (21514 ^ _777959) ^ [_1186789, _1186791, _1186793] : [class_Rings_Olinordered__ring(_1186789), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1186789), c_Groups_Ozero__class_Ozero(_1186789)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1186789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186789), _1186791), _1186791)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1186789), _1186793), _1186793)))))], (44078 ^ _777959) ^ [_1654619, _1654621, _1654623, _1654625, _1654627, _1654629] : [hAPP(hAPP(c_Map_Omap__of(_1654619, _1654621), _1654623), _1654625) = hAPP(c_Option_Ooption_OSome(_1654621), _1654627), hBOOL(hAPP(hAPP(_1654629, _1654625), _1654627)), -(hAPP(hAPP(c_Map_Omap__of(_1654619, _1654621), hAPP(c_List_Ofilter(tc_prod(_1654619, _1654621), hAPP(c_Product__Type_Oprod_Oprod__case(_1654619, _1654621, tc_HOL_Obool), _1654629)), _1654623)), _1654625) = hAPP(c_Option_Ooption_OSome(_1654621), _1654627))], (23349 ^ _777959) ^ [_1222763] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222763) = _1222763)], (50676 ^ _777959) ^ [_1805929, _1805931, _1805933] : [-(_1805929 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1805931), c_List_Oreplicate(_1805931, _1805929, _1805933)) = hAPP(hAPP(c_Set_Oinsert(_1805931), _1805933), c_Orderings_Obot__class_Obot(tc_fun(_1805931, tc_HOL_Obool))))], (47187 ^ _777959) ^ [_1724506] : [-(c_Nitpick_Ozero__frac(_1724506) = c_Nitpick_OAbs__Frac(_1724506, 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))))], (14474 ^ _777959) ^ [_1049544, _1049546, _1049548, _1049550] : [14476 ^ _777959 : [(14479 ^ _777959) ^ [] : [hAPP(_1049550, 14475 ^ [_1049544, _1049546, _1049548, _1049550]) = c_Orderings_Otop__class_Otop(tc_fun(_1049544, tc_HOL_Obool))], (14477 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1049546), 14475 ^ [_1049544, _1049546, _1049548, _1049550]), _1049548)))]], -(c_Orderings_Otop__class_Otop(tc_fun(_1049544, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1049546, tc_fun(_1049544, tc_HOL_Obool)), _1049548), _1049550))], (15062 ^ _777959) ^ [_1064424, _1064426, _1064428] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1064424)), _1064426) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1064424)), _1064428), -(_1064426 = _1064428)], (13719 ^ _777959) ^ [_1031446, _1031448, _1031450] : [-(hAPP(hAPP(c_Set_Oinsert(_1031446), _1031448), hAPP(c_Set_OCollect(_1031446), _1031450)) = hAPP(c_Set_OCollect(_1031446), hAPP(hAPP(c_COMBS(_1031446, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1031446), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1031446), c_fNot), hAPP(hAPP(c_COMBC(_1031446, _1031446, tc_HOL_Obool), c_fequal), _1031448)))), _1031450)))], (22834 ^ _777959) ^ [_1213554] : [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), _1213554))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1213554)))], (10554 ^ _777959) ^ [_964830, _964832, _964834] : [class_Lattices_Olattice(_964830), hBOOL(hAPP(c_Finite__Set_Ofinite(_964830), _964832)), hBOOL(hAPP(hAPP(c_member(_964830), _964834), _964832)), 10565 ^ _777959 : [(10572 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964830, tc_HOL_Obool)), _964832), hAPP(hAPP(c_Set_Oinsert(_964830), _964834), c_Orderings_Obot__class_Obot(tc_fun(_964830, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_964830, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_964830, _964832) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_964830), _964834), c_Big__Operators_Olattice__class_OInf__fin(_964830, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964830, tc_HOL_Obool)), _964832), hAPP(hAPP(c_Set_Oinsert(_964830), _964834), c_Orderings_Obot__class_Obot(tc_fun(_964830, tc_HOL_Obool)))))))], (10566 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964830, tc_HOL_Obool)), _964832), hAPP(hAPP(c_Set_Oinsert(_964830), _964834), c_Orderings_Obot__class_Obot(tc_fun(_964830, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_964830, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_964830, _964832) = _964834)]]], (43751 ^ _777959) ^ [_1647884, _1647886, _1647888, _1647890, _1647892] : [-(c_Map_Omap__upds(_1647884, _1647886, _1647888, _1647890, _1647892) = hAPP(c_List_Ofoldl(tc_fun(_1647884, tc_Option_Ooption(_1647886)), tc_prod(_1647884, _1647886), hAPP(hAPP(c_COMBB(tc_fun(_1647884, tc_fun(_1647886, tc_fun(_1647884, tc_Option_Ooption(_1647886)))), tc_fun(tc_prod(_1647884, _1647886), tc_fun(_1647884, tc_Option_Ooption(_1647886))), tc_fun(_1647884, tc_Option_Ooption(_1647886))), c_Product__Type_Oprod_Oprod__case(_1647884, _1647886, tc_fun(_1647884, tc_Option_Ooption(_1647886)))), hAPP(hAPP(c_COMBC(tc_fun(_1647884, tc_Option_Ooption(_1647886)), tc_fun(_1647886, tc_Option_Ooption(_1647886)), tc_fun(_1647884, tc_fun(_1647886, tc_fun(_1647884, tc_Option_Ooption(_1647886))))), hAPP(hAPP(c_COMBB(tc_fun(_1647884, tc_fun(tc_fun(_1647886, tc_Option_Ooption(_1647886)), tc_fun(_1647886, tc_fun(_1647884, tc_Option_Ooption(_1647886))))), tc_fun(tc_fun(_1647886, tc_Option_Ooption(_1647886)), tc_fun(_1647884, tc_fun(_1647886, tc_fun(_1647884, tc_Option_Ooption(_1647886))))), tc_fun(_1647884, tc_Option_Ooption(_1647886))), c_COMBC(_1647884, tc_fun(_1647886, tc_Option_Ooption(_1647886)), tc_fun(_1647886, tc_fun(_1647884, tc_Option_Ooption(_1647886))))), hAPP(hAPP(c_COMBB(tc_fun(_1647884, tc_fun(tc_Option_Ooption(_1647886), tc_fun(_1647884, tc_Option_Ooption(_1647886)))), tc_fun(_1647884, tc_fun(tc_fun(_1647886, tc_Option_Ooption(_1647886)), tc_fun(_1647886, tc_fun(_1647884, tc_Option_Ooption(_1647886))))), tc_fun(_1647884, tc_Option_Ooption(_1647886))), hAPP(c_COMBB(tc_fun(tc_Option_Ooption(_1647886), tc_fun(_1647884, tc_Option_Ooption(_1647886))), tc_fun(tc_fun(_1647886, tc_Option_Ooption(_1647886)), tc_fun(_1647886, tc_fun(_1647884, tc_Option_Ooption(_1647886)))), _1647884), c_COMBB(tc_Option_Ooption(_1647886), tc_fun(_1647884, tc_Option_Ooption(_1647886)), _1647886))), c_Fun_Ofun__upd(_1647884, tc_Option_Ooption(_1647886))))), c_Option_Ooption_OSome(_1647886))), _1647888), hAPP(hAPP(c_List_Ozip(_1647884, _1647886), _1647890), _1647892)))], (21672 ^ _777959) ^ [_1189604, _1189606, _1189608] : [-(hBOOL(hAPP(_1189604, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1189606), _1189608)))), 21675 ^ _777959 : [(21678 ^ _777959) ^ [] : [hBOOL(hAPP(_1189604, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (21676 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189606), _1189608)))]], 21680 ^ _777959 : [(21683 ^ _777959) ^ [] : [hBOOL(hAPP(_1189604, 21679 ^ [_1189604, _1189606, _1189608]))], (21681 ^ _777959) ^ [] : [-(_1189606 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1189608), 21679 ^ [_1189604, _1189606, _1189608]))]]], (48429 ^ _777959) ^ [_1752354, _1752356] : [-(hAPP(c_Relation_ORange(_1752354, _1752354), c_Transitive__Closure_Otrancl(_1752354, _1752356)) = hAPP(c_Relation_ORange(_1752354, _1752354), _1752356))], (474 ^ _777959) ^ [_785340, _785342, _785344, _785346, _785348, _785350, _785352, _785354] : [-(c_Finite__Set_Ofolding(_785352, _785348, _785344, _785340)), c_Finite__Set_Ofolding(_785354, _785350, _785346, _785342), _785354 = _785352, _785350 = _785348, _785346 = _785344, _785342 = _785340], (10991 ^ _777959) ^ [_973320, _973322] : [-(_973320 = c_Option_Ooption_ONone(_973322)), -(_973320 = hAPP(c_Option_Ooption_OSome(_973322), 10994 ^ [_973320, _973322]))], (19396 ^ _777959) ^ [_1149742] : [class_Rings_Ozero__neq__one(_1149742), c_Groups_Oone__class_Oone(_1149742) = c_Groups_Ozero__class_Ozero(_1149742)], (4576 ^ _777959) ^ [_847324, _847326] : [_847326 = _847324, -(c_Lazy__Sequence_Oyieldn(_847326) = c_Lazy__Sequence_Oyieldn(_847324))], (41948 ^ _777959) ^ [_1604164, _1604166] : [-(c_List_Osublist(_1604164, c_List_Olist_ONil(_1604164), _1604166) = c_List_Olist_ONil(_1604164))], (30100 ^ _777959) ^ [_1347274, _1347276, _1347278] : [-(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, _1347274, _1347276)), _1347278), _1347276) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1347274), _1347278), _1347276))], (31520 ^ _777959) ^ [_1373284] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1373284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1373284), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (14053 ^ _777959) ^ [_1039029, _1039031, _1039033] : [-(c_Map_Odom(_1039029, _1039031, _1039033) = hAPP(c_Set_OCollect(_1039029), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1039029), c_fNot), hAPP(hAPP(c_COMBC(_1039029, tc_Option_Ooption(_1039031), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1039031), tc_fun(tc_Option_Ooption(_1039031), tc_HOL_Obool), _1039029), c_fequal), _1039033)), c_Option_Ooption_ONone(_1039031)))))], (51038 ^ _777959) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (25162 ^ _777959) ^ [_1254744, _1254746, _1254748] : [class_Orderings_Oorder(_1254744), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1254744, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1254744), _1254746)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1254744, _1254746), _1254748)) = c_Orderings_Obot__class_Obot(tc_fun(_1254744, tc_HOL_Obool)))], (41771 ^ _777959) ^ [_1599739, _1599741, _1599743] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1599739)), _1599741), c_List_Olists(_1599739, c_Wellfounded_Oacc(_1599739, _1599743)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1599739)), _1599741), c_Wellfounded_Oacc(tc_List_Olist(_1599739), c_List_Olistrel1(_1599739, _1599743)))))], (37168 ^ _777959) ^ [_1485835, _1485837, _1485839, _1485841, _1485843, _1485845] : [-(hAPP(c_Relation_OImage(_1485835, _1485837, _1485839), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485841, tc_fun(_1485835, tc_HOL_Obool)), _1485843), _1485845)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1485841, tc_fun(_1485837, tc_HOL_Obool)), _1485843), hAPP(hAPP(c_COMBB(tc_fun(_1485835, tc_HOL_Obool), tc_fun(_1485837, tc_HOL_Obool), _1485841), c_Relation_OImage(_1485835, _1485837, _1485839)), _1485845)))], (41451 ^ _777959) ^ [_1590432, _1590434, _1590436, _1590438, _1590440] : [-(hAPP(hAPP(c_List_Olist__update(_1590432, hAPP(hAPP(c_List_Olist_OCons(_1590432), _1590434), _1590436)), _1590438), _1590440) = c_Nat_Onat_Onat__case(tc_List_Olist(_1590432), hAPP(hAPP(c_List_Olist_OCons(_1590432), _1590440), _1590436), hAPP(hAPP(c_COMBB(tc_List_Olist(_1590432), tc_List_Olist(_1590432), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1590432), _1590434)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1590432, tc_List_Olist(_1590432)), c_List_Olist__update(_1590432, _1590436)), _1590440)), _1590438))], (32891 ^ _777959) ^ [_1399242] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399242)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1399242)))], (48252 ^ _777959) ^ [_1749255, _1749257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749255), _1749257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1749255)), hAPP(c_Code__Numeral_Oof__nat, _1749257))))], (12437 ^ _777959) ^ [_1003851, _1003853, _1003855] : [class_Lattices_Olattice(_1003851), hAPP(_1003853, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1003851), 12442 ^ [_1003851, _1003853, _1003855]), 12443 ^ [_1003851, _1003853, _1003855])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1003851), hAPP(_1003853, 12442 ^ [_1003851, _1003853, _1003855])), hAPP(_1003853, 12443 ^ [_1003851, _1003853, _1003855])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1003851), _1003855)), -(_1003855 = c_Orderings_Obot__class_Obot(tc_fun(_1003851, tc_HOL_Obool))), -(hAPP(_1003853, c_Big__Operators_Olattice__class_OInf__fin(_1003851, _1003855)) = c_Big__Operators_Olattice__class_OInf__fin(_1003851, hAPP(c_Set_Oimage(_1003851, _1003851, _1003853), _1003855)))], (11786 ^ _777959) ^ [_991299, _991301] : [-(c_Map_Oran(_991299, _991301, hAPP(c_COMBK(tc_Option_Ooption(_991301), _991299), c_Option_Ooption_ONone(_991301))) = c_Orderings_Obot__class_Obot(tc_fun(_991301, tc_HOL_Obool)))], (19548 ^ _777959) ^ [_1151886] : [_1151886 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1151886), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25338 ^ _777959) ^ [_1258119, _1258121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1258119), _1258121)), -(c_Nat__Transfer_Otsub(_1258121, _1258119) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1258121), _1258119))], (17497 ^ _777959) ^ [_1112346, _1112348, _1112350] : [class_Orderings_Olinorder(_1112346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112346), _1112348)), -(c_Big__Operators_Olinorder__class_OMin(_1112346, hAPP(hAPP(c_Set_Oinsert(_1112346), _1112350), _1112348)) = hAPP(hAPP(c_Finite__Set_Ofold(_1112346, _1112346, c_Orderings_Oord__class_Omin(_1112346)), _1112350), _1112348))], (45858 ^ _777959) ^ [_1693385, _1693387] : [class_Enum_Oenum(_1693385), 45861 ^ _777959 : [(45862 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1693385)), _1693387)), -(hBOOL(hAPP(_1693387, c_Option_Ooption_ONone(_1693385)))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1693385), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1693385), tc_HOL_Obool, _1693385), _1693387), c_Option_Ooption_OSome(_1693385)))))], (45872 ^ _777959) ^ [] : [45873 ^ _777959 : [(45876 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1693385), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1693385), tc_HOL_Obool, _1693385), _1693387), c_Option_Ooption_OSome(_1693385))))], (45874 ^ _777959) ^ [] : [hBOOL(hAPP(_1693387, c_Option_Ooption_ONone(_1693385)))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(_1693385)), _1693387)))]]], (24552 ^ _777959) ^ [_1244150, _1244152, _1244154, _1244156, _1244158] : [class_Orderings_Olinorder(_1244150), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244150, _1244152), _1244154) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244150, _1244156), _1244158), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244150), _1244152), _1244154)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244150), _1244156), _1244158)), -(_1244154 = _1244158)], (36483 ^ _777959) ^ [_1469482, _1469484, _1469486, _1469488] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1469482), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1469484), _1469486)))), -(hBOOL(hAPP(hAPP(hAPP(_1469488, _1469482), _1469484), _1469486))), 36491 ^ _777959 : [(36494 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 36489 ^ [_1469482, _1469484, _1469486, _1469488]), 36490 ^ [_1469482, _1469484, _1469486, _1469488]))), hAPP(36488 ^ [_1469482, _1469484, _1469486, _1469488], 36490 ^ [_1469482, _1469484, _1469486, _1469488]) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)), -(hBOOL(hAPP(hAPP(hAPP(_1469488, 36488 ^ [_1469482, _1469484, _1469486, _1469488]), 36489 ^ [_1469482, _1469484, _1469486, _1469488]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 36490 ^ [_1469482, _1469484, _1469486, _1469488]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (36504 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1469488, 36488 ^ [_1469482, _1469484, _1469486, _1469488]), 36489 ^ [_1469482, _1469484, _1469486, _1469488]), 36490 ^ [_1469482, _1469484, _1469486, _1469488]))], (36492 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), 36488 ^ [_1469482, _1469484, _1469486, _1469488]), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), 36489 ^ [_1469482, _1469484, _1469486, _1469488]), 36490 ^ [_1469482, _1469484, _1469486, _1469488])))))]]], (22495 ^ _777959) ^ [] : [-(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)))], (35862 ^ _777959) ^ [_1458528] : [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), _1458528))), 35865 ^ _777959 : [(35872 ^ _777959) ^ [] : [-(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), _1458528))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1458528)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1458528)), 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), _1458528)))))], (35866 ^ _777959) ^ [] : [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), _1458528)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1458528)) = 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), _1458528))))]]], (42048 ^ _777959) ^ [_1606585] : [-(c_List_Obutlast(_1606585, c_List_Olist_ONil(_1606585)) = c_List_Olist_ONil(_1606585))], (44076 ^ _777959) ^ [_1654583, _1654585, _1654587] : [-(c_List_Omap__filter(_1654583, _1654585, _1654587, c_List_Olist_ONil(_1654583)) = c_List_Olist_ONil(_1654585))], (48057 ^ _777959) ^ [_1745571, _1745573, _1745575, _1745577, _1745579] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1745571, _1745573, _1745571, _1745575), hAPP(c_Product__Type_OPair(_1745573, _1745571), _1745577)), _1745579) = hAPP(_1745579, _1745577))], (35527 ^ _777959) ^ [_1451309, _1451311, _1451313] : [class_Rings_Osemiring__1(_1451309), hBOOL(hAPP(hAPP(c_member(_1451309), _1451311), c_Nat_Osemiring__1__class_ONats(_1451309))), hBOOL(hAPP(hAPP(c_member(_1451309), _1451313), c_Nat_Osemiring__1__class_ONats(_1451309))), -(hBOOL(hAPP(hAPP(c_member(_1451309), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1451309), _1451311), _1451313)), c_Nat_Osemiring__1__class_ONats(_1451309))))], (22764 ^ _777959) ^ [_1212097, _1212099] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212097)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212099)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1212097), _1212099)))], (38920 ^ _777959) ^ [_1526062, _1526064, _1526066] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1526062, _1526064, _1526066, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1526064)], (13201 ^ _777959) ^ [_1018793, _1018795, _1018797, _1018799] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1018793), _1018795)), hBOOL(hAPP(hAPP(c_member(_1018793), _1018797), _1018795)), hBOOL(hAPP(hAPP(c_member(_1018793), _1018799), _1018795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1018793), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018793, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1018793, tc_HOL_Obool)), _1018795), hAPP(hAPP(c_Set_Oinsert(_1018793), _1018797), c_Orderings_Obot__class_Obot(tc_fun(_1018793, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1018793), _1018799), c_Orderings_Obot__class_Obot(tc_fun(_1018793, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1018793), _1018795))))], (12780 ^ _777959) ^ [_1009837, _1009839, _1009841] : [class_Groups_Oordered__ab__group__add(_1009837), 12783 ^ _777959 : [(12790 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009837), _1009841), hAPP(c_Groups_Ouminus__class_Ouminus(_1009837), _1009839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009837), _1009839), hAPP(c_Groups_Ouminus__class_Ouminus(_1009837), _1009841))))], (12784 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009837), _1009839), hAPP(c_Groups_Ouminus__class_Ouminus(_1009837), _1009841))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1009837), _1009841), hAPP(c_Groups_Ouminus__class_Ouminus(_1009837), _1009839))))]]], (46960 ^ _777959) ^ [_1719612, _1719614, _1719616] : [c_Wellfounded_Owf(_1719612, _1719614), hBOOL(hAPP(hAPP(c_member(tc_prod(_1719612, _1719612)), hAPP(hAPP(c_Product__Type_OPair(_1719612, _1719612), _1719616), _1719616)), _1719614))], (24265 ^ _777959) ^ [_1239179, _1239181] : [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)), _1239179)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1239181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1239179), _1239181)))], (5558 ^ _777959) ^ [_862889, _862891] : [_862891 = _862889, -(c_Option_Ooption_OSome(_862891) = c_Option_Ooption_OSome(_862889))], (50298 ^ _777959) ^ [_1797618, _1797620, _1797622, _1797624, _1797626, _1797628, _1797630] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1797618, _1797620, _1797622, _1797624), _1797626), _1797628), _1797630) = c_New__DSequence_Oneg__bind(_1797618, _1797620, hAPP(hAPP(hAPP(_1797622, _1797626), _1797628), _1797630), hAPP(hAPP(c_COMBC(_1797618, 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(_1797620)))), hAPP(hAPP(c_COMBC(_1797618, 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(_1797620))))), hAPP(hAPP(c_COMBC(_1797618, 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(_1797620)))))), _1797624), _1797626)), _1797628)), _1797630)))], (20653 ^ _777959) ^ [_1171600, _1171602] : [class_Groups_Olinordered__ab__group__add(_1171600), 20656 ^ _777959 : [(20663 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171600), c_Groups_Ozero__class_Ozero(_1171600)), _1171602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171600), hAPP(c_Groups_Ouminus__class_Ouminus(_1171600), _1171602)), _1171602)))], (20657 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171600), hAPP(c_Groups_Ouminus__class_Ouminus(_1171600), _1171602)), _1171602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171600), c_Groups_Ozero__class_Ozero(_1171600)), _1171602)))]]], (21154 ^ _777959) ^ [_1179711, _1179713, _1179715, _1179717] : [-(c_Nat_Onat_Onat__case(_1179711, _1179713, _1179715, hAPP(c_Nat_OSuc, _1179717)) = hAPP(_1179715, _1179717))], (48759 ^ _777959) ^ [_1761364, _1761366, _1761368] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1761364, _1761364)), hAPP(hAPP(c_Product__Type_OPair(_1761364, _1761364), _1761366), _1761368)), c_Relation_OId(_1761364))), -(_1761366 = _1761368)], (14444 ^ _777959) ^ [_1048668, _1048670, _1048672] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1048668, tc_HOL_Obool)), _1048670), _1048672))), 14450 ^ _777959 : [(14454 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1048668, tc_HOL_Obool)), 14452 ^ [_1048668, _1048670, _1048672]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1048668, tc_HOL_Obool)), _1048670), _1048672))))], (14456 ^ _777959) ^ [] : [14449 ^ [_1048668, _1048670, _1048672] = 14452 ^ [_1048668, _1048670, _1048672]], (14458 ^ _777959) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1048668, tc_HOL_Obool)), 14449 ^ [_1048668, _1048670, _1048672]), 14452 ^ [_1048668, _1048670, _1048672]) = c_Orderings_Obot__class_Obot(tc_fun(_1048668, tc_HOL_Obool))], (14451 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1048668, tc_HOL_Obool)), 14449 ^ [_1048668, _1048670, _1048672]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1048668, tc_HOL_Obool)), _1048670), _1048672))))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1048668, tc_HOL_Obool)), _1048670), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1048668, tc_HOL_Obool), _1048672)) = c_Orderings_Obot__class_Obot(tc_fun(_1048668, tc_HOL_Obool)))], (44088 ^ _777959) ^ [_1654862, _1654864, _1654866, _1654868, _1654870] : [-(c_List_Omap__filter(_1654862, _1654864, _1654866, hAPP(hAPP(c_List_Olist_OCons(_1654862), _1654868), _1654870)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(_1654864), _1654864, c_List_Omap__filter(_1654862, _1654864, _1654866, _1654870), hAPP(hAPP(c_COMBC(_1654864, tc_List_Olist(_1654864), tc_List_Olist(_1654864)), c_List_Olist_OCons(_1654864)), c_List_Omap__filter(_1654862, _1654864, _1654866, _1654870))), hAPP(_1654866, _1654868)))], (35621 ^ _777959) ^ [_1453230, _1453232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1453230), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1453232, _1453230) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1453232), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1453230)))], (45724 ^ _777959) ^ [_1690267, _1690269, _1690271, _1690273, _1690275] : [class_Orderings_Olinorder(_1690267), -(hAPP(c_List_Ofilter(_1690269, _1690271), c_List_Olinorder__class_Osort__key(_1690269, _1690267, _1690273, _1690275)) = c_List_Olinorder__class_Osort__key(_1690269, _1690267, _1690273, hAPP(c_List_Ofilter(_1690269, _1690271), _1690275)))], (48948 ^ _777959) ^ [_1766398, _1766400, _1766402, _1766404] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1766398), tc_List_Olist(_1766398))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1766398), tc_List_Olist(_1766398)), _1766400), _1766402)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1766398), tc_List_Olist(_1766398)), c_List_Olistrel1(_1766398, _1766404)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1766398), tc_List_Olist(_1766398))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1766398), tc_List_Olist(_1766398)), _1766400), _1766402)), c_List_Olistrel1(_1766398, hAPP(c_Relation_Oconverse(_1766398, _1766398), _1766404)))))], (31696 ^ _777959) ^ [_1376403, _1376405, _1376407, _1376409] : [class_Orderings_Olinorder(_1376403), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376403), _1376405)), 31706 ^ _777959 : [(31709 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376403), 31705 ^ [_1376403, _1376405, _1376407, _1376409]), _1376407))], (31707 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1376403), 31705 ^ [_1376403, _1376405, _1376407, _1376409]), _1376405)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1376403), hAPP(hAPP(c_Finite__Set_Ofold(_1376403, _1376403, c_Orderings_Oord__class_Omax(_1376403)), _1376409), _1376405)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376403), _1376407), _1376409))))], (43733 ^ _777959) ^ [_1647407, _1647409, _1647411] : [class_Orderings_Olinorder(_1647407), -(c_Big__Operators_Olattice_OSup__fin(_1647407, c_Orderings_Oord__class_Omax(_1647407), hAPP(c_List_Oset(_1647407), hAPP(hAPP(c_List_Olist_OCons(_1647407), _1647409), _1647411))) = hAPP(c_List_Ofoldl(_1647407, _1647407, c_Orderings_Oord__class_Omax(_1647407), _1647409), _1647411))], (14904 ^ _777959) ^ [_1060052, _1060054, _1060056] : [-(c_Map_Oran(_1060052, _1060054, _1060056) = hAPP(c_Set_OCollect(_1060054), hAPP(hAPP(c_COMBB(tc_fun(_1060052, tc_HOL_Obool), tc_HOL_Obool, _1060054), c_HOL_OEx(_1060052)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1060054), tc_fun(_1060052, tc_HOL_Obool), _1060054), hAPP(c_COMBC(_1060052, tc_Option_Ooption(_1060054), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1060054), tc_fun(tc_Option_Ooption(_1060054), tc_HOL_Obool), _1060052), c_fequal), _1060056))), c_Option_Ooption_OSome(_1060054)))))], (47330 ^ _777959) ^ [_1728375, _1728377, _1728379] : [hAPP(c_Relation_ODomain(_1728375, _1728377), _1728379) = c_Orderings_Obot__class_Obot(tc_fun(_1728375, tc_HOL_Obool)), -(_1728379 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1728375, _1728377), tc_HOL_Obool)))], (38430 ^ _777959) ^ [_1514792, _1514794, _1514796, _1514798] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1514792), _1514794)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1514796), _1514798)), 38437 ^ _777959 : [(38438 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1514792), _1514794)), hAPP(c_Finite__Set_Ocard(_1514796), _1514798)))), 38439 ^ _777959 : [(38440 ^ _777959) ^ [_1515003] : [c_Fun_Oinj__on(_1514792, _1514796, _1515003, _1514794), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1514796, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1514792, _1514796, _1515003), _1514794)), _1514798))]]], (38448 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1514792), _1514794)), hAPP(c_Finite__Set_Ocard(_1514796), _1514798))), 38452 ^ _777959 : [(38455 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1514796, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1514792, _1514796, 38451 ^ [_1514792, _1514794, _1514796, _1514798]), _1514794)), _1514798)))], (38453 ^ _777959) ^ [] : [-(c_Fun_Oinj__on(_1514792, _1514796, 38451 ^ [_1514792, _1514794, _1514796, _1514798], _1514794))]]]]], (36978 ^ _777959) ^ [_1480795, _1480797, _1480799, _1480801] : [c_Wellfounded_Omax__extp(_1480795, hAPP(hAPP(c_COMBC(_1480795, tc_fun(tc_prod(_1480795, _1480795), tc_HOL_Obool), tc_fun(_1480795, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1480795, tc_fun(tc_fun(tc_prod(_1480795, _1480795), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1480795, _1480795), tc_HOL_Obool), tc_fun(_1480795, tc_HOL_Obool)), _1480795), c_COMBC(_1480795, tc_fun(tc_prod(_1480795, _1480795), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1480795, tc_prod(_1480795, _1480795)), tc_fun(_1480795, tc_fun(tc_fun(tc_prod(_1480795, _1480795), tc_HOL_Obool), tc_HOL_Obool)), _1480795), hAPP(c_COMBB(tc_prod(_1480795, _1480795), tc_fun(tc_fun(tc_prod(_1480795, _1480795), tc_HOL_Obool), tc_HOL_Obool), _1480795), c_member(tc_prod(_1480795, _1480795)))), c_Product__Type_OPair(_1480795, _1480795)))), _1480797), _1480799, _1480801), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1480795, tc_HOL_Obool), tc_fun(_1480795, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1480795, tc_HOL_Obool), tc_fun(_1480795, tc_HOL_Obool)), _1480799), _1480801)), c_Wellfounded_Omax__ext(_1480795, _1480797))))], (9220 ^ _777959) ^ [_936276, _936278, _936280, _936282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936276, tc_HOL_Obool)), _936278), _936280)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936276, tc_HOL_Obool)), _936280), _936282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936276, tc_HOL_Obool)), _936278), _936282)))], (17041 ^ _777959) ^ [_1103813, _1103815, _1103817, _1103819] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1103813), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103813), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1103813), _1103815), _1103817)), _1103819) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1103813), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103813), _1103815), _1103819)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1103813), _1103817), _1103819)))], (43992 ^ _777959) ^ [_1652621, _1652623, _1652625, _1652627] : [-(hBOOL(hAPP(_1652621, _1652623))), -(hAPP(c_List_OremoveAll(_1652625, _1652623), hAPP(c_List_Ofilter(_1652625, _1652621), _1652627)) = hAPP(c_List_Ofilter(_1652625, _1652621), _1652627))], (24782 ^ _777959) ^ [_1247811, _1247813, _1247815] : [class_Orderings_Oorder(_1247811), 24785 ^ _777959 : [(24792 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247811), _1247813), _1247815))), -(c_Orderings_Obot__class_Obot(tc_fun(_1247811, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1247811, _1247813), _1247815))], (24786 ^ _777959) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1247811, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1247811, _1247813), _1247815), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247811), _1247813), _1247815))]]], (35796 ^ _777959) ^ [_1456756, _1456758, _1456760] : [hBOOL(hAPP(_1456756, hAPP(hAPP(c_Product__Type_OPair(_1456758, _1456760), 35797 ^ [_1456756, _1456758, _1456760]), 35798 ^ [_1456756, _1456758, _1456760]))), 35801 ^ _777959 : [(35802 ^ _777959) ^ [_1456903] : [-(hBOOL(hAPP(_1456756, _1456903)))]]], (43943 ^ _777959) ^ [_1651672, _1651674, _1651676] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651672)), hAPP(c_List_Ofilter(_1651672, _1651674), _1651676))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651672)), hAPP(c_List_Ofilter(_1651672, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1651672), c_fNot), _1651674)), _1651676))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651672)), _1651676))], (16629 ^ _777959) ^ [_1096740, _1096742, _1096744, _1096746] : [class_Orderings_Olinorder(_1096740), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096740), _1096742), _1096744)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096740), _1096746), _1096744)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1096740), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1096740), _1096742), _1096746)), _1096744)))], (3778 ^ _777959) ^ [_835119, _835121, _835123, _835125, _835127, _835129] : [-(c_FunDef_Oin__rel(_835129, _835125, _835121) = c_FunDef_Oin__rel(_835127, _835123, _835119)), _835129 = _835127, _835125 = _835123, _835121 = _835119], (33513 ^ _777959) ^ [_1409489, _1409491] : [class_Int_Onumber__ring(_1409489), class_Rings_Olinordered__idom(_1409489), 33520 ^ _777959 : [(33527 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1409491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409489), c_Groups_Ozero__class_Ozero(_1409489)), hAPP(c_Int_Onumber__class_Onumber__of(_1409489), _1409491))))], (33521 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409489), c_Groups_Ozero__class_Ozero(_1409489)), hAPP(c_Int_Onumber__class_Onumber__of(_1409489), _1409491))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1409491)))]]], (7210 ^ _777959) ^ [_898699, _898701, _898703, _898705] : [hBOOL(hAPP(_898699, _898701)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_898703, tc_HOL_Obool)), _898699), _898705), _898701)))], (19564 ^ _777959) ^ [_1152229] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152229), _1152229) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41735 ^ _777959) ^ [_1598538, _1598540, _1598542, _1598544, _1598546, _1598548, _1598550, _1598552] : [-(hAPP(c_Product__Type_Omap__pair(_1598538, _1598540, _1598542, _1598544, _1598546, _1598548), hAPP(hAPP(c_Product__Type_OPair(_1598538, _1598542), _1598550), _1598552)) = hAPP(hAPP(c_Product__Type_OPair(_1598540, _1598544), hAPP(_1598546, _1598550)), hAPP(_1598548, _1598552)))], (45228 ^ _777959) ^ [_1679448, _1679450, _1679452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679448)), c_List_OtakeWhile(_1679448, _1679450, _1679452))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679448)), _1679452))), hBOOL(hAPP(_1679450, hAPP(hAPP(c_List_Onth(_1679448), _1679452), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679448)), c_List_OtakeWhile(_1679448, _1679450, _1679452)))))], (43085 ^ _777959) ^ [_1632368, _1632370, _1632372, _1632374, _1632376] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632368), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632370)), _1632372)))), -(hAPP(hAPP(c_List_Olist__update(_1632370, hAPP(hAPP(c_List_Oappend(_1632370), _1632372), _1632374)), _1632368), _1632376) = hAPP(hAPP(c_List_Oappend(_1632370), _1632372), hAPP(hAPP(c_List_Olist__update(_1632370, _1632374), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1632368), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632370)), _1632372))), _1632376)))], (20023 ^ _777959) ^ [_1160271, _1160273, _1160275] : [class_Rings_Oordered__cancel__semiring(_1160271), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160271), _1160273), c_Groups_Ozero__class_Ozero(_1160271))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160271), c_Groups_Ozero__class_Ozero(_1160271)), _1160275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1160271), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1160271), _1160273), _1160275)), c_Groups_Ozero__class_Ozero(_1160271))))], (35299 ^ _777959) ^ [_1441472, _1441474] : [-(c_Divides_Odivmod__int__rel(_1441472, _1441474) = 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, _1441472))), 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), _1441474)))))), 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)), _1441474))), 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)), _1441474))))), 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)), _1441474)))), 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), _1441474))), 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))))))))], (50638 ^ _777959) ^ [_1805101, _1805103, _1805105] : [-(c_List_Oreplicate(_1805101, hAPP(c_Nat_OSuc, _1805103), _1805105) = hAPP(hAPP(c_List_Olist_OCons(_1805101), _1805105), c_List_Oreplicate(_1805101, _1805103, _1805105)))], (46030 ^ _777959) ^ [_1696340, _1696342, _1696344, _1696346] : [class_Orderings_Oorder(_1696340), class_Enum_Oenum(_1696342), 46037 ^ _777959 : [(46046 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1696342, _1696340)), _1696344), _1696346))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1696342, _1696340)), _1696344), _1696346)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1696342), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1696342), c_fNot), hAPP(hAPP(c_COMBS(_1696342, _1696340, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1696340, tc_fun(_1696340, tc_HOL_Obool), _1696342), c_fequal), _1696344)), _1696346))))], (46038 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1696342, _1696340)), _1696344), _1696346)), 46041 ^ _777959 : [(46044 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1696342), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1696342), c_fNot), hAPP(hAPP(c_COMBS(_1696342, _1696340, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1696340, tc_fun(_1696340, tc_HOL_Obool), _1696342), c_fequal), _1696344)), _1696346)))))], (46042 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1696342, _1696340)), _1696344), _1696346)))]]]]], (38322 ^ _777959) ^ [_1512343, _1512345, _1512347, _1512349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1512343), hAPP(c_Set_Oimage(_1512345, _1512343, _1512347), _1512349))), hAPP(c_Finite__Set_Ocard(_1512345), _1512349))), c_Fun_Oinj__on(_1512345, _1512343, _1512347, _1512349)], (42901 ^ _777959) ^ [_1628291, _1628293, _1628295] : [-(c_List_Olist_ONil(_1628291) = hAPP(hAPP(c_List_Oappend(_1628291), _1628293), _1628295)), _1628293 = c_List_Olist_ONil(_1628291), _1628295 = c_List_Olist_ONil(_1628291)], (14219 ^ _777959) ^ [_1042513, _1042515] : [class_Lattices_Oboolean__algebra(_1042513), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1042513), _1042515), hAPP(c_Groups_Ouminus__class_Ouminus(_1042513), _1042515)) = c_Orderings_Otop__class_Otop(_1042513))], (42774 ^ _777959) ^ [_1625350, _1625352, _1625354, _1625356, _1625358, _1625360] : [-(c_List_Ofoldr(_1625350, _1625352, _1625354, hAPP(hAPP(c_List_Oappend(_1625350), _1625356), _1625358), _1625360) = c_List_Ofoldr(_1625350, _1625352, _1625354, _1625356, c_List_Ofoldr(_1625350, _1625352, _1625354, _1625358, _1625360)))], (15040 ^ _777959) ^ [_1064002, _1064004, _1064006, _1064008] : [class_Groups_Oab__semigroup__mult(_1064002), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064002), _1064004), _1064006)), _1064008) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064002), _1064004), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1064002), _1064006), _1064008)))], (9650 ^ _777959) ^ [_944900, _944902] : [class_Lattices_Olattice(_944900), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944900), _944902), _944902) = _944902)], (18931 ^ _777959) ^ [_1141346, _1141348] : [class_Groups_Oab__semigroup__mult(_1141346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1141346), _1141348)), -(_1141348 = c_Orderings_Obot__class_Obot(tc_fun(_1141346, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1141346), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141346), 18944 ^ [_1141346, _1141348]), 18945 ^ [_1141346, _1141348])), hAPP(hAPP(c_Set_Oinsert(_1141346), 18944 ^ [_1141346, _1141348]), hAPP(hAPP(c_Set_Oinsert(_1141346), 18945 ^ [_1141346, _1141348]), c_Orderings_Obot__class_Obot(tc_fun(_1141346, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1141346), hAPP(c_Finite__Set_Ofold1(_1141346, c_Groups_Otimes__class_Otimes(_1141346)), _1141348)), _1141348)))], (42481 ^ _777959) ^ [_1617198, _1617200, _1617202] : [-(c_List_Olistset(_1617198, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1617198, tc_HOL_Obool)), _1617200), _1617202)) = c_List_Oset__Cons(_1617198, _1617200, c_List_Olistset(_1617198, _1617202)))], (42104 ^ _777959) ^ [_1607585, _1607587, _1607589, _1607591] : [42105 ^ _777959 : [(42108 ^ _777959) ^ [] : [_1607591 = c_Orderings_Obot__class_Obot(tc_fun(_1607587, tc_HOL_Obool))], (42106 ^ _777959) ^ [] : [_1607589 = c_Orderings_Obot__class_Obot(tc_fun(_1607585, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1607585, _1607587), _1607589), hAPP(c_COMBK(tc_fun(_1607587, tc_HOL_Obool), _1607585), _1607591)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1607585, _1607587), tc_HOL_Obool)))], (42050 ^ _777959) ^ [_1606615, _1606617, _1606619] : [c_Equiv__Relations_Oequiv(_1606615, _1606617, _1606619), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1606615, _1606615), tc_HOL_Obool)), _1606619), hAPP(hAPP(c_Product__Type_OSigma(_1606615, _1606615), _1606617), hAPP(c_COMBK(tc_fun(_1606615, tc_HOL_Obool), _1606615), _1606617)))))], (48370 ^ _777959) ^ [_1751277] : [-(_1751277 = 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, _1751277)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1751277))))], (23787 ^ _777959) ^ [_1230270, _1230272] : [class_Power_Opower(_1230270), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1230270), _1230272), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1230270))], (43205 ^ _777959) ^ [_1635777, _1635779] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635777)), hAPP(c_List_Orotate1(_1635777), _1635779)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1635777)), _1635779))], (39378 ^ _777959) ^ [_1537526, _1537528, _1537530, _1537532, _1537534, _1537536] : [c_Finite__Set_Ofolding(_1537526, _1537528, _1537530, _1537532), hBOOL(hAPP(c_Finite__Set_Ofinite(_1537526), _1537534)), -(hAPP(c_Fun_Ocomp(_1537528, _1537528, _1537528, hAPP(_1537530, _1537536)), hAPP(_1537532, _1537534)) = hAPP(c_Fun_Ocomp(_1537528, _1537528, _1537528, hAPP(_1537532, _1537534)), hAPP(_1537530, _1537536)))], (37122 ^ _777959) ^ [_1483975, _1483977, _1483979, _1483981] : [c_FunDef_Oreduction__pair(_1483975, _1483977), -(c_FunDef_Oreduction__pair(_1483979, hAPP(hAPP(c_FunDef_Orp__inv__image(_1483975, _1483979), _1483977), _1483981)))], (25619 ^ _777959) ^ [_1263625, _1263627, _1263629] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1263625)), 25622 ^ _777959 : [(25623 ^ _777959) ^ [] : [-(_1263627 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1263629), _1263625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1263625), _1263627)), _1263629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1263629), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1263625), hAPP(c_Nat_OSuc, _1263627))))], (25633 ^ _777959) ^ [] : [_1263627 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1263629), _1263625), 25636 ^ _777959 : [(25639 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1263629), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1263625), hAPP(c_Nat_OSuc, _1263627)))))], (25637 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1263625), _1263627)), _1263629)))]]]]], (8602 ^ _777959) ^ [_926502, _926504, _926506, _926508] : [class_Orderings_Oorder(_926502), _926504 = _926506, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926502), _926508), _926506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_926502), _926508), _926504)))], (7638 ^ _777959) ^ [_906738, _906740, _906742] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OCall(_906738, _906740, _906742)], (39225 ^ _777959) ^ [_1533771, _1533773, _1533775] : [hBOOL(hAPP(hAPP(c_member(_1533771), _1533773), c_Wellfounded_Oacc(_1533771, _1533775))), 39228 ^ _777959 : [(39229 ^ _777959) ^ [_1533885] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1533771, _1533771)), hAPP(hAPP(c_Product__Type_OPair(_1533771, _1533771), _1533885), _1533773)), _1533775)), -(hBOOL(hAPP(hAPP(c_member(_1533771), _1533885), c_Wellfounded_Oacc(_1533771, _1533775))))]]], (44090 ^ _777959) ^ [_1654945, _1654947, _1654949, _1654951] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1654945, tc_Nat_Onat), _1654945), c_Product__Type_Ofst(_1654945, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1654945, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1654945, tc_Nat_Onat)), _1654947), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1654945, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1654945, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1654945, tc_Nat_Onat), _1654949), _1654951))) = hAPP(hAPP(c_List_Omap(tc_prod(_1654945, tc_Nat_Onat), _1654945), c_Product__Type_Ofst(_1654945, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1654945, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1654945, tc_Nat_Onat)), _1654947), c_Product__Type_Osnd(_1654945, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1654945, tc_Nat_Onat), _1654949), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1654951)))))], (35303 ^ _777959) ^ [_1441747, _1441749] : [-(c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint, _1441747, _1441749) = c_Smallcheck_Ofull__small_H(_1441747, hAPP(c_Code__Numeral_Oint__of, _1441749), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1441749))))], (41328 ^ _777959) ^ [_1587447, _1587449, _1587451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1587447), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1587449)), _1587451))), -(c_List_Obutlast(_1587449, hAPP(hAPP(c_List_Otake(_1587449), _1587447), _1587451)) = hAPP(hAPP(c_List_Otake(_1587449), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1587447), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1587451))], (14329 ^ _777959) ^ [_1045449, _1045451, _1045453] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045449), _1045451)), -(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(_1045449), _1045453)), hAPP(c_Finite__Set_Ocard(_1045449), _1045451))), hAPP(c_Finite__Set_Ocard(_1045449), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1045449, tc_HOL_Obool)), _1045453), _1045451)))))], (27872 ^ _777959) ^ [_1304332, _1304334, _1304336] : [class_Int_Oring__char__0(_1304332), 27875 ^ _777959 : [(27882 ^ _777959) ^ [] : [_1304334 = _1304336, -(hAPP(c_Int_Oring__1__class_Oof__int(_1304332), _1304334) = hAPP(c_Int_Oring__1__class_Oof__int(_1304332), _1304336))], (27876 ^ _777959) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1304332), _1304334) = hAPP(c_Int_Oring__1__class_Oof__int(_1304332), _1304336), -(_1304334 = _1304336)]]], (40274 ^ _777959) ^ [_1559283, _1559285, _1559287] : [-(hAPP(c_List_Oset(_1559283), c_List_Osublist(_1559283, _1559285, _1559287)) = hAPP(c_Set_OCollect(_1559283), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1559283), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1559283, 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)), _1559283), 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)), _1559283), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1559283, tc_fun(tc_Nat_Onat, _1559283), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1559283, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1559283), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1559283), c_COMBB(_1559283, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1559283), _1559285))))), 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(_1559283)), _1559285)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1559287))))))], (37383 ^ _777959) ^ [_1491686, _1491688, _1491690, _1491692] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1491686, _1491686)), hAPP(hAPP(c_Product__Type_OPair(_1491686, _1491686), _1491688), _1491690)), c_Relation_OId__on(_1491686, _1491692)))), _1491688 = _1491690, hBOOL(hAPP(hAPP(c_member(_1491686), _1491688), _1491692))], (46349 ^ _777959) ^ [_1703542, _1703544, _1703546, _1703548, _1703550, _1703552, _1703554] : [-(c_List_Olist__all2(_1703542, _1703544, _1703546, hAPP(hAPP(c_List_Olist_OCons(_1703542), _1703548), _1703550), hAPP(hAPP(c_List_Olist_OCons(_1703544), _1703552), _1703554))), hBOOL(hAPP(hAPP(_1703546, _1703548), _1703552)), c_List_Olist__all2(_1703542, _1703544, _1703546, _1703550, _1703554)], (2584 ^ _777959) ^ [_816270, _816272, _816274, _816276] : [-(c_Divides_OposDivAlg(_816276, _816272) = c_Divides_OposDivAlg(_816274, _816270)), _816276 = _816274, _816272 = _816270], (49363 ^ _777959) ^ [_1776730, _1776732, _1776734] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776730, _1776730)), _1776732), c_Transitive__Closure_Otrancl(_1776730, _1776734))), 49367 ^ _777959 : [(49370 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776730, _1776730)), _1776732), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1776730, _1776730), tc_HOL_Obool), 49366 ^ [_1776730, _1776732, _1776734]), _1776734))))], (49368 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 49366 ^ [_1776730, _1776732, _1776734])))]]], (9230 ^ _777959) ^ [_936503, _936505, _936507, _936509, _936511, _936513, _936515] : [hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_936503, tc_Option_Ooption(_936505)), _936507), _936509), hAPP(c_Option_Ooption_OSome(_936505), _936511)), _936513) = hAPP(c_Option_Ooption_OSome(_936505), _936515), 9235 ^ _777959 : [(9238 ^ _777959) ^ [] : [-(_936511 = _936515)], (9236 ^ _777959) ^ [] : [-(_936513 = _936509)]], 9239 ^ _777959 : [(9242 ^ _777959) ^ [] : [-(hAPP(_936507, _936513) = hAPP(c_Option_Ooption_OSome(_936505), _936515))], (9240 ^ _777959) ^ [] : [_936513 = _936509]]], (42022 ^ _777959) ^ [_1606051, _1606053, _1606055, _1606057] : [_1606057 = c_List_Olist_ONil(_1606053), -(c_List_Olist_ONil(_1606051) = hAPP(hAPP(c_List_Omap(_1606053, _1606051), _1606055), _1606057))], (13187 ^ _777959) ^ [_1018558, _1018560, _1018562] : [class_Lattices_Oboolean__algebra(_1018558), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1018558), _1018560), _1018562) = c_Orderings_Obot__class_Obot(_1018558), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1018558), _1018560), _1018562) = c_Orderings_Otop__class_Otop(_1018558), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1018558), _1018560) = _1018562)], (10192 ^ _777959) ^ [_956663, _956665, _956667, _956669] : [class_Lattices_Olattice(_956663), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956663), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_956663), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956663), _956665), _956667)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956663), _956665), _956669))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956663), _956665), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_956663), _956667), _956669)))))], (7148 ^ _777959) ^ [_897386, _897388, _897390] : [class_Lattices_Osemilattice__sup(_897386), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897386), _897388), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897386), _897388), _897390)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897386), _897388), _897390))], (49467 ^ _777959) ^ [_1779675, _1779677, _1779679, _1779681, _1779683] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1779675, _1779675)), hAPP(hAPP(c_Product__Type_OPair(_1779675, _1779675), _1779677), _1779679)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1779675, _1779675), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1779681)), _1779683))), 49471 ^ _777959 : [(49474 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779675, _1779675)), hAPP(hAPP(c_Product__Type_OPair(_1779675, _1779675), 49470 ^ [_1779675, _1779677, _1779679, _1779681, _1779683]), _1779679)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1779675, _1779675), tc_HOL_Obool), _1779681), _1779683))))], (49472 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1779675, _1779675)), hAPP(hAPP(c_Product__Type_OPair(_1779675, _1779675), _1779677), 49470 ^ [_1779675, _1779677, _1779679, _1779681, _1779683])), _1779683)))]]], (31298 ^ _777959) ^ [_1369131, _1369133] : [class_Rings_Olinordered__idom(_1369131), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369131), c_Groups_Osgn__class_Osgn(_1369131, _1369133)), hAPP(c_Groups_Oabs__class_Oabs(_1369131), _1369133)) = _1369133)], (41721 ^ _777959) ^ [_1598016, _1598018, _1598020] : [-(hAPP(c_Product__Type_Omap__pair(_1598016, _1598016, _1598018, _1598018, c_COMBI(_1598016), c_COMBI(_1598018)), _1598020) = _1598020)], (50320 ^ _777959) ^ [_1798451, _1798453, _1798455, _1798457] : [-(c_Lazy__Sequence_Oappend(_1798451, c_Lazy__Sequence_Olazy__sequence_OInsert(_1798451, _1798453, _1798455), _1798457) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1798451, _1798453, c_Lazy__Sequence_Oappend(_1798451, _1798455, _1798457)))], (46237 ^ _777959) ^ [_1701031, _1701033, _1701035, _1701037] : [hBOOL(hAPP(c_List_Olistsp(_1701031, _1701033), hAPP(hAPP(c_List_Olist_OCons(_1701031), _1701035), _1701037))), 46240 ^ _777959 : [(46243 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1701031, _1701033), _1701037)))], (46241 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1701033, _1701035)))]]], (51254 ^ _777959) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (29902 ^ _777959) ^ [_1343265, _1343267] : [class_Divides_Osemiring__div(_1343265), -(c_Divides_Odiv__class_Omod(_1343265, c_Groups_Ozero__class_Ozero(_1343265), _1343267) = c_Groups_Ozero__class_Ozero(_1343265))], (30032 ^ _777959) ^ [_1345910, _1345912, _1345914, _1345916, _1345918, _1345920] : [class_Divides_Osemiring__div(_1345910), c_Divides_Odiv__class_Omod(_1345910, _1345912, _1345914) = c_Divides_Odiv__class_Omod(_1345910, _1345916, _1345914), c_Divides_Odiv__class_Omod(_1345910, _1345918, _1345914) = c_Divides_Odiv__class_Omod(_1345910, _1345920, _1345914), -(c_Divides_Odiv__class_Omod(_1345910, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345910), _1345912), _1345918), _1345914) = c_Divides_Odiv__class_Omod(_1345910, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345910), _1345916), _1345920), _1345914))], (23411 ^ _777959) ^ [_1223890] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223890), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1223890)], (46706 ^ _777959) ^ [_1712166, _1712168, _1712170, _1712172] : [c_Wellfounded_Omax__extp(_1712166, _1712168, _1712170, _1712172), 46709 ^ _777959 : [(46712 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1712166), _1712172)))], (46714 ^ _777959) ^ [] : [_1712172 = c_Orderings_Obot__class_Obot(tc_fun(_1712166, tc_HOL_Obool))], (46716 ^ _777959) ^ [_1712382] : [hBOOL(hAPP(hAPP(c_member(_1712166), _1712382), _1712170)), 46720 ^ _777959 : [(46723 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1712168, _1712382), 46719 ^ [_1712166, _1712168, _1712170, _1712172, _1712382])))], (46721 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1712166), 46719 ^ [_1712166, _1712168, _1712170, _1712172, _1712382]), _1712172)))]]], (46710 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1712166), _1712170)))]]], (12738 ^ _777959) ^ [_1009092, _1009094, _1009096] : [class_Groups_Oordered__ab__group__add(_1009092), 12741 ^ _777959 : [(12748 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009092), hAPP(c_Groups_Ouminus__class_Ouminus(_1009092), _1009096)), _1009094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009092), hAPP(c_Groups_Ouminus__class_Ouminus(_1009092), _1009094)), _1009096)))], (12742 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009092), hAPP(c_Groups_Ouminus__class_Ouminus(_1009092), _1009094)), _1009096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009092), hAPP(c_Groups_Ouminus__class_Ouminus(_1009092), _1009096)), _1009094)))]]], (51096 ^ _777959) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (48621 ^ _777959) ^ [_1757870, _1757872, _1757874, _1757876, _1757878] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1757870, _1757870)), hAPP(hAPP(c_Product__Type_OPair(_1757870, _1757870), _1757872), _1757874)), c_Transitive__Closure_Ortrancl(_1757870, _1757876))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1757870, _1757870)), hAPP(hAPP(c_Product__Type_OPair(_1757870, _1757870), _1757874), _1757878)), c_Transitive__Closure_Otrancl(_1757870, _1757876))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1757870, _1757870)), hAPP(hAPP(c_Product__Type_OPair(_1757870, _1757870), _1757872), _1757878)), c_Transitive__Closure_Otrancl(_1757870, _1757876))))], (2922 ^ _777959) ^ [_821645, _821647, _821649, _821651, _821653, _821655, _821657, _821659] : [-(c_Product__Type_Oapfst(_821659, _821655, _821651, _821647) = c_Product__Type_Oapfst(_821657, _821653, _821649, _821645)), _821659 = _821657, _821655 = _821653, _821651 = _821649, _821647 = _821645], (5190 ^ _777959) ^ [_857397, _857399] : [_857399 = _857397, -(c_Lattices_Osemilattice__sup__class_Osup(_857399) = c_Lattices_Osemilattice__sup__class_Osup(_857397))], (14996 ^ _777959) ^ [_1063133, _1063135] : [14997 ^ _777959 : [(14998 ^ _777959) ^ [_1063197, _1063199] : [_1063135 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1063133, _1063197), 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)), _1063199)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1063133), _1063135)))], (46255 ^ _777959) ^ [_1701353, _1701355, _1701357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1701353, tc_HOL_Obool)), _1701355), _1701357)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1701353), tc_HOL_Obool)), c_List_Olistsp(_1701353, _1701355)), c_List_Olistsp(_1701353, _1701357))))], (33035 ^ _777959) ^ [_1401860, _1401862] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401860)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401862)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1401860), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1401862))))], (25116 ^ _777959) ^ [_1253765, _1253767, _1253769] : [class_Divides_Osemiring__div(_1253765), -(_1253767 = c_Groups_Ozero__class_Ozero(_1253765)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1253765), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253765), _1253769), _1253767)), _1253767) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253765), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1253765), _1253769), _1253767)), c_Groups_Oone__class_Oone(_1253765)))], (27702 ^ _777959) ^ [_1301266, _1301268] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301266)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1301266), _1301268)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1301266)), hAPP(c_Int_Onat, _1301268)))], (47295 ^ _777959) ^ [_1727452, _1727454, _1727456, _1727458] : [47296 ^ _777959 : [(47297 ^ _777959) ^ [_1727506] : [hBOOL(hAPP(hAPP(_1727456, _1727506), _1727458))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1727452, _1727454, _1727456), _1727458)))], (23297 ^ _777959) ^ [_1221936, _1221938] : [_1221936 = _1221938, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221936) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221938))], (8418 ^ _777959) ^ [_924038, _924040, _924042, _924044] : [-(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_924038, _924040), _924042), _924044), hAPP(_924042, _924044)) = _924042)], (13367 ^ _777959) ^ [_1022542, _1022544, _1022546] : [13368 ^ _777959 : [(13371 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1022542), hAPP(c_Set_OCollect(_1022542), _1022546)))], (13369 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1022542), hAPP(c_Set_OCollect(_1022542), _1022544)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1022542), hAPP(c_Set_OCollect(_1022542), hAPP(hAPP(c_COMBS(_1022542, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1022542), c_fconj), _1022544)), _1022546)))))], (41465 ^ _777959) ^ [_1590836, _1590838, _1590840] : [-(hAPP(hAPP(c_List_Onth(_1590836), hAPP(hAPP(c_List_Olist_OCons(_1590836), _1590838), _1590840)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1590838)], (2458 ^ _777959) ^ [_814381, _814383, _814385, _814387, _814389, _814391] : [-(c_Smallcheck_Ofull__small_H(_814391, _814387, _814383) = c_Smallcheck_Ofull__small_H(_814389, _814385, _814381)), _814391 = _814389, _814387 = _814385, _814383 = _814381], (13401 ^ _777959) ^ [_1023648, _1023650, _1023652] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023648, tc_fun(_1023650, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1023648, tc_HOL_Obool))), _1023652) = c_Orderings_Otop__class_Otop(tc_fun(_1023650, tc_HOL_Obool)))], (8360 ^ _777959) ^ [_922761, _922763, _922765, _922767, _922769] : [-(c_Option_Ooption_Ooption__rec(_922761, _922763, _922765, _922767, hAPP(c_Option_Ooption_OSome(_922763), _922769)) = hAPP(_922767, _922769))], (34459 ^ _777959) ^ [] : [-(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))))], (29040 ^ _777959) ^ [_1325214, _1325216] : [class_Orderings_Olinorder(_1325214), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1325214, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1325214), _1325216)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1325214), _1325216))], (16257 ^ _777959) ^ [_1088615, _1088617, _1088619, _1088621, _1088623, _1088625] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1088615), _1088617)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088619), _1088621)), 16267 ^ _777959 : [(16270 ^ _777959) ^ [] : [hAPP(c_Finite__Set_Ocard(_1088615), hAPP(c_Set_OCollect(_1088615), hAPP(hAPP(c_COMBS(_1088615, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1088615), c_fconj), hAPP(hAPP(c_COMBC(_1088615, tc_fun(_1088615, tc_HOL_Obool), tc_HOL_Obool), c_member(_1088615)), _1088617))), hAPP(hAPP(c_COMBC(_1088615, _1088619, tc_HOL_Obool), _1088623), 16266 ^ [_1088615, _1088617, _1088619, _1088621, _1088623, _1088625])))) = _1088625], (16268 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1088619), 16266 ^ [_1088615, _1088617, _1088619, _1088621, _1088623, _1088625]), _1088621)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088615, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1088619, tc_HOL_Obool), tc_Nat_Onat, _1088615), c_Finite__Set_Ocard(_1088619)), hAPP(hAPP(c_COMBB(tc_fun(_1088619, tc_HOL_Obool), tc_fun(_1088619, tc_HOL_Obool), _1088615), c_Set_OCollect(_1088619)), hAPP(hAPP(c_COMBB(tc_fun(_1088619, tc_HOL_Obool), tc_fun(_1088619, tc_HOL_Obool), _1088615), hAPP(c_COMBS(_1088619, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1088619), c_fconj), hAPP(hAPP(c_COMBC(_1088619, tc_fun(_1088619, tc_HOL_Obool), tc_HOL_Obool), c_member(_1088619)), _1088621)))), _1088623)))), _1088617) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1088625), hAPP(c_Finite__Set_Ocard(_1088619), _1088621)))], (10122 ^ _777959) ^ [_954623, _954625, _954627, _954629] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954623, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954623, tc_HOL_Obool)), _954625), _954627)), _954629) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954623, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954623, tc_HOL_Obool)), _954625), _954629)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954623, tc_HOL_Obool)), _954627), _954629)))], (18558 ^ _777959) ^ [_1134738, _1134740, _1134742, _1134744] : [c_Finite__Set_Ofolding__one(_1134738, _1134740, _1134742), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134738), _1134744)), -(hAPP(_1134742, _1134744) = hAPP(c_Finite__Set_Ofold1(_1134738, _1134740), _1134744))], (44392 ^ _777959) ^ [_1660384, _1660386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1660384), _1660386)), -(c_List_Oupt(_1660386, _1660384) = c_List_Olist_ONil(tc_Nat_Onat))], (33217 ^ _777959) ^ [_1404990] : [c_Int_OBit1(_1404990) = c_Int_OPls], (39031 ^ _777959) ^ [_1529571, _1529573, _1529575, _1529577, _1529579, _1529581] : [-(hAPP(c_Set_Oimage(_1529571, _1529573, hAPP(c_Fun_Ocomp(_1529575, _1529573, _1529571, _1529577), _1529579)), _1529581) = hAPP(c_Set_Oimage(_1529575, _1529573, _1529577), hAPP(c_Set_Oimage(_1529571, _1529575, _1529579), _1529581)))], (43264 ^ _777959) ^ [_1637110, _1637112, _1637114] : [hBOOL(hAPP(c_List_Odistinct(_1637110), _1637112)), -(hBOOL(hAPP(c_List_Odistinct(_1637110), hAPP(hAPP(c_List_Odrop(_1637110), _1637114), _1637112))))], (35379 ^ _777959) ^ [_1446805, _1446807, _1446809, _1446811] : [_1446809 = _1446811, -(hAPP(hAPP(c_COMBC(_1446805, tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_fun(_1446807, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446807, tc_fun(tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_fun(_1446807, tc_HOL_Obool)), _1446805), c_COMBC(_1446807, tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446807, tc_prod(_1446805, _1446807)), tc_fun(_1446807, tc_fun(tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_HOL_Obool)), _1446805), hAPP(c_COMBB(tc_prod(_1446805, _1446807), tc_fun(tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_HOL_Obool), _1446807), c_member(tc_prod(_1446805, _1446807)))), c_Product__Type_OPair(_1446805, _1446807)))), _1446809) = hAPP(hAPP(c_COMBC(_1446805, tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_fun(_1446807, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446807, tc_fun(tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_fun(_1446807, tc_HOL_Obool)), _1446805), c_COMBC(_1446807, tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446807, tc_prod(_1446805, _1446807)), tc_fun(_1446807, tc_fun(tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_HOL_Obool)), _1446805), hAPP(c_COMBB(tc_prod(_1446805, _1446807), tc_fun(tc_fun(tc_prod(_1446805, _1446807), tc_HOL_Obool), tc_HOL_Obool), _1446807), c_member(tc_prod(_1446805, _1446807)))), c_Product__Type_OPair(_1446805, _1446807)))), _1446811))], (11016 ^ _777959) ^ [_973822, _973824, _973826, _973828, _973830] : [class_Groups_Oordered__cancel__ab__semigroup__add(_973822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_973822), _973824), _973826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973822), _973828), _973830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_973822), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973822), _973824), _973828)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_973822), _973826), _973830))))], (2514 ^ _777959) ^ [_815219, _815221, _815223, _815225] : [-(c_Divides_Opdivmod(_815225, _815221) = c_Divides_Opdivmod(_815223, _815219)), _815225 = _815223, _815221 = _815219], (41821 ^ _777959) ^ [_1600833, _1600835, _1600837] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1600833)), _1600835), c_List_Olists(_1600833, _1600837))), 41824 ^ _777959 : [(41825 ^ _777959) ^ [_1600941] : [hBOOL(hAPP(hAPP(c_member(_1600833), _1600941), hAPP(c_List_Oset(_1600833), _1600835))), -(hBOOL(hAPP(hAPP(c_member(_1600833), _1600941), _1600837)))]]], (17199 ^ _777959) ^ [_1106768, _1106770, _1106772, _1106774, _1106776, _1106778, _1106780] : [-(hBOOL(hAPP(hAPP(c_member(_1106768), _1106770), _1106772))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1106768, _1106774, _1106776, _1106778, _1106772), _1106780)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1106768, _1106774, _1106776, _1106778, hAPP(hAPP(c_Set_Oinsert(_1106768), _1106770), _1106772)), hAPP(hAPP(_1106776, _1106770), _1106780))))], (35361 ^ _777959) ^ [_1445027, _1445029, _1445031, _1445033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1445027, tc_fun(_1445029, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1445027, tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_fun(_1445029, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445029, tc_fun(tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_fun(_1445029, tc_HOL_Obool)), _1445027), c_COMBC(_1445029, tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445029, tc_prod(_1445027, _1445029)), tc_fun(_1445029, tc_fun(tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_HOL_Obool)), _1445027), hAPP(c_COMBB(tc_prod(_1445027, _1445029), tc_fun(tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_HOL_Obool), _1445029), c_member(tc_prod(_1445027, _1445029)))), c_Product__Type_OPair(_1445027, _1445029)))), _1445031)), hAPP(hAPP(c_COMBC(_1445027, tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_fun(_1445029, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445029, tc_fun(tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_fun(_1445029, tc_HOL_Obool)), _1445027), c_COMBC(_1445029, tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1445029, tc_prod(_1445027, _1445029)), tc_fun(_1445029, tc_fun(tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_HOL_Obool)), _1445027), hAPP(c_COMBB(tc_prod(_1445027, _1445029), tc_fun(tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool), tc_HOL_Obool), _1445029), c_member(tc_prod(_1445027, _1445029)))), c_Product__Type_OPair(_1445027, _1445029)))), _1445033))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1445027, _1445029), tc_HOL_Obool)), _1445031), _1445033)))], (6683 ^ _777959) ^ [_886492, _886494, _886496, _886498, _886500] : [-(hAPP(c_Set_Oimage(_886492, _886494, _886496), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886492, tc_HOL_Obool)), _886498), _886500)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886494, tc_HOL_Obool)), hAPP(c_Set_Oimage(_886492, _886494, _886496), _886498)), hAPP(c_Set_Oimage(_886492, _886494, _886496), _886500)))], (22798 ^ _777959) ^ [_1212765, _1212767, _1212769] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1212765, tc_Nat_Onat), _1212767), _1212769)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1212765, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1212765), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1212767)), _1212769))], (22016 ^ _777959) ^ [_1196670, _1196672, _1196674, _1196676, _1196678, _1196680] : [class_Rings_Olinordered__semiring__1(_1196670), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196670), _1196672), _1196674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196670), _1196676), _1196674)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196670), c_Groups_Ozero__class_Ozero(_1196670)), _1196678)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196670), c_Groups_Ozero__class_Ozero(_1196670)), _1196680)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1196670), _1196678), _1196680) = c_Groups_Oone__class_Oone(_1196670), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196670), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1196670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196670), _1196678), _1196672)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1196670), _1196680), _1196676))), _1196674)))], (45340 ^ _777959) ^ [_1681564, _1681566, _1681568] : [-(c_List_Oremdups(_1681564, hAPP(c_List_Ofilter(_1681564, _1681566), _1681568)) = hAPP(c_List_Ofilter(_1681564, _1681566), c_List_Oremdups(_1681564, _1681568)))], (51154 ^ _777959) ^ [] : [-(class_HOL_Oequal(tc_Com_Ovname))], (38512 ^ _777959) ^ [] : [-(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))))], (47510 ^ _777959) ^ [_1732933, _1732935] : [c_Wellfounded_Owf(_1732933, _1732935), -(c_Wellfounded_Oacyclic(_1732933, _1732935))], (34743 ^ _777959) ^ [_1431553, _1431555, _1431557] : [class_Rings_Olinordered__idom(_1431553), 34746 ^ _777959 : [(34747 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1431553), c_Groups_Ozero__class_Ozero(_1431553)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1431553), hAPP(hAPP(c_Power_Opower__class_Opower(_1431553), _1431555), 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(_1431553), _1431557), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1431555 = c_Groups_Ozero__class_Ozero(_1431553), _1431557 = c_Groups_Ozero__class_Ozero(_1431553)], (34757 ^ _777959) ^ [] : [34758 ^ _777959 : [(34761 ^ _777959) ^ [] : [-(_1431557 = c_Groups_Ozero__class_Ozero(_1431553))], (34759 ^ _777959) ^ [] : [-(_1431555 = c_Groups_Ozero__class_Ozero(_1431553))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1431553), c_Groups_Ozero__class_Ozero(_1431553)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1431553), hAPP(hAPP(c_Power_Opower__class_Opower(_1431553), _1431555), 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(_1431553), _1431557), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))]]], (11050 ^ _777959) ^ [_974493, _974495, _974497, _974499] : [-(hAPP(_974499, _974495) = c_Option_Ooption_ONone(_974497)), -(hBOOL(hAPP(hAPP(c_member(_974493), _974495), c_Map_Odom(_974493, _974497, _974499))))], (8908 ^ _777959) ^ [_931415, _931417, _931419] : [class_Orderings_Oorder(_931415), 8911 ^ _777959 : [(8912 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931415), _931417), _931419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931415), _931417), _931419))), -(_931417 = _931419)], (8922 ^ _777959) ^ [] : [8923 ^ _777959 : [(8926 ^ _777959) ^ [] : [_931417 = _931419], (8924 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_931415), _931417), _931419))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_931415), _931417), _931419)))]]], (26186 ^ _777959) ^ [_1274451, _1274453, _1274455] : [class_Fields_Olinordered__field__inverse__zero(_1274451), 26189 ^ _777959 : [(26204 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274451), c_Groups_Ozero__class_Ozero(_1274451)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274451), _1274453), _1274455)))), 26205 ^ _777959 : [(26212 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274451), _1274453), c_Groups_Ozero__class_Ozero(_1274451))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274451), _1274455), c_Groups_Ozero__class_Ozero(_1274451)))], (26206 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274451), c_Groups_Ozero__class_Ozero(_1274451)), _1274453)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274451), c_Groups_Ozero__class_Ozero(_1274451)), _1274455))]]], (26190 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274451), c_Groups_Ozero__class_Ozero(_1274451)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274451), _1274453), _1274455))), 26195 ^ _777959 : [(26198 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274451), c_Groups_Ozero__class_Ozero(_1274451)), _1274455)))], (26196 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274451), c_Groups_Ozero__class_Ozero(_1274451)), _1274453)))]], 26199 ^ _777959 : [(26202 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274451), _1274455), c_Groups_Ozero__class_Ozero(_1274451))))], (26200 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1274451), _1274453), c_Groups_Ozero__class_Ozero(_1274451))))]]]]], (41850 ^ _777959) ^ [_1601693, _1601695, _1601697, _1601699] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1601693) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1601695), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1601693)), hAPP(hAPP(c_List_Olist_OCons(_1601695), _1601697), _1601699)) = hAPP(hAPP(c_List_Olist_OCons(_1601695), _1601697), hAPP(hAPP(c_List_Otake(_1601695), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1601693)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1601699)))], (47969 ^ _777959) ^ [_1743805, _1743807, _1743809, _1743811] : [47970 ^ _777959 : [(47973 ^ _777959) ^ [] : [c_List_Olist__ex(_1743805, _1743807, _1743811)], (47971 ^ _777959) ^ [] : [hBOOL(hAPP(_1743807, _1743809))]], -(c_List_Olist__ex(_1743805, _1743807, hAPP(hAPP(c_List_Olist_OCons(_1743805), _1743809), _1743811)))], (14861 ^ _777959) ^ [_1058557, _1058559, _1058561] : [class_Lattices_Odistrib__lattice(_1058557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058557), _1058559)), -(_1058559 = c_Orderings_Obot__class_Obot(tc_fun(_1058557, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1058557), _1058561), c_Big__Operators_Olattice__class_OInf__fin(_1058557, _1058559)) = c_Big__Operators_Olattice__class_OInf__fin(_1058557, hAPP(c_Set_OCollect(_1058557), hAPP(hAPP(c_COMBB(tc_fun(_1058557, tc_HOL_Obool), tc_HOL_Obool, _1058557), c_HOL_OEx(_1058557)), hAPP(hAPP(c_COMBC(_1058557, tc_fun(_1058557, tc_HOL_Obool), tc_fun(_1058557, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1058557, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1058557, tc_HOL_Obool), tc_fun(_1058557, tc_HOL_Obool)), _1058557), c_COMBS(_1058557, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1058557, tc_HOL_Obool), tc_fun(_1058557, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1058557), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1058557), c_fconj)), hAPP(hAPP(c_COMBC(_1058557, tc_fun(_1058557, _1058557), tc_fun(_1058557, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1058557, tc_HOL_Obool), tc_fun(tc_fun(_1058557, _1058557), tc_fun(_1058557, tc_HOL_Obool)), _1058557), c_COMBB(_1058557, tc_HOL_Obool, _1058557)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1058557), _1058561))))), hAPP(hAPP(c_COMBC(_1058557, tc_fun(_1058557, tc_HOL_Obool), tc_HOL_Obool), c_member(_1058557)), _1058559))))))], (7634 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSKIP)))], (44897 ^ _777959) ^ [_1671012, _1671014, _1671016] : [-(hAPP(c_List_Orev(_1671012), hAPP(c_List_Ofilter(_1671012, _1671014), _1671016)) = hAPP(c_List_Ofilter(_1671012, _1671014), hAPP(c_List_Orev(_1671012), _1671016)))], (44531 ^ _777959) ^ [_1663016, _1663018, _1663020, _1663022] : [-(c_List_Oupt(_1663016, _1663018) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1663020), _1663022)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1663016), _1663018)), _1663016 = _1663020, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1663016), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1663018) = _1663022], (11094 ^ _777959) ^ [_975329, _975331, _975333, _975335, _975337] : [hBOOL(hAPP(hAPP(c_member(_975329), _975331), _975333)), -(hAPP(c_Map_Orestrict__map(_975329, _975335, _975337, _975333), _975331) = hAPP(_975337, _975331))], (5024 ^ _777959) ^ [_854654, _854656, _854658, _854660, _854662, _854664] : [-(c_Lazy__Sequence_Oappend(_854664, _854660, _854656) = c_Lazy__Sequence_Oappend(_854662, _854658, _854654)), _854664 = _854662, _854660 = _854658, _854656 = _854654], (22256 ^ _777959) ^ [_1201567, _1201569, _1201571, _1201573] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(_1201567)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1201567), _1201569), _1201571), _1201573)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29008 ^ _777959) ^ [_1324665, _1324667, _1324669] : [class_Orderings_Oorder(_1324665), 29011 ^ _777959 : [(29018 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324665), _1324667), _1324669)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1324665, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1324665), _1324667)), hAPP(c_SetInterval_Oord__class_OatMost(_1324665), _1324669))))], (29012 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1324665, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1324665), _1324667)), hAPP(c_SetInterval_Oord__class_OatMost(_1324665), _1324669))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324665), _1324667), _1324669)))]]], (11140 ^ _777959) ^ [_976330, _976332, _976334, _976336, _976338, _976340] : [c_Finite__Set_Ofun__left__comm(_976330, _976332, _976334), hBOOL(hAPP(c_Finite__Set_Ofinite(_976330), _976336)), -(hAPP(hAPP(_976334, _976338), hAPP(hAPP(c_Finite__Set_Ofold(_976330, _976332, _976334), _976340), _976336)) = hAPP(hAPP(c_Finite__Set_Ofold(_976330, _976332, _976334), hAPP(hAPP(_976334, _976338), _976340)), _976336))], (11954 ^ _777959) ^ [_995103, _995105, _995107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995103), _995105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995107), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _995105), _995107)), _995103))))], (17317 ^ _777959) ^ [_1109081, _1109083, _1109085, _1109087] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1109081, tc_HOL_Obool), hAPP(c_Set_Oimage(_1109083, tc_fun(_1109081, tc_HOL_Obool), _1109085), _1109087)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1109083, tc_fun(_1109081, tc_HOL_Obool)), _1109087), _1109085))], (11994 ^ _777959) ^ [_995691, _995693] : [11995 ^ _777959 : [(11998 ^ _777959) ^ [] : [_995691 = _995693], (11996 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995691), _995693))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995691), _995693)))], (29318 ^ _777959) ^ [_1330734, _1330736, _1330738] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1330734)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1330736), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1330738)), 29328 ^ _777959 : [(29334 ^ _777959) ^ [] : [-(_1330736 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 29330 ^ [_1330734, _1330736, _1330738]), 29327 ^ [_1330734, _1330736, _1330738]))], (29332 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29330 ^ [_1330734, _1330736, _1330738]), _1330738)))], (29329 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29327 ^ [_1330734, _1330736, _1330738]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1330734))))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1330736), _1330734) = _1330736)], (43955 ^ _777959) ^ [_1651966, _1651968, _1651970] : [43957 ^ _777959 : [(43960 ^ _777959) ^ [] : [hBOOL(hAPP(_1651968, 43956 ^ [_1651966, _1651968, _1651970]))], (43958 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1651966), 43956 ^ [_1651966, _1651968, _1651970]), hAPP(c_List_Oset(_1651966), _1651970))))]], -(hAPP(c_List_Ofilter(_1651966, _1651968), _1651970) = _1651970)], (42563 ^ _777959) ^ [_1620117, _1620119, _1620121, _1620123] : [-(c_Product__Type_Oapfst(_1620117, _1620119, _1620121, _1620123) = c_Product__Type_Omap__pair(_1620117, _1620119, _1620121, _1620121, _1620123, c_Fun_Oid(_1620121)))], (31376 ^ _777959) ^ [_1370726, _1370728] : [class_Groups_Oordered__ab__group__add__abs(_1370726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1370726), _1370728), c_Groups_Ozero__class_Ozero(_1370726))), -(hAPP(c_Groups_Oabs__class_Oabs(_1370726), _1370728) = hAPP(c_Groups_Ouminus__class_Ouminus(_1370726), _1370728))], (3664 ^ _777959) ^ [_833266, _833268, _833270, _833272] : [-(c_List_Omeasures(_833272, _833268) = c_List_Omeasures(_833270, _833266)), _833272 = _833270, _833268 = _833266], (19727 ^ _777959) ^ [_1154753, _1154755, _1154757, _1154759, _1154761] : [class_Groups_Ocomm__monoid__mult(_1154753), hBOOL(hAPP(c_Finite__Set_Ofinite(_1154755), _1154757)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1154755, _1154753), hAPP(hAPP(c_COMBS(_1154755, _1154753, _1154753), hAPP(hAPP(c_COMBB(_1154753, tc_fun(_1154753, _1154753), _1154755), c_Groups_Otimes__class_Otimes(_1154753)), _1154759)), _1154761)), _1154757) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1154753), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1154755, _1154753), _1154759), _1154757)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1154755, _1154753), _1154761), _1154757)))], (25126 ^ _777959) ^ [_1253929, _1253931, _1253933] : [class_Divides_Osemiring__div(_1253929), -(_1253931 = c_Groups_Ozero__class_Ozero(_1253929)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1253929), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253929), _1253931), _1253933)), _1253931) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253929), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1253929), _1253933), _1253931)), c_Groups_Oone__class_Oone(_1253929)))], (4052 ^ _777959) ^ [_839332, _839334, _839336, _839338] : [-(c_List_Olistrel(_839338, _839334) = c_List_Olistrel(_839336, _839332)), _839338 = _839336, _839334 = _839332], (50730 ^ _777959) ^ [_1807026, _1807028, _1807030] : [hBOOL(hAPP(hAPP(c_List_Omember(_1807026), _1807030), _1807028)), -(hBOOL(hAPP(hAPP(c_member(_1807026), _1807028), hAPP(c_List_Oset(_1807026), _1807030))))], (23409 ^ _777959) ^ [_1223847, _1223849] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1223847)), _1223849) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1223847), _1223849)))], (7930 ^ _777959) ^ [_913049, _913051] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_913049, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_913049, tc_HOL_Obool))), _913051) = c_Orderings_Obot__class_Obot(tc_fun(_913049, tc_HOL_Obool)))], (33991 ^ _777959) ^ [_1418238] : [class_Int_Onumber__ring(_1418238), c_Int_Oiszero(_1418238, hAPP(c_Int_Onumber__class_Onumber__of(_1418238), c_Int_OBit1(c_Int_OPls)))], (2400 ^ _777959) ^ [_813468, _813470, _813472, _813474, _813476, _813478] : [-(c_Nat_Onat_Onat__rec(_813478, _813474, _813470) = c_Nat_Onat_Onat__rec(_813476, _813472, _813468)), _813478 = _813476, _813474 = _813472, _813470 = _813468], (20321 ^ _777959) ^ [_1165612, _1165614, _1165616] : [class_Rings_Olinordered__semiring__strict(_1165612), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165612), c_Groups_Ozero__class_Ozero(_1165612)), _1165614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165612), c_Groups_Ozero__class_Ozero(_1165612)), _1165616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165612), c_Groups_Ozero__class_Ozero(_1165612)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165612), _1165614), _1165616))))], (39362 ^ _777959) ^ [_1537046, _1537048, _1537050, _1537052, _1537054, _1537056] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537046, tc_fun(_1537048, tc_HOL_Obool)), _1537050), hAPP(c_Fun_Ocomp(_1537052, tc_fun(_1537048, tc_HOL_Obool), _1537046, _1537054), _1537056)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1537052, tc_fun(_1537048, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1537046, _1537052, _1537056), _1537050)), _1537054))], (39904 ^ _777959) ^ [_1550432, _1550434, _1550436, _1550438, _1550440] : [c_Fun_Oinj__on(_1550432, _1550434, _1550436, hAPP(hAPP(c_Set_Oinsert(_1550432), _1550438), hAPP(c_List_Oset(_1550432), _1550440))), -(hAPP(hAPP(c_List_Omap(_1550432, _1550434), _1550436), hAPP(c_List_OremoveAll(_1550432, _1550438), _1550440)) = hAPP(c_List_OremoveAll(_1550434, hAPP(_1550436, _1550438)), hAPP(hAPP(c_List_Omap(_1550432, _1550434), _1550436), _1550440)))], (13555 ^ _777959) ^ [_1026701, _1026703, _1026705, _1026707, _1026709] : [_1026701 = c_Orderings_Obot__class_Obot(tc_fun(_1026703, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026703, tc_fun(_1026705, tc_HOL_Obool)), _1026701), hAPP(hAPP(c_COMBC(_1026703, tc_fun(_1026705, tc_HOL_Obool), tc_fun(_1026705, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1026705, tc_HOL_Obool), tc_fun(tc_fun(_1026705, tc_HOL_Obool), tc_fun(_1026705, tc_HOL_Obool)), _1026703), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026705, tc_HOL_Obool))), _1026707)), _1026709)) = c_Orderings_Otop__class_Otop(tc_fun(_1026705, tc_HOL_Obool)))], (11064 ^ _777959) ^ [_974643, _974645] : [class_Lattices_Olattice(_974643), -(c_Big__Operators_Olattice__class_OInf__fin(_974643, hAPP(hAPP(c_Set_Oinsert(_974643), _974645), c_Orderings_Obot__class_Obot(tc_fun(_974643, tc_HOL_Obool)))) = _974645)], (17875 ^ _777959) ^ [_1119631, _1119633, _1119635, _1119637] : [_1119635 = _1119637, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1119631, _1119633, hAPP(hAPP(c_Set_Oinsert(_1119631), _1119635), c_Orderings_Obot__class_Obot(tc_fun(_1119631, tc_HOL_Obool)))), _1119637)))], (45644 ^ _777959) ^ [_1688931] : [class_Enum_Oenum(_1688931), -(hBOOL(hAPP(c_List_Odistinct(_1688931), c_Enum_Oenum__class_Oenum(_1688931))))], (34995 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (6661 ^ _777959) ^ [_886018, _886020, _886022] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886018, tc_HOL_Obool)), _886020), _886022) = c_Orderings_Obot__class_Obot(tc_fun(_886018, tc_HOL_Obool)), 6664 ^ _777959 : [(6667 ^ _777959) ^ [] : [-(_886022 = c_Orderings_Obot__class_Obot(tc_fun(_886018, tc_HOL_Obool)))], (6665 ^ _777959) ^ [] : [-(_886020 = c_Orderings_Obot__class_Obot(tc_fun(_886018, tc_HOL_Obool)))]]], (29212 ^ _777959) ^ [_1328671, _1328673, _1328675] : [class_Orderings_Olinorder(_1328671), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1328671), _1328673), _1328675)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328671, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1328671, _1328673, _1328675)), hAPP(c_SetInterval_Oord__class_OatLeast(_1328671), _1328675)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1328671), _1328673))], (25582 ^ _777959) ^ [_1262923, _1262925, _1262927] : [hBOOL(hAPP(_1262923, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1262925), _1262927))), 25587 ^ _777959 : [(25590 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1262923, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (25588 ^ _777959) ^ [] : [-(_1262927 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25592 ^ _777959 : [(25597 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1262923, 25591 ^ [_1262923, _1262925, _1262927])))], (25595 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1262925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1262927), hAPP(c_Nat_OSuc, 25591 ^ [_1262923, _1262925, _1262927])))))], (25593 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1262927), 25591 ^ [_1262923, _1262925, _1262927])), _1262925)))]]], (22585 ^ _777959) ^ [_1208888, _1208890, _1208892] : [-(c_Option_Ooption_Ooption__size(_1208888, _1208890, hAPP(c_Option_Ooption_OSome(_1208888), _1208892)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1208890, _1208892)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9664 ^ _777959) ^ [_945254, _945256, _945258] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945254, tc_HOL_Obool)), _945256), _945258) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945254, tc_HOL_Obool)), _945258), _945256))], (17093 ^ _777959) ^ [_1104898, _1104900, _1104902, _1104904] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1104898, _1104900, _1104902, _1104904, c_Orderings_Obot__class_Obot(tc_fun(_1104898, tc_HOL_Obool))), _1104904)))], (35651 ^ _777959) ^ [_1453695, _1453697, _1453699, _1453701, _1453703, _1453705] : [35652 ^ _777959 : [(35655 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1453701, _1453697), _1453699))], (35653 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1453695, _1453697), _1453699))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1453703, tc_fun(_1453705, tc_HOL_Obool))), _1453701), _1453695), _1453697), _1453699)))], (6951 ^ _777959) ^ [_892128, _892130, _892132] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _892130))), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCall(_892128, _892130, _892132))))], (48881 ^ _777959) ^ [_1764509, _1764511] : [-(c_Relation_Orefl__on(_1764509, c_Orderings_Otop__class_Otop(tc_fun(_1764509, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1764509, _1764509), tc_HOL_Obool)), _1764511), c_Relation_OId(_1764509))))], (41010 ^ _777959) ^ [_1578796, _1578798, _1578800, _1578802] : [-(hAPP(c_Set_OCollect(_1578796), hAPP(hAPP(c_COMBB(tc_fun(_1578798, tc_HOL_Obool), tc_HOL_Obool, _1578796), c_HOL_OAll(_1578798)), hAPP(hAPP(c_COMBB(tc_fun(_1578798, tc_HOL_Obool), tc_fun(_1578798, tc_HOL_Obool), _1578796), hAPP(c_COMBS(_1578798, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1578798), c_fimplies), hAPP(hAPP(c_COMBC(_1578798, tc_fun(_1578798, tc_HOL_Obool), tc_HOL_Obool), c_member(_1578798)), _1578800)))), _1578802))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1578798, tc_fun(_1578796, tc_HOL_Obool)), _1578800), hAPP(hAPP(c_COMBB(tc_fun(_1578796, tc_HOL_Obool), tc_fun(_1578796, tc_HOL_Obool), _1578798), c_Set_OCollect(_1578796)), hAPP(c_COMBC(_1578796, _1578798, tc_HOL_Obool), _1578802))))], (7234 ^ _777959) ^ [_899215, _899217, _899219] : [class_Lattices_Olattice(_899215), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899215), _899217), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_899215), _899217), _899219))))], (12101 ^ _777959) ^ [_997502, _997504, _997506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997502), _997504)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997502), _997506))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997504), _997506)))], (35573 ^ _777959) ^ [_1452125, _1452127, _1452129, _1452131] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1452125, _1452127), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1452129), _1452131))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1452125), _1452127), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1452131), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1452129)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1452129)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1452131), 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), _1452127), _1452131))))))], (10116 ^ _777959) ^ [_954388, _954390, _954392] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_954388, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954388, tc_HOL_Obool)), _954390), _954392)), _954392)))], (33221 ^ _777959) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (33793 ^ _777959) ^ [_1414052, _1414054] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1414052))), _1414054) = 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)))), _1414052), _1414054))], (51310 ^ _777959) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (44160 ^ _777959) ^ [_1656620, _1656622] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656620), _1656622)), -(c_List_Oupt(_1656620, hAPP(c_Nat_OSuc, _1656622)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1656620, _1656622)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1656622), c_List_Olist_ONil(tc_Nat_Onat))))], (27148 ^ _777959) ^ [_1292182, _1292184, _1292186, _1292188, _1292190] : [class_Groups_Oordered__ab__group__add(_1292182), hBOOL(hAPP(c_Finite__Set_Ofinite(_1292184), _1292186)), 27158 ^ _777959 : [(27161 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1292182), c_Groups_Ozero__class_Ozero(_1292182)), hAPP(_1292188, 27157 ^ [_1292182, _1292184, _1292186, _1292188, _1292190])))], (27159 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1292184), 27157 ^ [_1292182, _1292184, _1292186, _1292188, _1292190]), _1292186)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1292184, _1292182), _1292188), _1292186) = c_Groups_Ozero__class_Ozero(_1292182), hBOOL(hAPP(hAPP(c_member(_1292184), _1292190), _1292186)), -(hAPP(_1292188, _1292190) = c_Groups_Ozero__class_Ozero(_1292182))], (13151 ^ _777959) ^ [_1017941, _1017943, _1017945] : [class_Complete__Lattice_Ocomplete__lattice(_1017941), -(c_Complete__Lattice_OSup__class_OSup(_1017941, hAPP(hAPP(c_Set_Oinsert(_1017941), _1017943), hAPP(hAPP(c_Set_Oinsert(_1017941), _1017945), c_Orderings_Obot__class_Obot(tc_fun(_1017941, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1017941), _1017943), _1017945))], (6042 ^ _777959) ^ [_874551, _874553] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874551, tc_HOL_Obool)), _874553), _874553)))], (50970 ^ _777959) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (12177 ^ _777959) ^ [_999013, _999015, _999017] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999013), _999015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999013), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999015), _999017))))], (33165 ^ _777959) ^ [_1404129, _1404131] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404129))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404129)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404131)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26324 ^ _777959) ^ [_1276920, _1276922, _1276924, _1276926] : [class_Fields_Olinordered__field(_1276920), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276920), _1276922), _1276924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276920), _1276926), c_Groups_Ozero__class_Ozero(_1276920))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276920), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276920), _1276924), _1276926)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276920), _1276922), _1276926))))], (25918 ^ _777959) ^ [_1269251, _1269253, _1269255] : [class_Groups_Oordered__ab__group__add(_1269251), -(hAPP(c_Set_Oimage(_1269251, _1269251, c_Groups_Ouminus__class_Ouminus(_1269251)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1269251, _1269253, _1269255)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1269251, hAPP(c_Groups_Ouminus__class_Ouminus(_1269251), _1269255), hAPP(c_Groups_Ouminus__class_Ouminus(_1269251), _1269253)))], (50974 ^ _777959) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (34013 ^ _777959) ^ [_1418605, _1418607] : [class_Int_Onumber__ring(_1418605), 34016 ^ _777959 : [(34023 ^ _777959) ^ [] : [c_Int_Oiszero(_1418605, hAPP(c_Int_Onumber__class_Onumber__of(_1418605), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1418607), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1418605), _1418607) = c_Groups_Ozero__class_Ozero(_1418605))], (34017 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1418605), _1418607) = c_Groups_Ozero__class_Ozero(_1418605), -(c_Int_Oiszero(_1418605, hAPP(c_Int_Onumber__class_Onumber__of(_1418605), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1418607), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))]]], (48308 ^ _777959) ^ [_1750219, _1750221] : [hAPP(c_Code__Numeral_Onat__of, _1750219) = hAPP(c_Code__Numeral_Onat__of, _1750221), -(_1750219 = _1750221)], (46848 ^ _777959) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (45453 ^ _777959) ^ [_1683928, _1683930, _1683932, _1683934, _1683936] : [hBOOL(hAPP(hAPP(c_member(_1683928), _1683930), hAPP(c_List_Oset(_1683928), _1683932))), -(hBOOL(hAPP(_1683934, _1683930))), -(c_List_OdropWhile(_1683928, _1683934, hAPP(hAPP(c_List_Oappend(_1683928), _1683932), _1683936)) = hAPP(hAPP(c_List_Oappend(_1683928), c_List_OdropWhile(_1683928, _1683934, _1683932)), _1683936))], (12119 ^ _777959) ^ [_997857, _997859, _997861] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997857), _997859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997861), _997859))))], (6587 ^ _777959) ^ [_884540, _884542, _884544, _884546, _884548, _884550, _884552] : [hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_884540), _884542), _884544), _884546) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_884540), _884548), _884550), _884552), 6590 ^ _777959 : [(6595 ^ _777959) ^ [] : [-(_884546 = _884552)], (6593 ^ _777959) ^ [] : [-(_884544 = _884550)], (6591 ^ _777959) ^ [] : [-(_884542 = _884548)]]], (42711 ^ _777959) ^ [_1623940, _1623942, _1623944, _1623946, _1623948] : [hAPP(hAPP(c_List_Oappend(_1623940), _1623942), _1623944) = hAPP(hAPP(c_List_Olist_OCons(_1623940), _1623946), _1623948), 42716 ^ _777959 : [(42719 ^ _777959) ^ [] : [-(_1623944 = hAPP(hAPP(c_List_Olist_OCons(_1623940), _1623946), _1623948))], (42717 ^ _777959) ^ [] : [-(_1623942 = c_List_Olist_ONil(_1623940))]], 42721 ^ _777959 : [(42724 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1623940), 42720 ^ [_1623940, _1623942, _1623944, _1623946, _1623948]), _1623944) = _1623948)], (42722 ^ _777959) ^ [] : [-(_1623942 = hAPP(hAPP(c_List_Olist_OCons(_1623940), _1623946), 42720 ^ [_1623940, _1623942, _1623944, _1623946, _1623948]))]]], (23749 ^ _777959) ^ [_1229572, _1229574, _1229576, _1229578] : [class_Rings_Olinordered__semidom(_1229572), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1229572), c_Groups_Oone__class_Oone(_1229572)), _1229574)), 23756 ^ _777959 : [(23763 ^ _777959) ^ [] : [_1229576 = _1229578, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1229572), _1229574), _1229576) = hAPP(hAPP(c_Power_Opower__class_Opower(_1229572), _1229574), _1229578))], (23757 ^ _777959) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1229572), _1229574), _1229576) = hAPP(hAPP(c_Power_Opower__class_Opower(_1229572), _1229574), _1229578), -(_1229576 = _1229578)]]], (51152 ^ _777959) ^ [] : [-(class_Nat_Osize(tc_Com_Ostate))], (11513 ^ _777959) ^ [_983577, _983579, _983581, _983583, _983585] : [class_Complete__Lattice_Ocomplete__lattice(_983577), hBOOL(hAPP(hAPP(c_member(_983579), _983581), _983583)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983577), hAPP(_983585, _983581)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_983579, _983577), _983583), _983585))))], (16735 ^ _777959) ^ [_1098554, _1098556, _1098558] : [class_Orderings_Olinorder(_1098554), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098554), _1098556), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1098554), _1098558), _1098556))))], (37294 ^ _777959) ^ [_1489375, _1489377, _1489379, _1489381] : [-(hAPP(c_Relation_OField(_1489375), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1489375, _1489375)), hAPP(hAPP(c_Product__Type_OPair(_1489375, _1489375), _1489377), _1489379)), _1489381)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1489375, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1489375), _1489377), hAPP(hAPP(c_Set_Oinsert(_1489375), _1489379), c_Orderings_Obot__class_Obot(tc_fun(_1489375, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1489375), _1489381)))], (48398 ^ _777959) ^ [_1751713, _1751715] : [c_Wellfounded_Oacyclic(_1751713, _1751715), 48401 ^ _777959 : [(48402 ^ _777959) ^ [_1751798] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1751713, _1751713)), hAPP(hAPP(c_Product__Type_OPair(_1751713, _1751713), _1751798), _1751798)), c_Transitive__Closure_Otrancl(_1751713, _1751715)))]]], (40582 ^ _777959) ^ [_1566170, _1566172, _1566174, _1566176] : [class_Groups_Oab__group__add(_1566170), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1566170), hAPP(c_List_Omonoid__add__class_Olistsum(_1566170), hAPP(hAPP(c_List_Omap(_1566172, _1566170), _1566174), _1566176))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1566170), hAPP(hAPP(c_List_Omap(_1566172, _1566170), hAPP(c_Fun_Ocomp(_1566170, _1566170, _1566172, c_Groups_Ouminus__class_Ouminus(_1566170)), _1566174)), _1566176)))], (13701 ^ _777959) ^ [_1031022, _1031024, _1031026] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1031022), hAPP(c_Set_OCollect(_1031022), hAPP(hAPP(c_COMBS(_1031022, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1031022), c_fdisj), _1031024)), _1031026)))), 13704 ^ _777959 : [(13707 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1031022), hAPP(c_Set_OCollect(_1031022), _1031026))))], (13705 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1031022), hAPP(c_Set_OCollect(_1031022), _1031024))))]]], (26874 ^ _777959) ^ [_1286884, _1286886, _1286888, _1286890] : [class_Fields_Ofield(_1286884), -(_1286886 = c_Groups_Ozero__class_Ozero(_1286884)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1286884), _1286888), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286884), _1286890), _1286886)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286884), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1286884), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286884), _1286886), _1286888)), _1286890)), _1286886))], (3060 ^ _777959) ^ [_823804, _823806, _823808, _823810] : [-(c_List_Olexord(_823810, _823806) = c_List_Olexord(_823808, _823804)), _823810 = _823808, _823806 = _823804], (14029 ^ _777959) ^ [_1038445, _1038447, _1038449] : [-(hAPP(hAPP(c_Set_Oinsert(_1038445), _1038447), _1038449) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1038445, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1038445), hAPP(hAPP(c_COMBC(_1038445, _1038445, tc_HOL_Obool), c_fequal), _1038447))), _1038449))], (47088 ^ _777959) ^ [_1721937] : [class_Orderings_Owellorder(_1721937), -(c_Wellfounded_Owf(_1721937, hAPP(c_Set_OCollect(tc_prod(_1721937, _1721937)), hAPP(c_Product__Type_Oprod_Oprod__case(_1721937, _1721937, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1721937)))))], (41247 ^ _777959) ^ [_1585298, _1585300, _1585302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1585298, _1585298), tc_HOL_Obool)), _1585300), _1585302)), c_Relation_Orefl__on(_1585298, c_Orderings_Otop__class_Otop(tc_fun(_1585298, tc_HOL_Obool)), _1585302), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1585298), tc_List_Olist(_1585298)), tc_HOL_Obool)), c_List_Olistrel1(_1585298, _1585300)), c_List_Olistrel(_1585298, _1585302))))], (38602 ^ _777959) ^ [_1518629, _1518631, _1518633, _1518635, _1518637, _1518639, _1518641] : [c_Typedef_Otype__definition(_1518629, _1518631, _1518633, _1518635, _1518637), 38605 ^ _777959 : [(38612 ^ _777959) ^ [] : [_1518639 = _1518641, -(hAPP(_1518633, _1518639) = hAPP(_1518633, _1518641))], (38606 ^ _777959) ^ [] : [hAPP(_1518633, _1518639) = hAPP(_1518633, _1518641), -(_1518639 = _1518641)]]], (42248 ^ _777959) ^ [_1610842, _1610844, _1610846, _1610848] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1610842, _1610844)), hAPP(hAPP(c_Product__Type_OSigma(_1610842, _1610844), _1610846), hAPP(c_COMBK(tc_fun(_1610844, tc_HOL_Obool), _1610842), _1610848)))), -(_1610848 = c_Orderings_Obot__class_Obot(tc_fun(_1610844, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1610842), _1610846)))], (36520 ^ _777959) ^ [_1470524, _1470526, _1470528, _1470530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1470530, _1470526)), hAPP(_1470530, _1470528))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1470524, _1470524)), hAPP(hAPP(c_Product__Type_OPair(_1470524, _1470524), _1470526), _1470528)), hAPP(c_Wellfounded_Omeasure(_1470524), _1470530))))], (47589 ^ _777959) ^ [_1734136, _1734138, _1734140, _1734142, _1734144] : [47590 ^ _777959 : [(47593 ^ _777959) ^ [] : [hBOOL(hAPP(_1734144, hAPP(hAPP(c_List_Ozip(_1734136, _1734140), hAPP(hAPP(c_List_Otake(_1734136), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734136)), _1734138)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734140)), _1734142))), _1734138)), hAPP(hAPP(c_List_Otake(_1734140), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734136)), _1734138)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734140)), _1734142))), _1734142))))], (47591 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734136)), hAPP(hAPP(c_List_Otake(_1734136), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734136)), _1734138)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734140)), _1734142))), _1734138)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734140)), hAPP(hAPP(c_List_Otake(_1734140), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734136)), _1734138)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734140)), _1734142))), _1734142)))]], -(hBOOL(hAPP(_1734144, hAPP(hAPP(c_List_Ozip(_1734136, _1734140), _1734138), _1734142))))], (44889 ^ _777959) ^ [_1670791, _1670793] : [-(hAPP(c_List_Oset(_1670791), hAPP(c_List_Orev(_1670791), _1670793)) = hAPP(c_List_Oset(_1670791), _1670793))], (2626 ^ _777959) ^ [_816957, _816959, _816961, _816963] : [-(c_Divides_Odivmod__nat__rel(_816963, _816959) = c_Divides_Odivmod__nat__rel(_816961, _816957)), _816963 = _816961, _816959 = _816957], (48280 ^ _777959) ^ [_1749727, _1749729] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1749727)), hAPP(c_Code__Numeral_Oof__nat, _1749729)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1749727), _1749729)))], (51384 ^ _777959) ^ [] : [-(hBOOL(c_fTrue))], (38068 ^ _777959) ^ [_1507219, _1507221, _1507223, _1507225, _1507227] : [c_Fun_Oinj__on(_1507219, _1507221, _1507223, c_Orderings_Otop__class_Otop(tc_fun(_1507219, tc_HOL_Obool))), 38071 ^ _777959 : [(38078 ^ _777959) ^ [] : [_1507225 = _1507227, -(hAPP(c_Set_Oimage(_1507219, _1507221, _1507223), _1507225) = hAPP(c_Set_Oimage(_1507219, _1507221, _1507223), _1507227))], (38072 ^ _777959) ^ [] : [hAPP(c_Set_Oimage(_1507219, _1507221, _1507223), _1507225) = hAPP(c_Set_Oimage(_1507219, _1507221, _1507223), _1507227), -(_1507225 = _1507227)]]], (9668 ^ _777959) ^ [_945339, _945341, _945343, _945345] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945339, tc_HOL_Obool)), _945341), _945343), _945345)), -(hBOOL(hAPP(_945343, _945345)))], (8204 ^ _777959) ^ [_919322, _919324, _919326, _919328, _919330, _919332, _919334, _919336] : [c_Finite__Set_Ofolding__image__simple__idem(_919322, _919324, _919326, _919328, _919330, _919332), hBOOL(hAPP(c_Finite__Set_Ofinite(_919324), _919334)), hBOOL(hAPP(hAPP(c_member(_919324), _919336), _919334)), -(hAPP(hAPP(_919326, hAPP(_919330, _919336)), hAPP(_919332, _919334)) = hAPP(_919332, _919334))], (28612 ^ _777959) ^ [_1316950, _1316952, _1316954, _1316956, _1316958] : [class_Groups_Ocomm__monoid__add(_1316950), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1316950), _1316952), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1316954), _1316956), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1316958), _1316956))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1316950), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1316950, tc_Nat_Onat), _1316952), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1316956))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1316954, _1316958)))], (1090 ^ _777959) ^ [_794308, _794310] : [-(class_Groups_Oordered__ab__group__add(_794308)), _794310 = _794308, class_Groups_Oordered__ab__group__add(_794310)], (5080 ^ _777959) ^ [_855546, _855548, _855550, _855552] : [-(c_Option_Omap(_855552, _855548) = c_Option_Omap(_855550, _855546)), _855552 = _855550, _855548 = _855546], (40811 ^ _777959) ^ [_1571444, _1571446, _1571448] : [-(c_List_Osublist(_1571444, _1571446, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1571448)) = hAPP(hAPP(c_List_Otake(_1571444), _1571448), _1571446))], (19672 ^ _777959) ^ [_1153867, _1153869, _1153871] : [class_Groups_Ocomm__monoid__mult(_1153867), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1153869, _1153867), _1153871), c_Orderings_Obot__class_Obot(tc_fun(_1153869, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1153867))], (29026 ^ _777959) ^ [_1324975, _1324977] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1324975)), -(c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1324975, _1324977)))], (13469 ^ _777959) ^ [_1025052, _1025054, _1025056] : [class_Orderings_Otop(_1025052), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1025054, _1025052)), _1025056) = c_Orderings_Otop__class_Otop(_1025052))], (42304 ^ _777959) ^ [_1612176, _1612178, _1612180, _1612182, _1612184, _1612186, _1612188, _1612190, _1612192, _1612194] : [hAPP(c_Set_Oimage(_1612176, _1612178, _1612180), _1612182) = _1612184, hAPP(c_Set_Oimage(_1612186, _1612188, _1612190), _1612192) = _1612194, -(hAPP(c_Set_Oimage(tc_prod(_1612176, _1612186), tc_prod(_1612178, _1612188), c_Product__Type_Omap__pair(_1612176, _1612178, _1612186, _1612188, _1612180, _1612190)), hAPP(hAPP(c_Product__Type_OSigma(_1612176, _1612186), _1612182), hAPP(c_COMBK(tc_fun(_1612186, tc_HOL_Obool), _1612176), _1612192))) = hAPP(hAPP(c_Product__Type_OSigma(_1612178, _1612188), _1612184), hAPP(c_COMBK(tc_fun(_1612188, tc_HOL_Obool), _1612178), _1612194)))], (10134 ^ _777959) ^ [_955127, _955129, _955131, _955133] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_955127, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_955127, tc_HOL_Obool)), _955129), _955131)), _955133) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_955127, tc_HOL_Obool)), _955129), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_955127, tc_HOL_Obool)), _955131), _955133)))], (38342 ^ _777959) ^ [_1512720, _1512722, _1512724, _1512726, _1512728, _1512730] : [c_Fun_Oinj__on(_1512720, _1512722, _1512724, _1512726), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1512722, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1512720, _1512722, _1512724), _1512726)), _1512728)), c_Fun_Oinj__on(_1512722, _1512720, _1512730, _1512728), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1512720, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1512722, _1512720, _1512730), _1512728)), _1512726)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512720), _1512726)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1512722), _1512728)), -(hAPP(c_Finite__Set_Ocard(_1512720), _1512726) = hAPP(c_Finite__Set_Ocard(_1512722), _1512728))], (46788 ^ _777959) ^ [_1714284, _1714286, _1714288, _1714290, _1714292, _1714294, _1714296] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1714284, _1714286, _1714288), hAPP(hAPP(c_Relation_Orel__comp(_1714284, _1714290, _1714286), _1714292), _1714294)), _1714296) = hAPP(hAPP(c_Relation_Orel__comp(_1714284, _1714290, _1714288), _1714292), hAPP(hAPP(c_Relation_Orel__comp(_1714290, _1714286, _1714288), _1714294), _1714296)))], (22446 ^ _777959) ^ [_1205835, _1205837, _1205839, _1205841, _1205843] : [class_Groups_Ocomm__monoid__add(_1205835), class_Groups_Oordered__ab__semigroup__add(_1205835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1205837), _1205839)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1205837, tc_HOL_Obool)), _1205841), _1205839)), 22464 ^ _777959 : [(22467 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205835), c_Groups_Ozero__class_Ozero(_1205835)), hAPP(_1205843, 22463 ^ [_1205835, _1205837, _1205839, _1205841, _1205843])))], (22465 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1205837), 22463 ^ [_1205835, _1205837, _1205839, _1205841, _1205843]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1205837, tc_HOL_Obool)), _1205839), _1205841))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1205835), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1205837, _1205835), _1205843), _1205841)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1205837, _1205835), _1205843), _1205839))))], (6225 ^ _777959) ^ [_878192, _878194, _878196, _878198] : [6229 ^ _777959 : [(6232 ^ _777959) ^ [] : [hBOOL(hAPP(_878198, 6228 ^ [_878192, _878194, _878196, _878198]))], (6230 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_878192), 6228 ^ [_878192, _878194, _878196, _878198]), _878194)))]], 6234 ^ _777959 : [(6237 ^ _777959) ^ [] : [hBOOL(hAPP(_878198, 6233 ^ [_878192, _878194, _878196, _878198]))], (6235 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_878192), 6233 ^ [_878192, _878194, _878196, _878198]), _878196)))]], 6238 ^ _777959 : [(6239 ^ _777959) ^ [_878525] : [hBOOL(hAPP(hAPP(c_member(_878192), _878525), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_878192, tc_HOL_Obool)), _878194), _878196))), -(hBOOL(hAPP(_878198, _878525)))]]], (39043 ^ _777959) ^ [_1529901] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1529901)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1529901), tc_HOL_Obool))))], (38084 ^ _777959) ^ [_1507500, _1507502, _1507504, _1507506, _1507508] : [c_Fun_Oinj__on(_1507500, _1507502, _1507504, c_Orderings_Otop__class_Otop(tc_fun(_1507500, tc_HOL_Obool))), hAPP(_1507504, _1507506) = hAPP(_1507504, _1507508), -(_1507506 = _1507508)], (29777 ^ _777959) ^ [_1340482, _1340484, _1340486] : [hBOOL(hAPP(c_Predicate_OPowp(_1340482, hAPP(hAPP(c_COMBC(_1340482, tc_fun(_1340482, tc_HOL_Obool), tc_HOL_Obool), c_member(_1340482)), _1340484)), _1340486)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1340482, tc_HOL_Obool)), _1340486), hAPP(c_Set_OPow(_1340482), _1340484))))], (33239 ^ _777959) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (23517 ^ _777959) ^ [_1225536, _1225538] : [23518 ^ _777959 : [(23521 ^ _777959) ^ [] : [_1225536 = _1225538], (23519 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225536), _1225538))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225536), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225538), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (29922 ^ _777959) ^ [_1343557] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1343557, _1343557) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22912 ^ _777959) ^ [_1214901, _1214903, _1214905] : [class_Rings_Olinordered__semidom(_1214901), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1214901), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1214901), _1214903)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1214901), _1214905))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1214903), _1214905)))], (44014 ^ _777959) ^ [_1653044, _1653046, _1653048] : [44016 ^ _777959 : [(44019 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1653046, 44015 ^ [_1653044, _1653046, _1653048])))], (44017 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653044), 44015 ^ [_1653044, _1653046, _1653048]), hAPP(c_List_Oset(_1653044), _1653048))))]], -(hAPP(c_List_Ofilter(_1653044, _1653046), _1653048) = c_List_Olist_ONil(_1653044))], (45572 ^ _777959) ^ [_1686697, _1686699, _1686701, _1686703] : [-(c_List_Opartition(_1686697, _1686699, hAPP(hAPP(c_List_Olist_OCons(_1686697), _1686701), _1686703)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1686697), tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1686697), tc_fun(tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697))), tc_fun(tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1686697), tc_fun(tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)))), tc_fun(tc_fun(tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697))), tc_fun(tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)))), tc_List_Olist(_1686697)), c_COMBS(tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697))), tc_fun(tc_List_Olist(_1686697), tc_fun(tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)))), tc_List_Olist(_1686697)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)), tc_fun(tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697))), tc_List_Olist(_1686697)), hAPP(c_If(tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697))), hAPP(_1686699, _1686701)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1686697), tc_fun(tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697))), tc_List_Olist(_1686697)), c_Product__Type_OPair(tc_List_Olist(_1686697), tc_List_Olist(_1686697))), hAPP(c_List_Olist_OCons(_1686697), _1686701))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1686697), tc_fun(tc_List_Olist(_1686697), tc_List_Olist(_1686697)), tc_fun(tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697))), tc_fun(tc_fun(tc_List_Olist(_1686697), tc_List_Olist(_1686697)), tc_fun(tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)))), tc_List_Olist(_1686697)), c_COMBB(tc_List_Olist(_1686697), tc_prod(tc_List_Olist(_1686697), tc_List_Olist(_1686697)), tc_List_Olist(_1686697))), c_Product__Type_OPair(tc_List_Olist(_1686697), tc_List_Olist(_1686697)))), hAPP(c_List_Olist_OCons(_1686697), _1686701)))), c_List_Opartition(_1686697, _1686699, _1686703)))], (2616 ^ _777959) ^ [_816808, _816810, _816812, _816814] : [-(c_Divides_Odivmod__nat(_816814, _816810) = c_Divides_Odivmod__nat(_816812, _816808)), _816814 = _816812, _816810 = _816808], (36141 ^ _777959) ^ [_1463298, _1463300, _1463302] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1463298), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1463300)), _1463302)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1463298, _1463300), hAPP(c_Divides_OnegateSnd, _1463302))))], (13848 ^ _777959) ^ [_1034077, _1034079, _1034081, _1034083, _1034085] : [class_Complete__Lattice_Ocomplete__lattice(_1034077), class_Orderings_Olinorder(_1034077), 13855 ^ _777959 : [(13865 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1034077), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1034079, _1034077), _1034081), _1034083)), _1034085))), 13866 ^ _777959 : [(13867 ^ _777959) ^ [_1034425] : [hBOOL(hAPP(hAPP(c_member(_1034079), _1034425), _1034081)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1034077), hAPP(_1034083, _1034425)), _1034085))]]], (13856 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1034077), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1034079, _1034077), _1034081), _1034083)), _1034085)), 13860 ^ _777959 : [(13863 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1034077), hAPP(_1034083, 13859 ^ [_1034077, _1034079, _1034081, _1034083, _1034085])), _1034085)))], (13861 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1034079), 13859 ^ [_1034077, _1034079, _1034081, _1034083, _1034085]), _1034081)))]]]]], (24307 ^ _777959) ^ [_1239918, _1239920, _1239922, _1239924] : [-(c_Sum__Type_OPlus(_1239918, _1239920, _1239922, _1239924) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(_1239918, _1239920), tc_HOL_Obool))), _1239922 = c_Orderings_Obot__class_Obot(tc_fun(_1239918, tc_HOL_Obool)), _1239924 = c_Orderings_Obot__class_Obot(tc_fun(_1239920, tc_HOL_Obool))], (3986 ^ _777959) ^ [_838329, _838331, _838333, _838335] : [-(c_Random_Oselect(_838335, _838331) = c_Random_Oselect(_838333, _838329)), _838335 = _838333, _838331 = _838329], (23845 ^ _777959) ^ [_1231397, _1231399, _1231401] : [class_Rings_Olinordered__semidom(_1231397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231397), c_Groups_Oone__class_Oone(_1231397)), _1231399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1231397), hAPP(hAPP(c_Power_Opower__class_Opower(_1231397), _1231399), _1231401)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1231397), _1231399), hAPP(hAPP(c_Power_Opower__class_Opower(_1231397), _1231399), _1231401)))))], (49664 ^ _777959) ^ [_1784889, _1784891, _1784893] : [hBOOL(hAPP(hAPP(c_member(_1784889), _1784891), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1784889, tc_HOL_Obool), _1784893))), 49668 ^ _777959 : [(49671 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1784889, tc_HOL_Obool)), 49667 ^ [_1784889, _1784891, _1784893]), _1784893)))], (49669 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1784889), _1784891), 49667 ^ [_1784889, _1784891, _1784893])))]]], (36888 ^ _777959) ^ [_1477943, _1477945, _1477947, _1477949, _1477951, _1477953] : [-(c_Product__Type_Oprod_Oprod__rec(_1477943, _1477945, _1477947, _1477949, hAPP(hAPP(c_Product__Type_OPair(_1477943, _1477945), _1477951), _1477953)) = hAPP(hAPP(_1477949, _1477951), _1477953))], (22808 ^ _777959) ^ [_1213012, _1213014, _1213016] : [class_Rings_Ocomm__semiring__1(_1213012), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213012), _1213014), hAPP(hAPP(c_Power_Opower__class_Opower(_1213012), _1213014), _1213016)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1213012), _1213014), hAPP(c_Nat_OSuc, _1213016)))], (48992 ^ _777959) ^ [_1767622, _1767624, _1767626] : [c_Equiv__Relations_Oequiv(_1767622, _1767624, _1767626), -(hAPP(hAPP(c_Relation_Orel__comp(_1767622, _1767622, _1767622), hAPP(c_Relation_Oconverse(_1767622, _1767622), _1767626)), _1767626) = _1767626)], (37277 ^ _777959) ^ [_1489131, _1489133] : [c_Relation_Oirrefl(_1489131, _1489133), 37280 ^ _777959 : [(37281 ^ _777959) ^ [_1489213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1489131, _1489131)), hAPP(hAPP(c_Product__Type_OPair(_1489131, _1489131), _1489213), _1489213)), _1489133))]]], (43526 ^ _777959) ^ [_1643045, _1643047] : [hBOOL(hAPP(c_List_Odistinct(_1643045), _1643047)), -(hBOOL(hAPP(c_List_Odistinct(_1643045), hAPP(c_List_Otl(_1643045), _1643047))))], (26572 ^ _777959) ^ [_1281239, _1281241, _1281243, _1281245] : [class_Fields_Olinordered__field__inverse__zero(_1281239), 26575 ^ _777959 : [(26576 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), _1281241), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281239), _1281243), _1281245))), 26579 ^ _777959 : [(26586 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), c_Groups_Ozero__class_Ozero(_1281239)), _1281245))), 26589 ^ _777959 : [(26596 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), _1281245), c_Groups_Ozero__class_Ozero(_1281239)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), _1281241), c_Groups_Ozero__class_Ozero(_1281239))))], (26590 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), _1281245), c_Groups_Ozero__class_Ozero(_1281239))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), _1281243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281239), _1281241), _1281245))))]]], (26580 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), c_Groups_Ozero__class_Ozero(_1281239)), _1281245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281239), _1281241), _1281245)), _1281243)))]]], (26602 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), _1281241), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1281239), _1281243), _1281245)))), 26605 ^ _777959 : [(26608 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281239), _1281241), _1281245)), _1281243))], (26606 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), c_Groups_Ozero__class_Ozero(_1281239)), _1281245)))]], 26609 ^ _777959 : [(26612 ^ _777959) ^ [] : [26613 ^ _777959 : [(26616 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), _1281243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1281239), _1281241), _1281245)))], (26614 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), _1281245), c_Groups_Ozero__class_Ozero(_1281239))))]], 26617 ^ _777959 : [(26620 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), _1281241), c_Groups_Ozero__class_Ozero(_1281239)))], (26618 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), _1281245), c_Groups_Ozero__class_Ozero(_1281239)))]]], (26610 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1281239), c_Groups_Ozero__class_Ozero(_1281239)), _1281245))]]]]], (9722 ^ _777959) ^ [_946556, _946558, _946560] : [class_Lattices_Osemilattice__inf(_946556), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946556), _946558), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946556), _946558), _946560)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946556), _946558), _946560))], (29146 ^ _777959) ^ [_1327340, _1327342, _1327344] : [class_Orderings_Oorder(_1327340), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327340, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1327340), _1327342)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1327340, _1327342, _1327344)) = c_Orderings_Obot__class_Obot(tc_fun(_1327340, tc_HOL_Obool)))], (4830 ^ _777959) ^ [_851569, _851571, _851573, _851575, _851577, _851579, _851581, _851583] : [-(c_Fun_Ocomp(_851583, _851579, _851575, _851571) = c_Fun_Ocomp(_851581, _851577, _851573, _851569)), _851583 = _851581, _851579 = _851577, _851575 = _851573, _851571 = _851569], (1300 ^ _777959) ^ [_796933, _796935] : [-(class_Lattices_Osemilattice__sup(_796933)), _796935 = _796933, class_Lattices_Osemilattice__sup(_796935)], (3080 ^ _777959) ^ [_824102, _824104, _824106, _824108, _824110, _824112, _824114, _824116] : [-(c_List_Omap__filter(_824116, _824112, _824108, _824104) = c_List_Omap__filter(_824114, _824110, _824106, _824102)), _824116 = _824114, _824112 = _824110, _824108 = _824106, _824104 = _824102], (5252 ^ _777959) ^ [_858328, _858330, _858332, _858334, _858336, _858338, _858340, _858342, _858344, _858346] : [-(c_Predicate_Opred__comp(_858346, _858342, _858338, _858334, _858330) = c_Predicate_Opred__comp(_858344, _858340, _858336, _858332, _858328)), _858346 = _858344, _858342 = _858340, _858338 = _858336, _858334 = _858332, _858330 = _858328], (26854 ^ _777959) ^ [_1286528, _1286530, _1286532, _1286534] : [class_Fields_Ofield(_1286528), -(_1286530 = c_Groups_Ozero__class_Ozero(_1286528)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1286528), _1286532), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286528), _1286534), _1286530)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286528), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1286528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286528), _1286530), _1286532)), _1286534)), _1286530))], (24271 ^ _777959) ^ [_1239305, _1239307] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239305) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1239307), -(_1239305 = _1239307)], (43819 ^ _777959) ^ [_1649352, _1649354, _1649356] : [_1649352 = c_List_Olist_ONil(_1649354), -(c_List_Olast(_1649354, hAPP(hAPP(c_List_Oappend(_1649354), _1649356), _1649352)) = c_List_Olast(_1649354, _1649356))], (25888 ^ _777959) ^ [_1268593, _1268595, _1268597] : [class_Fields_Ofield__inverse__zero(_1268593), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268593), c_Groups_Oone__class_Oone(_1268593)), hAPP(hAPP(c_Power_Opower__class_Opower(_1268593), _1268595), _1268597)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1268593), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268593), c_Groups_Oone__class_Oone(_1268593)), _1268595)), _1268597))], (45035 ^ _777959) ^ [_1674813, _1674815, _1674817, _1674819] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1674813), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1674815)), _1674817))), -(hAPP(c_List_Orev(_1674815), hAPP(hAPP(c_List_Olist__update(_1674815, _1674817), _1674813), _1674819)) = hAPP(hAPP(c_List_Olist__update(_1674815, hAPP(c_List_Orev(_1674815), _1674817)), 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(_1674815)), _1674817)), _1674813)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1674819))], (40546 ^ _777959) ^ [_1565020, _1565022, _1565024, _1565026, _1565028] : [class_Groups_Ocomm__monoid__add(_1565020), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1565020), hAPP(hAPP(c_List_Omap(_1565022, _1565020), hAPP(hAPP(c_COMBS(_1565022, _1565020, _1565020), hAPP(hAPP(c_COMBB(_1565020, tc_fun(_1565020, _1565020), _1565022), c_Groups_Oplus__class_Oplus(_1565020)), _1565024)), _1565026)), _1565028)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1565020), hAPP(c_List_Omonoid__add__class_Olistsum(_1565020), hAPP(hAPP(c_List_Omap(_1565022, _1565020), _1565024), _1565028))), hAPP(c_List_Omonoid__add__class_Olistsum(_1565020), hAPP(hAPP(c_List_Omap(_1565022, _1565020), _1565026), _1565028))))], (42334 ^ _777959) ^ [_1613135, _1613137, _1613139] : [-(c_Relation_Orefl__on(_1613135, _1613137, _1613139)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1613135, _1613135), tc_HOL_Obool)), _1613139), hAPP(hAPP(c_Product__Type_OSigma(_1613135, _1613135), _1613137), hAPP(c_COMBK(tc_fun(_1613135, tc_HOL_Obool), _1613135), _1613137)))), 42340 ^ _777959 : [(42343 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1613135, _1613135)), hAPP(hAPP(c_Product__Type_OPair(_1613135, _1613135), 42339 ^ [_1613135, _1613137, _1613139]), 42339 ^ [_1613135, _1613137, _1613139])), _1613139))], (42341 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1613135), 42339 ^ [_1613135, _1613137, _1613139]), _1613137)))]]], (18849 ^ _777959) ^ [_1139854, _1139856, _1139858] : [class_Lattices_Oab__semigroup__idem__mult(_1139854), hBOOL(hAPP(c_Finite__Set_Ofinite(_1139854), _1139856)), -(hAPP(c_Finite__Set_Ofold1(_1139854, c_Groups_Otimes__class_Otimes(_1139854)), hAPP(hAPP(c_Set_Oinsert(_1139854), _1139858), _1139856)) = hAPP(hAPP(c_Finite__Set_Ofold(_1139854, _1139854, c_Groups_Otimes__class_Otimes(_1139854)), _1139858), _1139856))], (29711 ^ _777959) ^ [_1338513, _1338515] : [hAPP(c_Set_OPow(_1338513), _1338515) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1338513, tc_HOL_Obool), tc_HOL_Obool))], (36532 ^ _777959) ^ [_1470790, _1470792, _1470794, _1470796] : [-(hAPP(c_Product__Type_Osnd(_1470790, _1470792), hAPP(hAPP(c_Product__Type_OPair(_1470790, _1470792), _1470794), _1470796)) = _1470796)], (46609 ^ _777959) ^ [_1709207, _1709209, _1709211] : [hBOOL(hAPP(c_List_Odistinct(_1709207), _1709209)), -(hBOOL(hAPP(c_List_Odistinct(_1709207), c_List_Oinsert(_1709207, _1709211, _1709209))))], (24476 ^ _777959) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48314 ^ _777959) ^ [_1750304, _1750306] : [_1750304 = _1750306, -(hAPP(c_Code__Numeral_Onat__of, _1750304) = hAPP(c_Code__Numeral_Onat__of, _1750306))], (20593 ^ _777959) ^ [_1170593] : [class_Rings_Olinordered__semidom(_1170593), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1170593), c_Groups_Ozero__class_Ozero(_1170593)), c_Groups_Oone__class_Oone(_1170593))))], (45564 ^ _777959) ^ [_1686604, _1686606] : [-(_1686604 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1686606, _1686604, c_List_Olist_ONil(_1686606)) = c_List_Olist_ONil(tc_List_Olist(_1686606)))], (5116 ^ _777959) ^ [_856180, _856182, _856184, _856186, _856188, _856190] : [-(c_New__DSequence_Oneg__union(_856190, _856186, _856182) = c_New__DSequence_Oneg__union(_856188, _856184, _856180)), _856190 = _856188, _856186 = _856184, _856182 = _856180], (4356 ^ _777959) ^ [_843908, _843910] : [_843910 = _843908, -(c_Int_Oring__1__class_Oof__int(_843910) = c_Int_Oring__1__class_Oof__int(_843908))], (14195 ^ _777959) ^ [_1042058] : [class_Lattices_Oboolean__algebra(_1042058), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1042058), c_Orderings_Obot__class_Obot(_1042058)) = c_Orderings_Otop__class_Otop(_1042058))], (10667 ^ _777959) ^ [_967197, _967199, _967201, _967203, _967205, _967207] : [hBOOL(hAPP(hAPP(c_member(_967197), _967199), _967201)), hBOOL(hAPP(hAPP(_967203, _967199), _967205)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_967197, tc_fun(_967207, tc_HOL_Obool)), _967201), _967203), _967205)))], (50035 ^ _777959) ^ [_1792541, _1792543, _1792545, _1792547] : [class_HOL_Oequal(_1792541), class_Enum_Oenum(_1792543), 50042 ^ _777959 : [(50043 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1792543, _1792541)), _1792545), _1792547)), 50046 ^ _777959 : [(50047 ^ _777959) ^ [_1792763] : [hBOOL(hAPP(hAPP(c_member(_1792543), _1792763), hAPP(c_List_Oset(_1792543), c_Enum_Oenum__class_Oenum(_1792543)))), -(hAPP(_1792545, _1792763) = hAPP(_1792547, _1792763))]]], (50053 ^ _777959) ^ [] : [50055 ^ _777959 : [(50058 ^ _777959) ^ [] : [hAPP(_1792545, 50054 ^ [_1792541, _1792543, _1792545, _1792547]) = hAPP(_1792547, 50054 ^ [_1792541, _1792543, _1792545, _1792547])], (50056 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1792543), 50054 ^ [_1792541, _1792543, _1792545, _1792547]), hAPP(c_List_Oset(_1792543), c_Enum_Oenum__class_Oenum(_1792543)))))]], -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(_1792543, _1792541)), _1792545), _1792547)))]]], (7696 ^ _777959) ^ [_908092, _908094, _908096, _908098, _908100, _908102] : [c_Hoare__Mirabelle_Ohoare__derivs(_908092, _908094, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_908092)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_908092), _908096), _908098), _908100)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_908092), tc_HOL_Obool)))), 7703 ^ _777959 : [(7706 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_908096, 7701 ^ [_908092, _908094, _908096, _908098, _908100, _908102]), 7702 ^ [_908092, _908094, _908096, _908098, _908100, _908102]))], (7704 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_908102, 7701 ^ [_908092, _908094, _908096, _908098, _908100, _908102]), 7702 ^ [_908092, _908094, _908096, _908098, _908100, _908102])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_908092, _908094, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_908092)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_908092), _908102), _908098), _908100)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_908092), tc_HOL_Obool)))))], (34701 ^ _777959) ^ [_1430751, _1430753, _1430755] : [class_Rings_Olinordered__semidom(_1430751), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430751), hAPP(hAPP(c_Power_Opower__class_Opower(_1430751), _1430753), 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(_1430751), _1430755), 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(_1430751), c_Groups_Ozero__class_Ozero(_1430751)), _1430755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1430751), _1430753), _1430755)))], (24415 ^ _777959) ^ [_1241735, _1241737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1241735), _1241737)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241735)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241737))))], (39870 ^ _777959) ^ [_1549248, _1549250, _1549252, _1549254, _1549256, _1549258, _1549260, _1549262] : [-(hAPP(hAPP(c_List_Ozip(_1549248, _1549250), hAPP(hAPP(c_List_Omap(_1549252, _1549248), _1549254), _1549256)), hAPP(hAPP(c_List_Omap(_1549258, _1549250), _1549260), _1549262)) = hAPP(hAPP(c_List_Omap(tc_prod(_1549252, _1549258), tc_prod(_1549248, _1549250)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549252, _1549258, tc_prod(_1549248, _1549250)), hAPP(hAPP(c_COMBC(_1549252, tc_fun(_1549258, _1549250), tc_fun(_1549258, tc_prod(_1549248, _1549250))), hAPP(hAPP(c_COMBB(tc_fun(_1549250, tc_prod(_1549248, _1549250)), tc_fun(tc_fun(_1549258, _1549250), tc_fun(_1549258, tc_prod(_1549248, _1549250))), _1549252), c_COMBB(_1549250, tc_prod(_1549248, _1549250), _1549258)), hAPP(hAPP(c_COMBB(_1549248, tc_fun(_1549250, tc_prod(_1549248, _1549250)), _1549252), c_Product__Type_OPair(_1549248, _1549250)), _1549254))), _1549260))), hAPP(hAPP(c_List_Ozip(_1549252, _1549258), _1549256), _1549262)))], (41791 ^ _777959) ^ [_1600198, _1600200, _1600202] : [c_Equiv__Relations_Oequiv(_1600198, _1600200, _1600202), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1600198), c_List_Olists(_1600198, _1600200), c_List_Olistrel(_1600198, _1600202)))], (11932 ^ _777959) ^ [_994602, _994604, _994606] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994602), _994604)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994602), _994606)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994604), _994606))], (13599 ^ _777959) ^ [_1027830, _1027832] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1027830, tc_HOL_Obool)), _1027832), c_Orderings_Otop__class_Otop(tc_fun(_1027830, tc_HOL_Obool)))))], (35223 ^ _777959) ^ [_1440175] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1440175), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1440175))], (45129 ^ _777959) ^ [_1677477, _1677479] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1677477), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1677477))), _1677479))), -(c_List_Otranspose(_1677477, c_List_Otranspose(_1677477, _1677479)) = c_List_OtakeWhile(tc_List_Olist(_1677477), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1677477)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1677477), tc_List_Olist(_1677477), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1677477))), _1677479))], (12086 ^ _777959) ^ [_997212, _997214] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997212), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997212), _997214))))], (44366 ^ _777959) ^ [_1660031] : [-(c_List_Oupt(_1660031, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (11114 ^ _777959) ^ [_975655, _975657] : [_975657 = c_Option_Ooption_ONone(_975655), -(c_Option_Oset(_975655, _975657) = c_Orderings_Obot__class_Obot(tc_fun(_975655, tc_HOL_Obool)))], (41453 ^ _777959) ^ [_1590529, _1590531, _1590533, _1590535, _1590537] : [-(hAPP(hAPP(c_List_Olist__update(_1590529, hAPP(hAPP(c_List_Olist_OCons(_1590529), _1590531), _1590533)), hAPP(c_Nat_OSuc, _1590535)), _1590537) = hAPP(hAPP(c_List_Olist_OCons(_1590529), _1590531), hAPP(hAPP(c_List_Olist__update(_1590529, _1590533), _1590535), _1590537)))], (6971 ^ _777959) ^ [_892871, _892873, _892875, _892877, _892879] : [c_Hoare__Mirabelle_Ohoare__valids(_892871, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_892871), tc_HOL_Obool)), _892873), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_892871), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892871)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892871))), hAPP(hAPP(c_COMBB(tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892871))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_892871)), _892875)), c_Com_Ocom_OBODY)), _892877)), _892879)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_892871), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892871)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892871))), hAPP(hAPP(c_COMBB(tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892871))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_892871)), _892875)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _892877)), _892879)), -(c_Hoare__Mirabelle_Ohoare__valids(_892871, _892873, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_892871), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892871)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892871))), hAPP(hAPP(c_COMBB(tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_892871, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892871))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_892871)), _892875)), c_Com_Ocom_OBODY)), _892877)), _892879)))], (51158 ^ _777959) ^ [_1811469] : [class_Lazy__Sequence_Osmall__lazy(_1811469), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1811469)))], (48525 ^ _777959) ^ [_1755563, _1755565, _1755567] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1755563, _1755563)), _1755565), _1755567)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1755563, _1755563)), _1755565), c_Transitive__Closure_Ortrancl(_1755563, _1755567))))], (12419 ^ _777959) ^ [_1003518, _1003520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1003518), _1003520)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1003518), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1003520), _1003518)) = _1003520)], (10693 ^ _777959) ^ [_967752, _967754, _967756, _967758] : [class_Groups_Oab__semigroup__add(_967752), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967752), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967752), _967754), _967756)), _967758) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967752), _967754), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_967752), _967756), _967758)))], (41191 ^ _777959) ^ [_1584091, _1584093, _1584095, _1584097, _1584099] : [c_Relation_Orefl__on(_1584091, _1584093, _1584095), c_Relation_Orefl__on(_1584091, _1584097, _1584099), -(c_Relation_Orefl__on(_1584091, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1584091, tc_HOL_Obool)), _1584093), _1584097), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1584091, _1584091), tc_HOL_Obool)), _1584095), _1584099)))], (4078 ^ _777959) ^ [_839715, _839717, _839719, _839721] : [-(c_List_Olistrel1(_839721, _839717) = c_List_Olistrel1(_839719, _839715)), _839721 = _839719, _839717 = _839715], (10246 ^ _777959) ^ [_957842, _957844, _957846, _957848, _957850] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957842, tc_HOL_Obool)), hAPP(c_Set_Oimage(_957844, _957842, _957846), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957844, tc_HOL_Obool)), _957848), _957850))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957842, tc_HOL_Obool)), hAPP(c_Set_Oimage(_957844, _957842, _957846), _957848)), hAPP(c_Set_Oimage(_957844, _957842, _957846), _957850)))))], (1690 ^ _777959) ^ [_801808, _801810] : [-(class_Groups_Omonoid__mult(_801808)), _801810 = _801808, class_Groups_Omonoid__mult(_801810)], (11473 ^ _777959) ^ [_982731, _982733, _982735] : [class_Lattices_Olattice(_982731), hBOOL(hAPP(c_Finite__Set_Ofinite(_982731), _982733)), -(hBOOL(hAPP(hAPP(c_member(_982731), _982735), _982733))), -(c_Big__Operators_Olattice__class_OInf__fin(_982731, hAPP(hAPP(c_Set_Oinsert(_982731), _982735), _982733)) = hAPP(hAPP(c_Finite__Set_Ofold(_982731, _982731, c_Lattices_Osemilattice__inf__class_Oinf(_982731)), _982735), _982733))], (30072 ^ _777959) ^ [_1346662, _1346664, _1346666, _1346668] : [class_Divides_Oring__div(_1346662), -(c_Divides_Odiv__class_Omod(_1346662, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346662), _1346664), _1346666), _1346668) = c_Divides_Odiv__class_Omod(_1346662, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346662), c_Divides_Odiv__class_Omod(_1346662, _1346664, _1346668)), _1346666), _1346668))], (39071 ^ _777959) ^ [_1530428, _1530430, _1530432, _1530434, _1530436, _1530438] : [c_Fun_Oinj__on(_1530428, _1530430, _1530432, _1530434), c_Fun_Oinj__on(_1530430, _1530436, _1530438, hAPP(c_Set_Oimage(_1530428, _1530430, _1530432), _1530434)), -(c_Fun_Oinj__on(_1530428, _1530436, hAPP(c_Fun_Ocomp(_1530430, _1530436, _1530428, _1530438), _1530432), _1530434))], (14696 ^ _777959) ^ [_1054127, _1054129, _1054131, _1054133] : [hBOOL(hAPP(hAPP(_1054131, _1054129), _1054133)), -(hBOOL(hAPP(hAPP(c_member(_1054127), _1054129), c_SetInterval_Oord_OlessThan(_1054127, _1054131, _1054133))))], (16449 ^ _777959) ^ [_1092811, _1092813, _1092815] : [class_Orderings_Olinorder(_1092811), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092811), _1092813), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092811), _1092813), _1092815)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092811), _1092813), _1092815))], (12864 ^ _777959) ^ [_1011468, _1011470, _1011472] : [hBOOL(hAPP(hAPP(c_member(_1011468), _1011470), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1011468, tc_HOL_Obool)), _1011472))), hBOOL(hAPP(hAPP(c_member(_1011468), _1011470), _1011472))], (6511 ^ _777959) ^ [_883146, _883148, _883150] : [class_Orderings_Oorder(_883146), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883146), _883148), _883150)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883146), _883150), _883148)), -(_883150 = _883148)], (45137 ^ _777959) ^ [_1677688, _1677690, _1677692, _1677694, _1677696] : [-(hAPP(hAPP(c_List_Ozip(_1677688, _1677690), c_List_OtakeWhile(_1677688, _1677692, _1677694)), _1677696) = c_List_OtakeWhile(tc_prod(_1677688, _1677690), hAPP(c_Fun_Ocomp(_1677688, tc_HOL_Obool, tc_prod(_1677688, _1677690), _1677692), c_Product__Type_Ofst(_1677688, _1677690)), hAPP(hAPP(c_List_Ozip(_1677688, _1677690), _1677694), _1677696)))], (49812 ^ _777959) ^ [_1788165, _1788167, _1788169] : [c_List_Olist__all(_1788165, _1788167, hAPP(c_List_Orev(_1788165), _1788169)), -(c_List_Olist__all(_1788165, _1788167, _1788169))], (14562 ^ _777959) ^ [_1051556, _1051558, _1051560, _1051562, _1051564, _1051566] : [-(hBOOL(hAPP(hAPP(c_member(_1051556), _1051558), _1051560))), -(hAPP(c_Fun_Ooverride__on(_1051556, _1051562, _1051564, _1051566, _1051560), _1051558) = hAPP(_1051564, _1051558))], (50276 ^ _777959) ^ [_1797096, _1797098, _1797100, _1797102] : [-(c_New__Random__Sequence_Opos__map(_1797096, _1797098, _1797100, _1797102) = c_New__Random__Sequence_Opos__bind(_1797096, _1797098, _1797102, hAPP(c_Fun_Ocomp(_1797098, 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(_1797098))))), _1797096, c_New__Random__Sequence_Opos__single(_1797098)), _1797100)))], (33877 ^ _777959) ^ [_1416097, _1416099] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416097)), hAPP(c_Nat_OSuc, _1416099))), -(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(_1416097))), 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)), _1416099)))))], (43452 ^ _777959) ^ [_1641945, _1641947, _1641949, _1641951] : [-(_1641945 = c_List_Olist_ONil(_1641947)), -(hAPP(c_List_Ohd(_1641949), hAPP(hAPP(c_List_Omap(_1641947, _1641949), _1641951), _1641945)) = hAPP(_1641951, hAPP(c_List_Ohd(_1641947), _1641945)))], (42012 ^ _777959) ^ [_1605847, _1605849, _1605851] : [-(hAPP(hAPP(c_List_Olist__update(_1605847, c_List_Olist_ONil(_1605847)), _1605849), _1605851) = c_List_Olist_ONil(_1605847))], (34891 ^ _777959) ^ [_1434653, _1434655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434653), 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)))), _1434655))), 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)))), _1434653)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1434655), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1434653))], (98 ^ _777959) ^ [_779578, _779580, _779582, _779584, _779586, _779588, _779590, _779592, _779594, _779596] : [-(c_Big__Operators_Ocomm__monoid__big(_779594, _779590, _779586, _779582, _779578)), c_Big__Operators_Ocomm__monoid__big(_779596, _779592, _779588, _779584, _779580), _779596 = _779594, _779592 = _779590, _779588 = _779586, _779584 = _779582, _779580 = _779578], (34069 ^ _777959) ^ [_1419681, _1419683] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1419681)), c_Int_OBit0(_1419683)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1419681), _1419683)))], (51448 ^ _777959) ^ [_1814847, _1814849] : [hBOOL(_1814847), -(hBOOL(hAPP(hAPP(c_fimplies, _1814849), _1814847)))], (51472 ^ _777959) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (16407 ^ _777959) ^ [_1092066, _1092068] : [class_Orderings_Olinorder(_1092066), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1092066), _1092068), _1092068) = _1092068)], (50118 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OPls))], (26918 ^ _777959) ^ [_1287702, _1287704, _1287706] : [class_Fields_Olinordered__field(_1287702), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287702), _1287704), _1287706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287702), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287702), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1287702), _1287704), _1287706)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1287702), c_Groups_Oone__class_Oone(_1287702)), c_Groups_Oone__class_Oone(_1287702)))), _1287706)))], (14103 ^ _777959) ^ [_1040221, _1040223, _1040225, _1040227, _1040229, _1040231] : [hAPP(c_Map_Omap__add(_1040221, _1040223, _1040225, _1040227), _1040229) = hAPP(c_Option_Ooption_OSome(_1040223), _1040231), -(hAPP(_1040227, _1040229) = hAPP(c_Option_Ooption_OSome(_1040223), _1040231)), 14110 ^ _777959 : [(14113 ^ _777959) ^ [] : [-(hAPP(_1040225, _1040229) = hAPP(c_Option_Ooption_OSome(_1040223), _1040231))], (14111 ^ _777959) ^ [] : [-(hAPP(_1040227, _1040229) = c_Option_Ooption_ONone(_1040223))]]], (43546 ^ _777959) ^ [_1643431, _1643433, _1643435] : [-(hAPP(c_List_Oset(_1643431), hAPP(c_List_Orotate(_1643431, _1643433), _1643435)) = hAPP(c_List_Oset(_1643431), _1643435))], (5374 ^ _777959) ^ [_860163, _860165] : [_860165 = _860163, -(c_Orderings_Oord__class_Omin(_860165) = c_Orderings_Oord__class_Omin(_860163))], (17687 ^ _777959) ^ [_1115951, _1115953, _1115955] : [class_Orderings_Olinorder(_1115951), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115951), _1115953)), -(_1115953 = c_Orderings_Obot__class_Obot(tc_fun(_1115951, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115951), _1115955)), -(_1115955 = c_Orderings_Obot__class_Obot(tc_fun(_1115951, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1115951, tc_HOL_Obool)), _1115953), _1115955) = c_Orderings_Obot__class_Obot(tc_fun(_1115951, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1115951, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1115951, tc_HOL_Obool)), _1115953), _1115955)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1115951), c_Big__Operators_Olinorder__class_OMin(_1115951, _1115953)), c_Big__Operators_Olinorder__class_OMin(_1115951, _1115955)))], (33087 ^ _777959) ^ [_1402713, _1402715] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402713) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1402715)), 33090 ^ _777959 : [(33093 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402715)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (33091 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402713))))]], 33094 ^ _777959 : [(33097 ^ _777959) ^ [] : [33098 ^ _777959 : [(33101 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402713) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (33099 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402715))))]], 33102 ^ _777959 : [(33105 ^ _777959) ^ [] : [_1402713 = _1402715], (33103 ^ _777959) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402715)))]]], (33095 ^ _777959) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1402713)))]]], (40946 ^ _777959) ^ [_1576032, _1576034, _1576036, _1576038] : [c_List_Olistrelp(_1576032, hAPP(hAPP(c_COMBC(_1576032, tc_fun(tc_prod(_1576032, _1576032), tc_HOL_Obool), tc_fun(_1576032, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576032, tc_fun(tc_fun(tc_prod(_1576032, _1576032), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1576032, _1576032), tc_HOL_Obool), tc_fun(_1576032, tc_HOL_Obool)), _1576032), c_COMBC(_1576032, tc_fun(tc_prod(_1576032, _1576032), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576032, tc_prod(_1576032, _1576032)), tc_fun(_1576032, tc_fun(tc_fun(tc_prod(_1576032, _1576032), tc_HOL_Obool), tc_HOL_Obool)), _1576032), hAPP(c_COMBB(tc_prod(_1576032, _1576032), tc_fun(tc_fun(tc_prod(_1576032, _1576032), tc_HOL_Obool), tc_HOL_Obool), _1576032), c_member(tc_prod(_1576032, _1576032)))), c_Product__Type_OPair(_1576032, _1576032)))), _1576034), _1576036, _1576038), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1576032), tc_List_Olist(_1576032))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1576032), tc_List_Olist(_1576032)), _1576036), _1576038)), c_List_Olistrel(_1576032, _1576034))))], (11748 ^ _777959) ^ [_989582, _989584, _989586, _989588, _989590, _989592] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989582, tc_fun(_989584, tc_HOL_Obool)), hAPP(c_Set_Oimage(_989586, _989582, _989588), _989590)), _989592) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989586, tc_fun(_989584, tc_HOL_Obool)), _989590), hAPP(hAPP(c_COMBB(_989582, tc_fun(_989584, tc_HOL_Obool), _989586), _989592), _989588)))], (19518 ^ _777959) ^ [_1151459, _1151461] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1151459), _1151461) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 19521 ^ _777959 : [(19524 ^ _777959) ^ [] : [-(_1151461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19522 ^ _777959) ^ [] : [-(_1151459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (34425 ^ _777959) ^ [_1426119, _1426121] : [class_Int_Onumber__ring(_1426119), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1426119), hAPP(c_Int_Onumber__class_Onumber__of(_1426119), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1426121) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426119), _1426121), _1426121))], (41473 ^ _777959) ^ [_1591009, _1591011, _1591013, _1591015] : [-(_1591009 = _1591011), -(hAPP(c_List_OremoveAll(_1591013, _1591009), hAPP(hAPP(c_List_Olist_OCons(_1591013), _1591011), _1591015)) = hAPP(hAPP(c_List_Olist_OCons(_1591013), _1591011), hAPP(c_List_OremoveAll(_1591013, _1591009), _1591015)))], (29757 ^ _777959) ^ [_1339565, _1339567, _1339569] : [-(hAPP(c_Set_OPow(_1339565), hAPP(hAPP(c_Set_Oinsert(_1339565), _1339567), _1339569)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1339565, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1339565), _1339569)), hAPP(c_Set_Oimage(tc_fun(_1339565, tc_HOL_Obool), tc_fun(_1339565, tc_HOL_Obool), hAPP(c_Set_Oinsert(_1339565), _1339567)), hAPP(c_Set_OPow(_1339565), _1339569))))], (23831 ^ _777959) ^ [_1231116, _1231118, _1231120, _1231122] : [class_Rings_Olinordered__semidom(_1231116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231116), hAPP(hAPP(c_Power_Opower__class_Opower(_1231116), _1231118), hAPP(c_Nat_OSuc, _1231120))), hAPP(hAPP(c_Power_Opower__class_Opower(_1231116), _1231122), hAPP(c_Nat_OSuc, _1231120)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231116), c_Groups_Ozero__class_Ozero(_1231116)), _1231122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1231116), _1231118), _1231122)))], (43458 ^ _777959) ^ [_1642021, _1642023, _1642025] : [_1642021 = c_List_Olist_ONil(_1642023), -(hAPP(c_List_Ohd(_1642023), hAPP(hAPP(c_List_Oappend(_1642023), _1642021), _1642025)) = hAPP(c_List_Ohd(_1642023), _1642025))], (51050 ^ _777959) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (47001 ^ _777959) ^ [_1720338, _1720340, _1720342, _1720344, _1720346, _1720348, _1720350] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1720338, _1720340, _1720342, _1720344, _1720346), _1720348), _1720350))), 47002 ^ _777959 : [(47003 ^ _777959) ^ [_1720409] : [hBOOL(hAPP(hAPP(_1720344, _1720348), _1720409)), hBOOL(hAPP(hAPP(_1720346, _1720409), _1720350))]]], (34795 ^ _777959) ^ [_1432726, _1432728] : [class_Rings_Oring__1(_1432726), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1432726), hAPP(c_Groups_Ouminus__class_Ouminus(_1432726), c_Groups_Oone__class_Oone(_1432726))), 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)))), _1432728)) = c_Groups_Oone__class_Oone(_1432726))], (42792 ^ _777959) ^ [_1625748, _1625750, _1625752, _1625754] : [_1625750 = _1625754, -(hAPP(hAPP(c_List_Oappend(_1625748), _1625750), _1625752) = hAPP(hAPP(c_List_Oappend(_1625748), _1625754), _1625752))], (27461 ^ _777959) ^ [_1297225, _1297227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1297225)), _1297227)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1297225), hAPP(c_Int_Onat, _1297227))))], (19995 ^ _777959) ^ [_1159747, _1159749, _1159751, _1159753] : [class_Rings_Oordered__semiring(_1159747), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159747), _1159749), _1159751)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159747), c_Groups_Ozero__class_Ozero(_1159747)), _1159753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159747), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159747), _1159749), _1159753)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159747), _1159751), _1159753))))], (25714 ^ _777959) ^ [_1265682, _1265684, _1265686, _1265688] : [class_Rings_Odivision__ring(_1265682), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265682), _1265684), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265682), _1265686), _1265688)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1265682), _1265684), _1265686)), _1265688))], (51314 ^ _777959) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (7884 ^ _777959) ^ [_912058, _912060, _912062, _912064, _912066] : [class_Groups_Ominus(_912058), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912060, _912058)), _912062), _912064), _912066) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_912058), hAPP(_912062, _912066)), hAPP(_912064, _912066)))], (10130 ^ _777959) ^ [_954959, _954961, _954963, _954965] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_954959, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954959, tc_HOL_Obool)), _954961), _954963)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954959, tc_HOL_Obool)), _954965), _954963)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_954959, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954959, tc_HOL_Obool)), _954961), _954963)), _954965))], (6685 ^ _777959) ^ [_886566, _886568] : [class_Orderings_Obot(_886566), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886566), c_Orderings_Obot__class_Obot(_886566)), _886568)))], (30179 ^ _777959) ^ [_1348668, _1348670] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1348668, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1348670)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1348668, _1348670) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (4252 ^ _777959) ^ [_842322, _842324, _842326, _842328, _842330, _842332] : [-(c_Divides_Odiv__class_Omod(_842332, _842328, _842324) = c_Divides_Odiv__class_Omod(_842330, _842326, _842322)), _842332 = _842330, _842328 = _842326, _842324 = _842322], (40491 ^ _777959) ^ [_1563907, _1563909] : [class_Groups_Ocomm__monoid__add(_1563907), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1563907), _1563909) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1563907), hAPP(c_List_Onth(_1563907), _1563909)), 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(_1563907)), _1563909))))], (41737 ^ _777959) ^ [_1598609, _1598611, _1598613, _1598615, _1598617, _1598619] : [-(c_Product__Type_Omap__pair(_1598609, _1598611, _1598613, _1598615, _1598617, _1598619) = hAPP(c_Product__Type_Oprod_Oprod__case(_1598609, _1598613, tc_prod(_1598611, _1598615)), hAPP(hAPP(c_COMBC(_1598609, tc_fun(_1598613, _1598615), tc_fun(_1598613, tc_prod(_1598611, _1598615))), hAPP(hAPP(c_COMBB(tc_fun(_1598615, tc_prod(_1598611, _1598615)), tc_fun(tc_fun(_1598613, _1598615), tc_fun(_1598613, tc_prod(_1598611, _1598615))), _1598609), c_COMBB(_1598615, tc_prod(_1598611, _1598615), _1598613)), hAPP(hAPP(c_COMBB(_1598611, tc_fun(_1598615, tc_prod(_1598611, _1598615)), _1598609), c_Product__Type_OPair(_1598611, _1598615)), _1598617))), _1598619)))], (2554 ^ _777959) ^ [_815823, _815825, _815827, _815829] : [-(c_Set_Othe__elem(_815829, _815825) = c_Set_Othe__elem(_815827, _815823)), _815829 = _815827, _815825 = _815823], (35846 ^ _777959) ^ [_1458104, _1458106, _1458108] : [-(hAPP(c_Divides_Oadjust(_1458104), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1458106), _1458108)) = 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), _1458108), _1458104)), 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)))), _1458106)), 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)))), _1458106)), _1458108))))], (24427 ^ _777959) ^ [_1241956] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1241956)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1241956)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29152 ^ _777959) ^ [_1327467, _1327469, _1327471] : [class_Orderings_Oorder(_1327467), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327467, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1327467, _1327469, _1327471)), hAPP(c_SetInterval_Oord__class_OatLeast(_1327467), _1327471)) = c_Orderings_Obot__class_Obot(tc_fun(_1327467, tc_HOL_Obool)))], (15422 ^ _777959) ^ [_1071291, _1071293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1071291)), _1071293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071291), _1071293)))], (22070 ^ _777959) ^ [_1197863, _1197865, _1197867, _1197869, _1197871] : [class_Groups_Ocomm__monoid__mult(_1197863), hBOOL(hAPP(c_Finite__Set_Ofinite(_1197865), _1197867)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1197865), _1197869)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1197865, tc_HOL_Obool)), _1197867), _1197869) = c_Orderings_Obot__class_Obot(tc_fun(_1197865, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1197865, _1197863), _1197871), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1197865, tc_HOL_Obool)), _1197867), _1197869)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1197863), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1197865, _1197863), _1197871), _1197867)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1197865, _1197863), _1197871), _1197869)))], (42441 ^ _777959) ^ [_1616010, _1616012] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1616010), tc_List_Olist(_1616010), c_List_Olistrel(_1616010, _1616012)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1616010)), c_List_Olist_ONil(_1616010)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1616010), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1616010)), c_List_Olist_ONil(_1616010)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1616010), tc_HOL_Obool))))], (17909 ^ _777959) ^ [_1120192, _1120194, _1120196] : [class_Orderings_Olinorder(_1120192), hBOOL(hAPP(c_Finite__Set_Ofinite(_1120192), _1120194)), -(_1120196 = c_Orderings_Obot__class_Obot(tc_fun(_1120192, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1120192, tc_HOL_Obool)), _1120196), _1120194)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1120192), c_Big__Operators_Olattice_OInf__fin(_1120192, c_Orderings_Oord__class_Omin(_1120192), _1120196)), c_Big__Operators_Olattice_OInf__fin(_1120192, c_Orderings_Oord__class_Omin(_1120192), _1120194)) = c_Big__Operators_Olattice_OInf__fin(_1120192, c_Orderings_Oord__class_Omin(_1120192), _1120194))], (48136 ^ _777959) ^ [_1747063, _1747065] : [-(_1747063 = _1747065), -(c_Random_Oinc__shift(_1747063, _1747065) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1747065), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (42086 ^ _777959) ^ [_1607264, _1607266] : [_1607266 = c_List_Olist_ONil(_1607264), -(c_Orderings_Obot__class_Obot(tc_fun(_1607264, tc_HOL_Obool)) = hAPP(c_List_Oset(_1607264), _1607266))], (35031 ^ _777959) ^ [_1437291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1437291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1437291))))], (39270 ^ _777959) ^ [_1534957, _1534959, _1534961] : [-(c_Map_Odom(_1534957, _1534959, hAPP(c_Map_Omap__of(_1534957, _1534959), _1534961)) = hAPP(c_Set_Oimage(tc_prod(_1534957, _1534959), _1534957, c_Product__Type_Ofst(_1534957, _1534959)), hAPP(c_List_Oset(tc_prod(_1534957, _1534959)), _1534961)))], (33143 ^ _777959) ^ [_1403745, _1403747] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403745))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403745), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403747)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (35327 ^ _777959) ^ [_1442153, _1442155] : [class_Int_Onumber__ring(_1442153), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1442155)), -(hBOOL(hAPP(hAPP(c_member(_1442153), hAPP(c_Int_Onumber__class_Onumber__of(_1442153), _1442155)), c_Nat_Osemiring__1__class_ONats(_1442153))))], (50718 ^ _777959) ^ [_1806776, _1806778, _1806780] : [hBOOL(hAPP(hAPP(c_member(_1806776), _1806780), hAPP(c_List_Oset(_1806776), _1806778))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1806776), _1806778), _1806780)))], (33195 ^ _777959) ^ [_1404602, _1404604] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404602)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404602)), _1404604)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1404602))), _1404604))], (12510 ^ _777959) ^ [_1005413, _1005415, _1005417, _1005419, _1005421] : [-(c_Map_Orestrict__map(_1005413, _1005415, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1005413, tc_Option_Ooption(_1005415)), _1005417), _1005419), hAPP(c_Option_Ooption_OSome(_1005415), _1005421)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1005413, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1005413), _1005419), c_Orderings_Obot__class_Obot(tc_fun(_1005413, tc_HOL_Obool))))) = c_Map_Orestrict__map(_1005413, _1005415, _1005417, hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1005413, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1005413), _1005419), c_Orderings_Obot__class_Obot(tc_fun(_1005413, tc_HOL_Obool))))))], (12642 ^ _777959) ^ [_1007403, _1007405] : [class_Groups_Ogroup__add(_1007403), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1007403), hAPP(c_Groups_Ouminus__class_Ouminus(_1007403), _1007405)) = _1007405)], (49052 ^ _777959) ^ [_1769057, _1769059, _1769061, _1769063] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1769057, _1769057)), hAPP(hAPP(c_Product__Type_OPair(_1769057, _1769057), _1769059), _1769061)), hAPP(c_Relation_Oconverse(_1769057, _1769057), c_Transitive__Closure_Otrancl(_1769057, _1769063)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1769057, _1769057)), hAPP(hAPP(c_Product__Type_OPair(_1769057, _1769057), _1769059), _1769061)), c_Transitive__Closure_Otrancl(_1769057, hAPP(c_Relation_Oconverse(_1769057, _1769057), _1769063)))))], (29222 ^ _777959) ^ [_1328866, _1328868, _1328870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1328866)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1328868), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1328870)), 29229 ^ _777959 : [(29230 ^ _777959) ^ [_1329074] : [29232 ^ _777959 : [(29238 ^ _777959) ^ [] : [-(_1329074 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 29234 ^ [_1328866, _1328868, _1328870, _1329074]), 29231 ^ [_1328866, _1328868, _1328870, _1329074]))], (29236 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29234 ^ [_1328866, _1328868, _1328870, _1329074]), _1328870)))], (29233 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29231 ^ [_1328866, _1328868, _1328870, _1329074]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1328866))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1329074), _1328868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1329074), _1328866)), _1328868)))]]], (10974 ^ _777959) ^ [_973074, _973076] : [c_Option_Ooption_ONone(_973074) = hAPP(c_Option_Ooption_OSome(_973074), _973076)], (42967 ^ _777959) ^ [_1629459, _1629461, _1629463] : [hAPP(hAPP(c_List_Oappend(_1629459), _1629461), _1629463) = _1629463, -(_1629461 = c_List_Olist_ONil(_1629459))], (41301 ^ _777959) ^ [_1586725, _1586727, _1586729] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586725, _1586725)), hAPP(hAPP(c_Product__Type_OPair(_1586725, _1586725), 41302 ^ [_1586725, _1586727, _1586729]), 41302 ^ [_1586725, _1586727, _1586729])), _1586727))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1586725), tc_List_Olist(_1586725))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1586725), tc_List_Olist(_1586725)), _1586729), _1586729)), c_List_Olexord(_1586725, _1586727)))], (35999 ^ _777959) ^ [_1460852, _1460854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1460852)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1460854)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1460852, _1460854), c_Divides_OposDivAlg(_1460852, _1460854))))], (23443 ^ _777959) ^ [_1224379, _1224381] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224379), _1224381)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1224381), _1224379)), -(_1224379 = _1224381)], (44238 ^ _777959) ^ [_1657986, _1657988, _1657990, _1657992, _1657994] : [class_Orderings_Olinorder(_1657986), 44241 ^ _777959 : [(44248 ^ _777959) ^ [] : [c_List_Olinorder__class_Osorted(_1657986, hAPP(hAPP(c_List_Omap(_1657988, _1657986), _1657990), _1657994)), -(c_List_Olinorder__class_Osorted(_1657986, hAPP(hAPP(c_List_Omap(_1657988, _1657986), _1657990), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1657988, _1657986, _1657990), _1657992), _1657994))))], (44242 ^ _777959) ^ [] : [c_List_Olinorder__class_Osorted(_1657986, hAPP(hAPP(c_List_Omap(_1657988, _1657986), _1657990), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1657988, _1657986, _1657990), _1657992), _1657994))), -(c_List_Olinorder__class_Osorted(_1657986, hAPP(hAPP(c_List_Omap(_1657988, _1657986), _1657990), _1657994)))]]], (38374 ^ _777959) ^ [_1513416, _1513418, _1513420, _1513422, _1513424] : [c_Fun_Oinj__on(_1513416, _1513418, _1513420, hAPP(hAPP(c_Set_Oinsert(_1513416), _1513422), _1513424)), 38377 ^ _777959 : [(38380 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1513418), hAPP(_1513420, _1513422)), hAPP(c_Set_Oimage(_1513416, _1513418, _1513420), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1513416, tc_HOL_Obool)), _1513424), hAPP(hAPP(c_Set_Oinsert(_1513416), _1513422), c_Orderings_Obot__class_Obot(tc_fun(_1513416, tc_HOL_Obool)))))))], (38378 ^ _777959) ^ [] : [-(c_Fun_Oinj__on(_1513416, _1513418, _1513420, _1513424))]]], (42859 ^ _777959) ^ [_1627409, _1627411, _1627413, _1627415, _1627417, _1627419] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627409)), _1627411) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627413)), _1627415), -(c_Map_Omap__upds(_1627409, _1627413, _1627417, _1627411, hAPP(hAPP(c_List_Oappend(_1627413), _1627415), _1627419)) = c_Map_Omap__upds(_1627409, _1627413, _1627417, _1627411, _1627415))], (46463 ^ _777959) ^ [_1706034, _1706036, _1706038, _1706040, _1706042, _1706044] : [c_List_Olist__all2(_1706034, _1706036, _1706038, _1706040, _1706042), -(c_List_Olist__all2(_1706034, _1706036, _1706038, hAPP(hAPP(c_List_Odrop(_1706034), _1706044), _1706040), hAPP(hAPP(c_List_Odrop(_1706036), _1706044), _1706042)))], (36165 ^ _777959) ^ [_1463620, _1463622] : [-(c_Divides_Opdivmod(_1463620, _1463622) = 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), _1463620)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1463622))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1463620), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1463622))))], (44004 ^ _777959) ^ [_1652839, _1652841, _1652843] : [hAPP(c_List_Ofilter(_1652839, _1652841), _1652843) = c_List_Olist_ONil(_1652839), 44007 ^ _777959 : [(44008 ^ _777959) ^ [_1652936] : [hBOOL(hAPP(hAPP(c_member(_1652839), _1652936), hAPP(c_List_Oset(_1652839), _1652843))), hBOOL(hAPP(_1652841, _1652936))]]], (1570 ^ _777959) ^ [_800308, _800310] : [-(class_Groups_Oab__semigroup__add(_800308)), _800310 = _800308, class_Groups_Oab__semigroup__add(_800310)], (5130 ^ _777959) ^ [_856401, _856403, _856405, _856407, _856409, _856411, _856413, _856415, _856417, _856419] : [-(c_New__DSequence_Oneg__map(_856419, _856415, _856411, _856407, _856403) = c_New__DSequence_Oneg__map(_856417, _856413, _856409, _856405, _856401)), _856419 = _856417, _856415 = _856413, _856411 = _856409, _856407 = _856405, _856403 = _856401], (33533 ^ _777959) ^ [_1409794, _1409796] : [class_Int_Onumber__ring(_1409794), class_Rings_Olinordered__idom(_1409794), 33540 ^ _777959 : [(33547 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409796), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409794), hAPP(c_Int_Onumber__class_Onumber__of(_1409794), _1409796)), c_Groups_Ozero__class_Ozero(_1409794))))], (33541 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409794), hAPP(c_Int_Onumber__class_Onumber__of(_1409794), _1409796)), c_Groups_Ozero__class_Ozero(_1409794))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409796), c_Int_OPls)))]]], (22184 ^ _777959) ^ [_1200072, _1200074, _1200076, _1200078, _1200080] : [class_Groups_Ocomm__monoid__add(_1200072), hBOOL(hAPP(c_Finite__Set_Ofinite(_1200074), _1200076)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1200074, _1200072), _1200078), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1200074, tc_HOL_Obool)), _1200076), _1200080)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1200074, _1200072), hAPP(hAPP(c_COMBC(_1200074, _1200072, _1200072), hAPP(hAPP(c_COMBS(_1200074, _1200072, tc_fun(_1200072, _1200072)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1200072, tc_fun(_1200072, _1200072)), _1200074), c_If(_1200072)), hAPP(hAPP(c_COMBC(_1200074, tc_fun(_1200074, tc_HOL_Obool), tc_HOL_Obool), c_member(_1200074)), _1200080))), _1200078)), c_Groups_Ozero__class_Ozero(_1200072))), _1200076))], (15648 ^ _777959) ^ [_1075789, _1075791, _1075793] : [class_Rings_Ocomm__semiring__1(_1075789), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075789), _1075791), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075789), _1075793), _1075791)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075789), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075789), _1075793), c_Groups_Oone__class_Oone(_1075789))), _1075791))], (34959 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (9568 ^ _777959) ^ [_943260, _943262, _943264] : [class_Lattices_Olattice(_943260), hBOOL(hAPP(c_Finite__Set_Ofinite(_943260), _943262)), hBOOL(hAPP(c_Finite__Set_Ofinite(_943260), _943264)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943260, tc_HOL_Obool)), _943262), _943264) = c_Orderings_Obot__class_Obot(tc_fun(_943260, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_943260), c_Big__Operators_Olattice__class_OSup__fin(_943260, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_943260, tc_HOL_Obool)), _943262), _943264))), c_Big__Operators_Olattice__class_OSup__fin(_943260, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943260, tc_HOL_Obool)), _943262), _943264))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_943260), c_Big__Operators_Olattice__class_OSup__fin(_943260, _943262)), c_Big__Operators_Olattice__class_OSup__fin(_943260, _943264)))], (41395 ^ _777959) ^ [_1589091, _1589093, _1589095, _1589097, _1589099, _1589101] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1589091), tc_List_Olist(_1589091))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1589091), tc_List_Olist(_1589091)), hAPP(hAPP(c_List_Olist_OCons(_1589091), _1589093), _1589095)), hAPP(hAPP(c_List_Olist_OCons(_1589091), _1589097), _1589099))), c_List_Olex(_1589091, _1589101)))), 41396 ^ _777959 : [(41403 ^ _777959) ^ [] : [_1589093 = _1589097, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1589091), tc_List_Olist(_1589091))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1589091), tc_List_Olist(_1589091)), _1589095), _1589099)), c_List_Olex(_1589091, _1589101)))], (41397 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589091, _1589091)), hAPP(hAPP(c_Product__Type_OPair(_1589091, _1589091), _1589093), _1589097)), _1589101)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1589091)), _1589095) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1589091)), _1589099)]]], (34765 ^ _777959) ^ [_1431928, _1431930, _1431932] : [class_Rings_Olinordered__idom(_1431928), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1431928), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1431928), hAPP(hAPP(c_Power_Opower__class_Opower(_1431928), _1431930), 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(_1431928), _1431932), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1431928)))], (1850 ^ _777959) ^ [_803804, _803806, _803808, _803810, _803812, _803814] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_803812, _803808, _803804)), c_Hoare__Mirabelle_Ohoare__derivs(_803814, _803810, _803806), _803814 = _803812, _803810 = _803808, _803806 = _803804], (51282 ^ _777959) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (12056 ^ _777959) ^ [_996630, _996632, _996634] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996630), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996632), _996634)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996632), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996630), _996634)))], (37241 ^ _777959) ^ [_1487973, _1487975] : [-(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), _1487973), _1487975)), 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), _1487975), _1487973)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (41467 ^ _777959) ^ [_1590894, _1590896, _1590898, _1590900] : [_1590894 = _1590896, -(hAPP(c_List_OremoveAll(_1590898, _1590894), hAPP(hAPP(c_List_Olist_OCons(_1590898), _1590896), _1590900)) = hAPP(c_List_OremoveAll(_1590898, _1590894), _1590900))], (44025 ^ _777959) ^ [_1653244, _1653246, _1653248, _1653250, _1653252] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653244)), hAPP(c_List_Ofilter(_1653244, _1653246), hAPP(hAPP(c_List_Omap(_1653248, _1653244), _1653250), _1653252))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653248)), hAPP(c_List_Ofilter(_1653248, hAPP(c_Fun_Ocomp(_1653244, tc_HOL_Obool, _1653248, _1653246), _1653250)), _1653252)))], (34321 ^ _777959) ^ [_1424004] : [-(c_Int_Osucc(c_Int_OBit1(_1424004)) = c_Int_OBit0(c_Int_Osucc(_1424004)))], (43290 ^ _777959) ^ [_1637765, _1637767, _1637769] : [-(hAPP(hAPP(c_List_Odrop(_1637765), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1637765), _1637767), _1637769)) = _1637769)], (17995 ^ _777959) ^ [_1121693, _1121695, _1121697] : [class_Orderings_Olinorder(_1121693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1121693), _1121695)), -(_1121695 = c_Orderings_Obot__class_Obot(tc_fun(_1121693, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1121693), _1121697)), -(_1121697 = c_Orderings_Obot__class_Obot(tc_fun(_1121693, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1121693, c_Orderings_Oord__class_Omax(_1121693), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1121693, tc_HOL_Obool)), _1121695), _1121697)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1121693), c_Big__Operators_Olattice_OSup__fin(_1121693, c_Orderings_Oord__class_Omax(_1121693), _1121695)), c_Big__Operators_Olattice_OSup__fin(_1121693, c_Orderings_Oord__class_Omax(_1121693), _1121697)))], (30381 ^ _777959) ^ [_1352373, _1352375, _1352377, _1352379] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352373)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352375)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1352375), _1352377)), -(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), _1352377), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1352379, _1352373))), _1352375)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1352377), _1352373))))], (37359 ^ _777959) ^ [_1491138, _1491140, _1491142, _1491144] : [hBOOL(hAPP(hAPP(c_member(_1491138), _1491140), _1491142)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1491138, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1491138, _1491138, _1491144), hAPP(hAPP(c_Set_Oinsert(_1491138), _1491140), c_Orderings_Obot__class_Obot(tc_fun(_1491138, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1491138), _1491142), _1491144))))], (34219 ^ _777959) ^ [_1422240, _1422242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1422240), _1422242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1422240)), c_Int_OBit1(_1422242))))], (552 ^ _777959) ^ [_786481, _786483, _786485, _786487, _786489, _786491] : [-(c_Enum_Oex__n__lists(_786489, _786485, _786481)), c_Enum_Oex__n__lists(_786491, _786487, _786483), _786491 = _786489, _786487 = _786485, _786483 = _786481], (43260 ^ _777959) ^ [_1636996, _1636998, _1637000] : [-(c_List_Obutlast(_1636996, hAPP(hAPP(c_List_Odrop(_1636996), _1636998), _1637000)) = hAPP(hAPP(c_List_Odrop(_1636996), _1636998), c_List_Obutlast(_1636996, _1637000)))], (43488 ^ _777959) ^ [_1642342, _1642344] : [-(_1642342 = c_List_Olist_ONil(_1642344)), -(hAPP(c_List_Orotate1(_1642344), _1642342) = hAPP(hAPP(c_List_Oappend(_1642344), hAPP(c_List_Otl(_1642344), _1642342)), hAPP(hAPP(c_List_Olist_OCons(_1642344), hAPP(c_List_Ohd(_1642344), _1642342)), c_List_Olist_ONil(_1642344))))], (32403 ^ _777959) ^ [_1389779, _1389781, _1389783, _1389785] : [class_Fields_Olinordered__field__inverse__zero(_1389779), class_Int_Onumber(_1389779), 32410 ^ _777959 : [(32411 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), hAPP(c_Int_Onumber__class_Onumber__of(_1389779), _1389781)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1389779), _1389783), _1389785))), 32414 ^ _777959 : [(32421 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), c_Groups_Ozero__class_Ozero(_1389779)), _1389785))), 32424 ^ _777959 : [(32431 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), _1389785), c_Groups_Ozero__class_Ozero(_1389779)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), hAPP(c_Int_Onumber__class_Onumber__of(_1389779), _1389781)), c_Groups_Ozero__class_Ozero(_1389779))))], (32425 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), _1389785), c_Groups_Ozero__class_Ozero(_1389779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), _1389783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389779), hAPP(c_Int_Onumber__class_Onumber__of(_1389779), _1389781)), _1389785))))]]], (32415 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), c_Groups_Ozero__class_Ozero(_1389779)), _1389785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389779), hAPP(c_Int_Onumber__class_Onumber__of(_1389779), _1389781)), _1389785)), _1389783)))]]], (32437 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), hAPP(c_Int_Onumber__class_Onumber__of(_1389779), _1389781)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1389779), _1389783), _1389785)))), 32440 ^ _777959 : [(32443 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389779), hAPP(c_Int_Onumber__class_Onumber__of(_1389779), _1389781)), _1389785)), _1389783))], (32441 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), c_Groups_Ozero__class_Ozero(_1389779)), _1389785)))]], 32444 ^ _777959 : [(32447 ^ _777959) ^ [] : [32448 ^ _777959 : [(32451 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), _1389783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389779), hAPP(c_Int_Onumber__class_Onumber__of(_1389779), _1389781)), _1389785)))], (32449 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), _1389785), c_Groups_Ozero__class_Ozero(_1389779))))]], 32452 ^ _777959 : [(32455 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), hAPP(c_Int_Onumber__class_Onumber__of(_1389779), _1389781)), c_Groups_Ozero__class_Ozero(_1389779)))], (32453 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), _1389785), c_Groups_Ozero__class_Ozero(_1389779)))]]], (32445 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1389779), c_Groups_Ozero__class_Ozero(_1389779)), _1389785))]]]]], (17869 ^ _777959) ^ [_1119516, _1119518, _1119520, _1119522] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1119516, _1119518, hAPP(hAPP(c_Set_Oinsert(_1119516), _1119520), c_Orderings_Obot__class_Obot(tc_fun(_1119516, tc_HOL_Obool)))), _1119522)), -(_1119520 = _1119522)], (19953 ^ _777959) ^ [_1158940, _1158942, _1158944, _1158946] : [class_Rings_Oordered__ring(_1158940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158940), _1158942), _1158944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158940), _1158946), c_Groups_Ozero__class_Ozero(_1158940))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158940), _1158944), _1158946)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158940), _1158942), _1158946))))], (26362 ^ _777959) ^ [_1277638, _1277640, _1277642, _1277644] : [class_Fields_Ofield__inverse__zero(_1277638), -(_1277640 = c_Groups_Ozero__class_Ozero(_1277638)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277638), _1277640), _1277642)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277638), _1277640), _1277644)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277638), _1277642), _1277644))], (25702 ^ _777959) ^ [_1265428, _1265430] : [class_Rings_Odivision__ring(_1265428), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265428), _1265430), c_Groups_Oone__class_Oone(_1265428)) = _1265430)], (10138 ^ _777959) ^ [_955284, _955286, _955288, _955290, _955292] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_955284, _955286, _955288), _955290), _955292), c_Orderings_Obot__class_Obot(tc_fun(_955286, tc_HOL_Obool))) = _955292)], (24147 ^ _777959) ^ [_1236996, _1236998, _1237000] : [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), _1236996), _1236998)), _1237000)), 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)), _1237000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1236996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1236998), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (3906 ^ _777959) ^ [_837129, _837131, _837133, _837135] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_837135, _837131) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_837133, _837129)), _837135 = _837133, _837131 = _837129], (43346 ^ _777959) ^ [_1639118, _1639120, _1639122, _1639124] : [-(_1639118 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1639120), _1639118), hAPP(hAPP(c_List_Olist_OCons(_1639120), _1639122), _1639124)) = hAPP(hAPP(c_List_Odrop(_1639120), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1639118), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1639124))], (35950 ^ _777959) ^ [_1460060, _1460062] : [c_Nitpick_Orefl_H(_1460060, _1460062), 35953 ^ _777959 : [(35954 ^ _777959) ^ [_1460138] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1460060, _1460060)), hAPP(hAPP(c_Product__Type_OPair(_1460060, _1460060), _1460138), _1460138)), _1460062)))]]], (13543 ^ _777959) ^ [_1026406, _1026408, _1026410, _1026412, _1026414] : [_1026406 = c_Orderings_Obot__class_Obot(tc_fun(_1026408, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026408, tc_fun(_1026410, tc_HOL_Obool)), _1026406), hAPP(hAPP(c_COMBB(tc_fun(_1026410, tc_HOL_Obool), tc_fun(_1026410, tc_HOL_Obool), _1026408), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026410, tc_HOL_Obool)), _1026412)), _1026414)) = c_Orderings_Otop__class_Otop(tc_fun(_1026410, tc_HOL_Obool)))], (23351 ^ _777959) ^ [_1222789] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1222789), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1222789)], (3458 ^ _777959) ^ [_830129, _830131, _830133, _830135, _830137, _830139] : [-(c_Enum_On__lists(_830139, _830135, _830131) = c_Enum_On__lists(_830137, _830133, _830129)), _830139 = _830137, _830135 = _830133, _830131 = _830129], (35373 ^ _777959) ^ [_1446256, _1446258, _1446260, _1446262] : [hAPP(hAPP(c_COMBC(_1446256, tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_fun(_1446258, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446258, tc_fun(tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_fun(_1446258, tc_HOL_Obool)), _1446256), c_COMBC(_1446258, tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446258, tc_prod(_1446256, _1446258)), tc_fun(_1446258, tc_fun(tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_HOL_Obool)), _1446256), hAPP(c_COMBB(tc_prod(_1446256, _1446258), tc_fun(tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_HOL_Obool), _1446258), c_member(tc_prod(_1446256, _1446258)))), c_Product__Type_OPair(_1446256, _1446258)))), _1446260) = hAPP(hAPP(c_COMBC(_1446256, tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_fun(_1446258, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446258, tc_fun(tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_fun(_1446258, tc_HOL_Obool)), _1446256), c_COMBC(_1446258, tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1446258, tc_prod(_1446256, _1446258)), tc_fun(_1446258, tc_fun(tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_HOL_Obool)), _1446256), hAPP(c_COMBB(tc_prod(_1446256, _1446258), tc_fun(tc_fun(tc_prod(_1446256, _1446258), tc_HOL_Obool), tc_HOL_Obool), _1446258), c_member(tc_prod(_1446256, _1446258)))), c_Product__Type_OPair(_1446256, _1446258)))), _1446262), -(_1446260 = _1446262)], (50528 ^ _777959) ^ [_1803171, _1803173, _1803175] : [-(_1803171 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1803173, c_List_Oreplicate(_1803173, _1803171, _1803175)) = _1803175)], (11764 ^ _777959) ^ [_990319, _990321, _990323, _990325, _990327] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990319, tc_HOL_Obool)), _990321), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990323, tc_fun(_990319, tc_HOL_Obool)), _990325), _990327)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990323, tc_fun(_990319, tc_HOL_Obool)), _990325), hAPP(hAPP(c_COMBB(tc_fun(_990319, tc_HOL_Obool), tc_fun(_990319, tc_HOL_Obool), _990323), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990319, tc_HOL_Obool)), _990321)), _990327)))], (28059 ^ _777959) ^ [_1307373] : [-(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)), _1307373)))], (44995 ^ _777959) ^ [_1673445, _1673447, _1673449] : [44997 ^ _777959 : [(45000 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1673445), tc_List_Olist(_1673445), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1673445), tc_fun(tc_List_Olist(_1673445), tc_Nat_Onat), tc_fun(tc_List_Olist(_1673445), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1673445), tc_Nat_Onat), tc_fun(tc_List_Olist(_1673445), tc_HOL_Obool)), tc_List_Olist(_1673445)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1673445))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1673445)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1673445))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1673445)))), 44996 ^ [_1673445, _1673447, _1673449]))], (44998 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1673445), tc_List_Olist(_1673445))), 44996 ^ [_1673445, _1673447, _1673449]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1673445), tc_List_Olist(_1673445))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1673445), tc_List_Olist(_1673445)), _1673447), _1673449)))))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1673445))), _1673447) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1673445))), _1673449), 45005 ^ _777959 : [(45012 ^ _777959) ^ [] : [_1673447 = _1673449, -(c_List_Oconcat(_1673445, _1673447) = c_List_Oconcat(_1673445, _1673449))], (45006 ^ _777959) ^ [] : [c_List_Oconcat(_1673445, _1673447) = c_List_Oconcat(_1673445, _1673449), -(_1673447 = _1673449)]]], (21350 ^ _777959) ^ [_1183670, _1183672, _1183674, _1183676] : [class_Rings_Olinordered__semiring(_1183670), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183670), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183670), _1183672), _1183674)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183670), _1183676), _1183674))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183670), c_Groups_Ozero__class_Ozero(_1183670)), _1183674)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183670), _1183672), _1183676)))], (14956 ^ _777959) ^ [_1062217, _1062219, _1062221] : [-(c_Smallcheck_Oorelse(_1062217, _1062219, _1062221) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1062217), _1062217, _1062221, c_Option_Ooption_OSome(_1062217)), _1062219))], (47841 ^ _777959) ^ [_1740835, _1740837, _1740839] : [47843 ^ _777959 : [(47846 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1740835), 47842 ^ [_1740835, _1740837, _1740839]), c_Wellfounded_Oacc(_1740835, _1740839)))], (47844 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1740835, _1740835)), hAPP(hAPP(c_Product__Type_OPair(_1740835, _1740835), 47842 ^ [_1740835, _1740837, _1740839]), _1740837)), _1740839)))]], -(hBOOL(hAPP(hAPP(c_member(_1740835), _1740837), c_Wellfounded_Oacc(_1740835, _1740839))))], (51312 ^ _777959) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (51238 ^ _777959) ^ [_1812489, _1812491] : [-(class_HOL_Oequal(tc_prod(_1812489, _1812491)))], (10484 ^ _777959) ^ [_963291, _963293, _963295, _963297, _963299] : [c_Finite__Set_Ofolding__one(_963291, _963293, _963295), hBOOL(hAPP(c_Finite__Set_Ofinite(_963291), _963297)), hBOOL(hAPP(c_Finite__Set_Ofinite(_963291), _963299)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963291, tc_HOL_Obool)), _963297), _963299) = c_Orderings_Obot__class_Obot(tc_fun(_963291, tc_HOL_Obool))), -(hAPP(hAPP(_963293, hAPP(_963295, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963291, tc_HOL_Obool)), _963297), _963299))), hAPP(_963295, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963291, tc_HOL_Obool)), _963297), _963299))) = hAPP(hAPP(_963293, hAPP(_963295, _963297)), hAPP(_963295, _963299)))], (38922 ^ _777959) ^ [_1526094, _1526096, _1526098, _1526100] : [hAPP(c_List_Oset(_1526094), _1526096) = c_Map_Odom(_1526094, _1526098, _1526100), -(hAPP(c_Map_Omap__of(_1526094, _1526098), hAPP(hAPP(c_List_Omap(_1526094, tc_prod(_1526094, _1526098)), hAPP(hAPP(c_COMBS(_1526094, _1526098, tc_prod(_1526094, _1526098)), c_Product__Type_OPair(_1526094, _1526098)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1526098), _1526098, _1526094), c_Option_Othe(_1526098)), _1526100))), _1526096)) = _1526100)], (48725 ^ _777959) ^ [_1760538, _1760540] : [-(c_Transitive__Closure_Ortrancl(_1760538, c_Transitive__Closure_Ortrancl(_1760538, _1760540)) = c_Transitive__Closure_Ortrancl(_1760538, _1760540))], (17219 ^ _777959) ^ [_1107234] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1107234, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1107234, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1107234, tc_HOL_Obool)))], (46992 ^ _777959) ^ [_1720148, _1720150, _1720152, _1720154, _1720156, _1720158, _1720160] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1720148, _1720150, _1720152, _1720154, _1720156), _1720158), _1720160)), 46996 ^ _777959 : [(46999 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1720156, 46995 ^ [_1720148, _1720150, _1720152, _1720154, _1720156, _1720158, _1720160]), _1720160)))], (46997 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1720154, _1720158), 46995 ^ [_1720148, _1720150, _1720152, _1720154, _1720156, _1720158, _1720160])))]]], (44300 ^ _777959) ^ [_1659006, _1659008, _1659010] : [class_Orderings_Olinorder(_1659006), 44303 ^ _777959 : [(44310 ^ _777959) ^ [] : [c_List_Olinorder__class_Osorted(_1659006, _1659010), -(c_List_Olinorder__class_Osorted(_1659006, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659006, _1659006, c_COMBI(_1659006)), _1659008), _1659010)))], (44304 ^ _777959) ^ [] : [c_List_Olinorder__class_Osorted(_1659006, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1659006, _1659006, c_COMBI(_1659006)), _1659008), _1659010)), -(c_List_Olinorder__class_Osorted(_1659006, _1659010))]]], (4316 ^ _777959) ^ [_843296, _843298, _843300, _843302, _843304, _843306] : [-(c_Nitpick_Otimes__frac(_843306, _843302, _843298) = c_Nitpick_Otimes__frac(_843304, _843300, _843296)), _843306 = _843304, _843302 = _843300, _843298 = _843296], (24766 ^ _777959) ^ [_1247586, _1247588, _1247590] : [class_Orderings_Oorder(_1247586), 24769 ^ _777959 : [(24776 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247586), _1247588), _1247590))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1247586, _1247588), _1247590) = c_Orderings_Obot__class_Obot(tc_fun(_1247586, tc_HOL_Obool)))], (24770 ^ _777959) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1247586, _1247588), _1247590) = c_Orderings_Obot__class_Obot(tc_fun(_1247586, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1247586), _1247588), _1247590))]]], (15144 ^ _777959) ^ [_1066331, _1066333, _1066335, _1066337] : [class_Rings_Ocomm__semiring(_1066331), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066331), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066331), _1066333), _1066335)), _1066337) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066331), _1066333), _1066337)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066331), _1066335), _1066337)))], (7046 ^ _777959) ^ [_895228, _895230, _895232, _895234, _895236] : [class_Lattices_Olattice(_895228), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895230, _895228)), _895232), _895234), _895236) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_895228), hAPP(_895232, _895236)), hAPP(_895234, _895236)))], (26980 ^ _777959) ^ [_1288870, _1288872, _1288874, _1288876] : [class_Fields_Olinordered__field__inverse__zero(_1288870), 26983 ^ _777959 : [(26984 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288870), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288870), _1288872), _1288874)), _1288876)), 26987 ^ _777959 : [(26994 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288870), c_Groups_Ozero__class_Ozero(_1288870)), _1288874))), 26997 ^ _777959 : [(27004 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288870), _1288874), c_Groups_Ozero__class_Ozero(_1288870)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288870), c_Groups_Ozero__class_Ozero(_1288870)), _1288876)))], (26998 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288870), _1288874), c_Groups_Ozero__class_Ozero(_1288870))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288870), _1288876), _1288874)), _1288872)))]]], (26988 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288870), c_Groups_Ozero__class_Ozero(_1288870)), _1288874)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288870), _1288872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288870), _1288876), _1288874))))]]], (27010 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288870), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1288870), _1288872), _1288874)), _1288876))), 27013 ^ _777959 : [(27016 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288870), _1288872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288870), _1288876), _1288874)))], (27014 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288870), c_Groups_Ozero__class_Ozero(_1288870)), _1288874)))]], 27017 ^ _777959 : [(27020 ^ _777959) ^ [] : [27021 ^ _777959 : [(27024 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1288870), _1288876), _1288874)), _1288872))], (27022 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288870), _1288874), c_Groups_Ozero__class_Ozero(_1288870))))]], 27025 ^ _777959 : [(27028 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288870), c_Groups_Ozero__class_Ozero(_1288870)), _1288876))], (27026 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288870), _1288874), c_Groups_Ozero__class_Ozero(_1288870)))]]], (27018 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1288870), c_Groups_Ozero__class_Ozero(_1288870)), _1288874))]]]]], (14115 ^ _777959) ^ [_1040426, _1040428, _1040430, _1040432, _1040434, _1040436] : [-(hAPP(c_Map_Omap__add(_1040426, _1040428, _1040430, _1040432), _1040434) = hAPP(c_Option_Ooption_OSome(_1040428), _1040436)), 14116 ^ _777959 : [(14119 ^ _777959) ^ [] : [hAPP(_1040432, _1040434) = c_Option_Ooption_ONone(_1040428), hAPP(_1040430, _1040434) = hAPP(c_Option_Ooption_OSome(_1040428), _1040436)], (14117 ^ _777959) ^ [] : [hAPP(_1040432, _1040434) = hAPP(c_Option_Ooption_OSome(_1040428), _1040436)]]], (39264 ^ _777959) ^ [_1534792, _1534794, _1534796, _1534798, _1534800] : [hAPP(hAPP(c_Map_Omap__of(_1534792, _1534794), _1534796), _1534798) = hAPP(c_Option_Ooption_OSome(_1534794), _1534800), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534792, _1534794)), hAPP(hAPP(c_Product__Type_OPair(_1534792, _1534794), _1534798), _1534800)), hAPP(c_List_Oset(tc_prod(_1534792, _1534794)), _1534796))))], (43151 ^ _777959) ^ [_1634363, _1634365, _1634367, _1634369] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634363), tc_List_Olist(_1634363))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634363), tc_List_Olist(_1634363)), _1634365), _1634367)), c_List_Olistrel1(_1634363, _1634369))), 43156 ^ _777959 : [(43163 ^ _777959) ^ [] : [-(_1634367 = hAPP(hAPP(c_List_Oappend(_1634363), 43158 ^ [_1634363, _1634365, _1634367, _1634369]), hAPP(hAPP(c_List_Olist_OCons(_1634363), 43155 ^ [_1634363, _1634365, _1634367, _1634369]), 43159 ^ [_1634363, _1634365, _1634367, _1634369])))], (43161 ^ _777959) ^ [] : [-(_1634365 = hAPP(hAPP(c_List_Oappend(_1634363), 43158 ^ [_1634363, _1634365, _1634367, _1634369]), hAPP(hAPP(c_List_Olist_OCons(_1634363), 43154 ^ [_1634363, _1634365, _1634367, _1634369]), 43159 ^ [_1634363, _1634365, _1634367, _1634369])))], (43157 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634363, _1634363)), hAPP(hAPP(c_Product__Type_OPair(_1634363, _1634363), 43154 ^ [_1634363, _1634365, _1634367, _1634369]), 43155 ^ [_1634363, _1634365, _1634367, _1634369])), _1634369)))]]], (9692 ^ _777959) ^ [_945841, _945843, _945845, _945847] : [class_Lattices_Olattice(_945841), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945841), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945841), _945843), _945845)), _945847) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945841), _945843), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945841), _945845), _945847)))], (33423 ^ _777959) ^ [_1408065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1408065), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1408065)), c_Int_OPls)))], (42985 ^ _777959) ^ [_1629754, _1629756, _1629758, _1629760] : [-(hAPP(hAPP(c_List_Onth(_1629754), hAPP(hAPP(c_List_Oappend(_1629754), _1629756), hAPP(hAPP(c_List_Olist_OCons(_1629754), _1629758), _1629760))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629754)), _1629756)) = _1629758)], (18895 ^ _777959) ^ [_1140674, _1140676, _1140678] : [class_Groups_Oab__semigroup__mult(_1140674), hBOOL(hAPP(c_Finite__Set_Ofinite(_1140674), _1140676)), -(_1140676 = c_Orderings_Obot__class_Obot(tc_fun(_1140674, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1140674), _1140678)), -(_1140678 = c_Orderings_Obot__class_Obot(tc_fun(_1140674, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1140674, tc_HOL_Obool)), _1140676), _1140678) = c_Orderings_Obot__class_Obot(tc_fun(_1140674, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1140674, c_Groups_Otimes__class_Otimes(_1140674)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1140674, tc_HOL_Obool)), _1140676), _1140678)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140674), hAPP(c_Finite__Set_Ofold1(_1140674, c_Groups_Otimes__class_Otimes(_1140674)), _1140676)), hAPP(c_Finite__Set_Ofold1(_1140674, c_Groups_Otimes__class_Otimes(_1140674)), _1140678)))], (14233 ^ _777959) ^ [_1042943, _1042945, _1042947, _1042949] : [class_Rings_Ocomm__semiring__1(_1042943), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042943), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042943), _1042945), _1042947)), _1042949) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042943), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1042943), _1042945), _1042949)), _1042947))], (17261 ^ _777959) ^ [_1107987, _1107989, _1107991] : [class_Complete__Lattice_Ocomplete__lattice(_1107987), -(c_Complete__Lattice_OInf__class_OInf(_1107987, hAPP(hAPP(c_Set_Oinsert(_1107987), _1107989), _1107991)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1107987), _1107989), c_Complete__Lattice_OInf__class_OInf(_1107987, _1107991)))], (11762 ^ _777959) ^ [_990229, _990231, _990233, _990235, _990237] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990229, tc_HOL_Obool)), _990231), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990233, tc_fun(_990229, tc_HOL_Obool)), _990235), _990237)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990233, tc_fun(_990229, tc_HOL_Obool)), _990235), hAPP(hAPP(c_COMBB(tc_fun(_990229, tc_HOL_Obool), tc_fun(_990229, tc_HOL_Obool), _990233), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990229, tc_HOL_Obool)), _990231)), _990237)))], (8720 ^ _777959) ^ [_928434, _928436, _928438, _928440, _928442] : [-(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928434, _928436), _928438), _928440), _928442), _928440) = _928442)], (18524 ^ _777959) ^ [_1133956, _1133958, _1133960, _1133962, _1133964] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1133956, _1133958, hAPP(hAPP(c_Set_Oinsert(_1133956), _1133960), _1133962)), _1133964)), 18529 ^ _777959 : [(18534 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1133956), 18527 ^ [_1133956, _1133958, _1133960, _1133962, _1133964]), 18528 ^ [_1133956, _1133958, _1133960, _1133962, _1133964]))], (18532 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1133956, _1133956, _1133958, 18527 ^ [_1133956, _1133958, _1133960, _1133962, _1133964], 18528 ^ [_1133956, _1133958, _1133960, _1133962, _1133964]), _1133964)))], (18530 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1133956), _1133960), _1133962) = hAPP(hAPP(c_Set_Oinsert(_1133956), 18527 ^ [_1133956, _1133958, _1133960, _1133962, _1133964]), 18528 ^ [_1133956, _1133958, _1133960, _1133962, _1133964]))]]], (17277 ^ _777959) ^ [_1108331, _1108333, _1108335, _1108337] : [class_Orderings_Olinorder(_1108331), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108331), _1108333)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1108331, _1108331, c_Orderings_Oord__class_Omin(_1108331)), _1108335), hAPP(hAPP(c_Set_Oinsert(_1108331), _1108337), _1108333)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1108331), _1108337), hAPP(hAPP(c_Finite__Set_Ofold(_1108331, _1108331, c_Orderings_Oord__class_Omin(_1108331)), _1108335), _1108333)))], (6022 ^ _777959) ^ [_874166, _874168, _874170, _874172] : [hBOOL(hAPP(hAPP(c_member(_874166), _874168), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_874166, tc_HOL_Obool)), _874170), _874172))), -(hBOOL(hAPP(hAPP(c_member(_874166), _874168), _874170))), -(hBOOL(hAPP(hAPP(c_member(_874166), _874168), _874172)))], (11563 ^ _777959) ^ [_984664, _984666, _984668, _984670, _984672] : [_984664 = c_Orderings_Obot__class_Obot(tc_fun(_984666, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_984666, tc_fun(_984668, tc_HOL_Obool)), _984664), hAPP(hAPP(c_COMBC(_984666, tc_fun(_984668, tc_HOL_Obool), tc_fun(_984668, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_984668, tc_HOL_Obool), tc_fun(tc_fun(_984668, tc_HOL_Obool), tc_fun(_984668, tc_HOL_Obool)), _984666), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984668, tc_HOL_Obool))), _984670)), _984672)) = c_Orderings_Obot__class_Obot(tc_fun(_984668, tc_HOL_Obool)))], (37253 ^ _777959) ^ [_1488311, _1488313, _1488315, _1488317] : [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), _1488311), _1488313)), 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), _1488315), _1488317)), 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), _1488311), _1488317)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1488315), _1488313))))], (17863 ^ _777959) ^ [_1119382, _1119384] : [class_Orderings_Olinorder(_1119382), -(c_Big__Operators_Olattice_OSup__fin(_1119382, c_Orderings_Oord__class_Omax(_1119382), hAPP(hAPP(c_Set_Oinsert(_1119382), _1119384), c_Orderings_Obot__class_Obot(tc_fun(_1119382, tc_HOL_Obool)))) = _1119384)], (10268 ^ _777959) ^ [_958510, _958512, _958514] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958510, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958510, tc_HOL_Obool)), _958512), _958514)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958510, tc_HOL_Obool)), _958512), _958514)) = _958512)], (38936 ^ _777959) ^ [_1526791, _1526793, _1526795] : [hBOOL(hAPP(hAPP(c_member(_1526791), _1526795), c_Wellfounded_Oacc(_1526791, _1526793))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1526791, hAPP(hAPP(c_COMBC(_1526791, tc_fun(tc_prod(_1526791, _1526791), tc_HOL_Obool), tc_fun(_1526791, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526791, tc_fun(tc_fun(tc_prod(_1526791, _1526791), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1526791, _1526791), tc_HOL_Obool), tc_fun(_1526791, tc_HOL_Obool)), _1526791), c_COMBC(_1526791, tc_fun(tc_prod(_1526791, _1526791), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1526791, tc_prod(_1526791, _1526791)), tc_fun(_1526791, tc_fun(tc_fun(tc_prod(_1526791, _1526791), tc_HOL_Obool), tc_HOL_Obool)), _1526791), hAPP(c_COMBB(tc_prod(_1526791, _1526791), tc_fun(tc_fun(tc_prod(_1526791, _1526791), tc_HOL_Obool), tc_HOL_Obool), _1526791), c_member(tc_prod(_1526791, _1526791)))), c_Product__Type_OPair(_1526791, _1526791)))), _1526793)), _1526795)))], (39934 ^ _777959) ^ [_1551123, _1551125, _1551127] : [-(hBOOL(hAPP(hAPP(c_member(_1551123), _1551125), hAPP(c_List_Oset(_1551123), _1551127)))), -(hAPP(c_List_OremoveAll(_1551123, _1551125), _1551127) = _1551127)], (44945 ^ _777959) ^ [_1672082, _1672084, _1672086, _1672088] : [-(hAPP(hAPP(c_List_Omap(_1672082, _1672084), _1672086), c_List_Oconcat(_1672082, _1672088)) = c_List_Oconcat(_1672084, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1672082), tc_List_Olist(_1672084)), hAPP(c_List_Omap(_1672082, _1672084), _1672086)), _1672088)))], (29908 ^ _777959) ^ [_1343356] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1343356) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (50 ^ _777959) ^ [_778764, _778766, _778768, _778770, _778772, _778774, _778776, _778778, _778780, _778782, _778784, _778786] : [-(c_Nitpick_Ofold__graph_H(_778784, _778780, _778776, _778772, _778768, _778764)), c_Nitpick_Ofold__graph_H(_778786, _778782, _778778, _778774, _778770, _778766), _778786 = _778784, _778782 = _778780, _778778 = _778776, _778774 = _778772, _778770 = _778768, _778766 = _778764], (24588 ^ _777959) ^ [_1244764, _1244766, _1244768, _1244770, _1244772] : [class_Orderings_Olinorder(_1244764), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244764), _1244766), _1244768)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1244764), _1244770), _1244772)), 24599 ^ _777959 : [(24608 ^ _777959) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244764, _1244766), _1244768) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244764, _1244770), _1244772)), _1244766 = _1244770, _1244768 = _1244772], (24600 ^ _777959) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244764, _1244766), _1244768) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1244764, _1244770), _1244772), 24603 ^ _777959 : [(24606 ^ _777959) ^ [] : [-(_1244768 = _1244772)], (24604 ^ _777959) ^ [] : [-(_1244766 = _1244770)]]]]], (46692 ^ _777959) ^ [_1711374, _1711376, _1711378, _1711380, _1711382] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1711374, _1711374)), hAPP(hAPP(c_Product__Type_OPair(_1711374, _1711374), _1711376), _1711378)), c_List_Omeasures(_1711374, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1711374, tc_Nat_Onat)), _1711380), _1711382))))), 46693 ^ _777959 : [(46696 ^ _777959) ^ [] : [hAPP(_1711380, _1711376) = hAPP(_1711380, _1711378), hBOOL(hAPP(hAPP(c_member(tc_prod(_1711374, _1711374)), hAPP(hAPP(c_Product__Type_OPair(_1711374, _1711374), _1711376), _1711378)), c_List_Omeasures(_1711374, _1711382)))], (46694 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1711380, _1711376)), hAPP(_1711380, _1711378)))]]], (47425 ^ _777959) ^ [_1731092, _1731094] : [c_Wellfounded_OwfP(_1731092, _1731094), -(c_Wellfounded_Owf(_1731092, hAPP(c_Set_OCollect(tc_prod(_1731092, _1731092)), hAPP(c_Product__Type_Oprod_Oprod__case(_1731092, _1731092, tc_HOL_Obool), _1731094))))], (45350 ^ _777959) ^ [_1681764, _1681766, _1681768] : [hBOOL(hAPP(hAPP(c_member(_1681764), _1681766), hAPP(c_List_Oset(_1681764), _1681768))), -(c_List_Oremdups(_1681764, hAPP(hAPP(c_List_Olist_OCons(_1681764), _1681766), _1681768)) = c_List_Oremdups(_1681764, _1681768))], (16747 ^ _777959) ^ [_1098768, _1098770, _1098772, _1098774] : [class_Orderings_Olinorder(_1098768), 16750 ^ _777959 : [(16751 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098768), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1098768), _1098770), _1098772)), _1098774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098768), _1098770), _1098774))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098768), _1098772), _1098774)))], (16761 ^ _777959) ^ [] : [16762 ^ _777959 : [(16765 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098768), _1098772), _1098774))], (16763 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098768), _1098770), _1098774))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098768), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1098768), _1098770), _1098772)), _1098774)))]]], (25868 ^ _777959) ^ [_1268267, _1268269, _1268271] : [class_Rings_Odivision__ring(_1268267), -(_1268269 = c_Groups_Ozero__class_Ozero(_1268267)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1268267), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268267), _1268271), _1268269)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268267), _1268271), hAPP(c_Groups_Ouminus__class_Ouminus(_1268267), _1268269)))], (3996 ^ _777959) ^ [_838478, _838480, _838482, _838484, _838486, _838488, _838490, _838492] : [-(c_Product__Type_Oscomp(_838492, _838488, _838484, _838480) = c_Product__Type_Oscomp(_838490, _838486, _838482, _838478)), _838492 = _838490, _838488 = _838486, _838484 = _838482, _838480 = _838478], (17747 ^ _777959) ^ [_1116957] : [class_Orderings_Olinorder(_1116957), -(c_Orderings_Oord_Omax(_1116957, hAPP(c_COMBC(_1116957, _1116957, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1116957))) = c_Orderings_Oord__class_Omin(_1116957))], (10270 ^ _777959) ^ [_958570, _958572, _958574, _958576] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958570, tc_HOL_Obool)), _958572), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958570, tc_HOL_Obool)), _958574), _958576)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958570, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958570, tc_HOL_Obool)), _958572), _958574)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_958570, tc_HOL_Obool)), _958572), _958576)))], (5940 ^ _777959) ^ [_872659, _872661, _872663, _872665, _872667] : [hBOOL(hAPP(hAPP(c_member(_872659), _872661), _872663)), -(hAPP(c_Set_Oimage(_872659, _872665, hAPP(c_COMBK(_872665, _872659), _872667)), _872663) = hAPP(hAPP(c_Set_Oinsert(_872665), _872667), c_Orderings_Obot__class_Obot(tc_fun(_872665, tc_HOL_Obool))))], (36051 ^ _777959) ^ [_1461747, _1461749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461747)), 36054 ^ _777959 : [(36061 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461749))), 36064 ^ _777959 : [(36071 ^ _777959) ^ [] : [-(_1461747 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1461747, _1461749) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1461747), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1461749))))], (36065 ^ _777959) ^ [] : [_1461747 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1461747, _1461749) = 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)))]]], (36055 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461749)), -(c_Divides_Odivmod__int(_1461747, _1461749) = c_Divides_OposDivAlg(_1461747, _1461749))]]], (51454 ^ _777959) ^ [_1814934, _1814936] : [hBOOL(hAPP(hAPP(c_fimplies, _1814934), _1814936)), hBOOL(_1814934), -(hBOOL(_1814936))], (50703 ^ _777959) ^ [_1806377, _1806379, _1806381, _1806383, _1806385] : [50705 ^ _777959 : [(50708 ^ _777959) ^ [] : [c_Relation_Orefl__on(_1806381, hAPP(_1806383, 50704 ^ [_1806377, _1806379, _1806381, _1806383, _1806385]), hAPP(_1806385, 50704 ^ [_1806377, _1806379, _1806381, _1806383, _1806385]))], (50706 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806377), 50704 ^ [_1806377, _1806379, _1806381, _1806383, _1806385]), _1806379)))]], -(c_Relation_Orefl__on(_1806381, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1806377, tc_fun(_1806381, tc_HOL_Obool)), _1806379), _1806383), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1806377, tc_fun(tc_prod(_1806381, _1806381), tc_HOL_Obool)), _1806379), _1806385)))], (26254 ^ _777959) ^ [_1275631, _1275633, _1275635] : [class_Fields_Olinordered__field(_1275631), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275631), c_Groups_Ozero__class_Ozero(_1275631)), _1275633)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275631), c_Groups_Ozero__class_Ozero(_1275631)), _1275635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275631), c_Groups_Ozero__class_Ozero(_1275631)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275631), _1275633), _1275635))))], (45598 ^ _777959) ^ [_1687906, _1687908, _1687910, _1687912, _1687914] : [-(c_Enum_Oproduct(_1687906, _1687908, hAPP(hAPP(c_List_Olist_OCons(_1687906), _1687910), _1687912), _1687914) = hAPP(hAPP(c_List_Oappend(tc_prod(_1687906, _1687908)), hAPP(hAPP(c_List_Omap(_1687908, tc_prod(_1687906, _1687908)), hAPP(c_Product__Type_OPair(_1687906, _1687908), _1687910)), _1687914)), c_Enum_Oproduct(_1687906, _1687908, _1687912, _1687914)))], (35649 ^ _777959) ^ [_1453634] : [-(c_Divides_Oadjust(_1453634) = 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)), _1453634))))), 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)), _1453634))))), 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))))))))], (32945 ^ _777959) ^ [_1400261, _1400263] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1400261)), c_Int_OBit1(_1400263))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1400261), _1400263)))], (452 ^ _777959) ^ [_784987, _784989, _784991, _784993, _784995, _784997, _784999, _785001] : [-(c_List_Olistrelp(_784999, _784995, _784991, _784987)), c_List_Olistrelp(_785001, _784997, _784993, _784989), _785001 = _784999, _784997 = _784995, _784993 = _784991, _784989 = _784987], (7730 ^ _777959) ^ [_908956, _908958, _908960, _908962, _908964, _908966, _908968] : [c_Hoare__Mirabelle_Ohoare__derivs(_908956, _908958, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_908956)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_908956), _908960), _908962), _908964)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_908956), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_908956, _908958, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_908956)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_908956), _908964), _908966), _908968)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_908956), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(_908956, _908958, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_908956)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_908956), _908960), c_Com_Ocom_OSemi(_908962, _908966)), _908968)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_908956), tc_HOL_Obool)))))], (47017 ^ _777959) ^ [_1720626, _1720628, _1720630] : [c_Wellfounded_Owf(_1720626, _1720628), -(hBOOL(hAPP(hAPP(c_member(_1720626), _1720630), c_Wellfounded_Oacc(_1720626, _1720628))))], (6731 ^ _777959) ^ [_887297, _887299] : [_887299 = c_Orderings_Obot__class_Obot(tc_fun(_887297, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887297, tc_HOL_Obool)), _887299), c_Orderings_Obot__class_Obot(tc_fun(_887297, tc_HOL_Obool)))))], (21336 ^ _777959) ^ [_1183401, _1183403, _1183405, _1183407] : [class_Rings_Olinordered__semiring__strict(_1183401), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183401), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183401), _1183403), _1183405)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1183401), _1183407), _1183405))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1183401), c_Groups_Ozero__class_Ozero(_1183401)), _1183405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1183401), _1183403), _1183407)))], (7878 ^ _777959) ^ [_911921, _911923, _911925, _911927, _911929] : [class_Groups_Ominus(_911921), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_911923, _911921)), _911925), _911927), _911929) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_911921), hAPP(_911925, _911929)), hAPP(_911927, _911929)))], (34085 ^ _777959) ^ [_1419948, _1419950] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1419948)), c_Int_OBit0(_1419950)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1419948), _1419950)))], (14640 ^ _777959) ^ [_1052941, _1052943, _1052945, _1052947] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052941), _1052943)), hBOOL(hAPP(hAPP(c_member(_1052941), _1052945), _1052943)), -(hBOOL(hAPP(hAPP(c_member(_1052941), _1052945), _1052947))), -(hAPP(c_Finite__Set_Ocard(_1052941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1052941, tc_HOL_Obool)), _1052943), hAPP(hAPP(c_Set_Oinsert(_1052941), _1052945), _1052947))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1052941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1052941, tc_HOL_Obool)), _1052943), _1052947))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (13687 ^ _777959) ^ [_1030751, _1030753, _1030755] : [hBOOL(hAPP(hAPP(c_member(_1030751), _1030753), hAPP(c_Set_OCollect(_1030751), _1030755))), -(hBOOL(hAPP(_1030755, _1030753)))], (24840 ^ _777959) ^ [_1248956, _1248958, _1248960, _1248962] : [class_Orderings_Olinorder(_1248956), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248956), _1248958), _1248960)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1248956, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1248956, _1248958), _1248962)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1248956, _1248958), _1248960)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1248956, _1248960), _1248962))], (50226 ^ _777959) ^ [_1795809] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), _1795809)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1795809))))], (2830 ^ _777959) ^ [_820213, _820215, _820217, _820219] : [-(c_Predicate_OPowp(_820219, _820215) = c_Predicate_OPowp(_820217, _820213)), _820219 = _820217, _820215 = _820213], (19132 ^ _777959) ^ [_1145551, _1145553, _1145555, _1145557] : [class_Rings_Ocomm__semiring__1(_1145551), hBOOL(hAPP(c_Finite__Set_Ofinite(_1145553), _1145555)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1145553, _1145551), _1145557), _1145555) = c_Groups_Ozero__class_Ozero(_1145551)), 19141 ^ _777959 : [(19142 ^ _777959) ^ [_1145732] : [hBOOL(hAPP(hAPP(c_member(_1145553), _1145732), _1145555)), hAPP(_1145557, _1145732) = c_Groups_Ozero__class_Ozero(_1145551)]]], (49014 ^ _777959) ^ [_1768085, _1768087] : [-(c_List_Olistrel1(_1768085, hAPP(c_Relation_Oconverse(_1768085, _1768085), _1768087)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1768085), tc_List_Olist(_1768085)), c_List_Olistrel1(_1768085, _1768087)))], (45919 ^ _777959) ^ [_1694333, _1694335] : [class_Enum_Oenum(_1694333), 45922 ^ _777959 : [(45929 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1694333), _1694335)), -(hBOOL(hAPP(_1694335, 45932 ^ [_1694333, _1694335])))], (45923 ^ _777959) ^ [] : [45924 ^ _777959 : [(45925 ^ _777959) ^ [_1694435] : [hBOOL(hAPP(_1694335, _1694435))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1694333), _1694335)))]]], (17249 ^ _777959) ^ [_1107801] : [class_Complete__Lattice_Ocomplete__lattice(_1107801), -(c_Complete__Lattice_OInf__class_OInf(_1107801, c_Orderings_Obot__class_Obot(tc_fun(_1107801, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1107801))], (50000 ^ _777959) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22748 ^ _777959) ^ [_1211764, _1211766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211764)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211766))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211764), _1211766)))], (19566 ^ _777959) ^ [_1152258, _1152260] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152258), _1152260) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152260), _1152258) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1152258 = _1152260)], (24756 ^ _777959) ^ [_1247419, _1247421, _1247423] : [class_Orderings_Oorder(_1247419), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247419), _1247421), _1247423)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1247419, _1247423), _1247421) = c_Orderings_Obot__class_Obot(tc_fun(_1247419, tc_HOL_Obool)))], (33785 ^ _777959) ^ [_1413904] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413904) = 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(_1413904)))))], (35099 ^ _777959) ^ [_1438297, _1438299] : [class_Int_Onumber__ring(_1438297), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1438297), _1438299), hAPP(c_Int_Onumber__class_Onumber__of(_1438297), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1438297), _1438299))], (49538 ^ _777959) ^ [_1781605, _1781607, _1781609] : [hBOOL(hAPP(hAPP(c_member(_1781605), _1781607), hAPP(c_List_Oset(_1781605), _1781609))), 49543 ^ _777959 : [(49546 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1781605), _1781607), hAPP(c_List_Oset(_1781605), 49541 ^ [_1781605, _1781607, _1781609])))], (49544 ^ _777959) ^ [] : [-(_1781609 = hAPP(hAPP(c_List_Oappend(_1781605), 49541 ^ [_1781605, _1781607, _1781609]), hAPP(hAPP(c_List_Olist_OCons(_1781605), _1781607), 49542 ^ [_1781605, _1781607, _1781609])))]]], (41954 ^ _777959) ^ [_1604283, _1604285] : [-(c_List_Oremove1(_1604283, _1604285, c_List_Olist_ONil(_1604283)) = c_List_Olist_ONil(_1604283))], (12876 ^ _777959) ^ [_1011648, _1011650, _1011652] : [class_Groups_Oab__group__add(_1011648), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1011648), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1011648), _1011650), _1011652)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1011648), _1011652), _1011650))], (51250 ^ _777959) ^ [_1812645, _1812647] : [-(class_Nat_Osize(tc_prod(_1812645, _1812647)))], (35804 ^ _777959) ^ [_1456934, _1456936, _1456938, _1456940, _1456942, _1456944] : [_1456934 = _1456936, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1456938, _1456940, _1456942), _1456944), _1456934) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1456938, _1456940, _1456942), _1456944), _1456936))], (3926 ^ _777959) ^ [_837427, _837429, _837431, _837433] : [-(c_Random_Olog(_837433, _837429) = c_Random_Olog(_837431, _837427)), _837433 = _837431, _837429 = _837427], (7100 ^ _777959) ^ [_896544, _896546] : [class_Finite__Set_Ofinite(_896544), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_896544), _896546)))], (12345 ^ _777959) ^ [_1002137, _1002139, _1002141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1002137), _1002141)), _1002139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1002137), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002139), _1002141))))], (32995 ^ _777959) ^ [_1401082] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1401082)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1401082)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401082)), 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)))))], (50390 ^ _777959) ^ [_1799877, _1799879, _1799881, _1799883, _1799885] : [-(c_New__DSequence_Oneg__map(_1799877, _1799879, _1799881, _1799883, _1799885) = c_Lazy__Sequence_Ohb__map(_1799877, _1799879, _1799881, hAPP(_1799883, _1799885)))], (31837 ^ _777959) ^ [_1379313, _1379315, _1379317, _1379319] : [hAPP(c_Com_Ocom_OBODY, _1379313) = c_Com_Ocom_OLocal(_1379315, _1379317, _1379319)], (20981 ^ _777959) ^ [_1176729, _1176731] : [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), _1176729), _1176731))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1176731), _1176729)))], (43604 ^ _777959) ^ [_1644601, _1644603, _1644605, _1644607] : [43605 ^ _777959 : [(43606 ^ _777959) ^ [_1644698, _1644700] : [_1644601 = hAPP(hAPP(c_List_Olist_OCons(_1644603), _1644700), _1644698)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644603), tc_List_Olist(_1644603))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644603), tc_List_Olist(_1644603)), _1644605), hAPP(hAPP(c_List_Oappend(_1644603), _1644605), _1644601))), c_List_Olexord(_1644603, _1644607))))], (30263 ^ _777959) ^ [_1350315, _1350317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1350315)), 30266 ^ _777959 : [(30269 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350317, _1350315)), _1350315)))], (30267 ^ _777959) ^ [] : [-(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, _1350317, _1350315))))]]], (23497 ^ _777959) ^ [_1225212, _1225214, _1225216, _1225218] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225212), _1225214)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225216), _1225218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225212), _1225216)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225214), _1225218))))], (15488 ^ _777959) ^ [_1072334, _1072336, _1072338] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1072334)), _1072336)), hAPP(c_Nat_OSuc, _1072338)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1072334), _1072336)), _1072338))], (5170 ^ _777959) ^ [_857091, _857093] : [_857093 = _857091, -(c_Set_OCollect(_857093) = c_Set_OCollect(_857091))], (39001 ^ _777959) ^ [_1528770, _1528772, _1528774, _1528776, _1528778, _1528780, _1528782, _1528784, _1528786] : [hAPP(c_Fun_Ocomp(_1528770, _1528772, _1528774, _1528776), _1528778) = hAPP(c_Fun_Ocomp(_1528780, _1528772, _1528774, _1528782), _1528784), -(hAPP(_1528776, hAPP(_1528778, _1528786)) = hAPP(_1528782, hAPP(_1528784, _1528786)))], (20167 ^ _777959) ^ [_1162835, _1162837, _1162839] : [class_Groups_Oordered__comm__monoid__add(_1162835), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162835), c_Groups_Ozero__class_Ozero(_1162835)), _1162837)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162835), c_Groups_Ozero__class_Ozero(_1162835)), _1162839)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1162835), c_Groups_Ozero__class_Ozero(_1162835)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1162835), _1162837), _1162839))))], (24742 ^ _777959) ^ [_1247219, _1247221] : [class_Divides_Osemiring__div(_1247219), -(_1247221 = c_Groups_Ozero__class_Ozero(_1247219)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1247219), _1247221), _1247221) = c_Groups_Oone__class_Oone(_1247219))], (5982 ^ _777959) ^ [_873446, _873448] : [hBOOL(hAPP(hAPP(c_member(_873446), _873448), c_Orderings_Obot__class_Obot(tc_fun(_873446, tc_HOL_Obool))))], (37532 ^ _777959) ^ [_1494946, _1494948, _1494950, _1494952, _1494954] : [c_Equiv__Relations_Oequiv(_1494946, _1494948, _1494950), 37535 ^ _777959 : [(37546 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1494946, _1494946)), hAPP(hAPP(c_Product__Type_OPair(_1494946, _1494946), _1494952), _1494954)), _1494950))), hAPP(c_Relation_OImage(_1494946, _1494946, _1494950), hAPP(hAPP(c_Set_Oinsert(_1494946), _1494952), c_Orderings_Obot__class_Obot(tc_fun(_1494946, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1494946, _1494946, _1494950), hAPP(hAPP(c_Set_Oinsert(_1494946), _1494954), c_Orderings_Obot__class_Obot(tc_fun(_1494946, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1494946), _1494952), _1494948)), hBOOL(hAPP(hAPP(c_member(_1494946), _1494954), _1494948))], (37536 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1494946, _1494946)), hAPP(hAPP(c_Product__Type_OPair(_1494946, _1494946), _1494952), _1494954)), _1494950)), 37539 ^ _777959 : [(37544 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494946), _1494954), _1494948)))], (37542 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1494946), _1494952), _1494948)))], (37540 ^ _777959) ^ [] : [-(hAPP(c_Relation_OImage(_1494946, _1494946, _1494950), hAPP(hAPP(c_Set_Oinsert(_1494946), _1494952), c_Orderings_Obot__class_Obot(tc_fun(_1494946, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1494946, _1494946, _1494950), hAPP(hAPP(c_Set_Oinsert(_1494946), _1494954), c_Orderings_Obot__class_Obot(tc_fun(_1494946, tc_HOL_Obool)))))]]]]], (25648 ^ _777959) ^ [_1264235, _1264237, _1264239] : [class_Orderings_Olinorder(_1264235), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1264235), _1264237), _1264239)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1264235, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1264235), _1264237), c_Orderings_Obot__class_Obot(tc_fun(_1264235, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_1264235, _1264237, _1264239)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1264235, _1264237), _1264239))], (48473 ^ _777959) ^ [_1753436, _1753438, _1753440, _1753442, _1753444] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1753436, _1753436)), hAPP(hAPP(c_Product__Type_OPair(_1753436, _1753436), _1753438), _1753440)), _1753442)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1753436, _1753436)), hAPP(hAPP(c_Product__Type_OPair(_1753436, _1753436), _1753440), _1753444)), _1753442)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1753436, _1753436)), hAPP(hAPP(c_Product__Type_OPair(_1753436, _1753436), _1753438), _1753444)), c_Transitive__Closure_Otrancl(_1753436, _1753442))))], (10860 ^ _777959) ^ [_970872, _970874, _970876, _970878] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_970872), 10863 ^ _777959 : [(10870 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970872), _970874), _970878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970872), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970872), _970874), _970876)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970872), _970878), _970876))))], (10864 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970872), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970872), _970874), _970876)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970872), _970878), _970876))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970872), _970874), _970878)))]]], (36880 ^ _777959) ^ [_1477755, _1477757, _1477759, _1477761, _1477763] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1477755, _1477757)), hAPP(_1477755, _1477759))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1477761, _1477761)), hAPP(hAPP(c_Product__Type_OPair(_1477761, _1477761), _1477757), _1477759)), c_Wellfounded_Omlex__prod(_1477761, _1477755, _1477763))))], (25599 ^ _777959) ^ [_1263227, _1263229, _1263231] : [-(hBOOL(hAPP(_1263227, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1263229), _1263231)))), 25600 ^ _777959 : [(25607 ^ _777959) ^ [_1263395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1263231), _1263395)), _1263229)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1263229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1263231), hAPP(c_Nat_OSuc, _1263395)))), hBOOL(hAPP(_1263227, _1263395))], (25601 ^ _777959) ^ [] : [_1263231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1263227, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (322 ^ _777959) ^ [_782980, _782982, _782984, _782986, _782988, _782990, _782992, _782994, _782996, _782998] : [-(c_Finite__Set_Ofolding__image(_782996, _782992, _782988, _782984, _782980)), c_Finite__Set_Ofolding__image(_782998, _782994, _782990, _782986, _782982), _782998 = _782996, _782994 = _782992, _782990 = _782988, _782986 = _782984, _782982 = _782980], (41581 ^ _777959) ^ [_1593291, _1593293, _1593295, _1593297, _1593299, _1593301] : [-(_1593291 = _1593293), -(hAPP(hAPP(c_Map_Omap__of(_1593295, _1593297), hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1593295, _1593297)), hAPP(hAPP(c_Product__Type_OPair(_1593295, _1593297), _1593291), _1593299)), _1593301)), _1593293) = hAPP(hAPP(c_Map_Omap__of(_1593295, _1593297), _1593301), _1593293))], (24500 ^ _777959) ^ [_1243258, _1243260, _1243262] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1243258), _1243260))), 24503 ^ _777959 : [(24510 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1243262), _1243260))), -(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)), _1243258)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1243262), _1243260)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (24504 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1243262), _1243260)), -(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)), _1243258)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1243262), _1243260)) = 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))))]]], (20771 ^ _777959) ^ [_1173579, _1173581] : [class_Groups_Ogroup__add(_1173579), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173579), _1173581), hAPP(c_Groups_Ouminus__class_Ouminus(_1173579), _1173581)) = c_Groups_Ozero__class_Ozero(_1173579))], (11487 ^ _777959) ^ [_982945, _982947, _982949, _982951, _982953] : [class_Groups_Ocomm__monoid__add(_982945), hBOOL(hAPP(c_Finite__Set_Ofinite(_982947), _982949)), hBOOL(hAPP(hAPP(c_member(_982947), _982951), _982949)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_982947, _982945), _982953), _982949) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_982945), hAPP(_982953, _982951)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_982947, _982945), _982953), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982947, tc_HOL_Obool)), _982949), hAPP(hAPP(c_Set_Oinsert(_982947), _982951), c_Orderings_Obot__class_Obot(tc_fun(_982947, tc_HOL_Obool)))))))], (50662 ^ _777959) ^ [_1805601, _1805603, _1805605] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1805601)), c_List_Oreplicate(_1805601, _1805603, _1805605)) = _1805603)], (5216 ^ _777959) ^ [_857788, _857790, _857792, _857794] : [-(c_Relation_Oconverse(_857794, _857790) = c_Relation_Oconverse(_857792, _857788)), _857794 = _857792, _857790 = _857788], (48378 ^ _777959) ^ [_1751381, _1751383] : [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), _1751381), _1751383)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1751381), _1751383)))], (22762 ^ _777959) ^ [_1212037, _1212039, _1212041] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212037)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212039)), _1212041)) = 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), _1212037), _1212039))), _1212041))], (12796 ^ _777959) ^ [_1010120, _1010122, _1010124] : [class_Groups_Oordered__ab__group__add(_1010120), 12799 ^ _777959 : [(12806 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010120), hAPP(c_Groups_Ouminus__class_Ouminus(_1010120), _1010124)), _1010122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010120), hAPP(c_Groups_Ouminus__class_Ouminus(_1010120), _1010122)), _1010124)))], (12800 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010120), hAPP(c_Groups_Ouminus__class_Ouminus(_1010120), _1010122)), _1010124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010120), hAPP(c_Groups_Ouminus__class_Ouminus(_1010120), _1010124)), _1010122)))]]], (45326 ^ _777959) ^ [_1681298, _1681300] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681298)), c_List_Oremdups(_1681298, _1681300)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681298)), _1681300), -(c_List_Oremdups(_1681298, _1681300) = _1681300)], (9176 ^ _777959) ^ [_935477, _935479, _935481] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_935477, tc_HOL_Obool)), _935479), _935481))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935477, tc_HOL_Obool)), _935479), _935481)), -(_935479 = _935481)], (17765 ^ _777959) ^ [_1117232, _1117234, _1117236, _1117238, _1117240] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1117232, _1117232, _1117234, _1117236, _1117238), _1117240)), -(hBOOL(hAPP(hAPP(c_member(_1117232), _1117236), _1117238))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1117232, _1117234, hAPP(hAPP(c_Set_Oinsert(_1117232), _1117236), _1117238)), _1117240)))], (44765 ^ _777959) ^ [_1668093, _1668095, _1668097] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1668093), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1668093))), _1668095))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1668097), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1668093))), _1668095))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1668093), _1668093), hAPP(hAPP(c_COMBC(tc_List_Olist(_1668093), tc_Nat_Onat, _1668093), c_List_Onth(_1668093)), _1668097)), hAPP(c_List_Ofilter(tc_List_Olist(_1668093), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1668093)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1668097)), c_Nat_Osize__class_Osize(tc_List_Olist(_1668093)))), c_List_Otranspose(_1668093, _1668095))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1668093)), _1668095), _1668097))], (5893 ^ _777959) ^ [_871570] : [hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, _871570))), -(hAPP(c_Com_Obody, _871570) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), 5896 ^ [_871570]))], (23074 ^ _777959) ^ [] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29613 ^ _777959) ^ [_1336459, _1336461, _1336463, _1336465, _1336467] : [class_Groups_Ocomm__monoid__mult(_1336459), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336461), _1336463)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1336461, tc_HOL_Obool)), _1336465), _1336463)), 29627 ^ _777959 : [(29630 ^ _777959) ^ [] : [hAPP(_1336467, 29626 ^ [_1336459, _1336461, _1336463, _1336465, _1336467]) = c_Groups_Oone__class_Oone(_1336459)], (29628 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1336461), 29626 ^ [_1336459, _1336461, _1336463, _1336465, _1336467]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336461, tc_HOL_Obool)), _1336463), _1336465))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336461, _1336459), _1336467), _1336465) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336461, _1336459), _1336467), _1336463))], (9186 ^ _777959) ^ [_935673, _935675, _935677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935673, tc_HOL_Obool)), _935675), _935677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_935673, tc_HOL_Obool)), _935675), _935677))), -(_935675 = _935677)], (9674 ^ _777959) ^ [_945450, _945452, _945454, _945456] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945450, tc_HOL_Obool)), _945452), _945454), _945456)), -(hBOOL(hAPP(_945452, _945456)))], (7978 ^ _777959) ^ [_914154, _914156, _914158] : [hAPP(c_Com_Ocom_OBODY, _914154) = c_Com_Ocom_OWhile(_914156, _914158)], (42401 ^ _777959) ^ [_1615231, _1615233, _1615235] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1615231)), -(c_List_Osublist(_1615233, hAPP(hAPP(c_List_Olist_OCons(_1615233), _1615235), c_List_Olist_ONil(_1615233)), _1615231) = hAPP(hAPP(c_List_Olist_OCons(_1615233), _1615235), c_List_Olist_ONil(_1615233)))], (9606 ^ _777959) ^ [_944045, _944047, _944049, _944051] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944045, tc_HOL_Obool)), _944047), _944049), _944051)), 9609 ^ _777959 : [(9612 ^ _777959) ^ [] : [-(hBOOL(hAPP(_944049, _944051)))], (9610 ^ _777959) ^ [] : [-(hBOOL(hAPP(_944047, _944051)))]]], (27898 ^ _777959) ^ [_1304708] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1304708)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1304708))], (51206 ^ _777959) ^ [_1812078] : [-(class_Nat_Osize(tc_Option_Ooption(_1812078)))], (28016 ^ _777959) ^ [_1306616, _1306618] : [class_Rings_Oring__1(_1306616), -(hAPP(c_Int_Oring__1__class_Oof__int(_1306616), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1306618)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1306616), _1306618))], (30367 ^ _777959) ^ [_1352102, _1352104, _1352106, _1352108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1352102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1352104), _1352106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1352106), 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), _1352104), _1352102)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1352104), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1352108, _1352102))), _1352106))))], (11826 ^ _777959) ^ [_992382, _992384, _992386, _992388, _992390] : [-(_992382 = c_Orderings_Obot__class_Obot(tc_fun(_992384, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992384, tc_fun(_992386, tc_HOL_Obool)), _992382), hAPP(hAPP(c_COMBB(tc_fun(_992386, tc_HOL_Obool), tc_fun(_992386, tc_HOL_Obool), _992384), hAPP(c_Set_Oinsert(_992386), _992388)), _992390)) = hAPP(hAPP(c_Set_Oinsert(_992386), _992388), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992384, tc_fun(_992386, tc_HOL_Obool)), _992382), _992390)))], (48751 ^ _777959) ^ [_1761181] : [-(c_Relation_Orefl__on(_1761181, c_Orderings_Otop__class_Otop(tc_fun(_1761181, tc_HOL_Obool)), c_Relation_OId(_1761181)))], (36534 ^ _777959) ^ [_1470861, _1470863, _1470865, _1470867, _1470869, _1470871] : [hAPP(c_Product__Type_Oapsnd(_1470861, _1470863, _1470865, _1470867), _1470869) = hAPP(c_Product__Type_Oapsnd(_1470861, _1470863, _1470865, _1470871), _1470869), -(hAPP(_1470867, hAPP(c_Product__Type_Osnd(_1470865, _1470861), _1470869)) = hAPP(_1470871, hAPP(c_Product__Type_Osnd(_1470865, _1470861), _1470869)))], (1160 ^ _777959) ^ [_795183, _795185] : [-(class_Groups_Ogroup__add(_795183)), _795185 = _795183, class_Groups_Ogroup__add(_795185)], (10715 ^ _777959) ^ [_968160, _968162, _968164, _968166] : [class_Groups_Ocancel__semigroup__add(_968160), 10718 ^ _777959 : [(10725 ^ _777959) ^ [] : [_968162 = _968166, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968160), _968162), _968164) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968160), _968166), _968164))], (10719 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968160), _968162), _968164) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_968160), _968166), _968164), -(_968162 = _968166)]]], (28958 ^ _777959) ^ [_1323796] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1323796)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1323796)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1323796)))], (47354 ^ _777959) ^ [_1728908, _1728910, _1728912] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1728908, _1728910)), _1728912)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1728908), hAPP(c_Relation_ODomain(_1728908, _1728910), _1728912))))], (46838 ^ _777959) ^ [_1717189, _1717191, _1717193] : [c_Wellfounded_Owf(_1717189, _1717191), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1717189, _1717189), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1717189, _1717189, _1717189), _1717191), _1717193)), _1717191)), -(c_FunDef_Oreduction__pair(_1717189, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1717189, _1717189), tc_HOL_Obool), tc_fun(tc_prod(_1717189, _1717189), tc_HOL_Obool)), _1717191), _1717193)))], (35733 ^ _777959) ^ [_1455434, _1455436, _1455438] : [_1455434 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1455436, _1455436), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1455436, _1455436), tc_HOL_Obool)), _1455434), _1455438)))], (42389 ^ _777959) ^ [_1615056, _1615058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1615056), _1615058)), -(c_List_Oupto(_1615056, _1615058) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1615056), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1615056), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1615058)))], (13127 ^ _777959) ^ [_1017473, _1017475, _1017477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017473, tc_HOL_Obool)), _1017475), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1017473, tc_HOL_Obool)), _1017477))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1017473, tc_HOL_Obool)), _1017475), _1017477) = c_Orderings_Obot__class_Obot(tc_fun(_1017473, tc_HOL_Obool)))], (17927 ^ _777959) ^ [_1120524, _1120526, _1120528] : [class_Orderings_Olinorder(_1120524), hBOOL(hAPP(c_Finite__Set_Ofinite(_1120524), _1120526)), -(_1120528 = c_Orderings_Obot__class_Obot(tc_fun(_1120524, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1120524, tc_HOL_Obool)), _1120528), _1120526)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1120524), c_Big__Operators_Olattice_OSup__fin(_1120524, c_Orderings_Oord__class_Omax(_1120524), _1120528)), c_Big__Operators_Olattice_OSup__fin(_1120524, c_Orderings_Oord__class_Omax(_1120524), _1120526)) = c_Big__Operators_Olattice_OSup__fin(_1120524, c_Orderings_Oord__class_Omax(_1120524), _1120526))], (22788 ^ _777959) ^ [_1212610, _1212612] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1212610), _1212612)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212610)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212612)))], (14025 ^ _777959) ^ [_1038347, _1038349] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1038347, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038347, tc_HOL_Obool)), _1038349)), _1038349) = c_Orderings_Otop__class_Otop(tc_fun(_1038347, tc_HOL_Obool)))], (30126 ^ _777959) ^ [_1347789, _1347791] : [class_Divides_Osemiring__div(_1347789), -(c_Divides_Odiv__class_Omod(_1347789, _1347791, c_Groups_Oone__class_Oone(_1347789)) = c_Groups_Ozero__class_Ozero(_1347789))], (37800 ^ _777959) ^ [_1501163, _1501165, _1501167, _1501169, _1501171, _1501173, _1501175] : [c_Equiv__Relations_Oequiv(_1501163, _1501165, _1501167), c_Equiv__Relations_Ocongruent(_1501163, tc_fun(_1501169, tc_HOL_Obool), _1501167, _1501171), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501163, tc_fun(_1501169, tc_HOL_Obool)), _1501173), _1501171) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1501163, tc_fun(_1501169, tc_HOL_Obool)), _1501175), _1501171), hBOOL(hAPP(hAPP(c_member(tc_fun(_1501163, tc_HOL_Obool)), _1501173), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1501163), _1501165), _1501167))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1501163, tc_HOL_Obool)), _1501175), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1501163), _1501165), _1501167))), 37822 ^ _777959 : [(37826 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501163), 37824 ^ [_1501163, _1501165, _1501167, _1501169, _1501171, _1501173, _1501175]), _1501165)))], (37828 ^ _777959) ^ [] : [-(hAPP(_1501171, 37821 ^ [_1501163, _1501165, _1501167, _1501169, _1501171, _1501173, _1501175]) = hAPP(_1501171, 37824 ^ [_1501163, _1501165, _1501167, _1501169, _1501171, _1501173, _1501175]))], (37830 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1501163, _1501163)), hAPP(hAPP(c_Product__Type_OPair(_1501163, _1501163), 37821 ^ [_1501163, _1501165, _1501167, _1501169, _1501171, _1501173, _1501175]), 37824 ^ [_1501163, _1501165, _1501167, _1501169, _1501171, _1501173, _1501175])), _1501167))], (37823 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1501163), 37821 ^ [_1501163, _1501165, _1501167, _1501169, _1501171, _1501173, _1501175]), _1501165)))]], -(_1501173 = _1501175)], (30247 ^ _777959) ^ [_1350059, _1350061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1350059), 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, _1350061, _1350059)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (1070 ^ _777959) ^ [_794058, _794060] : [-(class_Rings_Oring__no__zero__divisors(_794058)), _794060 = _794058, class_Rings_Oring__no__zero__divisors(_794060)], (23813 ^ _777959) ^ [_1230789, _1230791, _1230793, _1230795] : [class_Rings_Olinordered__semidom(_1230789), hAPP(hAPP(c_Power_Opower__class_Opower(_1230789), _1230791), hAPP(c_Nat_OSuc, _1230793)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1230789), _1230795), hAPP(c_Nat_OSuc, _1230793)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230789), c_Groups_Ozero__class_Ozero(_1230789)), _1230791)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1230789), c_Groups_Ozero__class_Ozero(_1230789)), _1230795)), -(_1230791 = _1230795)], (41483 ^ _777959) ^ [_1591203, _1591205, _1591207, _1591209, _1591211] : [hAPP(hAPP(c_List_Olist_OCons(_1591203), _1591205), _1591207) = hAPP(hAPP(c_List_Olist_OCons(_1591203), _1591209), _1591211), 41486 ^ _777959 : [(41489 ^ _777959) ^ [] : [-(_1591207 = _1591211)], (41487 ^ _777959) ^ [] : [-(_1591205 = _1591209)]]], (22489 ^ _777959) ^ [] : [-(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)))], (28626 ^ _777959) ^ [_1317254] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1317254)), -(c_Nat__Transfer_Ois__nat(_1317254))], (50670 ^ _777959) ^ [_1805828, _1805830, _1805832] : [_1805828 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1805830), c_List_Oreplicate(_1805830, _1805828, _1805832)) = c_Orderings_Obot__class_Obot(tc_fun(_1805830, tc_HOL_Obool)))], (25690 ^ _777959) ^ [_1265140, _1265142, _1265144, _1265146] : [class_Fields_Ofield__inverse__zero(_1265140), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1265140), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265140), _1265142), _1265144)), _1265146) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265140), hAPP(hAPP(c_Power_Opower__class_Opower(_1265140), _1265142), _1265146)), hAPP(hAPP(c_Power_Opower__class_Opower(_1265140), _1265144), _1265146)))], (51040 ^ _777959) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (24435 ^ _777959) ^ [_1242085] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1242085)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1242085)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (15224 ^ _777959) ^ [_1068044, _1068046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068046), hAPP(c_Nat_OSuc, _1068044))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068044), _1068046))], (6869 ^ _777959) ^ [_890170, _890172, _890174, _890176] : [c_Hoare__Mirabelle_Ohoare__derivs(_890170, _890172, _890174), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_890170), tc_HOL_Obool)), _890176), _890174)), -(c_Hoare__Mirabelle_Ohoare__derivs(_890170, _890172, _890176))], (2564 ^ _777959) ^ [_815972, _815974, _815976, _815978] : [-(c_Divides_Odivmod__int(_815978, _815974) = c_Divides_Odivmod__int(_815976, _815972)), _815978 = _815976, _815974 = _815972], (27052 ^ _777959) ^ [_1290204, _1290206, _1290208, _1290210] : [class_Fields_Olinordered__field(_1290204), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290204), c_Groups_Ozero__class_Ozero(_1290204)), _1290206)), 27059 ^ _777959 : [(27066 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290204), _1290208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290204), _1290210), _1290206))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290204), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290204), _1290208), _1290206)), _1290210)))], (27060 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290204), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290204), _1290208), _1290206)), _1290210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290204), _1290208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290204), _1290210), _1290206))))]]], (51010 ^ _777959) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (40791 ^ _777959) ^ [_1570949, _1570951, _1570953] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1570949)), hAPP(hAPP(c_List_Otake(_1570949), _1570951), _1570953)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1570949)), _1570953)), _1570951))], (23471 ^ _777959) ^ [_1224761, _1224763] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224761), _1224763)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1224761)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1224763)))], (3382 ^ _777959) ^ [_828931, _828933, _828935, _828937] : [-(c_Enum_Osublists(_828937, _828933) = c_Enum_Osublists(_828935, _828931)), _828937 = _828935, _828933 = _828931], (39015 ^ _777959) ^ [_1529142, _1529144, _1529146, _1529148, _1529150, _1529152] : [-(hAPP(hAPP(c_Fun_Ocomp(_1529142, _1529144, _1529146, _1529148), _1529150), _1529152) = hAPP(_1529148, hAPP(_1529150, _1529152)))], (37243 ^ _777959) ^ [] : [-(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))))))], (41789 ^ _777959) ^ [_1600160] : [-(c_List_Olists(_1600160, c_Orderings_Otop__class_Otop(tc_fun(_1600160, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1600160), tc_HOL_Obool)))], (20 ^ _777959) ^ [_778219, _778221, _778223, _778225, _778227, _778229, _778231, _778233, _778235, _778237, _778239, _778241] : [-(c_Finite__Set_Ofolding__image__simple__idem(_778239, _778235, _778231, _778227, _778223, _778219)), c_Finite__Set_Ofolding__image__simple__idem(_778241, _778237, _778233, _778229, _778225, _778221), _778241 = _778239, _778237 = _778235, _778233 = _778231, _778229 = _778227, _778225 = _778223, _778221 = _778219], (13157 ^ _777959) ^ [_1018082, _1018084, _1018086] : [class_Complete__Lattice_Ocomplete__lattice(_1018082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1018082), _1018084)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1018082), _1018086), c_Complete__Lattice_OSup__class_OSup(_1018082, _1018084)) = hAPP(hAPP(c_Finite__Set_Ofold(_1018082, _1018082, c_Lattices_Osemilattice__sup__class_Osup(_1018082)), _1018086), _1018084))], (33201 ^ _777959) ^ [_1404677, _1404679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1404677), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404679)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404677)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404679))], (1868 ^ _777959) ^ [_804814, _804816, _804818, _804820, _804822, _804824, _804826, _804828] : [-(c_Hoare__Mirabelle_Otriple_Otriple__rec(_804828, _804824, _804820, _804816) = c_Hoare__Mirabelle_Otriple_Otriple__rec(_804826, _804822, _804818, _804814)), _804828 = _804826, _804824 = _804822, _804820 = _804818, _804816 = _804814], (38036 ^ _777959) ^ [_1506636, _1506638, _1506640, _1506642, _1506644] : [c_Fun_Oinj__on(_1506636, _1506638, _1506640, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1506636, tc_HOL_Obool)), _1506642), _1506644)), 38039 ^ _777959 : [(38046 ^ _777959) ^ [] : [_1506642 = _1506644, -(hAPP(c_Set_Oimage(_1506636, _1506638, _1506640), _1506642) = hAPP(c_Set_Oimage(_1506636, _1506638, _1506640), _1506644))], (38040 ^ _777959) ^ [] : [hAPP(c_Set_Oimage(_1506636, _1506638, _1506640), _1506642) = hAPP(c_Set_Oimage(_1506636, _1506638, _1506640), _1506644), -(_1506642 = _1506644)]]], (51074 ^ _777959) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (27337 ^ _777959) ^ [] : [-(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))))], (15398 ^ _777959) ^ [_1070775, _1070777, _1070779] : [class_Rings_Oring(_1070775), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070775), hAPP(c_Groups_Ouminus__class_Ouminus(_1070775), _1070777)), hAPP(c_Groups_Ouminus__class_Ouminus(_1070775), _1070779)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070775), _1070777), _1070779))], (37680 ^ _777959) ^ [_1498809] : [-(c_Equiv__Relations_Oequivp(_1498809, c_fequal))], (13875 ^ _777959) ^ [_1034595, _1034597, _1034599, _1034601, _1034603, _1034605] : [hBOOL(hAPP(hAPP(c_member(_1034595), _1034597), _1034599)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1034595, tc_fun(_1034601, tc_HOL_Obool)), _1034599), hAPP(hAPP(c_COMBB(tc_fun(_1034601, tc_HOL_Obool), tc_fun(_1034601, tc_HOL_Obool), _1034595), hAPP(c_Set_Oinsert(_1034601), _1034603)), _1034605)) = hAPP(hAPP(c_Set_Oinsert(_1034601), _1034603), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1034595, tc_fun(_1034601, tc_HOL_Obool)), _1034599), _1034605)))], (39326 ^ _777959) ^ [_1536184, _1536186, _1536188, _1536190, _1536192, _1536194] : [c_Finite__Set_Ofolding(_1536184, _1536186, _1536188, _1536190), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536184), _1536192)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536184), _1536194)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1536184, tc_HOL_Obool)), _1536192), _1536194) = c_Orderings_Obot__class_Obot(tc_fun(_1536184, tc_HOL_Obool)), -(hAPP(_1536190, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1536184, tc_HOL_Obool)), _1536192), _1536194)) = hAPP(c_Fun_Ocomp(_1536186, _1536186, _1536186, hAPP(_1536190, _1536192)), hAPP(_1536190, _1536194)))], (7890 ^ _777959) ^ [_912195, _912197, _912199, _912201, _912203, _912205, _912207] : [c_Finite__Set_Ofolding__image__simple__idem(_912195, _912197, _912199, _912201, _912203, _912205), -(hAPP(hAPP(_912199, _912207), _912207) = _912207)], (10354 ^ _777959) ^ [_960418, _960420, _960422, _960424, _960426, _960428, _960430, _960432] : [c_Finite__Set_Ofolding__image__simple(_960418, _960420, _960422, _960424, _960426, _960428), hBOOL(hAPP(c_Finite__Set_Ofinite(_960420), _960430)), hBOOL(hAPP(c_Finite__Set_Ofinite(_960420), _960432)), -(hAPP(hAPP(_960422, hAPP(_960428, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960420, tc_HOL_Obool)), _960430), _960432))), hAPP(_960428, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960420, tc_HOL_Obool)), _960430), _960432))) = hAPP(hAPP(_960422, hAPP(_960428, _960430)), hAPP(_960428, _960432)))], (24253 ^ _777959) ^ [_1238968, _1238970] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238968) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238970), -(_1238968 = _1238970)], (39786 ^ _777959) ^ [_1547052, _1547054, _1547056, _1547058] : [hBOOL(hAPP(c_List_Odistinct(_1547052), _1547054)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1547056, _1547052)), hAPP(hAPP(c_List_Ozip(_1547056, _1547052), _1547058), _1547054))))], (37164 ^ _777959) ^ [_1485717, _1485719, _1485721] : [-(hAPP(c_Relation_OImage(_1485717, _1485719, _1485721), c_Orderings_Obot__class_Obot(tc_fun(_1485717, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1485719, tc_HOL_Obool)))], (42270 ^ _777959) ^ [_1611295, _1611297, _1611299, _1611301] : [-(hAPP(c_Set_OCollect(tc_prod(_1611295, _1611297)), hAPP(c_Product__Type_Oprod_Oprod__case(_1611295, _1611297, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1611295, tc_fun(_1611297, tc_HOL_Obool), tc_fun(_1611297, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1611297, tc_HOL_Obool), tc_fun(_1611297, tc_HOL_Obool)), _1611295), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1611297)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1611295), c_fconj), _1611299))), _1611301))) = hAPP(hAPP(c_Product__Type_OSigma(_1611295, _1611297), hAPP(c_Set_OCollect(_1611295), _1611299)), hAPP(c_COMBK(tc_fun(_1611297, tc_HOL_Obool), _1611295), hAPP(c_Set_OCollect(_1611297), _1611301))))], (7608 ^ _777959) ^ [_905918, _905920, _905922, _905924, _905926] : [7611 ^ _777959 : [(7614 ^ _777959) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(_905920, _905922, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_905920)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_905920), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _905920), hAPP(hAPP(c_COMBC(tc_Com_Ostate, tc_Com_Ostate, tc_HOL_Obool), c_fequal), 7610 ^ [_905918, _905920, _905922, _905924, _905926]))), _905924), hAPP(c_COMBK(tc_fun(tc_Com_Ostate, tc_HOL_Obool), _905920), hAPP(_905926, 7609 ^ [_905918, _905920, _905922, _905924, _905926])))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_905920), tc_HOL_Obool))))], (7612 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_905918, 7609 ^ [_905918, _905920, _905922, _905924, _905926]), 7610 ^ [_905918, _905920, _905922, _905924, _905926])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_905920, _905922, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_905920)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_905920), _905918), _905924), _905926)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_905920), tc_HOL_Obool)))))], (28684 ^ _777959) ^ [_1318381, _1318383, _1318385, _1318387, _1318389] : [class_Orderings_Oorder(_1318381), 28687 ^ _777959 : [(28708 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1318381, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1318381, _1318383, _1318385)), c_SetInterval_Oord__class_OatLeastAtMost(_1318381, _1318387, _1318389)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318381), _1318387), _1318389)), 28711 ^ _777959 : [(28714 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318381), _1318387), _1318383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318381), _1318385), _1318389)), 28721 ^ _777959 : [(28724 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318381), _1318385), _1318389))], (28722 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318381), _1318387), _1318383))]]], (28712 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318381), _1318383), _1318385)))]]], (28688 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1318381, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1318381, _1318383, _1318385)), c_SetInterval_Oord__class_OatLeastAtMost(_1318381, _1318387, _1318389))), 28691 ^ _777959 : [(28692 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318381), _1318383), _1318385)), 28695 ^ _777959 : [(28700 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318381), _1318387), _1318383))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1318381), _1318385), _1318389)))], (28698 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318381), _1318385), _1318389)))], (28696 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318381), _1318387), _1318383)))]]], (28706 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1318381), _1318387), _1318389)))]]]]], (5286 ^ _777959) ^ [_858887, _858889, _858891, _858893] : [-(c_List_Olast(_858893, _858889) = c_List_Olast(_858891, _858887)), _858893 = _858891, _858889 = _858887], (31430 ^ _777959) ^ [_1371652, _1371654] : [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), _1371652)), _1371654))), _1371652 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1371654 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5424 ^ _777959) ^ [_860916, _860918] : [_860918 = _860916, -(c_Orderings_Oord__class_Oless(_860918) = c_Orderings_Oord__class_Oless(_860916))], (26310 ^ _777959) ^ [_1276651, _1276653, _1276655, _1276657] : [class_Fields_Olinordered__field(_1276651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276651), _1276653), _1276655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276651), c_Groups_Ozero__class_Ozero(_1276651)), _1276657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276651), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276651), _1276653), _1276657)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276651), _1276655), _1276657))))], (18734 ^ _777959) ^ [_1137769, _1137771, _1137773] : [class_Orderings_Olinorder(_1137769), hBOOL(hAPP(c_Finite__Set_Ofinite(_1137769), _1137771)), -(_1137771 = c_Orderings_Obot__class_Obot(tc_fun(_1137769, tc_HOL_Obool))), 18745 ^ _777959 : [(18746 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137769), _1137773), hAPP(c_Finite__Set_Ofold1(_1137769, c_Orderings_Oord__class_Omin(_1137769)), _1137771))), 18749 ^ _777959 : [(18750 ^ _777959) ^ [_1138062] : [hBOOL(hAPP(hAPP(c_member(_1137769), _1138062), _1137771)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137769), _1137773), _1138062)))]]], (18756 ^ _777959) ^ [] : [18758 ^ _777959 : [(18761 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137769), _1137773), 18757 ^ [_1137769, _1137771, _1137773]))], (18759 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1137769), 18757 ^ [_1137769, _1137771, _1137773]), _1137771)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137769), _1137773), hAPP(c_Finite__Set_Ofold1(_1137769, c_Orderings_Oord__class_Omin(_1137769)), _1137771))))]]], (39655 ^ _777959) ^ [_1544333, _1544335] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1544333), _1544335) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1544333, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1544335), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (51260 ^ _777959) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (31526 ^ _777959) ^ [_1373369] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1373369), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1373369)))], (39125 ^ _777959) ^ [_1531558, _1531560, _1531562, _1531564, _1531566, _1531568] : [class_Groups_Ocomm__monoid__mult(_1531558), c_Fun_Oinj__on(_1531560, _1531562, _1531564, _1531566), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1531562, _1531558), _1531568), hAPP(c_Set_Oimage(_1531560, _1531562, _1531564), _1531566)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1531560, _1531558), hAPP(c_Fun_Ocomp(_1531562, _1531558, _1531560, _1531568), _1531564)), _1531566))], (10544 ^ _777959) ^ [_964559, _964561, _964563, _964565, _964567, _964569] : [c_Finite__Set_Ofun__left__comm(_964559, _964561, _964563), hBOOL(hAPP(c_Finite__Set_Ofinite(_964559), _964565)), -(hAPP(hAPP(c_Finite__Set_Ofold(_964559, _964561, _964563), _964567), hAPP(hAPP(c_Set_Oinsert(_964559), _964569), _964565)) = hAPP(hAPP(_964563, _964569), hAPP(hAPP(c_Finite__Set_Ofold(_964559, _964561, _964563), _964567), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964559, tc_HOL_Obool)), _964565), hAPP(hAPP(c_Set_Oinsert(_964559), _964569), c_Orderings_Obot__class_Obot(tc_fun(_964559, tc_HOL_Obool)))))))], (47940 ^ _777959) ^ [_1743280, _1743282, _1743284] : [c_List_Olist__ex(_1743280, _1743282, _1743284), 47944 ^ _777959 : [(47947 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1743282, hAPP(hAPP(c_List_Onth(_1743280), _1743284), 47943 ^ [_1743280, _1743282, _1743284]))))], (47945 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47943 ^ [_1743280, _1743282, _1743284]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743280)), _1743284))))]]], (35085 ^ _777959) ^ [_1438115] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1438115), c_Int_OMin) = c_Int_Opred(_1438115))], (20541 ^ _777959) ^ [_1169689, _1169691, _1169693] : [class_Rings_Olinordered__ring__strict(_1169689), 20544 ^ _777959 : [(20553 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169689), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169689), _1169691), _1169691)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169689), _1169693), _1169693)) = c_Groups_Ozero__class_Ozero(_1169689)), _1169691 = c_Groups_Ozero__class_Ozero(_1169689), _1169693 = c_Groups_Ozero__class_Ozero(_1169689)], (20545 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1169689), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169689), _1169691), _1169691)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1169689), _1169693), _1169693)) = c_Groups_Ozero__class_Ozero(_1169689), 20548 ^ _777959 : [(20551 ^ _777959) ^ [] : [-(_1169693 = c_Groups_Ozero__class_Ozero(_1169689))], (20549 ^ _777959) ^ [] : [-(_1169691 = c_Groups_Ozero__class_Ozero(_1169689))]]]]], (31557 ^ _777959) ^ [_1373842, _1373844, _1373846] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373842, _1373844) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1373846, _1373844), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1373846), _1373842)), -(_1373842 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1373846), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1373844), 31564 ^ [_1373842, _1373844, _1373846])))], (36009 ^ _777959) ^ [_1461005, _1461007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461005)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461007)), -(c_Divides_OposDivAlg(_1461005, _1461007) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1461005), _1461007)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1461005, _1461007)))], (10622 ^ _777959) ^ [_966264, _966266, _966268, _966270, _966272] : [-(hBOOL(hAPP(hAPP(c_member(_966264), _966266), _966268))), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_966264, tc_Option_Ooption(_966270)), c_Map_Orestrict__map(_966264, _966270, _966272, _966268)), _966266), c_Option_Ooption_ONone(_966270)) = c_Map_Orestrict__map(_966264, _966270, _966272, _966268))], (7476 ^ _777959) ^ [_903422, _903424, _903426] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_903422), _903424)), hBOOL(hAPP(c_Finite__Set_Ofinite(_903422), _903426)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_903422), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903422, tc_HOL_Obool)), _903424), _903426))))], (14684 ^ _777959) ^ [_1053882, _1053884, _1053886, _1053888] : [hBOOL(hAPP(hAPP(_1053886, _1053888), _1053884)), -(hBOOL(hAPP(hAPP(c_member(_1053882), _1053884), c_SetInterval_Oord_OatLeast(_1053882, _1053886, _1053888))))], (32653 ^ _777959) ^ [_1394672, _1394674, _1394676, _1394678] : [class_Fields_Olinordered__field__inverse__zero(_1394672), class_Int_Onumber(_1394672), 32660 ^ _777959 : [(32661 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394672), hAPP(c_Int_Onumber__class_Onumber__of(_1394672), _1394674)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1394672), _1394676), _1394678))), 32664 ^ _777959 : [(32671 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394672), c_Groups_Ozero__class_Ozero(_1394672)), _1394678))), 32674 ^ _777959 : [(32681 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394672), _1394678), c_Groups_Ozero__class_Ozero(_1394672)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394672), hAPP(c_Int_Onumber__class_Onumber__of(_1394672), _1394674)), c_Groups_Ozero__class_Ozero(_1394672))))], (32675 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394672), _1394678), c_Groups_Ozero__class_Ozero(_1394672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394672), _1394676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394672), hAPP(c_Int_Onumber__class_Onumber__of(_1394672), _1394674)), _1394678))))]]], (32665 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394672), c_Groups_Ozero__class_Ozero(_1394672)), _1394678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394672), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394672), hAPP(c_Int_Onumber__class_Onumber__of(_1394672), _1394674)), _1394678)), _1394676)))]]], (32687 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394672), hAPP(c_Int_Onumber__class_Onumber__of(_1394672), _1394674)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1394672), _1394676), _1394678)))), 32690 ^ _777959 : [(32693 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394672), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394672), hAPP(c_Int_Onumber__class_Onumber__of(_1394672), _1394674)), _1394678)), _1394676))], (32691 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394672), c_Groups_Ozero__class_Ozero(_1394672)), _1394678)))]], 32694 ^ _777959 : [(32697 ^ _777959) ^ [] : [32698 ^ _777959 : [(32701 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394672), _1394676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1394672), hAPP(c_Int_Onumber__class_Onumber__of(_1394672), _1394674)), _1394678)))], (32699 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394672), _1394678), c_Groups_Ozero__class_Ozero(_1394672))))]], 32702 ^ _777959 : [(32705 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1394672), hAPP(c_Int_Onumber__class_Onumber__of(_1394672), _1394674)), c_Groups_Ozero__class_Ozero(_1394672)))], (32703 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394672), _1394678), c_Groups_Ozero__class_Ozero(_1394672)))]]], (32695 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1394672), c_Groups_Ozero__class_Ozero(_1394672)), _1394678))]]]]], (49998 ^ _777959) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44039 ^ _777959) ^ [_1653579, _1653581, _1653583] : [hBOOL(hAPP(c_List_Odistinct(_1653579), _1653581)), -(hAPP(c_List_Ofilter(_1653579, hAPP(hAPP(c_COMBC(_1653579, tc_fun(_1653579, tc_HOL_Obool), tc_HOL_Obool), c_member(_1653579)), hAPP(c_List_Oset(_1653579), c_List_Osublist(_1653579, _1653581, _1653583)))), _1653581) = c_List_Osublist(_1653579, _1653581, _1653583))], (42523 ^ _777959) ^ [_1619393, _1619395] : [-(hAPP(c_Fun_Oid(_1619393), _1619395) = _1619395)], (7364 ^ _777959) ^ [_901457, _901459, _901461, _901463, _901465] : [class_Lattices_Osemilattice__sup(_901457), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901457), _901459), _901461)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901457), _901463), _901465)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901457), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901457), _901459), _901463)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_901457), _901461), _901465))))], (12922 ^ _777959) ^ [_1012739, _1012741, _1012743] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012739, tc_HOL_Obool)), _1012741), _1012743) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1012739, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1012739, tc_HOL_Obool)), _1012741), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1012739, tc_HOL_Obool)), _1012743), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1012739, tc_HOL_Obool), tc_HOL_Obool))))))], (23274 ^ _777959) ^ [_1221517, _1221519] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1221517), _1221519)), -(_1221519 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1221517), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23277 ^ [_1221517, _1221519])))], (18478 ^ _777959) ^ [_1132777, _1132779, _1132781] : [class_Orderings_Olinorder(_1132777), hAPP(_1132779, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1132777), 18483 ^ [_1132777, _1132779, _1132781]), 18484 ^ [_1132777, _1132779, _1132781])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1132777), hAPP(_1132779, 18483 ^ [_1132777, _1132779, _1132781])), hAPP(_1132779, 18484 ^ [_1132777, _1132779, _1132781])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132777), _1132781)), -(_1132781 = c_Orderings_Obot__class_Obot(tc_fun(_1132777, tc_HOL_Obool))), -(hAPP(_1132779, c_Big__Operators_Olinorder__class_OMin(_1132777, _1132781)) = c_Big__Operators_Olinorder__class_OMin(_1132777, hAPP(c_Set_Oimage(_1132777, _1132777, _1132779), _1132781)))], (29735 ^ _777959) ^ [_1339081, _1339083, _1339085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1339081, tc_HOL_Obool)), _1339083), _1339085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1339081, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_1339081), _1339083)), hAPP(c_Set_OPow(_1339081), _1339085))))], (49726 ^ _777959) ^ [_1786467, _1786469, _1786471] : [c_Nitpick_Oless__eq__frac(_1786467, _1786469, _1786471), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1786467), c_Nitpick_Oplus__frac(_1786467, _1786469, c_Nitpick_Ouminus__frac(_1786467, _1786471)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (15372 ^ _777959) ^ [_1070370, _1070372] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1070370)), _1070372) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1070370), _1070372)))], (51018 ^ _777959) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (30926 ^ _777959) ^ [_1362071, _1362073, _1362075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1362071)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1362073), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1362075), 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), _1362075), _1362073))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1362071)))))], (33599 ^ _777959) ^ [_1410824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1410824)), -(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), _1410824))))], (50278 ^ _777959) ^ [_1797177, _1797179, _1797181, _1797183, _1797185] : [_1797177 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1797179, _1797181, _1797183, _1797185), _1797177) = c_Lazy__Sequence_Ohit__bound(_1797181))], (22162 ^ _777959) ^ [_1199518, _1199520] : [_1199518 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1199518), _1199520) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (30120 ^ _777959) ^ [_1347662, _1347664, _1347666, _1347668] : [class_Divides_Osemiring__div(_1347662), -(c_Divides_Odiv__class_Omod(_1347662, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347662), _1347664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347662), _1347666), _1347668)), _1347668) = c_Divides_Odiv__class_Omod(_1347662, _1347664, _1347668))], (22754 ^ _777959) ^ [_1211869, _1211871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211869), _1211871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211869)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211871))))], (3606 ^ _777959) ^ [_832407, _832409] : [_832409 = _832407, -(c_Wellfounded_Omeasure(_832409) = c_Wellfounded_Omeasure(_832407))], (49000 ^ _777959) ^ [_1767804, _1767806, _1767808, _1767810] : [-(hAPP(c_Relation_Oconverse(_1767804, _1767806), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1767804, _1767806), tc_HOL_Obool)), _1767808), _1767810)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1767806, _1767804), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1767804, _1767806), _1767808)), hAPP(c_Relation_Oconverse(_1767804, _1767806), _1767810)))], (48396 ^ _777959) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (30740 ^ _777959) ^ [_1358686, _1358688, _1358690] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1358686), _1358688)), _1358690) = 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), _1358686), _1358690)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1358688), _1358690))), 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, _1358686, _1358690)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1358688, _1358690))), _1358690)))], (25894 ^ _777959) ^ [_1268742, _1268744, _1268746, _1268748, _1268750] : [class_Fields_Ofield__inverse__zero(_1268742), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268744), _1268746)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1268744, _1268742), hAPP(hAPP(c_COMBS(_1268744, _1268742, _1268742), hAPP(hAPP(c_COMBB(_1268742, tc_fun(_1268742, _1268742), _1268744), c_Rings_Oinverse__class_Odivide(_1268742)), _1268748)), _1268750)), _1268746) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268742), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1268744, _1268742), _1268748), _1268746)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1268744, _1268742), _1268750), _1268746)))], (36654 ^ _777959) ^ [_1473316, _1473318] : [hAPP(c_Int_ORep__Integ, _1473316) = hAPP(c_Int_ORep__Integ, _1473318), -(_1473316 = _1473318)], (50898 ^ _777959) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (45308 ^ _777959) ^ [_1680997, _1680999] : [hBOOL(hAPP(c_List_Odistinct(_1680997), _1680999)), -(c_List_Oremdups(_1680997, _1680999) = _1680999)], (17053 ^ _777959) ^ [_1104131, _1104133, _1104135, _1104137] : [class_Groups_Oordered__ab__group__add(_1104131), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1104131), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1104131), _1104133), _1104135)), _1104137) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1104131), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1104131), _1104133), _1104137)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1104131), _1104135), _1104137)))], (254 ^ _777959) ^ [_781924, _781926] : [-(class_Fields_Ofield__inverse__zero(_781924)), _781926 = _781924, class_Fields_Ofield__inverse__zero(_781926)], (16371 ^ _777959) ^ [_1091373, _1091375] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1091373), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1091373, tc_HOL_Obool), _1091375)))), 16372 ^ _777959 : [(16373 ^ _777959) ^ [_1091437] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1091373, tc_HOL_Obool)), _1091437), _1091375)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1091373), _1091437))]]], (6539 ^ _777959) ^ [_883592, _883594, _883596, _883598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883592, tc_HOL_Obool)), _883594), _883596)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883592, tc_HOL_Obool)), _883598), _883596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_883592, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_883592, tc_HOL_Obool)), _883594), _883598)), _883596)))], (5653 ^ _777959) ^ [_867161, _867163] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_867161, _867163, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_867161), tc_HOL_Obool))))], (50410 ^ _777959) ^ [_1800423, _1800425] : [-(c_List_Osplice(_1800423, _1800425, c_List_Olist_ONil(_1800423)) = _1800425)], (44027 ^ _777959) ^ [_1653318, _1653320, _1653322, _1653324] : [hBOOL(hAPP(hAPP(c_member(_1653318), _1653320), hAPP(c_List_Oset(_1653318), _1653322))), -(hBOOL(hAPP(_1653324, _1653320))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653318)), hAPP(c_List_Ofilter(_1653318, _1653324), _1653322))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653318)), _1653322))))], (23537 ^ _777959) ^ [_1225931, _1225933] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225931), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1225933), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225931), _1225933)))], (49353 ^ _777959) ^ [_1776442, _1776444, _1776446] : [49354 ^ _777959 : [(49355 ^ _777959) ^ [_1776518] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1776442, _1776442)), _1776444), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1776442, _1776442), tc_HOL_Obool), _1776518), _1776446)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1776442, _1776442)), _1776444), c_Transitive__Closure_Ortrancl(_1776442, _1776446))))], (34857 ^ _777959) ^ [_1433964, _1433966] : [class_Rings_Oring__1(_1433964), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1433964), hAPP(c_Groups_Ouminus__class_Ouminus(_1433964), c_Groups_Oone__class_Oone(_1433964))), 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)))), _1433966))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1433964), c_Groups_Oone__class_Oone(_1433964)))], (37966 ^ _777959) ^ [_1505444, _1505446, _1505448, _1505450, _1505452] : [c_Fun_Oinj__on(_1505444, _1505446, _1505448, _1505450), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1505444, tc_HOL_Obool)), _1505452), _1505450)), -(c_Fun_Oinj__on(_1505444, _1505446, _1505448, _1505452))], (31949 ^ _777959) ^ [_1381137, _1381139] : [class_Int_Onumber__ring(_1381137), 31952 ^ _777959 : [(31959 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1381139)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1381137), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1381139)) = hAPP(c_Int_Onumber__class_Onumber__of(_1381137), _1381139))], (31953 ^ _777959) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1381139))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1381137), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1381139)) = c_Groups_Ozero__class_Ozero(_1381137))]]], (34327 ^ _777959) ^ [_1424101, _1424103] : [class_Int_Onumber__ring(_1424101), -(hAPP(c_Int_Onumber__class_Onumber__of(_1424101), c_Int_OBit0(_1424103)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1424101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1424101), c_Groups_Ozero__class_Ozero(_1424101)), hAPP(c_Int_Onumber__class_Onumber__of(_1424101), _1424103))), hAPP(c_Int_Onumber__class_Onumber__of(_1424101), _1424103)))], (45081 ^ _777959) ^ [_1675750, _1675752, _1675754, _1675756] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1675750)), c_List_Otranspose__rel(_1675750)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1675750)), hAPP(hAPP(c_List_Olist_OCons(_1675750), _1675752), _1675754)), _1675756))), -(c_List_Otranspose(_1675750, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1675750)), hAPP(hAPP(c_List_Olist_OCons(_1675750), _1675752), _1675754)), _1675756)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1675750)), hAPP(hAPP(c_List_Olist_OCons(_1675750), _1675752), c_List_Oconcat(_1675750, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1675750), tc_List_Olist(_1675750)), c_List_Olist_Olist__case(tc_List_Olist(_1675750), _1675750, c_List_Olist_ONil(_1675750), hAPP(hAPP(c_COMBB(tc_List_Olist(_1675750), tc_fun(tc_List_Olist(_1675750), tc_List_Olist(_1675750)), _1675750), c_COMBK(tc_List_Olist(_1675750), tc_List_Olist(_1675750))), hAPP(hAPP(c_COMBC(_1675750, tc_List_Olist(_1675750), tc_List_Olist(_1675750)), c_List_Olist_OCons(_1675750)), c_List_Olist_ONil(_1675750))))), _1675756)))), c_List_Otranspose(_1675750, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1675750)), _1675754), c_List_Oconcat(tc_List_Olist(_1675750), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1675750), tc_List_Olist(tc_List_Olist(_1675750))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1675750)), _1675750, c_List_Olist_ONil(tc_List_Olist(_1675750)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1675750), tc_List_Olist(tc_List_Olist(_1675750))), _1675750), hAPP(hAPP(c_COMBC(tc_List_Olist(_1675750), tc_List_Olist(tc_List_Olist(_1675750)), tc_List_Olist(tc_List_Olist(_1675750))), c_List_Olist_OCons(tc_List_Olist(_1675750))), c_List_Olist_ONil(tc_List_Olist(_1675750)))))), _1675756))))))], (36920 ^ _777959) ^ [_1479093, _1479095, _1479097, _1479099, _1479101, _1479103, _1479105] : [-(hAPP(c_Product__Type_Oapsnd(_1479093, _1479095, _1479097, _1479099), hAPP(c_Product__Type_Oapfst(_1479101, _1479097, _1479093, _1479103), _1479105)) = hAPP(hAPP(c_Product__Type_OPair(_1479097, _1479095), hAPP(_1479103, hAPP(c_Product__Type_Ofst(_1479101, _1479093), _1479105))), hAPP(_1479099, hAPP(c_Product__Type_Osnd(_1479101, _1479093), _1479105))))], (50954 ^ _777959) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (28215 ^ _777959) ^ [_1309996, _1309998] : [class_Rings_Oring__1(_1309996), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309998)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1309996), hAPP(c_Int_Onat, _1309998)) = hAPP(c_Int_Oring__1__class_Oof__int(_1309996), _1309998))], (16413 ^ _777959) ^ [_1092157, _1092159, _1092161] : [class_Orderings_Olinorder(_1092157), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092157), _1092159), _1092161) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1092157), _1092161), _1092159))], (39364 ^ _777959) ^ [_1537121, _1537123, _1537125, _1537127, _1537129, _1537131, _1537133] : [-(c_List_Ofoldr(_1537121, _1537123, _1537125, hAPP(hAPP(c_List_Omap(_1537127, _1537121), _1537129), _1537131), _1537133) = c_List_Ofoldr(_1537127, _1537123, hAPP(c_Fun_Ocomp(_1537121, tc_fun(_1537123, _1537123), _1537127, _1537125), _1537129), _1537131, _1537133))], (42094 ^ _777959) ^ [_1607423, _1607425, _1607427, _1607429] : [hAPP(hAPP(c_Product__Type_OSigma(_1607423, _1607425), _1607427), hAPP(c_COMBK(tc_fun(_1607425, tc_HOL_Obool), _1607423), _1607429)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1607423, _1607425), tc_HOL_Obool)), -(_1607427 = c_Orderings_Obot__class_Obot(tc_fun(_1607423, tc_HOL_Obool))), -(_1607429 = c_Orderings_Obot__class_Obot(tc_fun(_1607425, tc_HOL_Obool)))], (46862 ^ _777959) ^ [_1717654, _1717656, _1717658, _1717660] : [c_Wellfounded_Owf(_1717654, _1717656), -(c_Wellfounded_Owf(_1717658, hAPP(hAPP(c_Relation_Oinv__image(_1717654, _1717658), _1717656), _1717660)))], (38971 ^ _777959) ^ [_1527962, _1527964, _1527966, _1527968, _1527970, _1527972] : [-(hAPP(hAPP(c_List_Omap(_1527962, _1527964), _1527966), hAPP(hAPP(c_List_Omap(_1527968, _1527962), _1527970), _1527972)) = hAPP(hAPP(c_List_Omap(_1527968, _1527964), hAPP(c_Fun_Ocomp(_1527962, _1527964, _1527968, _1527966), _1527970)), _1527972))], (43831 ^ _777959) ^ [_1649525, _1649527, _1649529] : [_1649525 = c_List_Olist_ONil(_1649527), -(c_List_Olast(_1649527, hAPP(hAPP(c_List_Oappend(_1649527), _1649529), _1649525)) = c_List_Olast(_1649527, _1649529))], (22968 ^ _777959) ^ [_1215954, _1215956, _1215958] : [class_Rings_Oring__1(_1215954), hBOOL(hAPP(hAPP(c_member(_1215954), _1215956), c_Int_Oring__1__class_OInts(_1215954))), hBOOL(hAPP(hAPP(c_member(_1215954), _1215958), c_Int_Oring__1__class_OInts(_1215954))), -(hBOOL(hAPP(hAPP(c_member(_1215954), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215954), _1215956), _1215958)), c_Int_Oring__1__class_OInts(_1215954))))], (43328 ^ _777959) ^ [_1638689, _1638691, _1638693, _1638695] : [-(hAPP(hAPP(c_List_Oappend(_1638689), _1638691), _1638693) = _1638695), _1638691 = hAPP(hAPP(c_List_Otake(_1638689), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638689)), _1638691)), _1638695), _1638693 = hAPP(hAPP(c_List_Odrop(_1638689), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638689)), _1638691)), _1638695)], (51228 ^ _777959) ^ [_1812360, _1812362] : [-(class_Smallcheck_Osmall(tc_prod(_1812360, _1812362))), class_Smallcheck_Osmall(_1812360), class_Smallcheck_Osmall(_1812362)], (20425 ^ _777959) ^ [_1167523, _1167525, _1167527] : [class_Rings_Olinordered__ring__strict(_1167523), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167523), _1167525), c_Groups_Ozero__class_Ozero(_1167523))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167523), _1167527), c_Groups_Ozero__class_Ozero(_1167523))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167523), c_Groups_Ozero__class_Ozero(_1167523)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167523), _1167525), _1167527))))], (7326 ^ _777959) ^ [_900798, _900800, _900802] : [class_Lattices_Osemilattice__sup(_900798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900798), _900800), _900802)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_900798), _900802), _900800) = _900802)], (41203 ^ _777959) ^ [_1584416, _1584418, _1584420, _1584422] : [c_Relation_Orefl__on(_1584416, _1584418, _1584420), hBOOL(hAPP(hAPP(c_member(_1584416), _1584422), _1584418)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584416, _1584416)), hAPP(hAPP(c_Product__Type_OPair(_1584416, _1584416), _1584422), _1584422)), _1584420)))], (45638 ^ _777959) ^ [_1688784, _1688786] : [class_Orderings_Olinorder(_1688784), -(c_List_Olinorder__class_Osort__key(_1688784, _1688784, c_COMBI(_1688784), _1688786) = hAPP(c_List_Ofoldl(tc_List_Olist(_1688784), _1688784, hAPP(c_COMBC(_1688784, tc_List_Olist(_1688784), tc_List_Olist(_1688784)), c_List_Olinorder__class_Oinsort__key(_1688784, _1688784, c_COMBI(_1688784))), c_List_Olist_ONil(_1688784)), _1688786))], (32821 ^ _777959) ^ [_1397924, _1397926, _1397928] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(_1397924, _1397926, _1397928)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1397928)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (48352 ^ _777959) ^ [_1750949, _1750951] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1750949), _1750951) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1750949)), hAPP(c_Code__Numeral_Onat__of, _1750951))))], (9888 ^ _777959) ^ [_949762, _949764, _949766] : [class_Lattices_Osemilattice__inf(_949762), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949762), _949764), _949766)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949762), _949766), _949764) = _949764)], (4766 ^ _777959) ^ [_850517, _850519, _850521, _850523] : [-(c_New__DSequence_Opos__single(_850523, _850519) = c_New__DSequence_Opos__single(_850521, _850517)), _850523 = _850521, _850519 = _850517], (19476 ^ _777959) ^ [_1150910] : [hAPP(c_Nat_OSuc, _1150910) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (40290 ^ _777959) ^ [_1559738, _1559740, _1559742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1559738), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1559740)), _1559742))), -(hBOOL(hAPP(hAPP(c_member(_1559740), hAPP(hAPP(c_List_Onth(_1559740), _1559742), _1559738)), hAPP(c_List_Oset(_1559740), _1559742))))], (37474 ^ _777959) ^ [_1493765, _1493767, _1493769, _1493771, _1493773, _1493775, _1493777] : [c_Equiv__Relations_Oequiv(_1493765, _1493767, _1493769), hBOOL(hAPP(hAPP(c_member(tc_fun(_1493765, tc_HOL_Obool)), _1493771), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1493765), _1493767), _1493769))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1493765, tc_HOL_Obool)), _1493773), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1493765), _1493767), _1493769))), hBOOL(hAPP(hAPP(c_member(_1493765), _1493775), _1493771)), hBOOL(hAPP(hAPP(c_member(_1493765), _1493777), _1493773)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1493765, _1493765)), hAPP(hAPP(c_Product__Type_OPair(_1493765, _1493765), _1493775), _1493777)), _1493769)), -(_1493771 = _1493773)], (5544 ^ _777959) ^ [_862668, _862670, _862672, _862674, _862676, _862678] : [-(c_COMBS(_862678, _862674, _862670) = c_COMBS(_862676, _862672, _862668)), _862678 = _862676, _862674 = _862672, _862670 = _862668], (51360 ^ _777959) ^ [_1813668, _1813670] : [-(hAPP(c_COMBI(_1813668), _1813670) = _1813670)], (15548 ^ _777959) ^ [_1073512, _1073514] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073512), _1073514) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 15551 ^ _777959 : [(15554 ^ _777959) ^ [] : [-(_1073514 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15552 ^ _777959) ^ [] : [-(_1073512 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (45356 ^ _777959) ^ [_1681889, _1681891, _1681893] : [-(hBOOL(hAPP(hAPP(c_member(_1681889), _1681891), hAPP(c_List_Oset(_1681889), _1681893)))), -(c_List_Oremdups(_1681889, hAPP(hAPP(c_List_Olist_OCons(_1681889), _1681891), _1681893)) = hAPP(hAPP(c_List_Olist_OCons(_1681889), _1681891), c_List_Oremdups(_1681889, _1681893)))], (23607 ^ _777959) ^ [_1227110, _1227112] : [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), _1227110), _1227112))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1227110))), -(_1227112 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (39988 ^ _777959) ^ [_1552219, _1552221, _1552223] : [hBOOL(hAPP(hAPP(c_member(_1552219), _1552221), hAPP(c_List_Oset(_1552219), _1552223))), -(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(_1552219)), _1552223))))], (37140 ^ _777959) ^ [_1484833, _1484835] : [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)), _1484833), _1484835)), 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)), _1484833), 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)), _1484835), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (29789 ^ _777959) ^ [_1340778, _1340780, _1340782] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1340778, tc_HOL_Obool)), _1340780)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1340778), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1340778, tc_HOL_Obool), _1340780))), 29799 ^ _777959 : [(29802 ^ _777959) ^ [] : [hAPP(c_Finite__Set_Ocard(_1340778), 29798 ^ [_1340778, _1340780, _1340782]) = _1340782], (29800 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1340778, tc_HOL_Obool)), 29798 ^ [_1340778, _1340780, _1340782]), _1340780)))]], 29806 ^ _777959 : [(29810 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1340778, tc_HOL_Obool)), 29808 ^ [_1340778, _1340780, _1340782]), _1340780)))], (29812 ^ _777959) ^ [] : [29805 ^ [_1340778, _1340780, _1340782] = 29808 ^ [_1340778, _1340780, _1340782]], (29814 ^ _777959) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1340778, tc_HOL_Obool)), 29805 ^ [_1340778, _1340780, _1340782]), 29808 ^ [_1340778, _1340780, _1340782]) = c_Orderings_Obot__class_Obot(tc_fun(_1340778, tc_HOL_Obool))], (29807 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1340778, tc_HOL_Obool)), 29805 ^ [_1340778, _1340780, _1340782]), _1340780)))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1340782), hAPP(c_Finite__Set_Ocard(tc_fun(_1340778, tc_HOL_Obool)), _1340780)) = hAPP(c_Finite__Set_Ocard(_1340778), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1340778, tc_HOL_Obool), _1340780)))], (23637 ^ _777959) ^ [_1227653, _1227655] : [class_Groups_Omonoid__mult(_1227653), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1227653), c_Groups_Oone__class_Oone(_1227653)), _1227655) = c_Groups_Oone__class_Oone(_1227653))], (12834 ^ _777959) ^ [_1010805, _1010807, _1010809] : [class_Groups_Ogroup__add(_1010805), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010805), _1010807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1010805), hAPP(c_Groups_Ouminus__class_Ouminus(_1010805), _1010807)), _1010809)) = _1010809)], (34481 ^ _777959) ^ [_1427016] : [class_Rings_Osemiring__1(_1427016), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427016), c_Groups_Oone__class_Oone(_1427016)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1427016))], (46904 ^ _777959) ^ [_1718331, _1718333] : [c_Wellfounded_Owf(_1718331, hAPP(hAPP(c_Relation_Orel__comp(_1718331, _1718331, _1718331), _1718333), _1718333)), -(c_Wellfounded_Owf(_1718331, _1718333))], (7240 ^ _777959) ^ [_899322, _899324, _899326] : [class_Lattices_Osemilattice__sup(_899322), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899322), _899324), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_899322), _899324), _899326))))], (2046 ^ _777959) ^ [_807749, _807751, _807753, _807755, _807757, _807759, _807761, _807763] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_807763, _807759, _807755, _807751) = c_SetInterval_Oord_OgreaterThanLessThan(_807761, _807757, _807753, _807749)), _807763 = _807761, _807759 = _807757, _807755 = _807753, _807751 = _807749], (15677 ^ _777959) ^ [_1076405, _1076407] : [class_Rings_Oring__1__no__zero__divisors(_1076405), 15680 ^ _777959 : [(15681 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076405), _1076407), _1076407) = c_Groups_Oone__class_Oone(_1076405), -(_1076407 = c_Groups_Oone__class_Oone(_1076405)), -(_1076407 = hAPP(c_Groups_Ouminus__class_Ouminus(_1076405), c_Groups_Oone__class_Oone(_1076405)))], (15691 ^ _777959) ^ [] : [15692 ^ _777959 : [(15695 ^ _777959) ^ [] : [_1076407 = hAPP(c_Groups_Ouminus__class_Ouminus(_1076405), c_Groups_Oone__class_Oone(_1076405))], (15693 ^ _777959) ^ [] : [_1076407 = c_Groups_Oone__class_Oone(_1076405)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076405), _1076407), _1076407) = c_Groups_Oone__class_Oone(_1076405))]]], (13561 ^ _777959) ^ [_1026908, _1026910, _1026912, _1026914, _1026916] : [-(_1026908 = c_Orderings_Obot__class_Obot(tc_fun(_1026910, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026910, tc_fun(_1026912, tc_HOL_Obool)), _1026908), hAPP(hAPP(c_COMBC(_1026910, tc_fun(_1026912, tc_HOL_Obool), tc_fun(_1026912, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1026912, tc_HOL_Obool), tc_fun(tc_fun(_1026912, tc_HOL_Obool), tc_fun(_1026912, tc_HOL_Obool)), _1026910), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026912, tc_HOL_Obool))), _1026914)), _1026916)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026912, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026910, tc_fun(_1026912, tc_HOL_Obool)), _1026908), _1026914)), _1026916))], (5342 ^ _777959) ^ [_859695, _859697] : [_859697 = _859695, -(c_List_Olist_OCons(_859697) = c_List_Olist_OCons(_859695))], (7142 ^ _777959) ^ [_897261, _897263, _897265] : [class_Lattices_Olattice(_897261), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897261), _897263), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897261), _897263), _897265)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897261), _897263), _897265))], (36744 ^ _777959) ^ [_1475159, _1475161, _1475163, _1475165, _1475167] : [hBOOL(hAPP(hAPP(_1475159, _1475161), _1475163)), -(hBOOL(hAPP(hAPP(_1475159, hAPP(c_Product__Type_Osnd(_1475165, _1475167), hAPP(hAPP(c_Product__Type_OPair(_1475165, _1475167), _1475163), _1475161))), hAPP(c_Product__Type_Ofst(_1475165, _1475167), hAPP(hAPP(c_Product__Type_OPair(_1475165, _1475167), _1475163), _1475161)))))], (30904 ^ _777959) ^ [_1361732] : [-(_1361732 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30907 ^ _777959 : [(30914 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1361732))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1361732) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30908 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1361732)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1361732) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (45139 ^ _777959) ^ [_1677762, _1677764, _1677766, _1677768, _1677770] : [-(hAPP(hAPP(c_List_Ozip(_1677762, _1677764), _1677766), c_List_OtakeWhile(_1677764, _1677768, _1677770)) = c_List_OtakeWhile(tc_prod(_1677762, _1677764), hAPP(c_Fun_Ocomp(_1677764, tc_HOL_Obool, tc_prod(_1677762, _1677764), _1677768), c_Product__Type_Osnd(_1677762, _1677764)), hAPP(hAPP(c_List_Ozip(_1677762, _1677764), _1677766), _1677770)))], (13359 ^ _777959) ^ [_1022404] : [-(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)), _1022404)))))], (5859 ^ _777959) ^ [_870983, _870985, _870987, _870989, _870991] : [-(hAPP(hAPP(c_Set_Oinsert(_870983), _870985), hAPP(hAPP(c_Set_Oinsert(_870983), _870987), c_Orderings_Obot__class_Obot(tc_fun(_870983, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_870983), _870989), hAPP(hAPP(c_Set_Oinsert(_870983), _870991), c_Orderings_Obot__class_Obot(tc_fun(_870983, tc_HOL_Obool))))), 5860 ^ _777959 : [(5867 ^ _777959) ^ [] : [_870985 = _870991, _870987 = _870989], (5861 ^ _777959) ^ [] : [_870985 = _870989, _870987 = _870991]]], (24470 ^ _777959) ^ [] : [-(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))], (4042 ^ _777959) ^ [_839183, _839185, _839187, _839189] : [-(c_Wellfounded_Oacc(_839189, _839185) = c_Wellfounded_Oacc(_839187, _839183)), _839189 = _839187, _839185 = _839183], (25404 ^ _777959) ^ [_1259369, _1259371] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1259369))), -(c_SMT_Oz3div(_1259371, _1259369) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1259371), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1259369))))], (38744 ^ _777959) ^ [_1521600, _1521602, _1521604, _1521606, _1521608, _1521610] : [-(hAPP(c_Set_Ovimage(_1521600, _1521602, _1521604), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1521606, tc_fun(_1521602, tc_HOL_Obool)), _1521608), _1521610)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1521606, tc_fun(_1521600, tc_HOL_Obool)), _1521608), hAPP(hAPP(c_COMBB(tc_fun(_1521602, tc_HOL_Obool), tc_fun(_1521600, tc_HOL_Obool), _1521606), c_Set_Ovimage(_1521600, _1521602, _1521604)), _1521610)))], (48184 ^ _777959) ^ [_1748041, _1748043] : [-(c_Random_Oselect__weight(_1748041, _1748043) = 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(_1748041, 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, _1748041), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1748041)), _1748043)))), hAPP(hAPP(c_COMBB(_1748041, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1748041, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1748041, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1748041, _1748043))))], (30084 ^ _777959) ^ [_1346940, _1346942, _1346944, _1346946, _1346948, _1346950] : [class_Divides_Oring__div(_1346940), c_Divides_Odiv__class_Omod(_1346940, _1346942, _1346944) = c_Divides_Odiv__class_Omod(_1346940, _1346946, _1346944), c_Divides_Odiv__class_Omod(_1346940, _1346948, _1346944) = c_Divides_Odiv__class_Omod(_1346940, _1346950, _1346944), -(c_Divides_Odiv__class_Omod(_1346940, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346940), _1346942), _1346948), _1346944) = c_Divides_Odiv__class_Omod(_1346940, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346940), _1346946), _1346950), _1346944))], (13945 ^ _777959) ^ [_1036361, _1036363, _1036365] : [-(hAPP(hAPP(c_Set_Oinsert(_1036361), _1036363), _1036365) = hAPP(c_Set_OCollect(_1036361), hAPP(hAPP(c_COMBS(_1036361, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1036361), c_fdisj), hAPP(hAPP(c_COMBC(_1036361, _1036361, tc_HOL_Obool), c_fequal), _1036363))), hAPP(hAPP(c_COMBC(_1036361, tc_fun(_1036361, tc_HOL_Obool), tc_HOL_Obool), c_member(_1036361)), _1036365))))], (44967 ^ _777959) ^ [_1672693, _1672695] : [-(_1672693 = c_List_Olist_ONil(_1672695)), -(c_List_Olast(_1672695, hAPP(c_List_Orev(_1672695), _1672693)) = hAPP(c_List_Ohd(_1672695), _1672693))], (7184 ^ _777959) ^ [_898226, _898228, _898230, _898232] : [class_Lattices_Osemilattice__sup(_898226), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898226), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898226), _898228), _898230)), _898232) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898226), _898228), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_898226), _898230), _898232)))], (5090 ^ _777959) ^ [_855695, _855697, _855699, _855701, _855703, _855705, _855707, _855709, _855711, _855713, _855715, _855717] : [-(c_New__Random__Sequence_Oneg__union(_855717, _855713, _855709, _855705, _855701, _855697) = c_New__Random__Sequence_Oneg__union(_855715, _855711, _855707, _855703, _855699, _855695)), _855717 = _855715, _855713 = _855711, _855709 = _855707, _855705 = _855703, _855701 = _855699, _855697 = _855695], (13479 ^ _777959) ^ [_1025230, _1025232] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1025230), c_Orderings_Otop__class_Otop(tc_fun(_1025230, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1025230), _1025232) = hAPP(c_Finite__Set_Ocard(_1025230), c_Orderings_Otop__class_Otop(tc_fun(_1025230, tc_HOL_Obool))), -(_1025232 = c_Orderings_Otop__class_Otop(tc_fun(_1025230, tc_HOL_Obool)))], (50190 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (40044 ^ _777959) ^ [_1553559, _1553561, _1553563, _1553565, _1553567] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553559)), _1553561) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1553563)), _1553565), 40047 ^ _777959 : [(40055 ^ _777959) ^ [] : [40056 ^ _777959 : [(40057 ^ _777959) ^ [_1553851] : [hAPP(hAPP(c_Map_Omap__of(_1553559, _1553563), hAPP(hAPP(c_List_Ozip(_1553559, _1553563), _1553561), _1553565)), _1553567) = hAPP(c_Option_Ooption_OSome(_1553563), _1553851)]], -(hBOOL(hAPP(hAPP(c_member(_1553559), _1553567), hAPP(c_List_Oset(_1553559), _1553561))))], (40048 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1553559), _1553567), hAPP(c_List_Oset(_1553559), _1553561))), -(hAPP(hAPP(c_Map_Omap__of(_1553559, _1553563), hAPP(hAPP(c_List_Ozip(_1553559, _1553563), _1553561), _1553565)), _1553567) = hAPP(c_Option_Ooption_OSome(_1553563), 40051 ^ [_1553559, _1553561, _1553563, _1553565, _1553567]))]]], (17323 ^ _777959) ^ [_1109255, _1109257, _1109259, _1109261, _1109263] : [class_Groups_Oab__semigroup__mult(_1109255), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1109255, _1109255, c_Groups_Otimes__class_Otimes(_1109255), _1109257, _1109259), _1109261)), -(hBOOL(hAPP(hAPP(c_member(_1109255), _1109257), _1109259))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1109255, _1109255, c_Groups_Otimes__class_Otimes(_1109255), _1109263, hAPP(hAPP(c_Set_Oinsert(_1109255), _1109257), _1109259)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1109255), _1109263), _1109261))))], (24820 ^ _777959) ^ [_1248488, _1248490, _1248492, _1248494] : [class_Orderings_Olinorder(_1248488), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248488), _1248490), _1248492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248488), _1248492), _1248494)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1248488, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1248488, _1248490), _1248492)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1248488, _1248492), _1248494)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1248488, _1248490), _1248494))], (42268 ^ _777959) ^ [_1611170, _1611172, _1611174, _1611176] : [-(hAPP(c_Set_OCollect(tc_prod(_1611170, _1611172)), hAPP(c_Product__Type_Oprod_Oprod__case(_1611170, _1611172, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1611170, tc_fun(_1611172, tc_HOL_Obool), tc_fun(_1611172, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1611172, tc_HOL_Obool), tc_fun(_1611172, tc_HOL_Obool)), _1611170), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1611172)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1611170), c_fconj), _1611174))), _1611176))) = hAPP(hAPP(c_Product__Type_OSigma(_1611170, _1611172), hAPP(c_Set_OCollect(_1611170), _1611174)), hAPP(hAPP(c_COMBB(tc_fun(_1611172, tc_HOL_Obool), tc_fun(_1611172, tc_HOL_Obool), _1611170), c_Set_OCollect(_1611172)), _1611176)))], (15486 ^ _777959) ^ [_1072303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1072303)), _1072303))], (48404 ^ _777959) ^ [_1751841, _1751843] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1751841, _1751841)), hAPP(hAPP(c_Product__Type_OPair(_1751841, _1751841), 48405 ^ [_1751841, _1751843]), 48405 ^ [_1751841, _1751843])), c_Transitive__Closure_Otrancl(_1751841, _1751843)))), -(c_Wellfounded_Oacyclic(_1751841, _1751843))], (23309 ^ _777959) ^ [_1222129] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1222129)), -(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)), _1222129))))], (2122 ^ _777959) ^ [_809049, _809051, _809053, _809055, _809057, _809059, _809061, _809063, _809065, _809067, _809069, _809071] : [-(c_Map_Omap__comp(_809071, _809067, _809063, _809059, _809055, _809051) = c_Map_Omap__comp(_809069, _809065, _809061, _809057, _809053, _809049)), _809071 = _809069, _809067 = _809065, _809063 = _809061, _809059 = _809057, _809055 = _809053, _809051 = _809049], (31614 ^ _777959) ^ [_1374917, _1374919, _1374921, _1374923, _1374925, _1374927] : [c_Com_Ocom_OCond(_1374917, _1374919, _1374921) = c_Com_Ocom_OCond(_1374923, _1374925, _1374927), 31617 ^ _777959 : [(31622 ^ _777959) ^ [] : [-(_1374921 = _1374927)], (31620 ^ _777959) ^ [] : [-(_1374919 = _1374925)], (31618 ^ _777959) ^ [] : [-(_1374917 = _1374923)]]], (23525 ^ _777959) ^ [_1225700, _1225702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1225700), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1225702), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1225700), _1225702)))], (15556 ^ _777959) ^ [_1073623, _1073625] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073623), _1073625) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1073623 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1073625 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (28910 ^ _777959) ^ [_1322955, _1322957, _1322959] : [class_Orderings_Olinorder(_1322955), 28913 ^ _777959 : [(28920 ^ _777959) ^ [] : [_1322957 = _1322959, -(hAPP(c_SetInterval_Oord__class_OatLeast(_1322955), _1322957) = hAPP(c_SetInterval_Oord__class_OatLeast(_1322955), _1322959))], (28914 ^ _777959) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_1322955), _1322957) = hAPP(c_SetInterval_Oord__class_OatLeast(_1322955), _1322959), -(_1322957 = _1322959)]]], (51364 ^ _777959) ^ [_1813736, _1813738, _1813740, _1813742, _1813744, _1813746] : [-(hAPP(hAPP(hAPP(c_COMBB(_1813736, _1813738, _1813740), _1813742), _1813744), _1813746) = hAPP(_1813742, hAPP(_1813744, _1813746)))], (47499 ^ _777959) ^ [_1732751, _1732753] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1732751), c_Int_OInteg)), hBOOL(hAPP(_1732753, hAPP(c_Int_ORep__Integ, 47504 ^ [_1732751, _1732753]))), -(hBOOL(hAPP(_1732753, _1732751)))], (3300 ^ _777959) ^ [_827694, _827696, _827698, _827700] : [-(c_List_Obutlast(_827700, _827696) = c_List_Obutlast(_827698, _827694)), _827700 = _827698, _827696 = _827694], (4670 ^ _777959) ^ [_848855, _848857] : [_848857 = _848855, -(c_Lazy__Sequence_Oyield(_848857) = c_Lazy__Sequence_Oyield(_848855))], (27291 ^ _777959) ^ [_1294562, _1294564, _1294566] : [class_Orderings_Oorder(_1294562), 27294 ^ _777959 : [(27301 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294562), _1294564), _1294566))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1294562, _1294564, _1294566) = c_Orderings_Obot__class_Obot(tc_fun(_1294562, tc_HOL_Obool)))], (27295 ^ _777959) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1294562, _1294564, _1294566) = c_Orderings_Obot__class_Obot(tc_fun(_1294562, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294562), _1294564), _1294566))]]], (8006 ^ _777959) ^ [_914686, _914688, _914690] : [c_Com_Ocom_OSemi(_914686, _914688) = hAPP(c_Com_Ocom_OBODY, _914690)], (46940 ^ _777959) ^ [_1719184, _1719186, _1719188, _1719190] : [c_Wellfounded_Owf(_1719184, _1719186), hBOOL(hAPP(hAPP(c_member(tc_prod(_1719184, _1719184)), hAPP(hAPP(c_Product__Type_OPair(_1719184, _1719184), _1719188), _1719190)), _1719186)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1719184, _1719184)), hAPP(hAPP(c_Product__Type_OPair(_1719184, _1719184), _1719190), _1719188)), _1719186))], (11044 ^ _777959) ^ [_974385, _974387, _974389, _974391] : [hBOOL(hAPP(hAPP(c_member(_974385), _974387), c_Map_Odom(_974385, _974389, _974391))), hAPP(_974391, _974387) = c_Option_Ooption_ONone(_974389)], (43703 ^ _777959) ^ [_1646756, _1646758, _1646760] : [class_Lattices_Olattice(_1646756), -(c_Big__Operators_Olattice__class_OSup__fin(_1646756, hAPP(c_List_Oset(_1646756), hAPP(hAPP(c_List_Olist_OCons(_1646756), _1646758), _1646760))) = hAPP(c_List_Ofoldl(_1646756, _1646756, c_Lattices_Osemilattice__sup__class_Osup(_1646756), _1646758), _1646760))], (46141 ^ _777959) ^ [_1698816, _1698818, _1698820, _1698822] : [46143 ^ _777959 : [(46146 ^ _777959) ^ [] : [hBOOL(hAPP(_1698818, hAPP(hAPP(c_List_Onth(_1698820), _1698822), 46142 ^ [_1698816, _1698818, _1698820, _1698822])))], (46144 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46142 ^ [_1698816, _1698818, _1698820, _1698822]), _1698816)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1698816), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698820)), _1698822))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1698816), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698820)), c_List_OtakeWhile(_1698820, _1698818, _1698822)))))], (35878 ^ _777959) ^ [_1458818, _1458820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1458818), 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)), _1458820)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1458818, _1458820), c_Divides_OnegDivAlg(_1458818, _1458820))))], (42535 ^ _777959) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (19939 ^ _777959) ^ [_1158671, _1158673, _1158675, _1158677] : [class_Rings_Oordered__ring(_1158671), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158671), _1158673), _1158675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158671), _1158677), c_Groups_Ozero__class_Ozero(_1158671))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158671), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158671), _1158677), _1158675)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158671), _1158677), _1158673))))], (41113 ^ _777959) ^ [_1582055, _1582057, _1582059] : [-(c_Relation_Orefl__on(_1582055, _1582057, _1582059)), 41117 ^ _777959 : [(41120 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1582055, _1582055, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1582055, tc_fun(_1582055, tc_HOL_Obool), tc_fun(_1582055, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1582055, tc_HOL_Obool), tc_fun(_1582055, tc_HOL_Obool)), _1582055), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1582055)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1582055), c_fconj), hAPP(hAPP(c_COMBC(_1582055, tc_fun(_1582055, tc_HOL_Obool), tc_HOL_Obool), c_member(_1582055)), _1582057)))), hAPP(hAPP(c_COMBC(_1582055, tc_fun(_1582055, tc_HOL_Obool), tc_HOL_Obool), c_member(_1582055)), _1582057))), 41116 ^ [_1582055, _1582057, _1582059]))], (41118 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582055, _1582055)), 41116 ^ [_1582055, _1582057, _1582059]), _1582059)))]], 41122 ^ _777959 : [(41125 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582055, _1582055)), hAPP(hAPP(c_Product__Type_OPair(_1582055, _1582055), 41121 ^ [_1582055, _1582057, _1582059]), 41121 ^ [_1582055, _1582057, _1582059])), _1582059))], (41123 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1582055), 41121 ^ [_1582055, _1582057, _1582059]), _1582057)))]]], (1020 ^ _777959) ^ [_793433, _793435] : [-(class_Rings_Olinordered__semiring__1__strict(_793433)), _793435 = _793433, class_Rings_Olinordered__semiring__1__strict(_793435)], (27958 ^ _777959) ^ [] : [-(c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (32969 ^ _777959) ^ [_1400652] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1400652) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1400652))], (49740 ^ _777959) ^ [_1786730] : [-(c_Nitpick_Onum(_1786730) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1786730, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1786730)))], (15994 ^ _777959) ^ [_1082552, _1082554, _1082556, _1082558, _1082560] : [class_Groups_Ocomm__monoid__mult(_1082552), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082554), _1082556)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1082552, _1082554, c_Groups_Otimes__class_Otimes(_1082552)), hAPP(hAPP(c_COMBS(_1082554, _1082552, _1082552), hAPP(hAPP(c_COMBB(_1082552, tc_fun(_1082552, _1082552), _1082554), c_Groups_Otimes__class_Otimes(_1082552)), _1082558)), _1082560)), c_Groups_Oone__class_Oone(_1082552)), _1082556) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082552), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1082552, _1082554, c_Groups_Otimes__class_Otimes(_1082552)), _1082558), c_Groups_Oone__class_Oone(_1082552)), _1082556)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1082552, _1082554, c_Groups_Otimes__class_Otimes(_1082552)), _1082560), c_Groups_Oone__class_Oone(_1082552)), _1082556)))], (14434 ^ _777959) ^ [_1048440, _1048442, _1048444] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048440), _1048442)), hBOOL(hAPP(hAPP(c_member(_1048440), _1048444), _1048442)), -(hAPP(c_Finite__Set_Ocard(_1048440), _1048442) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1048440), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1048440, tc_HOL_Obool)), _1048442), hAPP(hAPP(c_Set_Oinsert(_1048440), _1048444), c_Orderings_Obot__class_Obot(tc_fun(_1048440, tc_HOL_Obool)))))))], (10800 ^ _777959) ^ [_969709, _969711, _969713, _969715] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_969709), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969709), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969709), _969711), _969713)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969709), _969715), _969713))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969709), _969711), _969715)))], (17495 ^ _777959) ^ [_1112217, _1112219, _1112221, _1112223, _1112225] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1112217, tc_fun(_1112219, tc_HOL_Obool)), _1112221), hAPP(hAPP(c_COMBS(_1112217, tc_fun(_1112219, tc_HOL_Obool), tc_fun(_1112219, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1112219, tc_HOL_Obool), tc_fun(tc_fun(_1112219, tc_HOL_Obool), tc_fun(_1112219, tc_HOL_Obool)), _1112217), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1112219, tc_HOL_Obool))), _1112223)), _1112225)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1112219, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1112219, tc_HOL_Obool), hAPP(c_Set_Oimage(_1112217, tc_fun(_1112219, tc_HOL_Obool), _1112223), _1112221))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1112219, tc_HOL_Obool), hAPP(c_Set_Oimage(_1112217, tc_fun(_1112219, tc_HOL_Obool), _1112225), _1112221))))], (7648 ^ _777959) ^ [_906930, _906932, _906934, _906936, _906938] : [c_Finite__Set_Ofolding__one__idem(_906930, _906932, _906934), hBOOL(hAPP(c_Finite__Set_Ofinite(_906930), _906936)), hBOOL(hAPP(hAPP(c_member(_906930), _906938), _906936)), -(hAPP(hAPP(_906932, _906938), hAPP(_906934, _906936)) = hAPP(_906934, _906936))], (23146 ^ _777959) ^ [_1219106, _1219108, _1219110, _1219112] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1219106, _1219108)), c_Sum__Type_OPlus(_1219106, _1219108, _1219110, _1219112))), 23149 ^ _777959 : [(23152 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1219108), _1219112)))], (23150 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1219106), _1219110)))]]], (27072 ^ _777959) ^ [_1290585, _1290587, _1290589, _1290591] : [class_Fields_Olinordered__field(_1290585), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1290585), c_Groups_Ozero__class_Ozero(_1290585)), _1290587)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290585), _1290589), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290585), _1290591), _1290587))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1290585), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290585), _1290589), _1290587)), _1290591)))], (10274 ^ _777959) ^ [_958738, _958740, _958742, _958744, _958746, _958748, _958750] : [c_Finite__Set_Ofolding__image__simple(_958738, _958740, _958742, _958744, _958746, _958748), hBOOL(hAPP(c_Finite__Set_Ofinite(_958740), _958750)), -(hAPP(_958748, _958750) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_958738, _958740, _958742), _958746), _958744), _958750))], (39181 ^ _777959) ^ [_1532799, _1532801, _1532803, _1532805] : [hAPP(c_Map_Omap__of(_1532799, _1532801), _1532803) = hAPP(c_Map_Omap__of(_1532799, _1532801), _1532805), -(hAPP(c_Set_Oimage(tc_prod(_1532799, _1532801), _1532799, c_Product__Type_Ofst(_1532799, _1532801)), hAPP(c_List_Oset(tc_prod(_1532799, _1532801)), _1532803)) = hAPP(c_Set_Oimage(tc_prod(_1532799, _1532801), _1532799, c_Product__Type_Ofst(_1532799, _1532801)), hAPP(c_List_Oset(tc_prod(_1532799, _1532801)), _1532805)))], (11667 ^ _777959) ^ [_987550, _987552, _987554, _987556, _987558] : [-(hBOOL(hAPP(hAPP(c_member(_987550), _987552), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_987554, tc_fun(_987550, tc_HOL_Obool)), _987556), _987558)))), 11668 ^ _777959 : [(11669 ^ _777959) ^ [_987632] : [hBOOL(hAPP(hAPP(c_member(_987554), _987632), _987556)), hBOOL(hAPP(hAPP(c_member(_987550), _987552), hAPP(_987558, _987632)))]]], (18689 ^ _777959) ^ [_1136949, _1136951, _1136953] : [class_Lattices_Oab__semigroup__idem__mult(_1136949), -(_1136951 = c_Orderings_Obot__class_Obot(tc_fun(_1136949, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1136949), _1136951)), -(hAPP(c_Finite__Set_Ofold1(_1136949, c_Groups_Otimes__class_Otimes(_1136949)), hAPP(hAPP(c_Set_Oinsert(_1136949), _1136953), _1136951)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136949), _1136953), hAPP(c_Finite__Set_Ofold1(_1136949, c_Groups_Otimes__class_Otimes(_1136949)), _1136951)))], (39952 ^ _777959) ^ [_1551417, _1551419, _1551421, _1551423, _1551425] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551417)), _1551419) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551421)), _1551423), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551417)), _1551425) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551421)), _1551423), hBOOL(hAPP(c_List_Odistinct(_1551421), _1551423)), hAPP(c_Map_Omap__of(_1551421, _1551417), hAPP(hAPP(c_List_Ozip(_1551421, _1551417), _1551423), _1551419)) = hAPP(c_Map_Omap__of(_1551421, _1551417), hAPP(hAPP(c_List_Ozip(_1551421, _1551417), _1551423), _1551425)), -(_1551419 = _1551425)], (14225 ^ _777959) ^ [_1042618, _1042620, _1042622, _1042624, _1042626, _1042628] : [-(hAPP(c_Set_Oimage(_1042618, _1042620, hAPP(hAPP(c_COMBS(_1042618, _1042620, _1042620), hAPP(hAPP(c_COMBS(_1042618, _1042620, tc_fun(_1042620, _1042620)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1042620, tc_fun(_1042620, _1042620)), _1042618), c_If(_1042620)), _1042622)), _1042624)), _1042626)), _1042628) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1042620, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1042618, _1042620, _1042624), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1042618, tc_HOL_Obool)), _1042628), hAPP(c_Set_OCollect(_1042618), _1042622)))), hAPP(c_Set_Oimage(_1042618, _1042620, _1042626), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1042618, tc_HOL_Obool)), _1042628), hAPP(c_Set_OCollect(_1042618), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1042618), c_fNot), _1042622))))))], (50062 ^ _777959) ^ [] : [-(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)))], (30710 ^ _777959) ^ [_1358230, _1358232] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1358230), _1358232))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1358230, _1358232) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1358230), _1358232), _1358232))], (12046 ^ _777959) ^ [_996519, _996521] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996519), _996521))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _996521), _996519)))], (48723 ^ _777959) ^ [_1760504, _1760506] : [-(c_Relation_Orefl__on(_1760504, c_Orderings_Otop__class_Otop(tc_fun(_1760504, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1760504, _1760506)))], (29759 ^ _777959) ^ [_1339647] : [-(hAPP(c_Set_OPow(_1339647), c_Orderings_Otop__class_Otop(tc_fun(_1339647, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1339647, tc_HOL_Obool), tc_HOL_Obool)))], (51164 ^ _777959) ^ [_1811544] : [-(class_HOL_Oequal(tc_List_Olist(_1811544)))], (22491 ^ _777959) ^ [_1206666] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206666)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1206666), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1206666)))], (6411 ^ _777959) ^ [_881476, _881478, _881480, _881482] : [class_Orderings_Oorder(_881476), _881478 = _881480, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881476), _881482), _881480)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881476), _881482), _881478)))], (19011 ^ _777959) ^ [_1143031, _1143033, _1143035, _1143037] : [_1143037 = c_Option_Ooption_ONone(_1143031), -(hAPP(hAPP(c_Option_Omap(_1143031, _1143033), _1143035), _1143037) = c_Option_Ooption_ONone(_1143033))], (42670 ^ _777959) ^ [_1623037, _1623039, _1623041, _1623043, _1623045] : [-(hAPP(hAPP(c_List_Oappend(_1623037), _1623039), hAPP(hAPP(c_List_Olist_OCons(_1623037), _1623041), c_List_Olist_ONil(_1623037))) = hAPP(hAPP(c_List_Oappend(_1623037), _1623043), hAPP(hAPP(c_List_Olist_OCons(_1623037), _1623045), c_List_Olist_ONil(_1623037)))), _1623039 = _1623043, _1623041 = _1623045], (26416 ^ _777959) ^ [_1278456, _1278458, _1278460, _1278462] : [class_Fields_Ofield__inverse__zero(_1278456), 26419 ^ _777959 : [(26420 ^ _777959) ^ [] : [_1278458 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278456), _1278460), _1278462), 26423 ^ _777959 : [(26430 ^ _777959) ^ [] : [_1278462 = c_Groups_Ozero__class_Ozero(_1278456), -(_1278458 = c_Groups_Ozero__class_Ozero(_1278456))], (26424 ^ _777959) ^ [] : [-(_1278462 = c_Groups_Ozero__class_Ozero(_1278456)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278456), _1278458), _1278462) = _1278460)]]], (26436 ^ _777959) ^ [] : [-(_1278458 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1278456), _1278460), _1278462)), 26439 ^ _777959 : [(26442 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1278456), _1278458), _1278462) = _1278460], (26440 ^ _777959) ^ [] : [_1278462 = c_Groups_Ozero__class_Ozero(_1278456)]], 26443 ^ _777959 : [(26446 ^ _777959) ^ [] : [_1278458 = c_Groups_Ozero__class_Ozero(_1278456)], (26444 ^ _777959) ^ [] : [-(_1278462 = c_Groups_Ozero__class_Ozero(_1278456))]]]]], (15126 ^ _777959) ^ [_1065800, _1065802, _1065804, _1065806, _1065808] : [class_Rings_Ocomm__semiring__1(_1065800), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065800), _1065802), _1065804)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065800), _1065806), _1065808)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065800), _1065802), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065800), _1065804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065800), _1065806), _1065808))))], (51000 ^ _777959) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (1480 ^ _777959) ^ [_799183, _799185] : [-(class_Groups_Oordered__comm__monoid__add(_799183)), _799185 = _799183, class_Groups_Oordered__comm__monoid__add(_799185)], (39412 ^ _777959) ^ [_1538273, _1538275, _1538277, _1538279, _1538281, _1538283, _1538285, _1538287] : [c_Finite__Set_Ofolding(_1538273, _1538275, _1538277, _1538279), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538273), _1538281)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1538273), _1538283)), -(hAPP(c_Fun_Ocomp(_1538275, _1538275, _1538285, hAPP(_1538279, _1538283)), hAPP(c_Fun_Ocomp(_1538275, _1538275, _1538285, hAPP(_1538279, _1538281)), _1538287)) = hAPP(c_Fun_Ocomp(_1538275, _1538275, _1538285, hAPP(_1538279, _1538281)), hAPP(c_Fun_Ocomp(_1538275, _1538275, _1538285, hAPP(_1538279, _1538283)), _1538287)))], (8056 ^ _777959) ^ [_915671, _915673, _915675, _915677] : [hBOOL(hAPP(hAPP(c_member(_915671), _915673), _915675)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915671, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_915671), _915673), _915677)), _915675) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915671, tc_HOL_Obool)), _915677), _915675))], (29192 ^ _777959) ^ [_1328281, _1328283, _1328285] : [class_Orderings_Olinorder(_1328281), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1328281), _1328283), _1328285)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1328281, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1328281, _1328283, _1328285)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1328281), _1328285)) = hAPP(c_SetInterval_Oord__class_OatLeast(_1328281), _1328283))], (47487 ^ _777959) ^ [_1732329, _1732331] : [c_Wellfounded_Owf(_1732329, _1732331), -(c_Wellfounded_OwfP(_1732329, hAPP(hAPP(c_COMBC(_1732329, tc_fun(tc_prod(_1732329, _1732329), tc_HOL_Obool), tc_fun(_1732329, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1732329, tc_fun(tc_fun(tc_prod(_1732329, _1732329), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1732329, _1732329), tc_HOL_Obool), tc_fun(_1732329, tc_HOL_Obool)), _1732329), c_COMBC(_1732329, tc_fun(tc_prod(_1732329, _1732329), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1732329, tc_prod(_1732329, _1732329)), tc_fun(_1732329, tc_fun(tc_fun(tc_prod(_1732329, _1732329), tc_HOL_Obool), tc_HOL_Obool)), _1732329), hAPP(c_COMBB(tc_prod(_1732329, _1732329), tc_fun(tc_fun(tc_prod(_1732329, _1732329), tc_HOL_Obool), tc_HOL_Obool), _1732329), c_member(tc_prod(_1732329, _1732329)))), c_Product__Type_OPair(_1732329, _1732329)))), _1732331)))], (48691 ^ _777959) ^ [_1759655, _1759657, _1759659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1759655, _1759655), tc_HOL_Obool)), c_Relation_OId(_1759655)), _1759657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1759655, _1759655), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1759655, _1759655, _1759655), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1759655, _1759655), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1759655, _1759659)), _1759657)), _1759659)), _1759657)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1759655, _1759655), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1759655, _1759659)), _1759657)))], (33273 ^ _777959) ^ [_1405748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1405748))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1405748)))], (30898 ^ _777959) ^ [_1361656] : [_1361656 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1361656) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (15358 ^ _777959) ^ [_1070137, _1070139] : [class_Rings_Ocomm__semiring__1(_1070137), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070137), c_Groups_Oone__class_Oone(_1070137)), _1070139) = _1070139)], (12926 ^ _777959) ^ [_1012874, _1012876, _1012878, _1012880] : [class_Groups_Oab__group__add(_1012874), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012876, _1012874), hAPP(hAPP(c_COMBB(_1012874, _1012874, _1012876), c_Groups_Ouminus__class_Ouminus(_1012874)), _1012878)), _1012880) = hAPP(c_Groups_Ouminus__class_Ouminus(_1012874), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1012876, _1012874), _1012878), _1012880)))], (47244 ^ _777959) ^ [_1725765, _1725767, _1725769, _1725771] : [hBOOL(hAPP(hAPP(c_member(_1725765), _1725767), hAPP(c_Relation_ORange(_1725769, _1725765), _1725771))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1725769, _1725765)), hAPP(hAPP(c_Product__Type_OPair(_1725769, _1725765), 47247 ^ [_1725765, _1725767, _1725769, _1725771]), _1725767)), _1725771)))], (42786 ^ _777959) ^ [_1625639, _1625641, _1625643, _1625645] : [hAPP(hAPP(c_List_Oappend(_1625639), _1625641), _1625643) = hAPP(hAPP(c_List_Oappend(_1625639), _1625645), _1625643), -(_1625641 = _1625645)], (16161 ^ _777959) ^ [_1086189] : [-(hAPP(c_Nat_OSuc, _1086189) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1086189))], (48366 ^ _777959) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (34919 ^ _777959) ^ [_1435136, _1435138] : [class_Rings_Oring__1(_1435136), 34922 ^ _777959 : [(34929 ^ _777959) ^ [] : [-(_1435138 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 34932 ^ _777959 : [(34939 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435138), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1435136), _1435138) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1435136), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1435136, _1435136)), tc_fun(tc_Int_Oint, _1435136)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1435136, _1435136), _1435136), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1435136, _1435136)), tc_fun(tc_Int_Oint, _1435136)), tc_Int_Oint), c_COMBB(tc_fun(_1435136, _1435136), _1435136, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1435136, tc_fun(tc_fun(_1435136, _1435136), _1435136), tc_Int_Oint), c_HOL_OLet(_1435136, _1435136)), c_Int_Oring__1__class_Oof__int(_1435136)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1435136, _1435136), tc_fun(_1435136, _1435136)), hAPP(hAPP(c_COMBB(tc_fun(_1435136, tc_fun(_1435136, _1435136)), tc_fun(tc_fun(_1435136, _1435136), tc_fun(_1435136, _1435136)), tc_Int_Oint), c_COMBS(_1435136, _1435136, _1435136)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1435136, _1435136), tc_fun(_1435136, tc_fun(_1435136, _1435136))), hAPP(hAPP(c_COMBB(tc_fun(_1435136, tc_fun(_1435136, _1435136)), tc_fun(tc_fun(_1435136, _1435136), tc_fun(_1435136, tc_fun(_1435136, _1435136))), tc_Int_Oint), c_COMBB(_1435136, tc_fun(_1435136, _1435136), _1435136)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1435136, tc_fun(_1435136, _1435136)), tc_Int_Oint), c_If(_1435136)), 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(_1435136, _1435136, _1435136), c_Groups_Oplus__class_Oplus(_1435136)), c_COMBI(_1435136))))), hAPP(hAPP(c_COMBC(_1435136, _1435136, _1435136), hAPP(hAPP(c_COMBB(_1435136, tc_fun(_1435136, _1435136), _1435136), c_Groups_Oplus__class_Oplus(_1435136)), hAPP(hAPP(c_COMBS(_1435136, _1435136, _1435136), c_Groups_Oplus__class_Oplus(_1435136)), c_COMBI(_1435136)))), c_Groups_Oone__class_Oone(_1435136))))), c_Divides_Odivmod__int(_1435138, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (34933 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435138), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1435136), _1435138) = hAPP(c_Groups_Ouminus__class_Ouminus(_1435136), hAPP(c_Int_Oring__1__class_Oof__int(_1435136), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1435138))))]]], (34923 ^ _777959) ^ [] : [_1435138 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1435136), _1435138) = c_Groups_Ozero__class_Ozero(_1435136))]]], (51268 ^ _777959) ^ [_1812816] : [-(class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(_1812816)))], (51112 ^ _777959) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (17287 ^ _777959) ^ [_1108554, _1108556, _1108558] : [class_Orderings_Olinorder(_1108554), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108554), _1108556)), hBOOL(hAPP(hAPP(c_member(_1108554), _1108558), _1108556)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1108554), _1108558), c_Big__Operators_Olinorder__class_OMax(_1108554, _1108556)) = c_Big__Operators_Olinorder__class_OMax(_1108554, _1108556))], (6717 ^ _777959) ^ [_887028, _887030] : [hBOOL(hAPP(hAPP(c_member(_887028), _887030), c_Orderings_Obot__class_Obot(tc_fun(_887028, tc_HOL_Obool))))], (15240 ^ _777959) ^ [_1068277, _1068279] : [15241 ^ _777959 : [(15244 ^ _777959) ^ [] : [_1068277 = _1068279], (15242 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068277), _1068279))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068277), hAPP(c_Nat_OSuc, _1068279))))], (27662 ^ _777959) ^ [_1300496, _1300498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300496)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300498)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1300496)), hAPP(c_Int_Onat, _1300498)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1300496), _1300498)))], (22296 ^ _777959) ^ [_1202444, _1202446, _1202448, _1202450, _1202452] : [class_Groups_Ocomm__monoid__mult(_1202444), hBOOL(hAPP(c_Finite__Set_Ofinite(_1202446), _1202448)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1202446), _1202450)), 22310 ^ _777959 : [(22313 ^ _777959) ^ [] : [hAPP(_1202452, 22309 ^ [_1202444, _1202446, _1202448, _1202450, _1202452]) = c_Groups_Oone__class_Oone(_1202444)], (22311 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1202446), 22309 ^ [_1202444, _1202446, _1202448, _1202450, _1202452]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1202446, tc_HOL_Obool)), _1202448), _1202450))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1202446, _1202444), _1202452), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1202446, tc_HOL_Obool)), _1202448), _1202450)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1202444), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1202446, _1202444), _1202452), _1202448)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1202446, _1202444), _1202452), _1202450)))], (38676 ^ _777959) ^ [_1520168, _1520170, _1520172, _1520174, _1520176, _1520178] : [hAPP(_1520168, _1520170) = _1520172, hBOOL(hAPP(hAPP(c_member(_1520174), _1520172), _1520176)), -(hBOOL(hAPP(hAPP(c_member(_1520178), _1520170), hAPP(c_Set_Ovimage(_1520178, _1520174, _1520168), _1520176))))], (21718 ^ _777959) ^ [_1190507, _1190509] : [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), _1190507), _1190509))), 21721 ^ _777959 : [(21724 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1190509)))], (21722 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1190507)))]]], (50928 ^ _777959) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (6597 ^ _777959) ^ [_884717, _884719, _884721, _884723, _884725, _884727, _884729] : [-(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_884717), _884719), _884721), _884723) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_884717), _884725), _884727), _884729)), _884719 = _884725, _884721 = _884727, _884723 = _884729], (24902 ^ _777959) ^ [_1250133, _1250135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1250133), 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)), _1250135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1250133), _1250135)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32335 ^ _777959) ^ [_1388379, _1388381, _1388383] : [class_Int_Onumber__ring(_1388379), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388379), hAPP(c_Groups_Ouminus__class_Ouminus(_1388379), hAPP(c_Int_Onumber__class_Onumber__of(_1388379), _1388381))), _1388383) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1388379), hAPP(c_Int_Onumber__class_Onumber__of(_1388379), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1388381))), _1388383))], (9746 ^ _777959) ^ [_947040, _947042, _947044] : [class_Lattices_Olattice(_947040), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_947040), _947042), _947044) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_947040), _947044), _947042))], (13817 ^ _777959) ^ [_1033384] : [-(c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1033384), tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(_1033384)), c_Option_Ooption_ONone(_1033384)), hAPP(c_Set_Oimage(_1033384, tc_Option_Ooption(_1033384), c_Option_Ooption_OSome(_1033384)), c_Orderings_Otop__class_Otop(tc_fun(_1033384, tc_HOL_Obool)))))], (44254 ^ _777959) ^ [_1658293, _1658295, _1658297, _1658299, _1658301] : [class_Orderings_Olinorder(_1658293), c_List_Olinorder__class_Osorted(_1658293, hAPP(hAPP(c_List_Omap(_1658295, _1658293), _1658297), _1658299)), -(c_List_Olinorder__class_Osorted(_1658293, hAPP(hAPP(c_List_Omap(_1658295, _1658293), _1658297), c_List_Oremove1(_1658295, _1658301, _1658299))))], (6091 ^ _777959) ^ [_875459, _875461, _875463] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875459, tc_HOL_Obool)), _875461), _875463)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_875459, tc_HOL_Obool)), _875461), _875463) = _875463)], (38848 ^ _777959) ^ [_1524220, _1524222, _1524224, _1524226] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1524220), _1524222)), c_Fun_Oinj__on(_1524224, _1524220, _1524226, c_Orderings_Otop__class_Otop(tc_fun(_1524224, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1524224), hAPP(c_Set_Ovimage(_1524224, _1524220, _1524226), _1524222))))], (28840 ^ _777959) ^ [_1321545, _1321547, _1321549, _1321551] : [class_Orderings_Olinorder(_1321545), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321545), _1321547), _1321549)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1321545), _1321549), _1321551)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321545, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1321545, _1321547, _1321549)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1321545, _1321549, _1321551)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1321545, _1321547), _1321551))], (13953 ^ _777959) ^ [_1036613, _1036615, _1036617] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1036613, tc_HOL_Obool)), _1036615), _1036617) = hAPP(c_Set_OCollect(_1036613), hAPP(hAPP(c_COMBS(_1036613, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1036613), c_fdisj), hAPP(hAPP(c_COMBC(_1036613, tc_fun(_1036613, tc_HOL_Obool), tc_HOL_Obool), c_member(_1036613)), _1036615))), hAPP(hAPP(c_COMBC(_1036613, tc_fun(_1036613, tc_HOL_Obool), tc_HOL_Obool), c_member(_1036613)), _1036617))))], (5839 ^ _777959) ^ [_870566, _870568, _870570] : [hAPP(hAPP(c_Set_Oinsert(_870566), _870568), c_Orderings_Obot__class_Obot(tc_fun(_870566, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_870566), _870570), c_Orderings_Obot__class_Obot(tc_fun(_870566, tc_HOL_Obool))), -(_870568 = _870570)], (32571 ^ _777959) ^ [_1393031, _1393033] : [class_Int_Onumber__ring(_1393031), class_Rings_Olinordered__idom(_1393031), 32578 ^ _777959 : [(32585 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393031), hAPP(c_Int_Onumber__class_Onumber__of(_1393031), _1393033)), c_Groups_Ozero__class_Ozero(_1393031)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1393031), hAPP(c_Int_Onumber__class_Onumber__of(_1393031), _1393033)) = hAPP(c_Int_Onumber__class_Onumber__of(_1393031), _1393033))], (32579 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1393031), hAPP(c_Int_Onumber__class_Onumber__of(_1393031), _1393033)), c_Groups_Ozero__class_Ozero(_1393031))), -(hAPP(c_Groups_Oabs__class_Oabs(_1393031), hAPP(c_Int_Onumber__class_Onumber__of(_1393031), _1393033)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1393031), hAPP(c_Int_Onumber__class_Onumber__of(_1393031), _1393033)))]]], (35169 ^ _777959) ^ [_1439438] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1439438)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1439438)))], (49683 ^ _777959) ^ [_1785334, _1785336, _1785338, _1785340, _1785342, _1785344] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1785334, _1785336)), _1785338), hAPP(hAPP(c_Relation_Orel__comp(_1785334, _1785340, _1785336), _1785342), _1785344))), 49689 ^ _777959 : [(49694 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785340, _1785336)), hAPP(hAPP(c_Product__Type_OPair(_1785340, _1785336), 49687 ^ [_1785334, _1785336, _1785338, _1785340, _1785342, _1785344]), 49688 ^ [_1785334, _1785336, _1785338, _1785340, _1785342, _1785344])), _1785344)))], (49692 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1785334, _1785340)), hAPP(hAPP(c_Product__Type_OPair(_1785334, _1785340), 49686 ^ [_1785334, _1785336, _1785338, _1785340, _1785342, _1785344]), 49687 ^ [_1785334, _1785336, _1785338, _1785340, _1785342, _1785344])), _1785342)))], (49690 ^ _777959) ^ [] : [-(_1785338 = hAPP(hAPP(c_Product__Type_OPair(_1785334, _1785336), 49686 ^ [_1785334, _1785336, _1785338, _1785340, _1785342, _1785344]), 49688 ^ [_1785334, _1785336, _1785338, _1785340, _1785342, _1785344]))]]], (49406 ^ _777959) ^ [_1777762, _1777764, _1777766, _1777768, _1777770] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1777762, _1777762)), hAPP(hAPP(c_Product__Type_OPair(_1777762, _1777762), _1777764), _1777766)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777762, _1777762), tc_HOL_Obool), _1777768), _1777770))), 49411 ^ _777959 : [(49414 ^ _777959) ^ [] : [-(_1777764 = _1777766)], (49412 ^ _777959) ^ [] : [-(_1777768 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 49417 ^ _777959 : [(49422 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777762, _1777762)), hAPP(hAPP(c_Product__Type_OPair(_1777762, _1777762), 49415 ^ [_1777762, _1777764, _1777766, _1777768, _1777770]), _1777766)), _1777770)))], (49420 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1777762, _1777762)), hAPP(hAPP(c_Product__Type_OPair(_1777762, _1777762), _1777764), 49415 ^ [_1777762, _1777764, _1777766, _1777768, _1777770])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1777762, _1777762), tc_HOL_Obool), 49416 ^ [_1777762, _1777764, _1777766, _1777768, _1777770]), _1777770))))], (49418 ^ _777959) ^ [] : [-(_1777768 = hAPP(c_Nat_OSuc, 49416 ^ [_1777762, _1777764, _1777766, _1777768, _1777770]))]]], (36618 ^ _777959) ^ [_1472586] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1472586)), 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), _1472586)) = 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), _1472586))))))], (13675 ^ _777959) ^ [_1030539, _1030541, _1030543] : [hBOOL(hAPP(hAPP(c_member(_1030539), _1030541), hAPP(c_Set_OCollect(_1030539), _1030543))), -(hBOOL(hAPP(_1030543, _1030541)))], (4388 ^ _777959) ^ [_844376, _844378, _844380, _844382, _844384, _844386] : [-(c_Nitpick_Oplus__frac(_844386, _844382, _844378) = c_Nitpick_Oplus__frac(_844384, _844380, _844376)), _844386 = _844384, _844382 = _844380, _844378 = _844376], (51020 ^ _777959) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (48332 ^ _777959) ^ [_1750586] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1750586)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1750586))], (45222 ^ _777959) ^ [_1679295, _1679297, _1679299, _1679301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1679295), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679297)), c_List_OtakeWhile(_1679297, _1679299, _1679301)))), -(hAPP(hAPP(c_List_Onth(_1679297), c_List_OtakeWhile(_1679297, _1679299, _1679301)), _1679295) = hAPP(hAPP(c_List_Onth(_1679297), _1679301), _1679295))], (15578 ^ _777959) ^ [_1073924, _1073926, _1073928, _1073930, _1073932] : [class_Rings_Osemiring__0(_1073924), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073924), _1073926), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1073928, _1073924), _1073930), _1073932)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1073928, _1073924), hAPP(hAPP(c_COMBB(_1073924, _1073924, _1073928), hAPP(c_Groups_Otimes__class_Otimes(_1073924), _1073926)), _1073930)), _1073932))], (50752 ^ _777959) ^ [_1807348, _1807350] : [class_Lattices_Obounded__lattice(_1807348), -(class_Lattices_Obounded__lattice__top(tc_fun(_1807350, _1807348)))], (36349 ^ _777959) ^ [_1467182, _1467184] : [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), _1467182), _1467184))), 36352 ^ _777959 : [(36361 ^ _777959) ^ [] : [-(c_Divides_OposDivAlg(_1467182, _1467184) = hAPP(c_Divides_Oadjust(_1467184), c_Divides_OposDivAlg(_1467182, 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)))), _1467184)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467182), _1467184))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1467184), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36353 ^ _777959) ^ [] : [36354 ^ _777959 : [(36357 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1467184), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36355 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1467182), _1467184))]], -(c_Divides_OposDivAlg(_1467182, _1467184) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467182))]]], (30691 ^ _777959) ^ [_1357903, _1357905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1357903)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1357905, _1357903)), _1357903)))], (40389 ^ _777959) ^ [_1561914, _1561916, _1561918, _1561920, _1561922] : [class_Orderings_Olinorder(_1561914), hBOOL(hAPP(c_List_Odistinct(_1561916), _1561918)), -(hBOOL(hAPP(c_List_Odistinct(_1561916), c_List_Olinorder__class_Oinsort__insert__key(_1561916, _1561914, _1561920, _1561922, _1561918))))], (23289 ^ _777959) ^ [_1221793, _1221795] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221793)), _1221795) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1221793), _1221795)))], (16020 ^ _777959) ^ [_1083161, _1083163, _1083165] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1083161), _1083163)), -(hBOOL(hAPP(hAPP(c_member(_1083161), _1083165), _1083163))), -(hAPP(c_Finite__Set_Ocard(_1083161), hAPP(hAPP(c_Set_Oinsert(_1083161), _1083165), _1083163)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1083161), _1083163)))], (43482 ^ _777959) ^ [_1642295, _1642297] : [-(_1642295 = c_List_Olist_ONil(_1642297)), -(hAPP(c_List_Ohd(_1642297), _1642295) = hAPP(hAPP(c_List_Onth(_1642297), _1642295), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (40260 ^ _777959) ^ [_1558851, _1558853] : [40262 ^ _777959 : [(40266 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40264 ^ [_1558851, _1558853]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1558851)), _1558853))))], (40268 ^ _777959) ^ [] : [40261 ^ [_1558851, _1558853] = 40264 ^ [_1558851, _1558853]], (40270 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1558851), _1558853), 40261 ^ [_1558851, _1558853]) = hAPP(hAPP(c_List_Onth(_1558851), _1558853), 40264 ^ [_1558851, _1558853]))], (40263 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40261 ^ [_1558851, _1558853]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1558851)), _1558853))))]], -(hBOOL(hAPP(c_List_Odistinct(_1558851), _1558853)))], (24484 ^ _777959) ^ [_1242979, _1242981] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1242979), _1242981))), -(c_Nat__Transfer_Otsub(_1242981, _1242979) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (8448 ^ _777959) ^ [_924426, _924428, _924430] : [class_Orderings_Olinorder(_924426), 8451 ^ _777959 : [(8452 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924426), _924428), _924430))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924426), _924430), _924428))), -(_924428 = _924430)], (8462 ^ _777959) ^ [] : [8463 ^ _777959 : [(8466 ^ _777959) ^ [] : [_924428 = _924430], (8464 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924426), _924430), _924428))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924426), _924428), _924430))]]], (25460 ^ _777959) ^ [_1260682] : [-(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)), _1260682))))], (25550 ^ _777959) ^ [_1262248, _1262250, _1262252] : [-(hBOOL(hAPP(_1262248, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1262250), _1262252)))), 25553 ^ _777959 : [(25556 ^ _777959) ^ [] : [hBOOL(hAPP(_1262248, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (25554 ^ _777959) ^ [] : [-(_1262252 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 25557 ^ _777959 : [(25562 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25560 ^ [_1262248, _1262250, _1262252]), _1262252)))], (25564 ^ _777959) ^ [] : [-(_1262250 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1262252), 25559 ^ [_1262248, _1262250, _1262252])), 25560 ^ [_1262248, _1262250, _1262252]))], (25566 ^ _777959) ^ [] : [hBOOL(hAPP(_1262248, 25559 ^ [_1262248, _1262250, _1262252]))], (25558 ^ _777959) ^ [] : [_1262252 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (24031 ^ _777959) ^ [_1234881, _1234883, _1234885] : [hBOOL(hAPP(_1234881, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1234883), _1234885)))), 24034 ^ _777959 : [(24041 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1234883), _1234885)), -(hBOOL(hAPP(_1234881, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24035 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1234885), _1234883)), -(hBOOL(hAPP(_1234881, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234883)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1234885)))))]]], (46786 ^ _777959) ^ [_1714193, _1714195, _1714197, _1714199, _1714201, _1714203] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1714193, _1714195, _1714197), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1714193, _1714195), tc_HOL_Obool)), _1714199), _1714201)), _1714203) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1714193, _1714197), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1714193, _1714195, _1714197), _1714199), _1714203)), hAPP(hAPP(c_Relation_Orel__comp(_1714193, _1714195, _1714197), _1714201), _1714203)))], (39201 ^ _777959) ^ [_1533263, _1533265, _1533267, _1533269, _1533271] : [class_Groups_Ocomm__monoid__mult(_1533263), hBOOL(hAPP(c_Finite__Set_Ofinite(_1533265), _1533267)), c_Fun_Oinj__on(_1533265, _1533265, _1533269, _1533267), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1533265, _1533263), _1533271), hAPP(c_Set_Oimage(_1533265, _1533265, _1533269), _1533267)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1533265, _1533263), hAPP(c_Fun_Ocomp(_1533265, _1533263, _1533265, _1533271), _1533269)), _1533267))], (9444 ^ _777959) ^ [_940388, _940390, _940392, _940394, _940396, _940398, _940400] : [c_Nitpick_Ofold__graph_H(_940388, _940390, _940392, _940394, _940396, hAPP(hAPP(_940392, _940398), _940400)), 9449 ^ _777959 : [(9452 ^ _777959) ^ [] : [-(hAPP(hAPP(_940392, _940398), _940400) = _940394)], (9450 ^ _777959) ^ [] : [-(_940396 = c_Orderings_Obot__class_Obot(tc_fun(_940388, tc_HOL_Obool)))]], 9455 ^ _777959 : [(9460 ^ _777959) ^ [] : [-(c_Nitpick_Ofold__graph_H(_940388, _940390, _940392, _940394, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940388, tc_HOL_Obool)), _940396), hAPP(hAPP(c_Set_Oinsert(_940388), 9453 ^ [_940388, _940390, _940392, _940394, _940396, _940398, _940400]), c_Orderings_Obot__class_Obot(tc_fun(_940388, tc_HOL_Obool)))), 9454 ^ [_940388, _940390, _940392, _940394, _940396, _940398, _940400]))], (9458 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_940388), 9453 ^ [_940388, _940390, _940392, _940394, _940396, _940398, _940400]), _940396)))], (9456 ^ _777959) ^ [] : [-(hAPP(hAPP(_940392, _940398), _940400) = hAPP(hAPP(_940392, 9453 ^ [_940388, _940390, _940392, _940394, _940396, _940398, _940400]), 9454 ^ [_940388, _940390, _940392, _940394, _940396, _940398, _940400]))]]], (51408 ^ _777959) ^ [_1814365, _1814367] : [hBOOL(hAPP(hAPP(c_fconj, _1814365), _1814367)), -(hBOOL(_1814365))], (35918 ^ _777959) ^ [_1459433, _1459435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1459433)), 35921 ^ _777959 : [(35928 ^ _777959) ^ [] : [-(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), _1459435), _1459433)))), -(c_Divides_OnegDivAlg(_1459435, _1459433) = hAPP(c_Divides_Oadjust(_1459433), c_Divides_OnegDivAlg(_1459435, 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)))), _1459433))))], (35922 ^ _777959) ^ [] : [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), _1459435), _1459433))), -(c_Divides_OnegDivAlg(_1459435, _1459433) = 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), _1459435), _1459433)))]]], (32829 ^ _777959) ^ [_1398064] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1398064)))), -(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), _1398064)) = 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), _1398064))))], (40127 ^ _777959) ^ [_1555875, _1555877, _1555879] : [-(_1555875 = _1555877), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555879)), _1555875) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555879)), _1555877), 40133 ^ _777959 : [(40136 ^ _777959) ^ [] : [hAPP(hAPP(c_List_Onth(_1555879), _1555875), 40132 ^ [_1555875, _1555877, _1555879]) = hAPP(hAPP(c_List_Onth(_1555879), _1555877), 40132 ^ [_1555875, _1555877, _1555879])], (40134 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40132 ^ [_1555875, _1555877, _1555879]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555879)), _1555875))))]]], (33475 ^ _777959) ^ [_1408929, _1408931] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1408929), _1408931), hAPP(c_Int_Onumber__class_Onumber__of(_1408929), c_Int_OBit1(c_Int_OPls))) = _1408931), class_Fields_Ofield(_1408929), class_Int_Onumber__ring(_1408929)], (38812 ^ _777959) ^ [_1523342, _1523344, _1523346, _1523348, _1523350] : [hBOOL(hAPP(hAPP(c_member(_1523342), _1523344), hAPP(c_Set_Ovimage(_1523342, _1523346, _1523348), hAPP(hAPP(c_Set_Oinsert(_1523346), _1523350), c_Orderings_Obot__class_Obot(tc_fun(_1523346, tc_HOL_Obool)))))), -(hAPP(_1523348, _1523344) = _1523350)], (42517 ^ _777959) ^ [_1619282, _1619284] : [-(c_Product__Type_Omap__pair(_1619282, _1619282, _1619284, _1619284, c_Fun_Oid(_1619282), c_Fun_Oid(_1619284)) = c_Fun_Oid(tc_prod(_1619282, _1619284)))], (43199 ^ _777959) ^ [_1635672, _1635674] : [hBOOL(hAPP(c_List_Odistinct(_1635672), _1635674)), -(hBOOL(hAPP(c_List_Odistinct(_1635672), hAPP(c_List_Orotate1(_1635672), _1635674))))], (26072 ^ _777959) ^ [_1272298, _1272300, _1272302, _1272304, _1272306] : [class_Fields_Ofield__inverse__zero(_1272298), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1272298), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272298), _1272300), _1272302)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272298), _1272304), _1272306)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1272298), _1272300), _1272304)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1272298), _1272302), _1272306)))], (45103 ^ _777959) ^ [_1676593, _1676595, _1676597] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1676593), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1676593))), _1676595))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1676597), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1676593))), _1676595))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1676593))), hAPP(c_List_Ofilter(tc_List_Olist(_1676593), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1676593)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1676597)), c_Nat_Osize__class_Osize(tc_List_Olist(_1676593)))), c_List_Otranspose(_1676593, _1676595))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676593)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1676593)), _1676595), _1676597)))], (8746 ^ _777959) ^ [_928822, _928824, _928826, _928828, _928830] : [hAPP(_928822, _928824) = _928826, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928828, _928830), _928822), _928824), _928826) = _928822)], (8038 ^ _777959) ^ [_915216, _915218, _915220, _915222, _915224] : [c_Com_Ocom_OCall(_915216, _915218, _915220) = c_Com_Ocom_OSemi(_915222, _915224)], (45268 ^ _777959) ^ [_1680350, _1680352, _1680354, _1680356] : [-(c_List_Oremdups(_1680350, hAPP(hAPP(c_List_Omap(_1680352, _1680350), _1680354), c_List_Oremdups(_1680352, _1680356))) = c_List_Oremdups(_1680350, hAPP(hAPP(c_List_Omap(_1680352, _1680350), _1680354), _1680356)))], (33007 ^ _777959) ^ [_1401282, _1401284, _1401286] : [class_Int_Onumber__ring(_1401282), 33010 ^ _777959 : [(33017 ^ _777959) ^ [] : [-(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), _1401284)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1401282), _1401286), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1401284))) = c_Groups_Oone__class_Oone(_1401282))], (33011 ^ _777959) ^ [] : [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), _1401284))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1401282), _1401286), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1401284))) = hAPP(hAPP(c_HOL_OLet(_1401282, _1401282), hAPP(hAPP(c_Power_Opower__class_Opower(_1401282), _1401286), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401284))), hAPP(hAPP(c_COMBS(_1401282, _1401282, _1401282), hAPP(hAPP(c_COMBB(_1401282, tc_fun(_1401282, _1401282), _1401282), c_Groups_Otimes__class_Otimes(_1401282)), hAPP(c_Groups_Otimes__class_Otimes(_1401282), _1401286))), c_COMBI(_1401282))))]]], (23587 ^ _777959) ^ [_1226759, _1226761] : [23588 ^ _777959 : [(23591 ^ _777959) ^ [] : [_1226759 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23589 ^ _777959) ^ [] : [_1226761 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1226759), _1226761) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18859 ^ _777959) ^ [_1140049, _1140051, _1140053] : [class_Groups_Oab__semigroup__mult(_1140049), -(_1140051 = c_Orderings_Obot__class_Obot(tc_fun(_1140049, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1140049), _1140051)), -(hBOOL(hAPP(hAPP(c_member(_1140049), _1140053), _1140051))), -(hAPP(c_Finite__Set_Ofold1(_1140049, c_Groups_Otimes__class_Otimes(_1140049)), hAPP(hAPP(c_Set_Oinsert(_1140049), _1140053), _1140051)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140049), _1140053), hAPP(c_Finite__Set_Ofold1(_1140049, c_Groups_Otimes__class_Otimes(_1140049)), _1140051)))], (22323 ^ _777959) ^ [_1203080, _1203082] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1203080)), _1203082) = 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), _1203080)), _1203082))], (42363 ^ _777959) ^ [_1613944, _1613946, _1613948, _1613950, _1613952, _1613954, _1613956, _1613958] : [c_Fun_Oinj__on(_1613944, _1613946, _1613948, _1613950), c_Fun_Oinj__on(_1613952, _1613954, _1613956, _1613958), -(c_Fun_Oinj__on(tc_prod(_1613944, _1613952), tc_prod(_1613946, _1613954), c_Product__Type_Omap__pair(_1613944, _1613946, _1613952, _1613954, _1613948, _1613956), hAPP(hAPP(c_Product__Type_OSigma(_1613944, _1613952), _1613950), hAPP(c_COMBK(tc_fun(_1613952, tc_HOL_Obool), _1613944), _1613958))))], (33593 ^ _777959) ^ [_1410739] : [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), _1410739))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1410739)))], (34067 ^ _777959) ^ [_1419652, _1419654] : [c_Int_OBit0(_1419652) = c_Int_OBit1(_1419654)], (44384 ^ _777959) ^ [_1660251, _1660253] : [44385 ^ _777959 : [(44388 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1660253), _1660251))], (44386 ^ _777959) ^ [] : [_1660253 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_List_Oupt(_1660251, _1660253) = c_List_Olist_ONil(tc_Nat_Onat))], (10140 ^ _777959) ^ [_955333, _955335, _955337, _955339] : [class_Lattices_Osemilattice__inf(_955333), hBOOL(hAPP(c_Finite__Set_Ofinite(_955333), _955335)), hBOOL(hAPP(hAPP(c_member(_955333), _955337), _955335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_955333), hAPP(hAPP(c_Finite__Set_Ofold(_955333, _955333, c_Lattices_Osemilattice__inf__class_Oinf(_955333)), _955339), _955335)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_955333), _955337), _955339))))], (36692 ^ _777959) ^ [_1474133, _1474135, _1474137, _1474139, _1474141] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1474133, _1474135, _1474137), _1474139), _1474141) = hAPP(hAPP(_1474139, hAPP(c_Product__Type_Ofst(_1474133, _1474135), _1474141)), hAPP(c_Product__Type_Osnd(_1474133, _1474135), _1474141)))], (5720 ^ _777959) ^ [_868254, _868256] : [c_Hoare__Mirabelle_Ostate__not__singleton, 5726 ^ _777959 : [(5729 ^ _777959) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _868254, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, 5725 ^ [_868254, _868256]))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))], (5727 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Com_Opname), 5725 ^ [_868254, _868256]), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))]], hBOOL(hAPP(c_Com_OWT, _868256)), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _868254, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, _868256)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (32153 ^ _777959) ^ [_1385340, _1385342, _1385344] : [class_Int_Onumber__ring(_1385340), -(hAPP(c_Int_Onumber__class_Onumber__of(_1385340), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385342), _1385344)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1385340), hAPP(c_Int_Onumber__class_Onumber__of(_1385340), _1385342)), hAPP(c_Int_Onumber__class_Onumber__of(_1385340), _1385344)))], (23307 ^ _777959) ^ [_1222095] : [-(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), _1222095))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (51398 ^ _777959) ^ [_1814226, _1814228] : [hBOOL(_1814226), hBOOL(_1814228), -(hBOOL(hAPP(hAPP(c_fconj, _1814226), _1814228)))], (3250 ^ _777959) ^ [_826855, _826857, _826859, _826861] : [-(c_List_Otranspose(_826861, _826857) = c_List_Otranspose(_826859, _826855)), _826861 = _826859, _826857 = _826855], (30102 ^ _777959) ^ [_1347325, _1347327, _1347329] : [class_Divides_Osemiring__div(_1347325), -(c_Divides_Odiv__class_Omod(_1347325, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347325), _1347327), _1347329), _1347329) = c_Groups_Ozero__class_Ozero(_1347325))], (24115 ^ _777959) ^ [_1236408, _1236410, _1236412, _1236414, _1236416] : [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), _1236408), _1236410)), _1236412)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1236408), _1236414)), _1236416))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1236416), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236408), _1236416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1236408), _1236412)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1236414), _1236410)))], (1230 ^ _777959) ^ [_796058, _796060] : [-(class_Rings_Oring(_796058)), _796060 = _796058, class_Rings_Oring(_796060)], (13917 ^ _777959) ^ [_1035583, _1035585, _1035587, _1035589, _1035591] : [-(_1035583 = c_Orderings_Obot__class_Obot(tc_fun(_1035585, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1035587, tc_HOL_Obool)), _1035589), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1035585, tc_fun(_1035587, tc_HOL_Obool)), _1035583), _1035591)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1035585, tc_fun(_1035587, tc_HOL_Obool)), _1035583), hAPP(hAPP(c_COMBB(tc_fun(_1035587, tc_HOL_Obool), tc_fun(_1035587, tc_HOL_Obool), _1035585), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1035587, tc_HOL_Obool)), _1035589)), _1035591)))], (43660 ^ _777959) ^ [_1645944, _1645946] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1645944), _1645946) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43663 ^ _777959 : [(43666 ^ _777959) ^ [_1646058] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1646058), hAPP(c_List_Oset(tc_Nat_Onat), _1645946))), -(_1646058 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43664 ^ _777959) ^ [] : [-(_1645944 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20755 ^ _777959) ^ [_1173323, _1173325, _1173327] : [class_Groups_Ogroup__add(_1173323), 20758 ^ _777959 : [(20765 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173323), _1173325), _1173327) = c_Groups_Ozero__class_Ozero(_1173323), -(_1173325 = hAPP(c_Groups_Ouminus__class_Ouminus(_1173323), _1173327))], (20759 ^ _777959) ^ [] : [_1173325 = hAPP(c_Groups_Ouminus__class_Ouminus(_1173323), _1173327), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1173323), _1173325), _1173327) = c_Groups_Ozero__class_Ozero(_1173323))]]], (42258 ^ _777959) ^ [_1611006, _1611008, _1611010, _1611012] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1611006, _1611008)), hAPP(hAPP(c_Product__Type_OSigma(_1611006, _1611008), _1611010), hAPP(c_COMBK(tc_fun(_1611008, tc_HOL_Obool), _1611006), _1611012)))), -(_1611010 = c_Orderings_Obot__class_Obot(tc_fun(_1611006, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1611008), _1611012)))], (10677 ^ _777959) ^ [_967394, _967396, _967398, _967400, _967402, _967404, _967406, _967408] : [hBOOL(hAPP(hAPP(c_member(_967394), _967396), _967398)), hBOOL(hAPP(hAPP(hAPP(_967400, _967396), _967402), _967404)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_967394, tc_fun(_967406, tc_fun(_967408, tc_HOL_Obool))), _967398), _967400), _967402), _967404)))], (43189 ^ _777959) ^ [_1635424, _1635426] : [-(hAPP(c_List_Orotate1(_1635424), _1635426) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1635424), _1635424, c_List_Olist_ONil(_1635424), hAPP(hAPP(c_COMBB(tc_List_Olist(_1635424), tc_fun(tc_List_Olist(_1635424), tc_List_Olist(_1635424)), _1635424), hAPP(c_COMBC(tc_List_Olist(_1635424), tc_List_Olist(_1635424), tc_List_Olist(_1635424)), c_List_Oappend(_1635424))), hAPP(hAPP(c_COMBC(_1635424, tc_List_Olist(_1635424), tc_List_Olist(_1635424)), c_List_Olist_OCons(_1635424)), c_List_Olist_ONil(_1635424)))), _1635426))], (50724 ^ _777959) ^ [_1806913, _1806915, _1806917] : [hBOOL(hAPP(hAPP(c_member(_1806913), _1806915), hAPP(c_List_Oset(_1806913), _1806917))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1806913), _1806917), _1806915)))], (47741 ^ _777959) ^ [_1738111, _1738113] : [47743 ^ _777959 : [(47746 ^ _777959) ^ [] : [47742 ^ [_1738111, _1738113] = c_Orderings_Obot__class_Obot(tc_fun(_1738111, tc_HOL_Obool))], (47744 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1738111, tc_HOL_Obool)), 47742 ^ [_1738111, _1738113]), hAPP(c_Relation_OImage(_1738111, _1738111, _1738113), 47742 ^ [_1738111, _1738113]))))]], -(c_Wellfounded_Owf(_1738111, _1738113))], (29060 ^ _777959) ^ [_1325586] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1325586)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1325586))], (1510 ^ _777959) ^ [_799558, _799560] : [-(class_Rings_Oordered__comm__semiring(_799558)), _799560 = _799558, class_Rings_Oordered__comm__semiring(_799560)], (29108 ^ _777959) ^ [_1326489, _1326491, _1326493, _1326495] : [class_Orderings_Olinorder(_1326489), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326489, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1326489, _1326491, _1326493)), hAPP(c_SetInterval_Oord__class_OatMost(_1326489), _1326495)) = c_SetInterval_Oord__class_OatLeastAtMost(_1326489, _1326491, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1326489), _1326493), _1326495)))], (40564 ^ _777959) ^ [_1565637, _1565639, _1565641, _1565643, _1565645] : [class_Groups_Oab__group__add(_1565637), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1565637), hAPP(hAPP(c_List_Omap(_1565639, _1565637), hAPP(hAPP(c_COMBS(_1565639, _1565637, _1565637), hAPP(hAPP(c_COMBB(_1565637, tc_fun(_1565637, _1565637), _1565639), c_Groups_Ominus__class_Ominus(_1565637)), _1565641)), _1565643)), _1565645)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1565637), hAPP(c_List_Omonoid__add__class_Olistsum(_1565637), hAPP(hAPP(c_List_Omap(_1565639, _1565637), _1565641), _1565645))), hAPP(c_List_Omonoid__add__class_Olistsum(_1565637), hAPP(hAPP(c_List_Omap(_1565639, _1565637), _1565643), _1565645))))], (48192 ^ _777959) ^ [_1748298, _1748300] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1748298), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1748300), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 48199 ^ _777959 : [(48206 ^ _777959) ^ [] : [_1748298 = _1748300, -(hAPP(c_Code__Numeral_Oof__nat, _1748298) = hAPP(c_Code__Numeral_Oof__nat, _1748300))], (48200 ^ _777959) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1748298) = hAPP(c_Code__Numeral_Oof__nat, _1748300), -(_1748298 = _1748300)]]], (24682 ^ _777959) ^ [_1246275] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1246275), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (42298 ^ _777959) ^ [_1611984, _1611986, _1611988] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1611984), tc_List_Olist(_1611984))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1611984), tc_List_Olist(_1611984)), _1611986), c_List_Olist_ONil(_1611984))), c_List_Olistrel1(_1611984, _1611988)))], (29126 ^ _777959) ^ [] : [-(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)))], (13721 ^ _777959) ^ [_1031555, _1031557, _1031559, _1031561, _1031563] : [hAPP(c_Map_Omap__add(_1031555, _1031557, _1031559, _1031561), _1031563) = c_Option_Ooption_ONone(_1031557), 13724 ^ _777959 : [(13727 ^ _777959) ^ [] : [-(hAPP(_1031559, _1031563) = c_Option_Ooption_ONone(_1031557))], (13725 ^ _777959) ^ [] : [-(hAPP(_1031561, _1031563) = c_Option_Ooption_ONone(_1031557))]]], (13929 ^ _777959) ^ [_1035842, _1035844, _1035846, _1035848, _1035850] : [-(_1035842 = c_Orderings_Obot__class_Obot(tc_fun(_1035844, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1035846, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1035844, tc_fun(_1035846, tc_HOL_Obool)), _1035842), _1035848)), _1035850) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1035844, tc_fun(_1035846, tc_HOL_Obool)), _1035842), hAPP(hAPP(c_COMBC(_1035844, tc_fun(_1035846, tc_HOL_Obool), tc_fun(_1035846, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1035846, tc_HOL_Obool), tc_fun(tc_fun(_1035846, tc_HOL_Obool), tc_fun(_1035846, tc_HOL_Obool)), _1035844), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1035846, tc_HOL_Obool))), _1035848)), _1035850)))], (34993 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (10324 ^ _777959) ^ [_959779, _959781, _959783, _959785, _959787, _959789] : [c_Finite__Set_Ofun__left__comm__idem(_959779, _959781, _959783), hBOOL(hAPP(c_Finite__Set_Ofinite(_959779), _959785)), -(hAPP(hAPP(c_Finite__Set_Ofold(_959779, _959781, _959783), _959787), hAPP(hAPP(c_Set_Oinsert(_959779), _959789), _959785)) = hAPP(hAPP(c_Finite__Set_Ofold(_959779, _959781, _959783), hAPP(hAPP(_959783, _959789), _959787)), _959785))], (6797 ^ _777959) ^ [_888538, _888540, _888542, _888544] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888538, tc_HOL_Obool)), _888540), _888542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888538, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_888538), _888544), _888540)), hAPP(hAPP(c_Set_Oinsert(_888538), _888544), _888542))))], (24732 ^ _777959) ^ [_1247057, _1247059, _1247061, _1247063] : [class_Divides_Osemiring__div(_1247057), -(_1247059 = c_Groups_Ozero__class_Ozero(_1247057)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1247057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247057), _1247059), _1247061)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247057), _1247059), _1247063)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1247057), _1247061), _1247063))], (15769 ^ _777959) ^ [_1077929, _1077931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077929)), _1077931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077929), _1077931)))], (15496 ^ _777959) ^ [_1072548, _1072550, _1072552, _1072554] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072548), _1072550)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072552), _1072554)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072548), _1072552)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072550), _1072554))))], (40642 ^ _777959) ^ [_1567499, _1567501, _1567503, _1567505, _1567507] : [class_Groups_Ocomm__monoid__add(_1567499), hBOOL(hAPP(hAPP(c_member(_1567501), _1567503), hAPP(c_List_Oset(_1567501), _1567505))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1567499), hAPP(hAPP(c_List_Omap(_1567501, _1567499), _1567507), _1567505)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1567499), hAPP(_1567507, _1567503)), hAPP(c_List_Omonoid__add__class_Olistsum(_1567499), hAPP(hAPP(c_List_Omap(_1567501, _1567499), _1567507), c_List_Oremove1(_1567501, _1567503, _1567505)))))], (7618 ^ _777959) ^ [_906340, _906342, _906344] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_906340, _906342, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_906340)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_906340), _906344), c_Com_Ocom_OSKIP), _906344)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_906340), tc_HOL_Obool)))))], (43272 ^ _777959) ^ [_1637254, _1637256, _1637258, _1637260] : [-(hAPP(hAPP(c_List_Odrop(_1637254), _1637256), hAPP(hAPP(c_List_Odrop(_1637254), _1637258), _1637260)) = hAPP(hAPP(c_List_Odrop(_1637254), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1637256), _1637258)), _1637260))], (27123 ^ _777959) ^ [_1291662, _1291664, _1291666, _1291668, _1291670, _1291672] : [class_Groups_Oordered__ab__group__add(_1291662), hBOOL(hAPP(c_Finite__Set_Ofinite(_1291664), _1291666)), 27133 ^ _777959 : [(27136 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291662), c_Groups_Ozero__class_Ozero(_1291662)), hAPP(_1291668, 27132 ^ [_1291662, _1291664, _1291666, _1291668, _1291670, _1291672])))], (27134 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1291664), 27132 ^ [_1291662, _1291664, _1291666, _1291668, _1291670, _1291672]), _1291666)))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1291664, _1291662), _1291668), _1291666) = _1291670, hBOOL(hAPP(hAPP(c_member(_1291664), _1291672), _1291666)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1291662), hAPP(_1291668, _1291672)), _1291670)))], (16213 ^ _777959) ^ [_1087531, _1087533, _1087535, _1087537, _1087539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1087531), _1087533)), 16216 ^ _777959 : [(16223 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1087537), 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), _1087533), _1087531)), _1087535)), _1087539))), -(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), _1087531), _1087535)), _1087537)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087533), _1087535)), _1087539))))], (16217 ^ _777959) ^ [] : [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), _1087531), _1087535)), _1087537)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087533), _1087535)), _1087539))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1087537), 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), _1087533), _1087531)), _1087535)), _1087539))))]]], (45902 ^ _777959) ^ [_1694080, _1694082] : [class_Enum_Oenum(_1694080), 45905 ^ _777959 : [(45913 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1694080), _1694082)), 45916 ^ _777959 : [(45917 ^ _777959) ^ [_1694298] : [-(hBOOL(hAPP(_1694082, _1694298)))]]], (45906 ^ _777959) ^ [] : [hBOOL(hAPP(_1694082, 45907 ^ [_1694080, _1694082])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1694080), _1694082)))]]], (5743 ^ _777959) ^ [_868701, _868703, _868705, _868707] : [-(_868701 = c_Orderings_Obot__class_Obot(tc_fun(_868703, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_868703, _868705, hAPP(c_COMBK(_868705, _868703), _868707)), _868701) = hAPP(hAPP(c_Set_Oinsert(_868705), _868707), c_Orderings_Obot__class_Obot(tc_fun(_868705, tc_HOL_Obool))))], (43067 ^ _777959) ^ [_1631943, _1631945, _1631947, _1631949] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1631943), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631945)), _1631947))), -(hAPP(hAPP(c_List_Onth(_1631945), hAPP(hAPP(c_List_Oappend(_1631945), _1631947), _1631949)), _1631943) = hAPP(hAPP(c_List_Onth(_1631945), _1631947), _1631943))], (12221 ^ _777959) ^ [_999841, _999843, _999845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999841), _999843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _999841), _999845)), _999843)))], (31448 ^ _777959) ^ [_1371937, _1371939] : [-(c_Nitpick_Oint__lcm(_1371937, _1371939) = 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), _1371937)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1371939)))))], (44843 ^ _777959) ^ [_1669910, _1669912] : [hBOOL(hAPP(c_List_Odistinct(_1669910), _1669912)), -(hBOOL(hAPP(c_List_Odistinct(_1669910), hAPP(c_List_Orev(_1669910), _1669912))))], (11070 ^ _777959) ^ [_974750, _974752, _974754, _974756, _974758] : [class_Groups_Ocomm__monoid__add(_974750), hBOOL(hAPP(c_Finite__Set_Ofinite(_974752), _974754)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_974752, _974750), hAPP(hAPP(c_COMBS(_974752, _974750, _974750), hAPP(hAPP(c_COMBB(_974750, tc_fun(_974750, _974750), _974752), c_Groups_Oplus__class_Oplus(_974750)), _974756)), _974758)), _974754) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974750), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_974752, _974750), _974756), _974754)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_974752, _974750), _974758), _974754)))], (43274 ^ _777959) ^ [_1637313, _1637315, _1637317, _1637319, _1637321] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1637313, _1637315)), _1637317), hAPP(hAPP(c_List_Ozip(_1637313, _1637315), _1637319), _1637321)) = hAPP(hAPP(c_List_Ozip(_1637313, _1637315), hAPP(hAPP(c_List_Odrop(_1637313), _1637317), _1637319)), hAPP(hAPP(c_List_Odrop(_1637315), _1637317), _1637321)))], (37182 ^ _777959) ^ [_1486242, _1486244, _1486246, _1486248, _1486250] : [-(hAPP(c_Relation_OImage(_1486242, _1486244, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1486242, _1486244), tc_HOL_Obool)), _1486246), _1486248)), _1486250) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1486244, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1486242, _1486244, _1486246), _1486250)), hAPP(c_Relation_OImage(_1486242, _1486244, _1486248), _1486250)))], (45172 ^ _777959) ^ [_1678505, _1678507, _1678509] : [hBOOL(hAPP(c_List_Odistinct(_1678505), _1678507)), -(hBOOL(hAPP(c_List_Odistinct(_1678505), c_List_OtakeWhile(_1678505, _1678509, _1678507))))], (43709 ^ _777959) ^ [_1646885, _1646887, _1646889] : [class_Lattices_Olattice(_1646885), -(c_Big__Operators_Olattice__class_OInf__fin(_1646885, hAPP(c_List_Oset(_1646885), hAPP(hAPP(c_List_Olist_OCons(_1646885), _1646887), _1646889))) = hAPP(c_List_Ofoldl(_1646885, _1646885, c_Lattices_Osemilattice__inf__class_Oinf(_1646885), _1646887), _1646889))], (45616 ^ _777959) ^ [_1688301, _1688303, _1688305, _1688307] : [class_Enum_Oenum(_1688301), class_Enum_Oenum(_1688303), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688303)), _1688305) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688301)), c_Enum_Oenum__class_Oenum(_1688301)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688303)), _1688307) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688301)), c_Enum_Oenum__class_Oenum(_1688301)), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1688303), _1688303, _1688301, c_Option_Othe(_1688303)), hAPP(c_Map_Omap__of(_1688301, _1688303), hAPP(hAPP(c_List_Ozip(_1688301, _1688303), c_Enum_Oenum__class_Oenum(_1688301)), _1688305))) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1688303), _1688303, _1688301, c_Option_Othe(_1688303)), hAPP(c_Map_Omap__of(_1688301, _1688303), hAPP(hAPP(c_List_Ozip(_1688301, _1688303), c_Enum_Oenum__class_Oenum(_1688301)), _1688307))), -(_1688305 = _1688307)], (19003 ^ _777959) ^ [_1142867, _1142869, _1142871] : [-(hAPP(hAPP(c_Option_Omap(_1142867, _1142869), _1142871), c_Option_Ooption_ONone(_1142867)) = c_Option_Ooption_ONone(_1142869))], (50152 ^ _777959) ^ [_1794505, _1794507] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1794505)), c_Int_OBit0(_1794507))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1794505), _1794507)))], (9614 ^ _777959) ^ [_944190, _944192, _944194, _944196] : [hBOOL(hAPP(_944190, _944192)), hBOOL(hAPP(_944194, _944192)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944196, tc_HOL_Obool)), _944190), _944194), _944192)))], (39173 ^ _777959) ^ [_1532538, _1532540, _1532542, _1532544] : [c_Fun_Oinj__on(_1532538, _1532540, _1532542, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1532538, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1532538), tc_fun(_1532538, tc_HOL_Obool), c_List_Oset(_1532538)), _1532544))), -(c_Fun_Oinj__on(tc_List_Olist(_1532538), tc_List_Olist(_1532540), hAPP(c_List_Omap(_1532538, _1532540), _1532542), _1532544))], (48008 ^ _777959) ^ [_1744541, _1744543, _1744545, _1744547] : [c_List_Olist__ex(_1744541, _1744543, hAPP(hAPP(c_List_Oappend(_1744541), _1744545), _1744547)), -(c_List_Olist__ex(_1744541, _1744543, _1744545)), -(c_List_Olist__ex(_1744541, _1744543, _1744547))], (34065 ^ _777959) ^ [_1419611, _1419613] : [c_Int_OBit1(_1419611) = c_Int_OBit0(_1419613)], (34299 ^ _777959) ^ [_1423682] : [-(c_Int_Opred(c_Int_OBit1(_1423682)) = c_Int_OBit0(_1423682))], (2374 ^ _777959) ^ [_813077, _813079] : [_813079 = _813077, -(c_Int_Oring__1__class_OInts(_813079) = c_Int_Oring__1__class_OInts(_813077))], (46552 ^ _777959) ^ [_1708028, _1708030, _1708032, _1708034, _1708036, _1708038, _1708040, _1708042] : [c_List_Olist__all2(_1708028, _1708030, _1708032, _1708034, _1708036), hBOOL(hAPP(hAPP(_1708032, _1708038), _1708040)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708042), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708030)), _1708036))), -(c_List_Olist__all2(_1708028, _1708030, _1708032, hAPP(hAPP(c_List_Olist__update(_1708028, _1708034), _1708042), _1708038), hAPP(hAPP(c_List_Olist__update(_1708030, _1708036), _1708042), _1708040)))], (15526 ^ _777959) ^ [_1073173] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1073173) = _1073173)], (5364 ^ _777959) ^ [_860014, _860016, _860018, _860020] : [-(c_List_Ozip(_860020, _860016) = c_List_Ozip(_860018, _860014)), _860020 = _860018, _860016 = _860014], (46538 ^ _777959) ^ [_1707729, _1707731, _1707733, _1707735, _1707737, _1707739, _1707741, _1707743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707729), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707731)), _1707733))), c_List_Olist__all2(_1707731, _1707735, _1707737, _1707733, _1707739), hBOOL(hAPP(hAPP(_1707737, _1707741), _1707743)), -(c_List_Olist__all2(_1707731, _1707735, _1707737, hAPP(hAPP(c_List_Olist__update(_1707731, _1707733), _1707729), _1707741), hAPP(hAPP(c_List_Olist__update(_1707735, _1707739), _1707729), _1707743)))], (45953 ^ _777959) ^ [_1694829, _1694831] : [class_Enum_Oenum(_1694829), 45956 ^ _777959 : [(45964 ^ _777959) ^ [] : [45965 ^ _777959 : [(45966 ^ _777959) ^ [_1695009] : [hBOOL(hAPP(_1694831, _1695009))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1694829), _1694831)))], (45957 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1694829), _1694831)), -(hBOOL(hAPP(_1694831, 45960 ^ [_1694829, _1694831])))]]], (50254 ^ _777959) ^ [_1796686, _1796688, _1796690, _1796692, _1796694, _1796696] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1796686, _1796688, _1796690, _1796692, c_Lazy__Sequence_Olazy__sequence_OInsert(_1796688, _1796694, _1796696)) = hAPP(hAPP(_1796692, _1796694), _1796696))], (13609 ^ _777959) ^ [_1028068, _1028070, _1028072, _1028074, _1028076] : [hBOOL(hAPP(hAPP(c_member(_1028068), _1028070), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1028072, tc_fun(_1028068, tc_HOL_Obool)), _1028074), _1028076))), 13612 ^ _777959 : [(13613 ^ _777959) ^ [_1028192] : [hBOOL(hAPP(hAPP(c_member(_1028072), _1028192), _1028074)), -(hBOOL(hAPP(hAPP(c_member(_1028068), _1028070), hAPP(_1028076, _1028192))))]]], (30722 ^ _777959) ^ [_1358383, _1358385] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1358383), _1358385))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1358383, _1358385) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1358383), _1358385), _1358385))], (33833 ^ _777959) ^ [_1414954, _1414956] : [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(_1414954))), 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)), _1414956))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414954) = hAPP(c_Nat_OSuc, _1414956))], (49384 ^ _777959) ^ [_1777249] : [-(c_Nat_Ofunpow(_1777249) = c_Nat_Ocompow(_1777249, _1777249))], (22862 ^ _777959) ^ [_1214026, _1214028] : [class_Rings_Olinordered__semidom(_1214026), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1214026), c_Groups_Ozero__class_Ozero(_1214026)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1214026), _1214028))))], (1260 ^ _777959) ^ [_796433, _796435] : [-(class_Orderings_Owellorder(_796433)), _796435 = _796433, class_Orderings_Owellorder(_796435)], (2904 ^ _777959) ^ [_821344, _821346, _821348, _821350, _821352, _821354, _821356, _821358] : [-(c_Product__Type_Oapsnd(_821358, _821354, _821350, _821346) = c_Product__Type_Oapsnd(_821356, _821352, _821348, _821344)), _821358 = _821356, _821354 = _821352, _821350 = _821348, _821346 = _821344], (30098 ^ _777959) ^ [_1347223, _1347225, _1347227] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1347223), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1347225, _1347227)), _1347227) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1347223), _1347225), _1347227))], (43424 ^ _777959) ^ [_1641105, _1641107, _1641109, _1641111, _1641113] : [-(hAPP(hAPP(c_List_Ozip(_1641105, _1641107), hAPP(hAPP(c_List_Oappend(_1641105), _1641109), _1641111)), _1641113) = hAPP(hAPP(c_List_Oappend(tc_prod(_1641105, _1641107)), hAPP(hAPP(c_List_Ozip(_1641105, _1641107), _1641109), hAPP(hAPP(c_List_Otake(_1641107), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641105)), _1641109)), _1641113))), hAPP(hAPP(c_List_Ozip(_1641105, _1641107), _1641111), hAPP(hAPP(c_List_Odrop(_1641107), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641105)), _1641109)), _1641113))))], (11926 ^ _777959) ^ [_994477, _994479] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994477), _994479)), _994479) = _994477)], (41980 ^ _777959) ^ [_1605288] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605288)), c_List_Olist_ONil(_1605288)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43721 ^ _777959) ^ [_1647143, _1647145, _1647147] : [class_Orderings_Olinorder(_1647143), -(c_Big__Operators_Olinorder__class_OMax(_1647143, hAPP(c_List_Oset(_1647143), hAPP(hAPP(c_List_Olist_OCons(_1647143), _1647145), _1647147))) = hAPP(c_List_Ofoldl(_1647143, _1647143, c_Orderings_Oord__class_Omax(_1647143), _1647145), _1647147))], (10078 ^ _777959) ^ [_953515, _953517] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953515, tc_HOL_Obool)), _953517), c_Orderings_Obot__class_Obot(tc_fun(_953515, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_953515, tc_HOL_Obool)))], (37598 ^ _777959) ^ [_1496427, _1496429, _1496431, _1496433, _1496435] : [c_Equiv__Relations_Oequiv(_1496427, _1496429, _1496431), hBOOL(hAPP(hAPP(c_member(tc_prod(_1496427, _1496427)), hAPP(hAPP(c_Product__Type_OPair(_1496427, _1496427), _1496433), _1496435)), _1496431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1496427, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1496427, _1496427, _1496431), hAPP(hAPP(c_Set_Oinsert(_1496427), _1496433), c_Orderings_Obot__class_Obot(tc_fun(_1496427, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1496427, _1496427, _1496431), hAPP(hAPP(c_Set_Oinsert(_1496427), _1496435), c_Orderings_Obot__class_Obot(tc_fun(_1496427, tc_HOL_Obool)))))))], (41858 ^ _777959) ^ [_1601821, _1601823, _1601825, _1601827, _1601829, _1601831] : [hBOOL(hAPP(hAPP(c_member(_1601821), _1601823), _1601825)), hBOOL(hAPP(hAPP(c_member(_1601827), _1601829), hAPP(_1601831, _1601823))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601821, _1601827)), hAPP(hAPP(c_Product__Type_OPair(_1601821, _1601827), _1601823), _1601829)), hAPP(hAPP(c_Product__Type_OSigma(_1601821, _1601827), _1601825), _1601831))))], (46393 ^ _777959) ^ [_1704690, _1704692, _1704694, _1704696, _1704698, _1704700, _1704702] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704690)), _1704692) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1704694)), _1704696), 46396 ^ _777959 : [(46405 ^ _777959) ^ [] : [-(c_List_Olist__all2(_1704690, _1704694, _1704698, hAPP(hAPP(c_List_Oappend(_1704690), _1704692), _1704700), hAPP(hAPP(c_List_Oappend(_1704694), _1704696), _1704702))), c_List_Olist__all2(_1704690, _1704694, _1704698, _1704692, _1704696), c_List_Olist__all2(_1704690, _1704694, _1704698, _1704700, _1704702)], (46397 ^ _777959) ^ [] : [c_List_Olist__all2(_1704690, _1704694, _1704698, hAPP(hAPP(c_List_Oappend(_1704690), _1704692), _1704700), hAPP(hAPP(c_List_Oappend(_1704694), _1704696), _1704702)), 46400 ^ _777959 : [(46403 ^ _777959) ^ [] : [-(c_List_Olist__all2(_1704690, _1704694, _1704698, _1704700, _1704702))], (46401 ^ _777959) ^ [] : [-(c_List_Olist__all2(_1704690, _1704694, _1704698, _1704692, _1704696))]]]]], (9502 ^ _777959) ^ [_941749, _941751, _941753, _941755] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_941749), _941751)), -(hAPP(c_Set_Oimage(_941749, _941753, _941755), _941751) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_941753, tc_HOL_Obool), _941749, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941753, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_941749, tc_fun(_941753, tc_HOL_Obool), tc_fun(_941753, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_941753, tc_fun(tc_fun(_941753, tc_HOL_Obool), tc_fun(_941753, tc_HOL_Obool)), _941749), c_Set_Oinsert(_941753)), _941755)), c_Orderings_Obot__class_Obot(tc_fun(_941753, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_941753, tc_HOL_Obool))), _941751))], (9868 ^ _777959) ^ [_949422, _949424, _949426, _949428] : [class_Lattices_Osemilattice__inf(_949422), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949422), _949424), _949426)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949422), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949422), _949428), _949424)), _949426)))], (4378 ^ _777959) ^ [_844227, _844229, _844231, _844233] : [-(c_Nitpick_OAbs__Frac(_844233, _844229) = c_Nitpick_OAbs__Frac(_844231, _844227)), _844233 = _844231, _844229 = _844227], (43037 ^ _777959) ^ [_1631177, _1631179, _1631181, _1631183, _1631185] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631177), tc_List_Olist(_1631177))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631177), tc_List_Olist(_1631177)), _1631179), _1631181)), c_List_Olexord(_1631177, _1631183))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631177), tc_List_Olist(_1631177))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631177), tc_List_Olist(_1631177)), hAPP(hAPP(c_List_Oappend(_1631177), _1631185), _1631179)), hAPP(hAPP(c_List_Oappend(_1631177), _1631185), _1631181))), c_List_Olexord(_1631177, _1631183))))], (1720 ^ _777959) ^ [_802183, _802185] : [-(class_Rings_Osemiring__0(_802183)), _802185 = _802183, class_Rings_Osemiring__0(_802185)], (6245 ^ _777959) ^ [_878683, _878685, _878687, _878689, _878691, _878693] : [c_Com_Ocom_OCall(_878683, _878685, _878687) = c_Com_Ocom_OCall(_878689, _878691, _878693), 6248 ^ _777959 : [(6253 ^ _777959) ^ [] : [-(_878687 = _878693)], (6251 ^ _777959) ^ [] : [-(_878685 = _878691)], (6249 ^ _777959) ^ [] : [-(_878683 = _878689)]]], (41421 ^ _777959) ^ [_1589788, _1589790, _1589792, _1589794, _1589796, _1589798] : [hBOOL(hAPP(hAPP(_1589788, _1589790), _1589792)), c_List_Olistrelp(_1589794, _1589788, _1589796, _1589798), -(c_List_Olistrelp(_1589794, _1589788, hAPP(hAPP(c_List_Olist_OCons(_1589794), _1589790), _1589796), hAPP(hAPP(c_List_Olist_OCons(_1589794), _1589792), _1589798)))], (3646 ^ _777959) ^ [_833011, _833013] : [_833013 = _833011, -(c_Wellfounded_Ofinite__psubset(_833013) = c_Wellfounded_Ofinite__psubset(_833011))], (49245 ^ _777959) ^ [_1773693, _1773695, _1773697, _1773699, _1773701] : [c_Relation_Osingle__valued(_1773693, _1773693, _1773695), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773693, _1773693)), hAPP(hAPP(c_Product__Type_OPair(_1773693, _1773693), _1773697), _1773699)), c_Transitive__Closure_Ortrancl(_1773693, _1773695))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1773693, _1773693)), hAPP(hAPP(c_Product__Type_OPair(_1773693, _1773693), _1773697), _1773701)), c_Transitive__Closure_Ortrancl(_1773693, _1773695))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773693, _1773693)), hAPP(hAPP(c_Product__Type_OPair(_1773693, _1773693), _1773699), _1773701)), c_Transitive__Closure_Ortrancl(_1773693, _1773695)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1773693, _1773693)), hAPP(hAPP(c_Product__Type_OPair(_1773693, _1773693), _1773701), _1773699)), c_Transitive__Closure_Ortrancl(_1773693, _1773695))))], (43133 ^ _777959) ^ [_1633808, _1633810, _1633812, _1633814, _1633816, _1633818] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633808), tc_List_Olist(_1633808))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633808), tc_List_Olist(_1633808)), hAPP(hAPP(c_List_Oappend(_1633808), _1633810), hAPP(hAPP(c_List_Olist_OCons(_1633808), _1633812), c_List_Olist_ONil(_1633808)))), hAPP(hAPP(c_List_Oappend(_1633808), _1633814), hAPP(hAPP(c_List_Olist_OCons(_1633808), _1633816), c_List_Olist_ONil(_1633808))))), c_List_Olistrel1(_1633808, _1633818)))), 43134 ^ _777959 : [(43141 ^ _777959) ^ [] : [_1633810 = _1633814, hBOOL(hAPP(hAPP(c_member(tc_prod(_1633808, _1633808)), hAPP(hAPP(c_Product__Type_OPair(_1633808, _1633808), _1633812), _1633816)), _1633818))], (43135 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633808), tc_List_Olist(_1633808))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633808), tc_List_Olist(_1633808)), _1633810), _1633814)), c_List_Olistrel1(_1633808, _1633818))), _1633812 = _1633816]]], (20733 ^ _777959) ^ [_1172952, _1172954, _1172956] : [class_Groups_Ogroup__add(_1172952), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1172952), _1172954), _1172956) = c_Groups_Ozero__class_Ozero(_1172952), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1172952), _1172954) = _1172956)], (4372 ^ _777959) ^ [_844142, _844144] : [_844144 = _844142, -(c_Nitpick_Ofrac(_844144) = c_Nitpick_Ofrac(_844142))], (39671 ^ _777959) ^ [_1544581, _1544583, _1544585, _1544587, _1544589, _1544591] : [c_Finite__Set_Ofolding__idem(_1544581, _1544583, _1544585, _1544587), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544581), _1544589)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544581), _1544591)), -(hAPP(_1544587, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1544581, tc_HOL_Obool)), _1544589), _1544591)) = hAPP(c_Fun_Ocomp(_1544583, _1544583, _1544583, hAPP(_1544587, _1544589)), hAPP(_1544587, _1544591)))], (44642 ^ _777959) ^ [_1665182] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1665182) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1665182))))], (6681 ^ _777959) ^ [_886425, _886427, _886429, _886431] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886425, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_886425), _886427), _886429)), _886431) = hAPP(hAPP(c_Set_Oinsert(_886425), _886427), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886425, tc_HOL_Obool)), _886429), _886431)))], (49765 ^ _777959) ^ [_1787293, _1787295, _1787297] : [49767 ^ _777959 : [(49770 ^ _777959) ^ [] : [hBOOL(hAPP(_1787295, hAPP(hAPP(c_List_Onth(_1787293), _1787297), 49766 ^ [_1787293, _1787295, _1787297])))], (49768 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49766 ^ [_1787293, _1787295, _1787297]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1787293)), _1787297))))]], -(c_List_Olist__all(_1787293, _1787295, _1787297))], (12858 ^ _777959) ^ [_1011326, _1011328, _1011330] : [hBOOL(hAPP(hAPP(c_member(_1011326), _1011328), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1011326, tc_HOL_Obool)), _1011330))), hBOOL(hAPP(hAPP(c_member(_1011326), _1011328), _1011330))], (49338 ^ _777959) ^ [_1776075, _1776077] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1776075, _1776075), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1776077) = c_Relation_OId(_1776075))], (28010 ^ _777959) ^ [_1306481, _1306483, _1306485] : [class_Rings_Oring__1(_1306481), -(hAPP(c_Int_Oring__1__class_Oof__int(_1306481), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1306483), _1306485)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1306481), hAPP(c_Int_Oring__1__class_Oof__int(_1306481), _1306483)), hAPP(c_Int_Oring__1__class_Oof__int(_1306481), _1306485)))], (38946 ^ _777959) ^ [_1527251, _1527253, _1527255, _1527257, _1527259] : [hAPP(hAPP(c_List_Omap(_1527251, _1527253), _1527255), _1527257) = hAPP(hAPP(c_List_Omap(_1527251, _1527253), _1527259), _1527257), 38949 ^ _777959 : [(38950 ^ _777959) ^ [_1527374] : [hBOOL(hAPP(hAPP(c_member(_1527251), _1527374), hAPP(c_List_Oset(_1527251), _1527257))), -(hAPP(_1527255, _1527374) = hAPP(_1527259, _1527374))]]], (34133 ^ _777959) ^ [_1420840, _1420842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1420840), _1420842)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1420840)), c_Int_OBit0(_1420842))))], (3632 ^ _777959) ^ [_832790, _832792, _832794, _832796, _832798, _832800] : [-(c_Wellfounded_Omlex__prod(_832800, _832796, _832792) = c_Wellfounded_Omlex__prod(_832798, _832794, _832790)), _832800 = _832798, _832796 = _832794, _832792 = _832790], (41543 ^ _777959) ^ [_1592478, _1592480, _1592482, _1592484] : [hBOOL(hAPP(hAPP(c_member(_1592478), _1592480), hAPP(c_List_Oset(_1592478), hAPP(hAPP(c_List_Olist_OCons(_1592478), _1592482), _1592484)))), -(_1592480 = _1592482), -(hBOOL(hAPP(hAPP(c_member(_1592478), _1592480), hAPP(c_List_Oset(_1592478), _1592484))))], (14660 ^ _777959) ^ [_1053398, _1053400] : [class_Rings_Olinordered__semidom(_1053398), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1053398), _1053400), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1053398), _1053400), c_Groups_Oone__class_Oone(_1053398)))))], (38784 ^ _777959) ^ [_1522627, _1522629, _1522631, _1522633, _1522635] : [hBOOL(hAPP(hAPP(c_member(_1522627), _1522629), hAPP(c_Set_Ovimage(_1522627, _1522631, _1522633), _1522635))), -(hBOOL(hAPP(hAPP(c_member(_1522631), hAPP(_1522633, _1522629)), _1522635)))], (782 ^ _777959) ^ [_789974, _789976, _789978, _789980, _789982, _789984] : [-(c_Equiv__Relations_Oequiv(_789982, _789978, _789974)), c_Equiv__Relations_Oequiv(_789984, _789980, _789976), _789984 = _789982, _789980 = _789978, _789976 = _789974], (47996 ^ _777959) ^ [_1744336, _1744338, _1744340] : [c_List_Olist__ex(_1744336, _1744338, hAPP(c_List_Orev(_1744336), _1744340)), -(c_List_Olist__ex(_1744336, _1744338, _1744340))], (11768 ^ _777959) ^ [_990518, _990520, _990522, _990524, _990526, _990528, _990530] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990518, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990520, tc_fun(_990518, tc_HOL_Obool)), _990522), _990524)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990526, tc_fun(_990518, tc_HOL_Obool)), _990528), _990530)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990520, tc_fun(_990518, tc_HOL_Obool)), _990522), hAPP(hAPP(c_COMBB(tc_fun(_990526, tc_fun(_990518, tc_HOL_Obool)), tc_fun(_990518, tc_HOL_Obool), _990520), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990526, tc_fun(_990518, tc_HOL_Obool)), _990528)), hAPP(hAPP(c_COMBC(_990520, tc_fun(_990526, tc_fun(_990518, tc_HOL_Obool)), tc_fun(_990526, tc_fun(_990518, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_990518, tc_HOL_Obool), tc_fun(_990518, tc_HOL_Obool)), tc_fun(tc_fun(_990526, tc_fun(_990518, tc_HOL_Obool)), tc_fun(_990526, tc_fun(_990518, tc_HOL_Obool))), _990520), c_COMBB(tc_fun(_990518, tc_HOL_Obool), tc_fun(_990518, tc_HOL_Obool), _990526)), hAPP(hAPP(c_COMBB(tc_fun(_990518, tc_HOL_Obool), tc_fun(tc_fun(_990518, tc_HOL_Obool), tc_fun(_990518, tc_HOL_Obool)), _990520), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990518, tc_HOL_Obool))), _990524))), _990530))))], (42142 ^ _777959) ^ [_1608465, _1608467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1608465), _1608467)), -(c_List_Oupto(_1608467, _1608465) = c_List_Olist_ONil(tc_Int_Oint))], (40022 ^ _777959) ^ [_1552951, _1552953, _1552955] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1552951), _1552953)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1552951)), hAPP(c_Set_OCollect(tc_List_Olist(_1552951)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1552951), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1552951)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1552951), tc_fun(_1552951, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1552951, tc_HOL_Obool), tc_fun(tc_fun(_1552951, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1552951)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1552951, tc_HOL_Obool))), c_List_Oset(_1552951))), _1552953))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1552951), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1552951)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1552951)))), _1552955))))))], (51308 ^ _777959) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (48885 ^ _777959) ^ [_1764685, _1764687] : [-(c_Relation_Oirrefl(_1764685, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1764685, _1764685), tc_HOL_Obool)), _1764687), c_Relation_OId(_1764685))))], (22565 ^ _777959) ^ [_1208276, _1208278, _1208280, _1208282, _1208284, _1208286] : [class_Groups_Ocomm__monoid__mult(_1208276), hBOOL(hAPP(c_Finite__Set_Ofinite(_1208278), _1208280)), 22572 ^ _777959 : [(22579 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1208278), _1208282), _1208280))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1208278, _1208276), hAPP(hAPP(c_COMBC(_1208278, _1208276, _1208276), hAPP(hAPP(c_COMBS(_1208278, _1208276, tc_fun(_1208276, _1208276)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1208276, tc_fun(_1208276, _1208276)), _1208278), c_If(_1208276)), hAPP(hAPP(c_COMBC(_1208278, _1208278, tc_HOL_Obool), c_fequal), _1208282))), _1208284)), _1208286)), _1208280) = hAPP(hAPP(c_Power_Opower__class_Opower(_1208276), _1208286), hAPP(c_Finite__Set_Ocard(_1208278), _1208280)))], (22573 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1208278), _1208282), _1208280)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1208278, _1208276), hAPP(hAPP(c_COMBC(_1208278, _1208276, _1208276), hAPP(hAPP(c_COMBS(_1208278, _1208276, tc_fun(_1208276, _1208276)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1208276, tc_fun(_1208276, _1208276)), _1208278), c_If(_1208276)), hAPP(hAPP(c_COMBC(_1208278, _1208278, tc_HOL_Obool), c_fequal), _1208282))), _1208284)), _1208286)), _1208280) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1208276), hAPP(_1208284, _1208282)), hAPP(hAPP(c_Power_Opower__class_Opower(_1208276), _1208286), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208278), _1208280)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (8640 ^ _777959) ^ [_927137, _927139, _927141, _927143] : [class_Orderings_Oorder(_927137), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927137), _927139), _927141)), _927139 = _927143, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927137), _927143), _927141)))], (15874 ^ _777959) ^ [_1080023, _1080025, _1080027, _1080029, _1080031, _1080033] : [class_Rings_Oordered__ring(_1080023), 15877 ^ _777959 : [(15884 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080023), _1080029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080023), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080023), _1080031), _1080025)), _1080027)), _1080033))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080023), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080023), _1080025), _1080027)), _1080029)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080023), _1080031), _1080027)), _1080033))))], (15878 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080023), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080023), _1080025), _1080027)), _1080029)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080023), _1080031), _1080027)), _1080033))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1080023), _1080029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1080023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080023), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080023), _1080031), _1080025)), _1080027)), _1080033))))]]], (28620 ^ _777959) ^ [_1317181] : [c_Nat__Transfer_Ois__nat(_1317181), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1317181)))], (35513 ^ _777959) ^ [_1451054, _1451056, _1451058] : [class_Rings_Osemiring__1(_1451054), hBOOL(hAPP(hAPP(c_member(_1451054), _1451056), c_Nat_Osemiring__1__class_ONats(_1451054))), hBOOL(hAPP(hAPP(c_member(_1451054), _1451058), c_Nat_Osemiring__1__class_ONats(_1451054))), -(hBOOL(hAPP(hAPP(c_member(_1451054), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1451054), _1451056), _1451058)), c_Nat_Osemiring__1__class_ONats(_1451054))))], (14257 ^ _777959) ^ [_1043515, _1043517, _1043519] : [class_Rings_Ocomm__semiring__1(_1043515), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043515), _1043517), _1043519) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043515), _1043519), _1043517))], (33573 ^ _777959) ^ [_1410422, _1410424] : [class_Int_Onumber__ring(_1410422), class_Rings_Olinordered__idom(_1410422), 33580 ^ _777959 : [(33587 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1410424)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410422), c_Groups_Ozero__class_Ozero(_1410422)), hAPP(c_Int_Onumber__class_Onumber__of(_1410422), _1410424))))], (33581 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410422), c_Groups_Ozero__class_Ozero(_1410422)), hAPP(c_Int_Onumber__class_Onumber__of(_1410422), _1410424))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1410424)))]]], (17059 ^ _777959) ^ [_1104290, _1104292, _1104294, _1104296] : [class_Groups_Oordered__ab__group__add(_1104290), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1104290), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1104290), _1104292), _1104294)), _1104296) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1104290), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1104290), _1104292), _1104296)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1104290), _1104294), _1104296)))], (26268 ^ _777959) ^ [_1275886, _1275888, _1275890] : [class_Fields_Olinordered__field(_1275886), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275886), c_Groups_Ozero__class_Ozero(_1275886)), _1275888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275886), _1275890), c_Groups_Ozero__class_Ozero(_1275886))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1275886), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1275886), _1275888), _1275890)), c_Groups_Ozero__class_Ozero(_1275886))))], (31490 ^ _777959) ^ [_1372892, _1372894] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1372892)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1372894)), hAPP(c_Int_Onat, _1372892)) = hAPP(c_Int_Onat, _1372894))], (24856 ^ _777959) ^ [_1249298, _1249300, _1249302] : [-(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)), _1249298)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1249300), _1249302)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1249300), _1249298)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1249302), _1249298)))], (23685 ^ _777959) ^ [_1228559, _1228561, _1228563] : [class_Rings_Olinordered__semidom(_1228559), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228559), c_Groups_Ozero__class_Ozero(_1228559)), _1228561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1228559), c_Groups_Ozero__class_Ozero(_1228559)), hAPP(hAPP(c_Power_Opower__class_Opower(_1228559), _1228561), _1228563))))], (26500 ^ _777959) ^ [_1279883, _1279885, _1279887, _1279889, _1279891] : [class_Fields_Olinordered__field(_1279883), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279883), c_Groups_Ozero__class_Ozero(_1279883)), _1279885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279883), _1279885), _1279887)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279883), c_Groups_Ozero__class_Ozero(_1279883)), _1279889)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279883), _1279889), _1279891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279883), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279883), _1279885), _1279891)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279883), _1279887), _1279889))))], (5900 ^ _777959) ^ [_871681, _871683] : [-(hAPP(c_Option_Othe(_871681), hAPP(c_Option_Ooption_OSome(_871681), _871683)) = _871683)], (16987 ^ _777959) ^ [_1102905, _1102907, _1102909, _1102911] : [class_Orderings_Olinorder(_1102905), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102905), _1102907), _1102909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102905), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1102905), _1102911), _1102907)), _1102909)))], (38276 ^ _777959) ^ [_1511358, _1511360, _1511362, _1511364] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1511358), _1511360)), 38279 ^ _777959 : [(38286 ^ _777959) ^ [] : [hAPP(c_Finite__Set_Ocard(_1511362), hAPP(c_Set_Oimage(_1511358, _1511362, _1511364), _1511360)) = hAPP(c_Finite__Set_Ocard(_1511358), _1511360), -(c_Fun_Oinj__on(_1511358, _1511362, _1511364, _1511360))], (38280 ^ _777959) ^ [] : [c_Fun_Oinj__on(_1511358, _1511362, _1511364, _1511360), -(hAPP(c_Finite__Set_Ocard(_1511362), hAPP(c_Set_Oimage(_1511358, _1511362, _1511364), _1511360)) = hAPP(c_Finite__Set_Ocard(_1511358), _1511360))]]], (23232 ^ _777959) ^ [_1220698, _1220700, _1220702, _1220704] : [class_Rings_Olinordered__semidom(_1220698), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220698), c_Groups_Oone__class_Oone(_1220698)), _1220700)), 23239 ^ _777959 : [(23246 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220702), _1220704)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220698), hAPP(hAPP(c_Power_Opower__class_Opower(_1220698), _1220700), _1220702)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220698), _1220700), _1220704))))], (23240 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220698), hAPP(hAPP(c_Power_Opower__class_Opower(_1220698), _1220700), _1220702)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220698), _1220700), _1220704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220702), _1220704)))]]], (34097 ^ _777959) ^ [_1420171, _1420173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420171), _1420173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1420171)), c_Int_OBit0(_1420173))))], (14085 ^ _777959) ^ [_1039818, _1039820, _1039822, _1039824, _1039826] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1039818), hAPP(c_Set_Oimage(_1039820, _1039818, _1039822), c_Orderings_Otop__class_Otop(tc_fun(_1039820, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1039824), hAPP(c_Set_Oimage(_1039820, _1039824, hAPP(hAPP(c_COMBB(_1039818, _1039824, _1039820), _1039826), _1039822)), c_Orderings_Otop__class_Otop(tc_fun(_1039820, tc_HOL_Obool))))))], (33269 ^ _777959) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (50660 ^ _777959) ^ [_1805546, _1805548, _1805550, _1805552] : [-(hAPP(hAPP(c_List_Omap(_1805546, _1805548), hAPP(c_COMBK(_1805548, _1805546), _1805550)), _1805552) = c_List_Oreplicate(_1805548, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1805546)), _1805552), _1805550))], (20953 ^ _777959) ^ [_1176301, _1176303] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176301), _1176303) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20956 ^ _777959 : [(20959 ^ _777959) ^ [] : [-(_1176303 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (20957 ^ _777959) ^ [] : [-(_1176301 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (13607 ^ _777959) ^ [_1028003, _1028005] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1028003, tc_HOL_Obool)), _1028005), c_Orderings_Otop__class_Otop(tc_fun(_1028003, tc_HOL_Obool))) = _1028005)], (13093 ^ _777959) ^ [_1016826, _1016828, _1016830] : [class_Complete__Lattice_Ocomplete__lattice(_1016826), hBOOL(hAPP(hAPP(c_member(_1016826), _1016828), _1016830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1016826), _1016828), c_Complete__Lattice_OSup__class_OSup(_1016826, _1016830))))], (8778 ^ _777959) ^ [_929432, _929434, _929436, _929438, _929440, _929442] : [_929432 = _929434, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_929436, _929438), _929440), _929434), _929442), _929432) = _929442)], (14411 ^ _777959) ^ [_1047946, _1047948, _1047950] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047946), _1047948)), hBOOL(hAPP(hAPP(c_member(_1047946), _1047950), _1047948)), -(hAPP(c_Finite__Set_Ocard(_1047946), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1047946, tc_HOL_Obool)), _1047948), hAPP(hAPP(c_Set_Oinsert(_1047946), _1047950), c_Orderings_Obot__class_Obot(tc_fun(_1047946, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1047946), _1047948)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (6812 ^ _777959) ^ [_888899, _888901, _888903, _888905, _888907] : [-(hBOOL(hAPP(hAPP(c_member(_888899), _888901), hAPP(c_Set_Oimage(_888903, _888899, _888905), _888907)))), 6813 ^ _777959 : [(6814 ^ _777959) ^ [_888969] : [hBOOL(hAPP(hAPP(c_member(_888903), _888969), _888907)), _888901 = hAPP(_888905, _888969)]]], (16557 ^ _777959) ^ [_1095273, _1095275, _1095277, _1095279] : [class_Orderings_Olinorder(_1095273), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095273), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095273), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095273), _1095275), _1095277)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095273), _1095275), _1095279))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095273), _1095275), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095273), _1095277), _1095279)))))], (28888 ^ _777959) ^ [_1322583, _1322585, _1322587] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1322583, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1322585)), _1322587) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322583, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1322583, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1322585)), _1322587)), hAPP(_1322587, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (45489 ^ _777959) ^ [_1684758, _1684760, _1684762, _1684764, _1684766] : [class_Groups_Omonoid__add(_1684758), 45495 ^ _777959 : [(45500 ^ _777959) ^ [] : [hAPP(_1684766, 45494 ^ [_1684758, _1684760, _1684762, _1684764, _1684766]) = c_Groups_Ozero__class_Ozero(_1684758)], (45498 ^ _777959) ^ [] : [hBOOL(hAPP(_1684764, 45494 ^ [_1684758, _1684760, _1684762, _1684764, _1684766]))], (45496 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1684760), 45494 ^ [_1684758, _1684760, _1684762, _1684764, _1684766]), hAPP(c_List_Oset(_1684760), _1684762))))]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1684758), hAPP(hAPP(c_List_Omap(_1684760, _1684758), _1684766), hAPP(c_List_Ofilter(_1684760, _1684764), _1684762))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1684758), hAPP(hAPP(c_List_Omap(_1684760, _1684758), _1684766), _1684762)))], (4596 ^ _777959) ^ [_847630, _847632, _847634, _847636, _847638, _847640, _847642, _847644] : [-(c_New__Random__Sequence_Opos__empty(_847644, _847640, _847636, _847632) = c_New__Random__Sequence_Opos__empty(_847642, _847638, _847634, _847630)), _847644 = _847642, _847640 = _847638, _847636 = _847634, _847632 = _847630], (11788 ^ _777959) ^ [_991343, _991345, _991347, _991349, _991351, _991353] : [hBOOL(hAPP(hAPP(c_member(_991343), _991345), _991347)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991343, tc_fun(_991349, tc_HOL_Obool)), _991347), hAPP(hAPP(c_COMBB(tc_fun(_991349, tc_HOL_Obool), tc_fun(_991349, tc_HOL_Obool), _991343), hAPP(c_Set_Oinsert(_991349), _991351)), _991353)) = hAPP(hAPP(c_Set_Oinsert(_991349), _991351), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991343, tc_fun(_991349, tc_HOL_Obool)), _991347), _991353)))], (9210 ^ _777959) ^ [_936079, _936081, _936083, _936085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936079, tc_HOL_Obool)), _936081), _936083)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_936079, tc_HOL_Obool)), _936083), _936085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_936079, tc_HOL_Obool)), _936081), _936085)))], (13056 ^ _777959) ^ [_1015645, _1015647] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1015645, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1015645, tc_HOL_Obool)), _1015647)), _1015647) = c_Orderings_Obot__class_Obot(tc_fun(_1015645, tc_HOL_Obool)))], (49193 ^ _777959) ^ [_1772321, _1772323, _1772325, _1772327, _1772329, _1772331] : [c_Relation_Osingle__valued(_1772321, _1772323, _1772325), hBOOL(hAPP(hAPP(c_member(tc_prod(_1772321, _1772323)), hAPP(hAPP(c_Product__Type_OPair(_1772321, _1772323), _1772327), _1772329)), _1772325)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1772321, _1772323)), hAPP(hAPP(c_Product__Type_OPair(_1772321, _1772323), _1772327), _1772331)), _1772325)), -(_1772329 = _1772331)], (6895 ^ _777959) ^ [_890685, _890687, _890689] : [hBOOL(hAPP(hAPP(c_member(_890685), _890687), hAPP(hAPP(c_Set_Oinsert(_890685), _890689), c_Orderings_Obot__class_Obot(tc_fun(_890685, tc_HOL_Obool))))), -(_890687 = _890689)], (14768 ^ _777959) ^ [_1055580, _1055582, _1055584] : [class_Rings_Olinordered__idom(_1055580), -(_1055582 = _1055584), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055580), _1055582), _1055584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1055580), _1055584), _1055582)))], (13070 ^ _777959) ^ [_1016029, _1016031, _1016033] : [13072 ^ _777959 : [(13075 ^ _777959) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1016029, tc_HOL_Obool)), 13071 ^ [_1016029, _1016031, _1016033]), _1016033) = c_Orderings_Obot__class_Obot(tc_fun(_1016029, tc_HOL_Obool))], (13073 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1016029, tc_HOL_Obool)), 13071 ^ [_1016029, _1016031, _1016033]), _1016031)))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1016029, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1016029, tc_HOL_Obool), _1016031)), _1016033) = c_Orderings_Obot__class_Obot(tc_fun(_1016029, tc_HOL_Obool)))], (22387 ^ _777959) ^ [_1204482, _1204484, _1204486, _1204488, _1204490] : [class_Groups_Ocomm__monoid__add(_1204482), hBOOL(hAPP(c_Finite__Set_Ofinite(_1204484), _1204486)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1204484), _1204488)), 22401 ^ _777959 : [(22404 ^ _777959) ^ [] : [hAPP(_1204490, 22400 ^ [_1204482, _1204484, _1204486, _1204488, _1204490]) = c_Groups_Ozero__class_Ozero(_1204482)], (22402 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1204484), 22400 ^ [_1204482, _1204484, _1204486, _1204488, _1204490]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1204484, tc_HOL_Obool)), _1204486), _1204488))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1204484, _1204482), _1204490), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1204484, tc_HOL_Obool)), _1204486), _1204488)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1204482), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1204484, _1204482), _1204490), _1204486)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1204484, _1204482), _1204490), _1204488)))], (28774 ^ _777959) ^ [_1320052, _1320054, _1320056, _1320058] : [class_Groups_Ocomm__monoid__add(_1320052), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1320054), _1320056)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1320052), _1320058), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1320054, _1320056)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1320052), hAPP(_1320058, _1320054)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1320052), _1320058), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1320054), _1320056))))], (46433 ^ _777959) ^ [_1705499, _1705501, _1705503, _1705505, _1705507] : [c_List_Olist__all2(_1705499, _1705501, _1705503, _1705505, hAPP(c_List_Orev(_1705501), _1705507)), -(c_List_Olist__all2(_1705499, _1705501, _1705503, hAPP(c_List_Orev(_1705499), _1705505), _1705507))], (47462 ^ _777959) ^ [_1731713, _1731715] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1731713, _1731715), 47463 ^ [_1731713, _1731715])), -(c_Wellfounded_OwfP(_1731713, _1731715))], (9266 ^ _777959) ^ [_937235, _937237, _937239, _937241, _937243, _937245, _937247] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_937235, tc_Option_Ooption(_937237)), _937239), _937241), hAPP(c_Option_Ooption_OSome(_937237), _937243)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_937235, tc_Option_Ooption(_937237)), _937245), _937241), hAPP(c_Option_Ooption_OSome(_937237), _937247)), -(_937243 = _937247)], (28384 ^ _777959) ^ [] : [-(c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (40878 ^ _777959) ^ [_1573345, _1573347, _1573349, _1573351] : [40880 ^ _777959 : [(40883 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1573349, 40879 ^ [_1573345, _1573347, _1573349, _1573351])), hAPP(_1573351, 40879 ^ [_1573345, _1573347, _1573349, _1573351])))], (40881 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1573345), 40879 ^ [_1573345, _1573347, _1573349, _1573351]), hAPP(c_List_Oset(_1573345), _1573347))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1573345, _1573349, _1573347)), c_List_Olist_Olist__size(_1573345, _1573351, _1573347))))], (44120 ^ _777959) ^ [_1655897, _1655899, _1655901] : [-(c_List_Osublist(_1655897, _1655899, _1655901) = hAPP(hAPP(c_List_Omap(tc_prod(_1655897, tc_Nat_Onat), _1655897), c_Product__Type_Ofst(_1655897, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1655897, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1655897, 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(_1655897, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1655897, tc_Nat_Onat))), _1655901)), hAPP(hAPP(c_List_Ozip(_1655897, tc_Nat_Onat), _1655899), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655897)), _1655899))))))], (4020 ^ _777959) ^ [_838864, _838866, _838868, _838870] : [-(c_Code__Numeral_Onat__of__aux(_838870, _838866) = c_Code__Numeral_Onat__of__aux(_838868, _838864)), _838870 = _838868, _838866 = _838864], (29964 ^ _777959) ^ [_1344380, _1344382, _1344384, _1344386] : [class_Divides_Osemiring__div(_1344380), -(c_Divides_Odiv__class_Omod(_1344380, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344380), _1344382), _1344384), _1344386) = c_Divides_Odiv__class_Omod(_1344380, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344380), c_Divides_Odiv__class_Omod(_1344380, _1344382, _1344386)), c_Divides_Odiv__class_Omod(_1344380, _1344384, _1344386)), _1344386))], (32879 ^ _777959) ^ [_1399026, _1399028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399026)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399028))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1399026), _1399028)))], (2530 ^ _777959) ^ [_815453, _815455, _815457, _815459, _815461, _815463] : [-(c_Smallcheck_Osmall_H(_815463, _815459, _815455) = c_Smallcheck_Osmall_H(_815461, _815457, _815453)), _815463 = _815461, _815459 = _815457, _815455 = _815453], (20391 ^ _777959) ^ [_1166887, _1166889, _1166891, _1166893] : [class_Rings_Olinordered__ring__strict(_1166887), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166887), _1166889), c_Groups_Ozero__class_Ozero(_1166887))), 20398 ^ _777959 : [(20405 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166887), _1166893), _1166891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166887), _1166889), _1166891)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166887), _1166889), _1166893))))], (20399 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166887), _1166889), _1166891)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166887), _1166889), _1166893))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1166887), _1166893), _1166891)))]]], (30643 ^ _777959) ^ [_1357176, _1357178] : [class_Rings_Olinordered__idom(_1357176), -(c_Groups_Osgn__class_Osgn(_1357176, c_Groups_Osgn__class_Osgn(_1357176, _1357178)) = c_Groups_Osgn__class_Osgn(_1357176, _1357178))], (5056 ^ _777959) ^ [_855176, _855178, _855180, _855182] : [-(c_Lazy__Sequence_Ohb__flat(_855182, _855178) = c_Lazy__Sequence_Ohb__flat(_855180, _855176)), _855182 = _855180, _855178 = _855176], (51304 ^ _777959) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (41972 ^ _777959) ^ [_1604888, _1604890, _1604892] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1604888, _1604890), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1604888, _1604890), _1604892), hAPP(c_COMBK(tc_fun(_1604890, tc_HOL_Obool), _1604888), c_Orderings_Otop__class_Otop(tc_fun(_1604890, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1604888, _1604890), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1604888, tc_HOL_Obool)), _1604892)), hAPP(c_COMBK(tc_fun(_1604890, tc_HOL_Obool), _1604888), c_Orderings_Otop__class_Otop(tc_fun(_1604890, tc_HOL_Obool)))))], (17669 ^ _777959) ^ [_1115603, _1115605, _1115607] : [class_Orderings_Olinorder(_1115603), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115603), _1115605)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1115603), _1115607)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1115603, tc_HOL_Obool)), _1115605), _1115607) = c_Orderings_Obot__class_Obot(tc_fun(_1115603, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1115603), c_Big__Operators_Olinorder__class_OMin(_1115603, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1115603, tc_HOL_Obool)), _1115605), _1115607))), c_Big__Operators_Olinorder__class_OMin(_1115603, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1115603, tc_HOL_Obool)), _1115605), _1115607))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1115603), c_Big__Operators_Olinorder__class_OMin(_1115603, _1115605)), c_Big__Operators_Olinorder__class_OMin(_1115603, _1115607)))], (40958 ^ _777959) ^ [_1576813, _1576815, _1576817, _1576819] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1576813), tc_List_Olist(_1576813))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1576813), tc_List_Olist(_1576813)), _1576815), _1576817)), c_List_Olistrel(_1576813, _1576819))), 40961 ^ _777959 : [(40964 ^ _777959) ^ [_1577149] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1576813, _1576813)), _1577149), hAPP(c_List_Oset(tc_prod(_1576813, _1576813)), hAPP(hAPP(c_List_Ozip(_1576813, _1576813), _1576815), _1576817)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1576813, _1576813, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1576813, tc_fun(tc_prod(_1576813, _1576813), tc_HOL_Obool), tc_fun(_1576813, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576813, tc_fun(tc_fun(tc_prod(_1576813, _1576813), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1576813, _1576813), tc_HOL_Obool), tc_fun(_1576813, tc_HOL_Obool)), _1576813), c_COMBC(_1576813, tc_fun(tc_prod(_1576813, _1576813), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1576813, tc_prod(_1576813, _1576813)), tc_fun(_1576813, tc_fun(tc_fun(tc_prod(_1576813, _1576813), tc_HOL_Obool), tc_HOL_Obool)), _1576813), hAPP(c_COMBB(tc_prod(_1576813, _1576813), tc_fun(tc_fun(tc_prod(_1576813, _1576813), tc_HOL_Obool), tc_HOL_Obool), _1576813), c_member(tc_prod(_1576813, _1576813)))), c_Product__Type_OPair(_1576813, _1576813)))), _1576819)), _1577149)))], (40962 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1576813)), _1576815) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1576813)), _1576817))]]], (37772 ^ _777959) ^ [_1500537, _1500539, _1500541, _1500543, _1500545, _1500547] : [c_Equiv__Relations_Ocongruent(_1500537, _1500539, _1500541, _1500543), hBOOL(hAPP(hAPP(c_member(tc_prod(_1500537, _1500537)), hAPP(hAPP(c_Product__Type_OPair(_1500537, _1500537), _1500545), _1500547)), _1500541)), -(hAPP(_1500543, _1500545) = hAPP(_1500543, _1500547))], (3178 ^ _777959) ^ [_825689, _825691, _825693, _825695, _825697, _825699] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_825699, _825695, _825691) = c_SetInterval_Oord__class_OgreaterThanLessThan(_825697, _825693, _825689)), _825699 = _825697, _825695 = _825693, _825691 = _825689], (33799 ^ _777959) ^ [_1414197, _1414199] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1414197)))), _1414199) = 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)))), _1414197)), _1414199))], (24425 ^ _777959) ^ [] : [-(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)))], (8044 ^ _777959) ^ [_915365, _915367] : [c_Com_Ocom_OSKIP = c_Com_Ocom_OSemi(_915365, _915367)], (42804 ^ _777959) ^ [_1625993, _1625995, _1625997, _1625999] : [_1625997 = _1625999, -(hAPP(hAPP(c_List_Oappend(_1625993), _1625995), _1625997) = hAPP(hAPP(c_List_Oappend(_1625993), _1625995), _1625999))], (50816 ^ _777959) ^ [_1808188, _1808190] : [class_Orderings_Otop(_1808188), -(class_Orderings_Otop(tc_fun(_1808190, _1808188)))], (40793 ^ _777959) ^ [_1571004, _1571006, _1571008, _1571010, _1571012] : [-(c_List_Olist_Olist__size(_1571004, _1571006, hAPP(hAPP(c_List_Omap(_1571008, _1571004), _1571010), _1571012)) = c_List_Olist_Olist__size(_1571008, hAPP(c_Fun_Ocomp(_1571004, tc_Nat_Onat, _1571008, _1571006), _1571010), _1571012))], (17233 ^ _777959) ^ [_1107511, _1107513, _1107515, _1107517, _1107519, _1107521] : [c_Finite__Set_Ofun__left__comm(_1107511, _1107513, _1107515), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1107511, _1107513, _1107515, _1107517, _1107519), _1107521)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1107511, _1107513, _1107515), _1107517), _1107519) = _1107521)], (39976 ^ _777959) ^ [_1551955, _1551957, _1551959, _1551961] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551955)), _1551957) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551959)), _1551961), -(hAPP(hAPP(c_List_Omap(tc_prod(_1551955, _1551959), _1551959), c_Product__Type_Osnd(_1551955, _1551959)), hAPP(hAPP(c_List_Ozip(_1551955, _1551959), _1551957), _1551961)) = _1551961)], (800 ^ _777959) ^ [_790243, _790245, _790247, _790249, _790251, _790253] : [-(c_Relation_Ototal__on(_790251, _790247, _790243)), c_Relation_Ototal__on(_790253, _790249, _790245), _790253 = _790251, _790249 = _790247, _790245 = _790243], (9168 ^ _777959) ^ [_935328, _935330, _935332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_935328, tc_HOL_Obool)), _935330), _935332)), 9171 ^ _777959 : [(9174 ^ _777959) ^ [] : [_935330 = _935332], (9172 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935328, tc_HOL_Obool)), _935330), _935332)))]]], (45576 ^ _777959) ^ [_1687171, _1687173, _1687175, _1687177, _1687179] : [c_List_Opartition(_1687171, _1687173, _1687175) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1687171), tc_List_Olist(_1687171)), _1687177), _1687179), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1687171, tc_HOL_Obool)), hAPP(c_List_Oset(_1687171), _1687177)), hAPP(c_List_Oset(_1687171), _1687179)) = hAPP(c_List_Oset(_1687171), _1687175))], (20783 ^ _777959) ^ [_1173789, _1173791, _1173793] : [class_Groups_Ocomm__monoid__add(_1173789), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1173791, _1173789), _1173793), c_Orderings_Obot__class_Obot(tc_fun(_1173791, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1173789))], (51144 ^ _777959) ^ [] : [-(class_HOL_Oequal(tc_HOL_Obool))], (21224 ^ _777959) ^ [_1181309, _1181311, _1181313, _1181315] : [class_Groups_Oordered__comm__monoid__add(_1181309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181309), c_Groups_Ozero__class_Ozero(_1181309)), _1181311)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181309), _1181313), _1181315)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181309), _1181313), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181309), _1181311), _1181315))))], (25424 ^ _777959) ^ [_1260034, _1260036] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1260034), _1260036))))], (28077 ^ _777959) ^ [_1307666, _1307668, _1307670] : [class_Orderings_Olinorder(_1307666), 28080 ^ _777959 : [(28087 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307666), _1307670), _1307668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307666, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1307666), _1307668)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1307666), _1307670))))], (28081 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1307666, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1307666), _1307668)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1307666), _1307670))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1307666), _1307670), _1307668)))]]], (35025 ^ _777959) ^ [_1437208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1437208))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1437208)))], (33801 ^ _777959) ^ [_1414246, _1414248] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1414246), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1414248)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1414246), 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)))), _1414248)))], (19875 ^ _777959) ^ [_1157449, _1157451, _1157453] : [class_Rings_Oordered__ring(_1157449), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157449), c_Groups_Ozero__class_Ozero(_1157449)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157449), _1157451), _1157453)))), 19880 ^ _777959 : [(19887 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157449), _1157451), c_Groups_Ozero__class_Ozero(_1157449))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157449), _1157453), c_Groups_Ozero__class_Ozero(_1157449)))], (19881 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157449), c_Groups_Ozero__class_Ozero(_1157449)), _1157451)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157449), c_Groups_Ozero__class_Ozero(_1157449)), _1157453))]]], (26296 ^ _777959) ^ [_1276396, _1276398, _1276400] : [class_Fields_Olinordered__field(_1276396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276396), _1276398), c_Groups_Ozero__class_Ozero(_1276396))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276396), _1276400), c_Groups_Ozero__class_Ozero(_1276396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1276396), c_Groups_Ozero__class_Ozero(_1276396)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1276396), _1276398), _1276400))))], (42178 ^ _777959) ^ [_1609176, _1609178, _1609180, _1609182, _1609184, _1609186] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1609176, _1609178)), hAPP(hAPP(c_Product__Type_OPair(_1609176, _1609178), _1609180), _1609182)), hAPP(hAPP(c_Product__Type_OSigma(_1609176, _1609178), _1609184), _1609186)))), hBOOL(hAPP(hAPP(c_member(_1609176), _1609180), _1609184)), hBOOL(hAPP(hAPP(c_member(_1609178), _1609182), hAPP(_1609186, _1609180)))], (50070 ^ _777959) ^ [_1793173, _1793175, _1793177] : [class_HOL_Oequal(_1793173), 50073 ^ _777959 : [(50080 ^ _777959) ^ [] : [_1793175 = _1793177, -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1793173), _1793175), _1793177)))], (50074 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(_1793173), _1793175), _1793177)), -(_1793175 = _1793177)]]], (1360 ^ _777959) ^ [_797683, _797685] : [-(class_Orderings_Obot(_797683)), _797685 = _797683, class_Orderings_Obot(_797685)], (23184 ^ _777959) ^ [_1219825, _1219827] : [-(c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(_1219825, _1219827)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Com_Ocom_Ocom__size(_1219827)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (1580 ^ _777959) ^ [_800433, _800435] : [-(class_Rings_Oordered__semiring(_800433)), _800435 = _800433, class_Rings_Oordered__semiring(_800435)], (37430 ^ _777959) ^ [_1492870, _1492872, _1492874] : [c_Equiv__Relations_Oequiv(_1492870, _1492872, _1492874), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1492870, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1492870), _1492872), _1492874)) = _1492872)], (19260 ^ _777959) ^ [_1147712, _1147714] : [class_Rings_Ocomm__semiring__1(_1147712), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1147712), _1147714), c_Groups_Ozero__class_Ozero(_1147712)) = _1147714)], (35213 ^ _777959) ^ [_1440016] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1440016)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1440016)))], (12882 ^ _777959) ^ [_1011767] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1011767, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1011767, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1011767, tc_HOL_Obool)))], (8010 ^ _777959) ^ [_914767, _914769] : [hBOOL(hAPP(c_Com_OWT, _914767)), hBOOL(hAPP(c_Com_OWT, _914769)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_914767, _914769))))], (49485 ^ _777959) ^ [_1780299, _1780301, _1780303, _1780305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1780299, _1780299)), hAPP(hAPP(c_Product__Type_OPair(_1780299, _1780299), _1780301), _1780303)), c_Transitive__Closure_Otrancl(_1780299, _1780305))), 49489 ^ _777959 : [(49492 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780299, _1780299)), hAPP(hAPP(c_Product__Type_OPair(_1780299, _1780299), 49488 ^ [_1780299, _1780301, _1780303, _1780305]), _1780303)), _1780305)))], (49490 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1780299, _1780299)), hAPP(hAPP(c_Product__Type_OPair(_1780299, _1780299), _1780301), 49488 ^ [_1780299, _1780301, _1780303, _1780305])), c_Transitive__Closure_Ortrancl(_1780299, _1780305))))]]], (7622 ^ _777959) ^ [_906452, _906454] : [-(c_Set_Othe__elem(_906452, _906454) = c_HOL_OThe(_906452, hAPP(hAPP(c_COMBB(tc_fun(_906452, tc_HOL_Obool), tc_HOL_Obool, _906452), hAPP(c_fequal, _906454)), hAPP(hAPP(c_COMBC(_906452, tc_fun(_906452, tc_HOL_Obool), tc_fun(_906452, tc_HOL_Obool)), c_Set_Oinsert(_906452)), c_Orderings_Obot__class_Obot(tc_fun(_906452, tc_HOL_Obool))))))], (14335 ^ _777959) ^ [_1045610, _1045612, _1045614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045610), _1045612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1045610, tc_HOL_Obool)), _1045614), _1045612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1045610), _1045614)), hAPP(c_Finite__Set_Ocard(_1045610), _1045612))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1045610, tc_HOL_Obool)), _1045614), _1045612)))], (42695 ^ _777959) ^ [_1623569, _1623571, _1623573, _1623575, _1623577] : [-(hAPP(hAPP(c_List_Olist_OCons(_1623569), _1623571), _1623573) = hAPP(hAPP(c_List_Oappend(_1623569), _1623575), _1623577)), 42696 ^ _777959 : [(42703 ^ _777959) ^ [_1623752] : [hAPP(hAPP(c_List_Olist_OCons(_1623569), _1623571), _1623752) = _1623575, _1623573 = hAPP(hAPP(c_List_Oappend(_1623569), _1623752), _1623577)], (42697 ^ _777959) ^ [] : [_1623575 = c_List_Olist_ONil(_1623569), hAPP(hAPP(c_List_Olist_OCons(_1623569), _1623571), _1623573) = _1623577]]], (1110 ^ _777959) ^ [_794558, _794560] : [-(class_Rings_Olinordered__ring(_794558)), _794560 = _794558, class_Rings_Olinordered__ring(_794560)], (5916 ^ _777959) ^ [_872232, _872234] : [-(c_Option_Oset(_872232, hAPP(c_Option_Ooption_OSome(_872232), _872234)) = hAPP(hAPP(c_Set_Oinsert(_872232), _872234), c_Orderings_Obot__class_Obot(tc_fun(_872232, tc_HOL_Obool))))], (10508 ^ _777959) ^ [_963885, _963887, _963889, _963891, _963893, _963895] : [-(hBOOL(hAPP(hAPP(c_member(_963885), _963887), _963889))), -(c_Map_Orestrict__map(_963885, _963891, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_963885, tc_Option_Ooption(_963891)), _963893), _963887), _963895), _963889) = c_Map_Orestrict__map(_963885, _963891, _963893, _963889))], (19560 ^ _777959) ^ [_1152174] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152174) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11942 ^ _777959) ^ [_994859, _994861, _994863] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994859), _994861)), _994863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994859), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994863), _994861))))], (39840 ^ _777959) ^ [_1548416, _1548418, _1548420, _1548422] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548416, _1548416)), hAPP(hAPP(c_Product__Type_OPair(_1548416, _1548416), _1548418), _1548420)), hAPP(c_List_Oset(tc_prod(_1548416, _1548416)), hAPP(hAPP(c_List_Ozip(_1548416, _1548416), _1548422), _1548422))))), hBOOL(hAPP(hAPP(c_member(_1548416), _1548418), hAPP(c_List_Oset(_1548416), _1548422))), _1548418 = _1548420], (14535 ^ _777959) ^ [_1051038, _1051040, _1051042, _1051044, _1051046, _1051048, _1051050] : [14537 ^ _777959 : [(14540 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_1051046, 14536 ^ [_1051038, _1051040, _1051042, _1051044, _1051046, _1051048, _1051050]), _1051048), _1051050))], (14538 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1051038), 14536 ^ [_1051038, _1051040, _1051042, _1051044, _1051046, _1051048, _1051050]), _1051044)))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1051038, tc_fun(_1051040, tc_fun(_1051042, tc_HOL_Obool))), _1051044), _1051046), _1051048), _1051050)))], (9080 ^ _777959) ^ [_933783, _933785, _933787, _933789] : [class_Orderings_Opreorder(_933783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933783), _933785), _933787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_933783), _933787), _933789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_933783), _933785), _933789)))], (9758 ^ _777959) ^ [_947258, _947260, _947262, _947264] : [-(hAPP(c_Finite__Set_Ofold__image(_947258, _947260, _947262), _947264) = c_Finite__Set_Ofold(_947260, _947258, hAPP(hAPP(c_COMBB(_947258, tc_fun(_947258, _947258), _947260), _947262), _947264)))], (610 ^ _777959) ^ [_787372, _787374, _787376, _787378] : [-(c_FunDef_Oreduction__pair(_787376, _787372)), c_FunDef_Oreduction__pair(_787378, _787374), _787378 = _787376, _787374 = _787372], (42320 ^ _777959) ^ [_1612741, _1612743, _1612745] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612741), tc_List_Olist(_1612741))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612741), tc_List_Olist(_1612741)), _1612743), c_List_Olist_ONil(_1612741))), c_List_Olex(_1612741, _1612745)))], (36167 ^ _777959) ^ [_1463685, _1463687] : [_1463685 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1463687, _1463685) = 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), _1463687)))], (4760 ^ _777959) ^ [_850432, _850434] : [_850434 = _850432, -(c_New__Random__Sequence_Opos__single(_850434) = c_New__Random__Sequence_Opos__single(_850432))], (10962 ^ _777959) ^ [_972844, _972846, _972848] : [class_Groups_Ogroup__add(_972844), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_972844), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972844), _972846), _972848)), _972848) = _972846)], (12131 ^ _777959) ^ [_998091, _998093, _998095, _998097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998091), _998093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _998095), _998097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998091), _998095)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998093), _998097))))], (17973 ^ _777959) ^ [_1121326, _1121328, _1121330] : [class_Orderings_Olinorder(_1121326), hBOOL(hAPP(c_Finite__Set_Ofinite(_1121326), _1121328)), -(_1121328 = c_Orderings_Obot__class_Obot(tc_fun(_1121326, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1121326), _1121330)), -(_1121330 = c_Orderings_Obot__class_Obot(tc_fun(_1121326, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1121326, c_Orderings_Oord__class_Omin(_1121326), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1121326, tc_HOL_Obool)), _1121328), _1121330)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1121326), c_Big__Operators_Olattice_OInf__fin(_1121326, c_Orderings_Oord__class_Omin(_1121326), _1121328)), c_Big__Operators_Olattice_OInf__fin(_1121326, c_Orderings_Oord__class_Omin(_1121326), _1121330)))], (6893 ^ _777959) ^ [_890608, _890610, _890612] : [-(hAPP(hAPP(c_Set_Oinsert(_890608), _890610), _890612) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_890608, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_890608), _890610), c_Orderings_Obot__class_Obot(tc_fun(_890608, tc_HOL_Obool)))), _890612))], (37235 ^ _777959) ^ [] : [-(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))))))], (27563 ^ _777959) ^ [_1298880, _1298882] : [hAPP(c_Int_Onat, _1298880) = _1298882, 27566 ^ _777959 : [(27573 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298880))), -(_1298882 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (27567 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1298880)), -(_1298880 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1298882))]]], (33403 ^ _777959) ^ [_1407760] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407760) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1407760), c_Int_OPls)))], (31662 ^ _777959) ^ [_1375761, _1375763, _1375765] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OCond(_1375761, _1375763, _1375765)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1375763)), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1375765))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (3916 ^ _777959) ^ [_837278, _837280, _837282, _837284] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_837284, _837280) = c_SetInterval_Oord__class_OatLeastLessThan(_837282, _837278)), _837284 = _837282, _837280 = _837278], (13103 ^ _777959) ^ [_1016991] : [class_Complete__Lattice_Ocomplete__lattice(_1016991), -(c_Complete__Lattice_OSup__class_OSup(_1016991, c_Orderings_Obot__class_Obot(tc_fun(_1016991, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_1016991))], (11539 ^ _777959) ^ [_984140, _984142, _984144, _984146] : [class_Complete__Lattice_Ocomplete__lattice(_984140), -(_984142 = c_Orderings_Obot__class_Obot(tc_fun(_984144, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_984144, _984140), _984142), hAPP(c_COMBK(_984140, _984144), _984146)) = _984146)], (50110 ^ _777959) ^ [_1793820, _1793822, _1793824, _1793826, _1793828] : [-(_1793820 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1793822, _1793824, _1793826, _1793828), _1793820) = hAPP(c_Lazy__Sequence_Obind(_1793822, _1793824, hAPP(_1793826, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1793820), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1793822, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1793824)), _1793828), _1793820)))], (51298 ^ _777959) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (45180 ^ _777959) ^ [_1678641, _1678643, _1678645] : [class_Orderings_Olinorder(_1678641), c_List_Olinorder__class_Osorted(_1678641, _1678643), -(c_List_Olinorder__class_Osorted(_1678641, c_List_OtakeWhile(_1678641, _1678645, _1678643)))], (40218 ^ _777959) ^ [_1557941, _1557943, _1557945, _1557947] : [hBOOL(hAPP(c_List_Odistinct(_1557941), _1557943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1557945), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1557941)), _1557943))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1557947), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1557941)), _1557943))), 40229 ^ _777959 : [(40236 ^ _777959) ^ [] : [_1557945 = _1557947, -(hAPP(hAPP(c_List_Onth(_1557941), _1557943), _1557945) = hAPP(hAPP(c_List_Onth(_1557941), _1557943), _1557947))], (40230 ^ _777959) ^ [] : [hAPP(hAPP(c_List_Onth(_1557941), _1557943), _1557945) = hAPP(hAPP(c_List_Onth(_1557941), _1557943), _1557947), -(_1557945 = _1557947)]]], (30577 ^ _777959) ^ [_1356074, _1356076] : [class_Groups_Osgn__if(_1356074), 30580 ^ _777959 : [(30587 ^ _777959) ^ [] : [-(_1356076 = c_Groups_Ozero__class_Ozero(_1356074)), 30590 ^ _777959 : [(30597 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356074), c_Groups_Ozero__class_Ozero(_1356074)), _1356076))), -(c_Groups_Osgn__class_Osgn(_1356074, _1356076) = hAPP(c_Groups_Ouminus__class_Ouminus(_1356074), c_Groups_Oone__class_Oone(_1356074)))], (30591 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356074), c_Groups_Ozero__class_Ozero(_1356074)), _1356076)), -(c_Groups_Osgn__class_Osgn(_1356074, _1356076) = c_Groups_Oone__class_Oone(_1356074))]]], (30581 ^ _777959) ^ [] : [_1356076 = c_Groups_Ozero__class_Ozero(_1356074), -(c_Groups_Osgn__class_Osgn(_1356074, _1356076) = c_Groups_Ozero__class_Ozero(_1356074))]]], (15340 ^ _777959) ^ [_1069852, _1069854] : [class_Groups_Ocomm__monoid__mult(_1069852), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1069852), c_Groups_Oone__class_Oone(_1069852)), _1069854) = _1069854)], (3718 ^ _777959) ^ [_834201, _834203] : [_834203 = _834201, -(c_Nitpick_Ozero__frac(_834203) = c_Nitpick_Ozero__frac(_834201))], (25292 ^ _777959) ^ [_1257258, _1257260, _1257262] : [-(hBOOL(hAPP(_1257258, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1257260), _1257262)))), 25295 ^ _777959 : [(25298 ^ _777959) ^ [] : [hBOOL(hAPP(_1257258, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (25296 ^ _777959) ^ [] : [-(_1257262 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], 25301 ^ _777959 : [(25302 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1257262)))], (25308 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 25304 ^ [_1257258, _1257260, _1257262]), _1257262)))], (25312 ^ _777959) ^ [] : [hBOOL(hAPP(_1257258, 25303 ^ [_1257258, _1257260, _1257262]))], (25310 ^ _777959) ^ [] : [-(_1257260 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1257262), 25303 ^ [_1257258, _1257260, _1257262])), 25304 ^ [_1257258, _1257260, _1257262]))], (25306 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25304 ^ [_1257258, _1257260, _1257262])))]], 25313 ^ _777959 : [(25314 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257262), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25320 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 25316 ^ [_1257258, _1257260, _1257262]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (25324 ^ _777959) ^ [] : [hBOOL(hAPP(_1257258, 25315 ^ [_1257258, _1257260, _1257262]))], (25322 ^ _777959) ^ [] : [-(_1257260 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1257262), 25315 ^ [_1257258, _1257260, _1257262])), 25316 ^ [_1257258, _1257260, _1257262]))], (25318 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1257262), 25316 ^ [_1257258, _1257260, _1257262])))]]], (40105 ^ _777959) ^ [_1555291, _1555293, _1555295, _1555297, _1555299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1555291), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555293)), _1555295))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1555291), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1555297)), _1555299))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1555293, _1555297)), hAPP(hAPP(c_List_Ozip(_1555293, _1555297), _1555295), _1555299)), _1555291) = hAPP(hAPP(c_Product__Type_OPair(_1555293, _1555297), hAPP(hAPP(c_List_Onth(_1555293), _1555295), _1555291)), hAPP(hAPP(c_List_Onth(_1555297), _1555299), _1555291)))], (37239 ^ _777959) ^ [_1487944] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1487944)) = _1487944)], (4472 ^ _777959) ^ [_845626, _845628, _845630, _845632] : [-(c_Product__Type_Osnd(_845632, _845628) = c_Product__Type_Osnd(_845630, _845626)), _845632 = _845630, _845628 = _845626], (13058 ^ _777959) ^ [_1015694, _1015696] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1015694, tc_HOL_Obool)), _1015696), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1015694, tc_HOL_Obool)), _1015696)) = c_Orderings_Obot__class_Obot(tc_fun(_1015694, tc_HOL_Obool)))], (50244 ^ _777959) ^ [_1796361, _1796363, _1796365, _1796367, _1796369] : [-(hAPP(c_New__DSequence_Opos__bind(_1796361, _1796363, _1796365, _1796367), _1796369) = hAPP(c_Lazy__Sequence_Obind(_1796361, _1796363, hAPP(_1796365, _1796369)), hAPP(hAPP(c_COMBC(_1796361, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1796363)), _1796367), _1796369)))], (48801 ^ _777959) ^ [_1762331, _1762333, _1762335, _1762337] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1762331, _1762331)), hAPP(hAPP(c_Product__Type_OPair(_1762331, _1762331), _1762333), _1762335)), c_Transitive__Closure_Ortrancl(_1762331, _1762337))), hBOOL(hAPP(hAPP(c_member(_1762331), _1762335), c_Wellfounded_Oacc(_1762331, _1762337))), -(hBOOL(hAPP(hAPP(c_member(_1762331), _1762333), c_Wellfounded_Oacc(_1762331, _1762337))))], (23066 ^ _777959) ^ [_1217768, _1217770, _1217772, _1217774] : [class_Rings_Osemiring__1(_1217768), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1217770, _1217768), hAPP(c_COMBK(_1217768, _1217770), _1217772)), _1217774) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1217768), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1217768), hAPP(c_Finite__Set_Ocard(_1217770), _1217774))), _1217772))], (30565 ^ _777959) ^ [_1355935, _1355937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1355935)), -(c_SMT_Oz3mod(_1355937, _1355935) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1355937, _1355935))], (30932 ^ _777959) ^ [_1362218, _1362220, _1362222, _1362224, _1362226] : [class_Groups_Ocomm__monoid__add(_1362218), class_Groups_Ocomm__monoid__mult(_1362218), _1362220 = _1362222, c_Nat__Transfer_Onat__set(_1362222), 30950 ^ _777959 : [(30953 ^ _777959) ^ [] : [hAPP(_1362224, 30949 ^ [_1362218, _1362220, _1362222, _1362224, _1362226]) = hAPP(_1362226, 30949 ^ [_1362218, _1362220, _1362222, _1362224, _1362226])], (30951 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30949 ^ [_1362218, _1362220, _1362222, _1362224, _1362226])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1362218), _1362224), _1362220) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1362218), _1362226), _1362222))], (51066 ^ _777959) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (3260 ^ _777959) ^ [_827004, _827006, _827008, _827010, _827012, _827014, _827016, _827018, _827020, _827022] : [-(c_Map_Omap__upds(_827022, _827018, _827014, _827010, _827006) = c_Map_Omap__upds(_827020, _827016, _827012, _827008, _827004)), _827022 = _827020, _827018 = _827016, _827014 = _827012, _827010 = _827008, _827006 = _827004], (24409 ^ _777959) ^ [_1241630, _1241632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241630)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241632))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1241630), _1241632)))], (28360 ^ _777959) ^ [_1312494, _1312496, _1312498, _1312500] : [class_Groups_Oab__group__add(_1312494), 28363 ^ _777959 : [(28370 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1312496), _1312498))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1312494), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1312494, _1312494), hAPP(hAPP(c_COMBB(_1312494, tc_fun(_1312494, _1312494), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1312494)), _1312500)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1312494, tc_Nat_Onat), _1312500), 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, _1312496, _1312498)) = c_Groups_Ozero__class_Ozero(_1312494))], (28364 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1312496), _1312498)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1312494), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1312494, _1312494), hAPP(hAPP(c_COMBB(_1312494, tc_fun(_1312494, _1312494), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1312494)), _1312500)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1312494, tc_Nat_Onat), _1312500), 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, _1312496, _1312498)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1312494), hAPP(_1312500, _1312496)), hAPP(_1312500, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1312498), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (21590 ^ _777959) ^ [_1188227, _1188229] : [hAPP(c_Finite__Set_Ocard(_1188227), _1188229) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1188229 = c_Orderings_Obot__class_Obot(tc_fun(_1188227, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1188227), _1188229))], (5274 ^ _777959) ^ [_858717, _858719] : [_858719 = _858717, -(c_List_Onth(_858719) = c_List_Onth(_858717))], (31546 ^ _777959) ^ [_1373617, _1373619] : [-(c_Nitpick_Onat__lcm(_1373617, _1373619) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1373617), _1373619)), c_Nitpick_Onat__gcd(_1373617, _1373619)))], (39095 ^ _777959) ^ [_1530911, _1530913, _1530915, _1530917] : [-(hAPP(c_Map_Omap__of(_1530911, _1530913), hAPP(hAPP(c_List_Omap(_1530911, tc_prod(_1530911, _1530913)), hAPP(hAPP(c_COMBS(_1530911, _1530913, tc_prod(_1530911, _1530913)), c_Product__Type_OPair(_1530911, _1530913)), _1530915)), _1530917)) = c_Map_Orestrict__map(_1530911, _1530913, hAPP(c_Fun_Ocomp(_1530913, tc_Option_Ooption(_1530913), _1530911, c_Option_Ooption_OSome(_1530913)), _1530915), hAPP(c_List_Oset(_1530911), _1530917)))], (13477 ^ _777959) ^ [_1025179, _1025181, _1025183, _1025185, _1025187] : [-(c_Map_Omap__add(_1025179, _1025181, _1025183, c_Map_Omap__add(_1025179, _1025181, _1025185, _1025187)) = c_Map_Omap__add(_1025179, _1025181, c_Map_Omap__add(_1025179, _1025181, _1025183, _1025185), _1025187))], (34339 ^ _777959) ^ [_1424362, _1424364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1424362), _1424364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1424362)), c_Int_OBit0(_1424364))))], (50164 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (12337 ^ _777959) ^ [_1001949, _1001951, _1001953] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001949), _1001951)), _1001953) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001949), _1001953)), _1001951))], (24474 ^ _777959) ^ [_1242793, _1242795, _1242797, _1242799, _1242801] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1242793, _1242795, _1242797), _1242799), hAPP(c_Nat_OSuc, _1242801)) = hAPP(hAPP(_1242797, _1242799), hAPP(hAPP(c_Power_Opower_Opower(_1242793, _1242795, _1242797), _1242799), _1242801)))], (24540 ^ _777959) ^ [_1243956, _1243958] : [class_Divides_Osemiring__div(_1243956), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1243956), c_Groups_Ozero__class_Ozero(_1243956)), _1243958) = c_Groups_Ozero__class_Ozero(_1243956))], (47393 ^ _777959) ^ [_1730196, _1730198, _1730200, _1730202] : [hBOOL(hAPP(hAPP(c_member(_1730196), _1730202), hAPP(c_Relation_ODomain(_1730196, _1730198), _1730200))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1730196, _1730198, hAPP(hAPP(c_COMBC(_1730196, tc_fun(tc_prod(_1730196, _1730198), tc_HOL_Obool), tc_fun(_1730198, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1730198, tc_fun(tc_fun(tc_prod(_1730196, _1730198), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1730196, _1730198), tc_HOL_Obool), tc_fun(_1730198, tc_HOL_Obool)), _1730196), c_COMBC(_1730198, tc_fun(tc_prod(_1730196, _1730198), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1730198, tc_prod(_1730196, _1730198)), tc_fun(_1730198, tc_fun(tc_fun(tc_prod(_1730196, _1730198), tc_HOL_Obool), tc_HOL_Obool)), _1730196), hAPP(c_COMBB(tc_prod(_1730196, _1730198), tc_fun(tc_fun(tc_prod(_1730196, _1730198), tc_HOL_Obool), tc_HOL_Obool), _1730198), c_member(tc_prod(_1730196, _1730198)))), c_Product__Type_OPair(_1730196, _1730198)))), _1730200)), _1730202)))], (6969 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody))))], (43825 ^ _777959) ^ [_1649459, _1649461, _1649463] : [-(_1649459 = c_List_Olist_ONil(_1649461)), -(c_List_Olast(_1649461, hAPP(hAPP(c_List_Oappend(_1649461), _1649463), _1649459)) = c_List_Olast(_1649461, _1649459))], (12205 ^ _777959) ^ [_999549, _999551, _999553, _999555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999549), _999551)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999553), _999551) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999549), _999555), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999553), _999555)))], (23473 ^ _777959) ^ [_1224807, _1224809] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224807), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1224809)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1224807), _1224809))], (44406 ^ _777959) ^ [_1660621, _1660623, _1660625] : [class_Orderings_Olinorder(_1660621), c_List_Olinorder__class_Osorted(_1660621, _1660623), -(c_List_Olinorder__class_Osorted(_1660621, hAPP(hAPP(c_List_Odrop(_1660621), _1660625), _1660623)))], (124 ^ _777959) ^ [_780023, _780025, _780027, _780029, _780031, _780033, _780035, _780037, _780039, _780041, _780043, _780045] : [-(c_Finite__Set_Ofolding__image__simple(_780043, _780039, _780035, _780031, _780027, _780023)), c_Finite__Set_Ofolding__image__simple(_780045, _780041, _780037, _780033, _780029, _780025), _780045 = _780043, _780041 = _780039, _780037 = _780035, _780033 = _780031, _780029 = _780027, _780025 = _780023], (12920 ^ _777959) ^ [_1012669, _1012671, _1012673] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1012669, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_1012669, tc_HOL_Obool), tc_HOL_Obool)), _1012671), _1012673)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012669, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1012669, tc_HOL_Obool), _1012671)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1012669, tc_HOL_Obool), _1012673)))], (6901 ^ _777959) ^ [_890800, _890802, _890804] : [_890802 = _890804, -(hBOOL(hAPP(hAPP(c_member(_890800), _890802), hAPP(hAPP(c_Set_Oinsert(_890800), _890804), c_Orderings_Obot__class_Obot(tc_fun(_890800, tc_HOL_Obool))))))], (40887 ^ _777959) ^ [_1573616, _1573618, _1573620, _1573622] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1573616), tc_List_Olist(_1573616))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1573616), tc_List_Olist(_1573616)), _1573618), _1573620)), c_List_Olistrel(_1573616, _1573622))), 40890 ^ _777959 : [(40893 ^ _777959) ^ [_1573845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1573845), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573616)), _1573618))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573616, _1573616)), hAPP(hAPP(c_Product__Type_OPair(_1573616, _1573616), hAPP(hAPP(c_List_Onth(_1573616), _1573618), _1573845)), hAPP(hAPP(c_List_Onth(_1573616), _1573620), _1573845))), _1573622)))], (40891 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573616)), _1573618) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1573616)), _1573620))]]], (46780 ^ _777959) ^ [_1713992, _1713994, _1713996, _1713998] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1713992, _1713994, _1713996), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1713992, _1713994), tc_HOL_Obool))), _1713998) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1713992, _1713996), tc_HOL_Obool)))], (10084 ^ _777959) ^ [_953682, _953684, _953686, _953688, _953690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953682, tc_HOL_Obool)), _953684), _953686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953682, tc_HOL_Obool)), _953688), _953690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_953682, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953682, tc_HOL_Obool)), _953684), _953688)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953682, tc_HOL_Obool)), _953686), _953690))))], (39093 ^ _777959) ^ [_1530847, _1530849, _1530851, _1530853, _1530855] : [-(hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1530847), tc_Option_Ooption(_1530849), _1530851, hAPP(c_Option_Omap(_1530847, _1530849), _1530853)), hAPP(c_COMBK(tc_Option_Ooption(_1530847), _1530851), c_Option_Ooption_ONone(_1530847))), _1530855) = c_Option_Ooption_ONone(_1530849))], (33859 ^ _777959) ^ [_1415620, _1415622] : [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(_1415622))), 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), _1415620)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415620)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415622))))], (35217 ^ _777959) ^ [_1440082] : [class_Int_Onumber__ring(_1440082), -(hAPP(c_Int_Oring__1__class_Oof__int(_1440082), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1440082), c_Int_OMin))], (47406 ^ _777959) ^ [_1730718, _1730720, _1730722, _1730724, _1730726] : [hBOOL(hAPP(hAPP(_1730718, _1730720), _1730722)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1730724, _1730726, _1730718), _1730720)))], (42347 ^ _777959) ^ [_1613484, _1613486, _1613488, _1613490, _1613492, _1613494] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1613484, _1613486), hAPP(hAPP(c_Set_Oinsert(_1613484), _1613488), _1613490)), hAPP(c_COMBK(tc_fun(_1613486, tc_HOL_Obool), _1613484), hAPP(hAPP(c_Set_Oinsert(_1613486), _1613492), _1613494))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1613484, _1613486)), hAPP(hAPP(c_Product__Type_OPair(_1613484, _1613486), _1613488), _1613492)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1613484, _1613486), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1613484, _1613486), _1613490), hAPP(c_COMBK(tc_fun(_1613486, tc_HOL_Obool), _1613484), hAPP(hAPP(c_Set_Oinsert(_1613486), _1613492), _1613494)))), hAPP(hAPP(c_Product__Type_OSigma(_1613484, _1613486), hAPP(hAPP(c_Set_Oinsert(_1613484), _1613488), _1613490)), hAPP(c_COMBK(tc_fun(_1613486, tc_HOL_Obool), _1613484), _1613494)))))], (3472 ^ _777959) ^ [_830350, _830352] : [_830352 = _830350, -(c_Option_Ooption_ONone(_830352) = c_Option_Ooption_ONone(_830350))], (3490 ^ _777959) ^ [_830605, _830607] : [_830607 = _830605, -(c_Option_Othe(_830607) = c_Option_Othe(_830605))], (35183 ^ _777959) ^ [_1439606, _1439608] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1439606), _1439608) = c_Groups_Oone__class_Oone(tc_Int_Oint), 35188 ^ _777959 : [(35191 ^ _777959) ^ [] : [-(_1439608 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (35189 ^ _777959) ^ [] : [-(_1439606 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 35192 ^ _777959 : [(35195 ^ _777959) ^ [] : [-(_1439608 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (35193 ^ _777959) ^ [] : [-(_1439606 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (40736 ^ _777959) ^ [_1569556, _1569558] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1569556), _1569558))), -(c_Nitpick_Ocard_H(_1569556, _1569558) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13403 ^ _777959) ^ [_1023712, _1023714, _1023716, _1023718] : [_1023712 = c_Orderings_Obot__class_Obot(tc_fun(_1023714, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023714, tc_fun(_1023716, tc_HOL_Obool)), _1023712), hAPP(c_COMBK(tc_fun(_1023716, tc_HOL_Obool), _1023714), _1023718)) = c_Orderings_Otop__class_Otop(tc_fun(_1023716, tc_HOL_Obool)))], (42158 ^ _777959) ^ [_1608708, _1608710] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1608708, _1608708), tc_HOL_Obool)), c_Relation_OId__on(_1608708, _1608710)), hAPP(hAPP(c_Product__Type_OSigma(_1608708, _1608708), _1608710), hAPP(c_COMBK(tc_fun(_1608708, tc_HOL_Obool), _1608708), _1608710)))))], (39019 ^ _777959) ^ [_1529242, _1529244, _1529246, _1529248, _1529250, _1529252, _1529254] : [-(hAPP(c_Fun_Ocomp(_1529242, _1529244, _1529246, _1529248), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1529246, _1529242), _1529250), _1529252), _1529254)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1529246, _1529244), hAPP(c_Fun_Ocomp(_1529242, _1529244, _1529246, _1529248), _1529250)), _1529252), hAPP(_1529248, _1529254)))], (49566 ^ _777959) ^ [_1782320, _1782322, _1782324] : [49567 ^ _777959 : [(49568 ^ _777959) ^ [_1782397, _1782399] : [_1782324 = hAPP(hAPP(c_List_Oappend(_1782320), _1782399), hAPP(hAPP(c_List_Olist_OCons(_1782320), _1782322), _1782397))]], -(hBOOL(hAPP(hAPP(c_member(_1782320), _1782322), hAPP(c_List_Oset(_1782320), _1782324))))], (23076 ^ _777959) ^ [_1217973, _1217975] : [_1217973 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1217975), _1217973) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (41587 ^ _777959) ^ [_1593375, _1593377, _1593379, _1593381, _1593383] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1593375), tc_List_Olist(_1593375))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1593375), tc_List_Olist(_1593375)), _1593377), _1593379)), c_List_Olistrel1(_1593375, _1593381))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1593375), tc_List_Olist(_1593375))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1593375), tc_List_Olist(_1593375)), hAPP(hAPP(c_List_Olist_OCons(_1593375), _1593383), _1593377)), hAPP(hAPP(c_List_Olist_OCons(_1593375), _1593383), _1593379))), c_List_Olistrel1(_1593375, _1593381))))], (27269 ^ _777959) ^ [_1294179] : [-(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)), _1294179)) = _1294179)], (12934 ^ _777959) ^ [_1013084, _1013086, _1013088] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013084, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1013084, tc_HOL_Obool), _1013086)), _1013088) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1013084, tc_HOL_Obool), tc_fun(_1013084, tc_HOL_Obool)), _1013086), hAPP(hAPP(c_COMBC(tc_fun(_1013084, tc_HOL_Obool), tc_fun(_1013084, tc_HOL_Obool), tc_fun(_1013084, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013084, tc_HOL_Obool))), _1013088)))], (8984 ^ _777959) ^ [_932472, _932474, _932476] : [class_Orderings_Oorder(_932472), -(_932474 = _932476), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932472), _932476), _932474)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932472), _932476), _932474)))], (49304 ^ _777959) ^ [_1775032, _1775034, _1775036] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775032, _1775032), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1775034)), _1775036) = hAPP(hAPP(c_Relation_Orel__comp(_1775032, _1775032, _1775032), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775032, _1775032), tc_HOL_Obool), _1775034), _1775036)), _1775036))], (15518 ^ _777959) ^ [_1072985] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1072985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072985), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1072985), _1072985)))))], (23415 ^ _777959) ^ [_1223941, _1223943] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223941), _1223943))), -(_1223941 = _1223943), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1223943), _1223941)))], (29761 ^ _777959) ^ [_1339688, _1339690, _1339692, _1339694] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1339688, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339690, tc_fun(tc_fun(_1339688, tc_HOL_Obool), tc_HOL_Obool)), _1339692), hAPP(hAPP(c_COMBB(tc_fun(_1339688, tc_HOL_Obool), tc_fun(tc_fun(_1339688, tc_HOL_Obool), tc_HOL_Obool), _1339690), c_Set_OPow(_1339688)), _1339694))), hAPP(c_Set_OPow(_1339688), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1339690, tc_fun(_1339688, tc_HOL_Obool)), _1339692), _1339694)))))], (264 ^ _777959) ^ [_782049, _782051, _782053, _782055] : [-(c_Nitpick_Orefl_H(_782053, _782049)), c_Nitpick_Orefl_H(_782055, _782051), _782055 = _782053, _782051 = _782049], (43406 ^ _777959) ^ [_1640680, _1640682, _1640684, _1640686] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1640680) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1640682), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1640680)), hAPP(hAPP(c_List_Olist_OCons(_1640682), _1640684), _1640686)) = hAPP(hAPP(c_List_Olist_OCons(_1640682), _1640684), _1640686))], (18630 ^ _777959) ^ [_1135897, _1135899, _1135901] : [class_Lattices_Osemilattice__inf(_1135897), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135897), _1135899)), hBOOL(hAPP(hAPP(c_member(_1135897), _1135901), _1135899)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135897), hAPP(c_Finite__Set_Ofold1(_1135897, c_Lattices_Osemilattice__inf__class_Oinf(_1135897)), _1135899)), _1135901)))], (7926 ^ _777959) ^ [_912967, _912969] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912967, tc_HOL_Obool)), _912969), _912969) = c_Orderings_Obot__class_Obot(tc_fun(_912967, tc_HOL_Obool)))], (28225 ^ _777959) ^ [_1310153, _1310155, _1310157] : [class_Groups_Ocomm__monoid__add(_1310153), class_Groups_Ocomm__monoid__mult(_1310153), c_Nat__Transfer_Onat__set(_1310155), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1310153), _1310157), _1310155) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1310153), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1310153, tc_Nat_Onat), _1310157), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1310155)))], (51134 ^ _777959) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (38328 ^ _777959) ^ [_1512473, _1512475, _1512477, _1512479, _1512481, _1512483] : [c_Fun_Oinj__on(_1512473, _1512475, _1512477, _1512479), -(hBOOL(hAPP(hAPP(c_member(_1512475), _1512481), hAPP(c_Set_Oimage(_1512473, _1512475, _1512477), _1512479)))), -(c_Fun_Oinj__on(_1512473, _1512475, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1512473, _1512475), _1512477), _1512483), _1512481), _1512479))], (16719 ^ _777959) ^ [_1098298, _1098300, _1098302] : [class_Orderings_Olinorder(_1098298), 16722 ^ _777959 : [(16729 ^ _777959) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1098298), _1098300), _1098302) = _1098302, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098298), _1098300), _1098302)))], (16723 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098298), _1098300), _1098302)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1098298), _1098300), _1098302) = _1098302)]]], (47216 ^ _777959) ^ [_1725140, _1725142, _1725144] : [hAPP(c_Relation_ORange(_1725140, _1725142), _1725144) = c_Orderings_Obot__class_Obot(tc_fun(_1725142, tc_HOL_Obool)), -(_1725144 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1725140, _1725142), tc_HOL_Obool)))], (45556 ^ _777959) ^ [_1686432, _1686434] : [-(c_List_Opartition(_1686432, _1686434, c_List_Olist_ONil(_1686432)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1686432), tc_List_Olist(_1686432)), c_List_Olist_ONil(_1686432)), c_List_Olist_ONil(_1686432)))], (50328 ^ _777959) ^ [_1798626, _1798628, _1798630, _1798632, _1798634, _1798636] : [-(c_New__Random__Sequence_Opos__union(_1798626, _1798628, _1798630, _1798632, _1798634, _1798636) = c_New__DSequence_Opos__union(_1798626, hAPP(hAPP(hAPP(_1798628, _1798632), _1798634), _1798636), hAPP(hAPP(hAPP(_1798630, _1798632), _1798634), _1798636)))], (47208 ^ _777959) ^ [_1724900, _1724902, _1724904] : [-(hAPP(c_Relation_ORange(_1724900, _1724902), hAPP(c_Set_OCollect(tc_prod(_1724900, _1724902)), hAPP(c_Product__Type_Oprod_Oprod__case(_1724900, _1724902, tc_HOL_Obool), _1724904))) = hAPP(c_Set_OCollect(_1724902), hAPP(hAPP(c_COMBB(tc_fun(_1724900, tc_HOL_Obool), tc_HOL_Obool, _1724902), c_HOL_OEx(_1724900)), hAPP(c_COMBC(_1724900, _1724902, tc_HOL_Obool), _1724904))))], (48055 ^ _777959) ^ [_1745525, _1745527, _1745529, _1745531] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1745525, _1745527, _1745529, tc_prod(_1745527, _1745529)), _1745531), c_Product__Type_OPair(_1745527, _1745529)) = _1745531)], (14750 ^ _777959) ^ [_1055234, _1055236, _1055238, _1055240, _1055242, _1055244] : [hBOOL(hAPP(hAPP(c_member(_1055234), _1055236), c_SetInterval_Oord_OatLeastLessThan(_1055234, _1055238, _1055240, _1055242, _1055244))), 14753 ^ _777959 : [(14756 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1055240, _1055236), _1055244)))], (14754 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1055238, _1055242), _1055236)))]]], (27443 ^ _777959) ^ [_1296976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1296976)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1296976)) = _1296976)], (24209 ^ _777959) ^ [_1238172, _1238174] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1238172)), _1238174) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1238172), _1238174)))], (42849 ^ _777959) ^ [_1627100, _1627102, _1627104, _1627106, _1627108, _1627110] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627100)), _1627102) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627104)), _1627106), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627100)), _1627108) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627104)), _1627110), -(hAPP(hAPP(c_List_Ozip(_1627100, _1627104), hAPP(hAPP(c_List_Oappend(_1627100), _1627102), _1627108)), hAPP(hAPP(c_List_Oappend(_1627104), _1627106), _1627110)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1627100, _1627104)), hAPP(hAPP(c_List_Ozip(_1627100, _1627104), _1627102), _1627106)), hAPP(hAPP(c_List_Ozip(_1627100, _1627104), _1627108), _1627110)))], (46427 ^ _777959) ^ [_1705388, _1705390, _1705392, _1705394, _1705396] : [c_List_Olist__all2(_1705388, _1705390, _1705392, hAPP(c_List_Orev(_1705388), _1705394), _1705396), -(c_List_Olist__all2(_1705388, _1705390, _1705392, _1705394, hAPP(c_List_Orev(_1705390), _1705396)))], (50408 ^ _777959) ^ [_1800352, _1800354, _1800356, _1800358, _1800360] : [-(c_List_Osplice(_1800352, hAPP(hAPP(c_List_Olist_OCons(_1800352), _1800354), _1800356), hAPP(hAPP(c_List_Olist_OCons(_1800352), _1800358), _1800360)) = hAPP(hAPP(c_List_Olist_OCons(_1800352), _1800354), hAPP(hAPP(c_List_Olist_OCons(_1800352), _1800358), c_List_Osplice(_1800352, _1800356, _1800360))))], (51348 ^ _777959) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (42074 ^ _777959) ^ [_1607049, _1607051] : [_1607051 = c_List_Olist_ONil(_1607049), -(hAPP(c_List_Oset(_1607049), _1607051) = c_Orderings_Obot__class_Obot(tc_fun(_1607049, tc_HOL_Obool)))], (1700 ^ _777959) ^ [_801933, _801935] : [-(class_Groups_Omonoid__add(_801933)), _801935 = _801933, class_Groups_Omonoid__add(_801935)], (42973 ^ _777959) ^ [_1629554, _1629556, _1629558] : [_1629556 = c_List_Olist_ONil(_1629554), -(hAPP(hAPP(c_List_Oappend(_1629554), _1629556), _1629558) = _1629558)], (4892 ^ _777959) ^ [_852562, _852564, _852566, _852568] : [-(c_New__DSequence_Oneg__single(_852568, _852564) = c_New__DSequence_Oneg__single(_852566, _852562)), _852568 = _852566, _852564 = _852562], (16521 ^ _777959) ^ [_1094487, _1094489, _1094491, _1094493] : [class_Orderings_Olinorder(_1094487), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094487), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094487), _1094489), _1094491)), _1094493) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094487), _1094489), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094487), _1094491), _1094493)))], (48390 ^ _777959) ^ [_1751597, _1751599] : [c_Wellfounded_Owf(_1751597, _1751599), -(c_Wellfounded_Owf(_1751597, c_Transitive__Closure_Otrancl(_1751597, _1751599)))], (15096 ^ _777959) ^ [_1065119, _1065121, _1065123] : [class_Rings_Ocomm__semiring__1(_1065119), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065119), _1065121), _1065123) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065119), _1065123), _1065121))], (34863 ^ _777959) ^ [_1434095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1434095)), -(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), _1434095), 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)))))))], (32983 ^ _777959) ^ [_1400889] : [-(c_Int_OBit1(_1400889) = 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)), _1400889)), _1400889))], (40936 ^ _777959) ^ [_1575178, _1575180, _1575182, _1575184] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1575178), tc_List_Olist(_1575178))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1575178), tc_List_Olist(_1575178)), _1575180), _1575182)), c_List_Olistrel(_1575178, _1575184))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1575178)), _1575180) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1575178)), _1575182))], (6983 ^ _777959) ^ [_893503, _893505, _893507] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_893503), _893505)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_893503), hAPP(hAPP(c_Set_Oinsert(_893503), _893507), _893505))))], (23353 ^ _777959) ^ [_1222833, _1222835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222833), _1222835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1222833), _1222835)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (6281 ^ _777959) ^ [_879251, _879253, _879255] : [class_Orderings_Opreorder(_879251), _879253 = _879255, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879251), _879253), _879255)))], (45382 ^ _777959) ^ [_1682493, _1682495, _1682497] : [hBOOL(hAPP(c_List_Odistinct(_1682493), _1682495)), hBOOL(hAPP(hAPP(c_member(_1682493), _1682497), hAPP(c_List_Oset(_1682493), _1682495))), -(c_List_OdropWhile(_1682493, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1682493), c_fNot), hAPP(hAPP(c_COMBC(_1682493, _1682493, tc_HOL_Obool), c_fequal), _1682497)), hAPP(c_List_Orev(_1682493), _1682495)) = hAPP(hAPP(c_List_Olist_OCons(_1682493), _1682497), hAPP(c_List_Orev(_1682493), c_List_OtakeWhile(_1682493, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1682493), c_fNot), hAPP(hAPP(c_COMBC(_1682493, _1682493, tc_HOL_Obool), c_fequal), _1682497)), _1682495))))], (6803 ^ _777959) ^ [_888715, _888717, _888719, _888721, _888723] : [hBOOL(hAPP(hAPP(c_member(_888715), _888717), hAPP(c_Set_Oimage(_888719, _888715, _888721), _888723))), 6807 ^ _777959 : [(6810 ^ _777959) ^ [] : [-(_888717 = hAPP(_888721, 6806 ^ [_888715, _888717, _888719, _888721, _888723]))], (6808 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_888719), 6806 ^ [_888715, _888717, _888719, _888721, _888723]), _888723)))]]], (12163 ^ _777959) ^ [_998715, _998717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _998715), _998717)), _998717))], (43795 ^ _777959) ^ [_1649085, _1649087, _1649089] : [-(_1649085 = c_List_Olist_ONil(_1649087)), -(c_List_Olast(_1649087, hAPP(hAPP(c_List_Olist_OCons(_1649087), _1649089), _1649085)) = c_List_Olast(_1649087, _1649085))], (4984 ^ _777959) ^ [_854034, _854036] : [_854036 = _854034, -(c_Groups_Ouminus__class_Ouminus(_854036) = c_Groups_Ouminus__class_Ouminus(_854034))], (50960 ^ _777959) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (12684 ^ _777959) ^ [_1008135, _1008137] : [class_Lattices_Oboolean__algebra(_1008135), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1008135), hAPP(c_Groups_Ouminus__class_Ouminus(_1008135), _1008137)) = _1008137)], (25916 ^ _777959) ^ [_1269213, _1269215] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1269213)), _1269215) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1269213, _1269215))], (36672 ^ _777959) ^ [_1473633, _1473635, _1473637, _1473639, _1473641] : [hAPP(c_Product__Type_Ofst(_1473633, _1473635), hAPP(hAPP(c_Product__Type_OPair(_1473633, _1473635), _1473637), _1473639)) = _1473641, -(_1473637 = _1473641)], (37245 ^ _777959) ^ [_1488055] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1488055) = 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), _1488055), 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))))))], (35888 ^ _777959) ^ [_1458977, _1458979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1458977), 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)), _1458979)), -(c_Divides_OnegDivAlg(_1458977, _1458979) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1458977), _1458979)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1458977, _1458979)))], (35111 ^ _777959) ^ [_1438519] : [class_Int_Onumber__ring(_1438519), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1438519), c_Groups_Oone__class_Oone(_1438519)) = hAPP(c_Int_Onumber__class_Onumber__of(_1438519), c_Int_OMin))], (8042 ^ _777959) ^ [_915325, _915327] : [c_Com_Ocom_OSemi(_915325, _915327) = c_Com_Ocom_OSKIP], (36862 ^ _777959) ^ [_1477488, _1477490] : [c_Code__Numeral_OSuc__code__numeral(_1477488) = c_Code__Numeral_OSuc__code__numeral(_1477490), -(_1477488 = _1477490)], (13771 ^ _777959) ^ [_1032669, _1032671] : [class_Lattices_Obounded__lattice__top(_1032669), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1032669), _1032671), c_Orderings_Otop__class_Otop(_1032669)) = c_Orderings_Otop__class_Otop(_1032669))], (24383 ^ _777959) ^ [_1241185] : [-(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), _1241185))))], (17119 ^ _777959) ^ [_1105316, _1105318, _1105320] : [class_Complete__Lattice_Ocomplete__lattice(_1105316), 17122 ^ _777959 : [(17123 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105316), _1105318), c_Complete__Lattice_OInf__class_OInf(_1105316, _1105320))), 17126 ^ _777959 : [(17127 ^ _777959) ^ [_1105474] : [hBOOL(hAPP(hAPP(c_member(_1105316), _1105474), _1105320)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105316), _1105318), _1105474)))]]], (17133 ^ _777959) ^ [] : [17135 ^ _777959 : [(17138 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105316), _1105318), 17134 ^ [_1105316, _1105318, _1105320]))], (17136 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1105316), 17134 ^ [_1105316, _1105318, _1105320]), _1105320)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1105316), _1105318), c_Complete__Lattice_OInf__class_OInf(_1105316, _1105320))))]]], (14139 ^ _777959) ^ [_1040998, _1041000, _1041002] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1040998), _1041000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1040998, tc_HOL_Obool)), _1041002), _1041000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1040998), _1041000)), hAPP(c_Finite__Set_Ocard(_1040998), _1041002))), -(_1041002 = _1041000)], (33303 ^ _777959) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (7390 ^ _777959) ^ [_901951] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_901951), c_Orderings_Obot__class_Obot(tc_fun(_901951, tc_HOL_Obool)))))], (35075 ^ _777959) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36962 ^ _777959) ^ [_1480244, _1480246, _1480248, _1480250, _1480252, _1480254] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1480244, tc_HOL_Obool), tc_fun(_1480244, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1480244, tc_HOL_Obool), tc_fun(_1480244, tc_HOL_Obool)), _1480246), _1480248)), c_Wellfounded_Omax__ext(_1480244, _1480250))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1480244, tc_HOL_Obool), tc_fun(_1480244, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1480244, tc_HOL_Obool), tc_fun(_1480244, tc_HOL_Obool)), _1480252), _1480254)), c_Wellfounded_Omax__ext(_1480244, _1480250))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1480244, tc_HOL_Obool), tc_fun(_1480244, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1480244, tc_HOL_Obool), tc_fun(_1480244, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480244, tc_HOL_Obool)), _1480246), _1480252)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1480244, tc_HOL_Obool)), _1480248), _1480254))), c_Wellfounded_Omax__ext(_1480244, _1480250))))], (18378 ^ _777959) ^ [_1130656, _1130658] : [class_Orderings_Olinorder(_1130656), hBOOL(hAPP(c_Finite__Set_Ofinite(_1130656), _1130658)), -(_1130658 = c_Orderings_Obot__class_Obot(tc_fun(_1130656, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1130656), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1130656), 18391 ^ [_1130656, _1130658]), 18392 ^ [_1130656, _1130658])), hAPP(hAPP(c_Set_Oinsert(_1130656), 18391 ^ [_1130656, _1130658]), hAPP(hAPP(c_Set_Oinsert(_1130656), 18392 ^ [_1130656, _1130658]), c_Orderings_Obot__class_Obot(tc_fun(_1130656, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1130656), c_Big__Operators_Olinorder__class_OMax(_1130656, _1130658)), _1130658)))], (8722 ^ _777959) ^ [_928501, _928503, _928505, _928507, _928509, _928511] : [_928501 = _928503, -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928505, _928507), _928509), _928503), _928511), _928501) = _928511)], (6255 ^ _777959) ^ [_878830, _878832, _878834, _878836, _878838, _878840] : [-(c_Com_Ocom_OCall(_878830, _878832, _878834) = c_Com_Ocom_OCall(_878836, _878838, _878840)), _878830 = _878836, _878832 = _878838, _878834 = _878840], (15312 ^ _777959) ^ [_1069427, _1069429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069427), hAPP(c_Nat_OSuc, _1069429))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069427), _1069429))), -(_1069427 = _1069429)], (43929 ^ _777959) ^ [_1651404, _1651406, _1651408, _1651410] : [hBOOL(hAPP(_1651404, _1651406)), -(hAPP(c_List_Ofilter(_1651408, _1651404), hAPP(hAPP(c_List_Olist_OCons(_1651408), _1651406), _1651410)) = hAPP(hAPP(c_List_Olist_OCons(_1651408), _1651406), hAPP(c_List_Ofilter(_1651408, _1651404), _1651410)))], (30792 ^ _777959) ^ [_1359734, _1359736, _1359738, _1359740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1359734)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1359736), _1359738)), -(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), _1359738), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1359740, _1359734))), _1359736)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1359738), _1359734))))], (50910 ^ _777959) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (37146 ^ _777959) ^ [_1484970] : [-(c_Wellfounded_Omeasure(_1484970) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1484970), c_Wellfounded_Oless__than))], (24241 ^ _777959) ^ [_1238757, _1238759] : [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)), _1238757)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238759))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1238757), _1238759)))], (31224 ^ _777959) ^ [_1367822, _1367824, _1367826] : [class_Groups_Oordered__ab__group__add__abs(_1367822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367822), _1367824), _1367826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367822), hAPP(c_Groups_Ouminus__class_Ouminus(_1367822), _1367824)), _1367826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367822), hAPP(c_Groups_Oabs__class_Oabs(_1367822), _1367824)), _1367826)))], (33397 ^ _777959) ^ [_1407655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1407655), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407655))], (46156 ^ _777959) ^ [_1699256, _1699258, _1699260, _1699262] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699256)), _1699258), c_List_Olists(_1699256, _1699260))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699256)), _1699258), c_List_Olists(_1699256, _1699262))), -(hBOOL(hAPP(c_List_Olistsp(_1699256, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1699256, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1699256, tc_fun(_1699256, tc_HOL_Obool), tc_HOL_Obool), c_member(_1699256)), _1699260)), hAPP(hAPP(c_COMBC(_1699256, tc_fun(_1699256, tc_HOL_Obool), tc_HOL_Obool), c_member(_1699256)), _1699262))), _1699258)))], (40276 ^ _777959) ^ [_1559427, _1559429, _1559431, _1559433] : [hBOOL(hAPP(hAPP(c_member(_1559427), _1559429), hAPP(c_List_Oset(_1559427), c_List_Osublist(_1559427, _1559431, _1559433)))), -(hBOOL(hAPP(hAPP(c_member(_1559427), _1559429), hAPP(c_List_Oset(_1559427), _1559431))))], (4620 ^ _777959) ^ [_848016, _848018, _848020, _848022, _848024, _848026, _848028, _848030] : [-(c_New__DSequence_Opos__bind(_848030, _848026, _848022, _848018) = c_New__DSequence_Opos__bind(_848028, _848024, _848020, _848016)), _848030 = _848028, _848026 = _848024, _848022 = _848020, _848018 = _848016], (44047 ^ _777959) ^ [_1653814, _1653816, _1653818, _1653820] : [-(c_List_Omap__filter(_1653814, _1653816, _1653818, _1653820) = hAPP(hAPP(c_List_Omap(_1653814, _1653816), hAPP(c_Fun_Ocomp(tc_Option_Ooption(_1653816), _1653816, _1653814, c_Option_Othe(_1653816)), _1653818)), hAPP(c_List_Ofilter(_1653814, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1653814), c_fNot), hAPP(hAPP(c_COMBC(_1653814, tc_Option_Ooption(_1653816), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Option_Ooption(_1653816), tc_fun(tc_Option_Ooption(_1653816), tc_HOL_Obool), _1653814), c_fequal), _1653818)), c_Option_Ooption_ONone(_1653816)))), _1653820)))], (46415 ^ _777959) ^ [_1705136, _1705138, _1705140, _1705142, _1705144] : [c_List_Olist__all2(_1705136, _1705138, _1705140, hAPP(c_List_Orev(_1705136), _1705142), hAPP(c_List_Orev(_1705138), _1705144)), -(c_List_Olist__all2(_1705136, _1705138, _1705140, _1705142, _1705144))], (38506 ^ _777959) ^ [_1516666] : [class_Nat_Osemiring__char__0(_1516666), -(c_Fun_Oinj__on(tc_Nat_Onat, _1516666, c_Nat_Osemiring__1__class_Oof__nat(_1516666), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (41888 ^ _777959) ^ [_1602710, _1602712, _1602714, _1602716, _1602718] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1602710, _1602712), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602710, tc_HOL_Obool)), _1602714), _1602716)), hAPP(c_COMBK(tc_fun(_1602712, tc_HOL_Obool), _1602710), _1602718)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1602710, _1602712), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1602710, _1602712), _1602714), hAPP(c_COMBK(tc_fun(_1602712, tc_HOL_Obool), _1602710), _1602718))), hAPP(hAPP(c_Product__Type_OSigma(_1602710, _1602712), _1602716), hAPP(c_COMBK(tc_fun(_1602712, tc_HOL_Obool), _1602710), _1602718))))], (2298 ^ _777959) ^ [_811941, _811943, _811945, _811947] : [-(c_Int_Onat__aux(_811947, _811943) = c_Int_Onat__aux(_811945, _811941)), _811947 = _811945, _811943 = _811941], (44178 ^ _777959) ^ [_1656921, _1656923, _1656925] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656921), _1656923)), -(c_List_Oupt(_1656921, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656923), _1656925)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1656921, _1656923)), c_List_Oupt(_1656923, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1656923), _1656925))))], (6659 ^ _777959) ^ [_885959, _885961] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_885959, tc_HOL_Obool)), _885961), c_Orderings_Obot__class_Obot(tc_fun(_885959, tc_HOL_Obool))) = _885961)], (33235 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (24247 ^ _777959) ^ [_1238883, _1238885] : [_1238883 = _1238885, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238883) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1238885))], (41960 ^ _777959) ^ [_1604436, _1604438, _1604440, _1604442, _1604444] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1604436, _1604438), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1604436, tc_HOL_Obool)), _1604440), _1604442)), hAPP(c_COMBK(tc_fun(_1604438, tc_HOL_Obool), _1604436), _1604444)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1604436, _1604438), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1604436, _1604438), _1604440), hAPP(c_COMBK(tc_fun(_1604438, tc_HOL_Obool), _1604436), _1604444))), hAPP(hAPP(c_Product__Type_OSigma(_1604436, _1604438), _1604442), hAPP(c_COMBK(tc_fun(_1604438, tc_HOL_Obool), _1604436), _1604444))))], (34285 ^ _777959) ^ [_1423455] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1423455)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1423455))))], (48745 ^ _777959) ^ [_1761072] : [-(hAPP(c_Relation_ORange(_1761072, _1761072), c_Relation_OId(_1761072)) = c_Orderings_Otop__class_Otop(tc_fun(_1761072, tc_HOL_Obool)))], (34103 ^ _777959) ^ [_1420293, _1420295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1420293)), c_Int_OBit0(_1420295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1420293), _1420295)))], (51118 ^ _777959) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (27714 ^ _777959) ^ [_1301548, _1301550, _1301552] : [class_Groups_Oordered__ab__group__add(_1301548), -(hAPP(c_Set_Oimage(_1301548, _1301548, c_Groups_Ouminus__class_Ouminus(_1301548)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1301548, _1301550, _1301552)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1301548, hAPP(c_Groups_Ouminus__class_Ouminus(_1301548), _1301552)), hAPP(c_Groups_Ouminus__class_Ouminus(_1301548), _1301550)))], (38116 ^ _777959) ^ [_1508071, _1508073, _1508075, _1508077, _1508079] : [c_Fun_Oinj__on(_1508071, _1508073, _1508075, _1508077), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1508071, tc_HOL_Obool)), _1508079), _1508077)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1508073, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1508071, _1508073, _1508075), _1508079)), hAPP(c_Set_Oimage(_1508071, _1508073, _1508075), _1508077))))], (29940 ^ _777959) ^ [_1343892, _1343894, _1343896] : [class_Divides_Osemiring__div(_1343892), -(c_Divides_Odiv__class_Omod(_1343892, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1343892), _1343894), _1343896), _1343896) = c_Divides_Odiv__class_Omod(_1343892, _1343894, _1343896))], (41856 ^ _777959) ^ [_1601782, _1601784] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1601782)), c_List_Olist_ONil(_1601782)), c_List_Olists(_1601782, _1601784))))], (33605 ^ _777959) ^ [] : [-(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)))))], (12812 ^ _777959) ^ [_1010403, _1010405, _1010407] : [class_Groups_Oordered__ab__group__add(_1010403), 12815 ^ _777959 : [(12822 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010403), _1010407), _1010405)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010403), hAPP(c_Groups_Ouminus__class_Ouminus(_1010403), _1010405)), hAPP(c_Groups_Ouminus__class_Ouminus(_1010403), _1010407))))], (12816 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010403), hAPP(c_Groups_Ouminus__class_Ouminus(_1010403), _1010405)), hAPP(c_Groups_Ouminus__class_Ouminus(_1010403), _1010407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1010403), _1010407), _1010405)))]]], (48290 ^ _777959) ^ [_1749895] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1749895)) = _1749895)], (38196 ^ _777959) ^ [_1509683, _1509685, _1509687] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1509683), _1509685)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509683, tc_HOL_Obool)), _1509685), hAPP(c_Set_Oimage(_1509683, _1509683, _1509687), _1509685))), -(c_Fun_Oinj__on(_1509683, _1509683, _1509687, _1509685))], (43191 ^ _777959) ^ [_1635518, _1635520] : [-(hAPP(c_List_Oset(_1635518), hAPP(c_List_Orotate1(_1635518), _1635520)) = hAPP(c_List_Oset(_1635518), _1635520))], (4912 ^ _777959) ^ [_852860, _852862, _852864, _852866, _852868, _852870, _852872, _852874, _852876, _852878, _852880, _852882] : [-(c_New__Random__Sequence_Opos__union(_852882, _852878, _852874, _852870, _852866, _852862) = c_New__Random__Sequence_Opos__union(_852880, _852876, _852872, _852868, _852864, _852860)), _852882 = _852880, _852878 = _852876, _852874 = _852872, _852870 = _852868, _852866 = _852864, _852862 = _852860], (43043 ^ _777959) ^ [_1631430, _1631432, _1631434] : [hBOOL(hAPP(c_List_Odistinct(_1631430), hAPP(hAPP(c_List_Oappend(_1631430), _1631432), _1631434))), 43046 ^ _777959 : [(43051 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1631430, tc_HOL_Obool)), hAPP(c_List_Oset(_1631430), _1631432)), hAPP(c_List_Oset(_1631430), _1631434)) = c_Orderings_Obot__class_Obot(tc_fun(_1631430, tc_HOL_Obool)))], (43049 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1631430), _1631434)))], (43047 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1631430), _1631432)))]]], (31650 ^ _777959) ^ [_1375636, _1375638] : [_1375636 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1375638, _1375636) = _1375638)], (1550 ^ _777959) ^ [_800058, _800060] : [-(class_Groups_Oab__semigroup__mult(_800058)), _800060 = _800058, class_Groups_Oab__semigroup__mult(_800060)], (48709 ^ _777959) ^ [_1760129, _1760131, _1760133] : [-(c_Transitive__Closure_Ortrancl(_1760129, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1760129, _1760129), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1760129, _1760131)), c_Transitive__Closure_Ortrancl(_1760129, _1760133))) = c_Transitive__Closure_Ortrancl(_1760129, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1760129, _1760129), tc_HOL_Obool)), _1760131), _1760133)))], (16509 ^ _777959) ^ [_1094201, _1094203, _1094205, _1094207] : [class_Orderings_Olinorder(_1094201), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094201), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094201), _1094203), _1094205)), _1094207) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094201), _1094203), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094201), _1094205), _1094207)))], (40369 ^ _777959) ^ [_1561400, _1561402, _1561404, _1561406, _1561408, _1561410] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1561400, _1561402), hAPP(hAPP(c_List_Ozip(_1561400, _1561402), _1561404), _1561406)), _1561408), _1561410) = hAPP(hAPP(c_List_Ozip(_1561400, _1561402), hAPP(hAPP(c_List_Olist__update(_1561400, _1561404), _1561408), hAPP(c_Product__Type_Ofst(_1561400, _1561402), _1561410))), hAPP(hAPP(c_List_Olist__update(_1561402, _1561406), _1561408), hAPP(c_Product__Type_Osnd(_1561400, _1561402), _1561410))))], (24722 ^ _777959) ^ [_1246895, _1246897, _1246899, _1246901] : [class_Divides_Osemiring__div(_1246895), -(_1246897 = c_Groups_Ozero__class_Ozero(_1246895)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1246895), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246895), _1246899), _1246897)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246895), _1246901), _1246897)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1246895), _1246899), _1246901))], (31644 ^ _777959) ^ [_1375494, _1375496, _1375498, _1375500, _1375502, _1375504] : [c_Com_Ocom_OCall(_1375494, _1375496, _1375498) = c_Com_Ocom_OCond(_1375500, _1375502, _1375504)], (38520 ^ _777959) ^ [_1516905, _1516907, _1516909, _1516911] : [c_Fun_Oinj__on(_1516905, tc_Option_Ooption(_1516907), _1516911, c_Map_Odom(_1516905, _1516907, _1516911)), -(c_Fun_Oinj__on(_1516905, tc_Option_Ooption(_1516907), c_Map_Omap__add(_1516905, _1516907, _1516909, _1516911), c_Map_Odom(_1516905, _1516907, _1516911)))], (46826 ^ _777959) ^ [_1715913, _1715915, _1715917, _1715919, _1715921, _1715923, _1715925] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1715913, _1715915, _1715917, hAPP(hAPP(c_COMBC(_1715913, tc_fun(tc_prod(_1715913, _1715915), tc_HOL_Obool), tc_fun(_1715915, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1715915, tc_fun(tc_fun(tc_prod(_1715913, _1715915), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1715913, _1715915), tc_HOL_Obool), tc_fun(_1715915, tc_HOL_Obool)), _1715913), c_COMBC(_1715915, tc_fun(tc_prod(_1715913, _1715915), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1715915, tc_prod(_1715913, _1715915)), tc_fun(_1715915, tc_fun(tc_fun(tc_prod(_1715913, _1715915), tc_HOL_Obool), tc_HOL_Obool)), _1715913), hAPP(c_COMBB(tc_prod(_1715913, _1715915), tc_fun(tc_fun(tc_prod(_1715913, _1715915), tc_HOL_Obool), tc_HOL_Obool), _1715915), c_member(tc_prod(_1715913, _1715915)))), c_Product__Type_OPair(_1715913, _1715915)))), _1715919), hAPP(hAPP(c_COMBC(_1715915, tc_fun(tc_prod(_1715915, _1715917), tc_HOL_Obool), tc_fun(_1715917, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1715917, tc_fun(tc_fun(tc_prod(_1715915, _1715917), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1715915, _1715917), tc_HOL_Obool), tc_fun(_1715917, tc_HOL_Obool)), _1715915), c_COMBC(_1715917, tc_fun(tc_prod(_1715915, _1715917), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1715917, tc_prod(_1715915, _1715917)), tc_fun(_1715917, tc_fun(tc_fun(tc_prod(_1715915, _1715917), tc_HOL_Obool), tc_HOL_Obool)), _1715915), hAPP(c_COMBB(tc_prod(_1715915, _1715917), tc_fun(tc_fun(tc_prod(_1715915, _1715917), tc_HOL_Obool), tc_HOL_Obool), _1715917), c_member(tc_prod(_1715915, _1715917)))), c_Product__Type_OPair(_1715915, _1715917)))), _1715921)), _1715923), _1715925)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1715913, _1715917)), hAPP(hAPP(c_Product__Type_OPair(_1715913, _1715917), _1715923), _1715925)), hAPP(hAPP(c_Relation_Orel__comp(_1715913, _1715915, _1715917), _1715919), _1715921))))], (13941 ^ _777959) ^ [_1036181, _1036183, _1036185, _1036187, _1036189] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1036181, tc_HOL_Obool)), _1036183), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1036185, tc_fun(_1036181, tc_HOL_Obool)), _1036187), _1036189)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1036185, tc_fun(_1036181, tc_HOL_Obool)), _1036187), hAPP(hAPP(c_COMBB(tc_fun(_1036181, tc_HOL_Obool), tc_fun(_1036181, tc_HOL_Obool), _1036185), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1036181, tc_HOL_Obool)), _1036183)), _1036189)))], (36225 ^ _777959) ^ [_1464799, _1464801] : [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), _1464799), _1464801))), 36228 ^ _777959 : [(36237 ^ _777959) ^ [] : [-(c_Divides_OnegDivAlg(_1464799, _1464801) = hAPP(c_Divides_Oadjust(_1464801), c_Divides_OnegDivAlg(_1464799, 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)))), _1464801)))), -(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), _1464799), _1464801)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1464801), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36229 ^ _777959) ^ [] : [36230 ^ _777959 : [(36233 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1464801), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (36231 ^ _777959) ^ [] : [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), _1464799), _1464801)))]], -(c_Divides_OnegDivAlg(_1464799, _1464801) = 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), _1464799), _1464801)))]]], (15132 ^ _777959) ^ [_1065977, _1065979, _1065981, _1065983, _1065985] : [class_Rings_Ocomm__semiring__1(_1065977), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065977), _1065979), _1065981)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065977), _1065983), _1065985)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065977), _1065983), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065977), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1065977), _1065979), _1065981)), _1065985)))], (27481 ^ _777959) ^ [_1297597] : [-(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)), _1297597)) = hAPP(c_Int_Onat, _1297597))], (43223 ^ _777959) ^ [_1636119, _1636121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636119)), _1636121)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1636119), _1636121) = _1636121)], (11820 ^ _777959) ^ [_992219, _992221, _992223, _992225, _992227] : [_992219 = c_Orderings_Obot__class_Obot(tc_fun(_992221, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992221, tc_fun(_992223, tc_HOL_Obool)), _992219), hAPP(hAPP(c_COMBB(tc_fun(_992223, tc_HOL_Obool), tc_fun(_992223, tc_HOL_Obool), _992221), hAPP(c_Set_Oinsert(_992223), _992225)), _992227)) = c_Orderings_Obot__class_Obot(tc_fun(_992223, tc_HOL_Obool)))], (51262 ^ _777959) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (33761 ^ _777959) ^ [_1413545, _1413547, _1413549] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413545), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413545)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413547)), _1413549)) = 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), _1413545), _1413547))), _1413549))], (46513 ^ _777959) ^ [_1707053, _1707055, _1707057, _1707059, _1707061] : [c_List_Olist__all2(_1707053, _1707055, _1707057, _1707059, _1707061), 46516 ^ _777959 : [(46519 ^ _777959) ^ [_1707216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1707216), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707053)), _1707059))), -(hBOOL(hAPP(hAPP(_1707057, hAPP(hAPP(c_List_Onth(_1707053), _1707059), _1707216)), hAPP(hAPP(c_List_Onth(_1707055), _1707061), _1707216))))], (46517 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707053)), _1707059) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707055)), _1707061))]]], (29643 ^ _777959) ^ [_1337040, _1337042, _1337044, _1337046, _1337048] : [class_Groups_Ocomm__monoid__add(_1337040), hBOOL(hAPP(c_Finite__Set_Ofinite(_1337042), _1337044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1337042, tc_HOL_Obool)), _1337046), _1337044)), 29657 ^ _777959 : [(29660 ^ _777959) ^ [] : [hAPP(_1337048, 29656 ^ [_1337040, _1337042, _1337044, _1337046, _1337048]) = c_Groups_Ozero__class_Ozero(_1337040)], (29658 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1337042), 29656 ^ [_1337040, _1337042, _1337044, _1337046, _1337048]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1337042, tc_HOL_Obool)), _1337044), _1337046))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1337042, _1337040), _1337048), _1337046) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1337042, _1337040), _1337048), _1337044))], (13965 ^ _777959) ^ [_1036987, _1036989, _1036991, _1036993] : [-(hBOOL(hAPP(hAPP(c_member(_1036987), _1036989), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1036987, tc_HOL_Obool)), _1036991), hAPP(c_Set_OCollect(_1036987), _1036993))))), hBOOL(hAPP(hAPP(c_member(_1036987), _1036989), _1036991)), hBOOL(hAPP(_1036993, _1036989))], (31580 ^ _777959) ^ [_1374289, _1374291, _1374293, _1374295] : [c_Com_Ocom_OCond(_1374289, _1374291, _1374293) = hAPP(c_Com_Ocom_OBODY, _1374295)], (8796 ^ _777959) ^ [_929718, _929720, _929722, _929724] : [-(c_Nitpick_Ofold__graph_H(_929718, _929720, _929722, _929724, c_Orderings_Obot__class_Obot(tc_fun(_929718, tc_HOL_Obool)), _929724))], (36313 ^ _777959) ^ [_1466378, _1466380] : [-(c_Divides_Odivmod__nat(_1466378, _1466380) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1466378, _1466380)))], (41982 ^ _777959) ^ [_1605335, _1605337] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1605335)), _1605337) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1605337 = c_List_Olist_ONil(_1605335))], (14393 ^ _777959) ^ [_1047443, _1047445, _1047447, _1047449, _1047451] : [-(c_Map_Odom(_1047443, _1047445, c_Fun_Ooverride__on(_1047443, tc_Option_Ooption(_1047445), _1047447, _1047449, _1047451)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1047443, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1047443, tc_HOL_Obool)), c_Map_Odom(_1047443, _1047445, _1047447)), hAPP(c_Set_OCollect(_1047443), hAPP(hAPP(c_COMBC(_1047443, tc_fun(_1047443, tc_HOL_Obool), tc_HOL_Obool), c_member(_1047443)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1047443, tc_HOL_Obool)), _1047451), c_Map_Odom(_1047443, _1047445, _1047449)))))), hAPP(c_Set_OCollect(_1047443), hAPP(hAPP(c_COMBC(_1047443, tc_fun(_1047443, tc_HOL_Obool), tc_HOL_Obool), c_member(_1047443)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1047443, tc_HOL_Obool)), _1047451), c_Map_Odom(_1047443, _1047445, _1047449))))))], (12066 ^ _777959) ^ [_996849, _996851, _996853] : [_996851 = _996853, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996849), _996851) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996849), _996853))], (9462 ^ _777959) ^ [_940825, _940827, _940829, _940831, _940833, _940835, _940837] : [-(c_Nitpick_Ofold__graph_H(_940825, _940827, _940829, _940831, _940833, hAPP(hAPP(_940829, _940835), _940837))), 9463 ^ _777959 : [(9470 ^ _777959) ^ [_941054, _941056] : [hAPP(hAPP(_940829, _940835), _940837) = hAPP(hAPP(_940829, _941056), _941054), hBOOL(hAPP(hAPP(c_member(_940825), _941056), _940833)), c_Nitpick_Ofold__graph_H(_940825, _940827, _940829, _940831, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_940825, tc_HOL_Obool)), _940833), hAPP(hAPP(c_Set_Oinsert(_940825), _941056), c_Orderings_Obot__class_Obot(tc_fun(_940825, tc_HOL_Obool)))), _941054)], (9464 ^ _777959) ^ [] : [_940833 = c_Orderings_Obot__class_Obot(tc_fun(_940825, tc_HOL_Obool)), hAPP(hAPP(_940829, _940835), _940837) = _940831]]], (1800 ^ _777959) ^ [_803183, _803185] : [-(class_Int_Onumber(_803183)), _803185 = _803183, class_Int_Onumber(_803185)], (17485 ^ _777959) ^ [_1112032, _1112034, _1112036] : [class_Orderings_Olinorder(_1112032), hBOOL(hAPP(c_Finite__Set_Ofinite(_1112032), _1112034)), -(c_Big__Operators_Olinorder__class_OMax(_1112032, hAPP(hAPP(c_Set_Oinsert(_1112032), _1112036), _1112034)) = hAPP(hAPP(c_Finite__Set_Ofold(_1112032, _1112032, c_Orderings_Oord__class_Omax(_1112032)), _1112036), _1112034))], (42772 ^ _777959) ^ [_1625289, _1625291, _1625293] : [-(hAPP(c_List_Oset(_1625289), hAPP(hAPP(c_List_Oappend(_1625289), _1625291), _1625293)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1625289, tc_HOL_Obool)), hAPP(c_List_Oset(_1625289), _1625291)), hAPP(c_List_Oset(_1625289), _1625293)))], (38664 ^ _777959) ^ [_1519816, _1519818, _1519820, _1519822, _1519824, _1519826, _1519828] : [c_Fun_Oinj__on(_1519816, _1519818, _1519820, c_Orderings_Otop__class_Otop(tc_fun(_1519816, tc_HOL_Obool))), hAPP(hAPP(c_Map_Omap__of(_1519816, _1519822), _1519824), _1519826) = hAPP(c_Option_Ooption_OSome(_1519822), _1519828), -(hAPP(hAPP(c_Map_Omap__of(_1519818, _1519822), hAPP(hAPP(c_List_Omap(tc_prod(_1519816, _1519822), tc_prod(_1519818, _1519822)), hAPP(c_Product__Type_Oprod_Oprod__case(_1519816, _1519822, tc_prod(_1519818, _1519822)), hAPP(hAPP(c_COMBB(_1519818, tc_fun(_1519822, tc_prod(_1519818, _1519822)), _1519816), c_Product__Type_OPair(_1519818, _1519822)), _1519820))), _1519824)), hAPP(_1519820, _1519826)) = hAPP(c_Option_Ooption_OSome(_1519822), _1519828))], (4290 ^ _777959) ^ [_842913, _842915, _842917, _842919] : [-(c_HOL_OLet(_842919, _842915) = c_HOL_OLet(_842917, _842913)), _842919 = _842917, _842915 = _842913], (46487 ^ _777959) ^ [_1706508, _1706510, _1706512] : [c_List_Olist__all2(_1706512, _1706512, c_fequal, _1706508, _1706510), -(_1706508 = _1706510)], (3144 ^ _777959) ^ [_825162, _825164, _825166, _825168, _825170, _825172] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_825172, _825168, _825164) = c_SetInterval_Oord__class_OatLeastAtMost(_825170, _825166, _825162)), _825172 = _825170, _825168 = _825166, _825164 = _825162], (8242 ^ _777959) ^ [_920109, _920111, _920113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_920109, tc_HOL_Obool)), _920111), hAPP(hAPP(c_Set_Oinsert(_920109), _920113), c_Orderings_Obot__class_Obot(tc_fun(_920109, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_920109, _920113, _920111) = _920113)], (48651 ^ _777959) ^ [_1758683, _1758685, _1758687, _1758689, _1758691] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1758683, _1758683)), hAPP(hAPP(c_Product__Type_OPair(_1758683, _1758683), _1758685), _1758687)), _1758689)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1758683, _1758683)), hAPP(hAPP(c_Product__Type_OPair(_1758683, _1758683), _1758687), _1758691)), c_Transitive__Closure_Ortrancl(_1758683, _1758689))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1758683, _1758683)), hAPP(hAPP(c_Product__Type_OPair(_1758683, _1758683), _1758685), _1758691)), c_Transitive__Closure_Ortrancl(_1758683, _1758689))))], (42662 ^ _777959) ^ [_1622860, _1622862, _1622864, _1622866, _1622868] : [hAPP(hAPP(c_List_Oappend(_1622860), _1622862), hAPP(hAPP(c_List_Olist_OCons(_1622860), _1622864), c_List_Olist_ONil(_1622860))) = hAPP(hAPP(c_List_Oappend(_1622860), _1622866), hAPP(hAPP(c_List_Olist_OCons(_1622860), _1622868), c_List_Olist_ONil(_1622860))), 42665 ^ _777959 : [(42668 ^ _777959) ^ [] : [-(_1622864 = _1622868)], (42666 ^ _777959) ^ [] : [-(_1622862 = _1622866)]]], (12084 ^ _777959) ^ [_997176, _997178] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _997176), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _997178), _997176))))], (44368 ^ _777959) ^ [_1660057] : [class_Orderings_Olinorder(_1660057), -(c_List_Olinorder__class_Osorted(_1660057, c_List_Olist_ONil(_1660057)))], (11080 ^ _777959) ^ [_975017, _975019] : [-(c_Map_Odom(_975017, _975019, hAPP(c_COMBK(tc_Option_Ooption(_975019), _975017), c_Option_Ooption_ONone(_975019))) = c_Orderings_Obot__class_Obot(tc_fun(_975017, tc_HOL_Obool)))], (33213 ^ _777959) ^ [_1404861, _1404863] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404861)), hAPP(c_Nat_OSuc, _1404863)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1404861))), 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)), _1404863)))))], (41964 ^ _777959) ^ [_1604661, _1604663, _1604665, _1604667] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1604661, _1604663)), hAPP(hAPP(c_Product__Type_OSigma(_1604661, _1604663), _1604665), hAPP(c_COMBK(tc_fun(_1604663, tc_HOL_Obool), _1604661), _1604667))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1604661), _1604665)), hAPP(c_Finite__Set_Ocard(_1604663), _1604667)))], (34965 ^ _777959) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (17113 ^ _777959) ^ [_1105237] : [class_Orderings_Olinorder(_1105237), -(c_Finite__Set_Ofun__left__comm__idem(_1105237, _1105237, c_Orderings_Oord__class_Omin(_1105237)))], (39524 ^ _777959) ^ [_1540947, _1540949, _1540951] : [hBOOL(hAPP(c_List_Odistinct(_1540947), hAPP(hAPP(c_List_Omap(tc_prod(_1540947, _1540949), _1540947), c_Product__Type_Ofst(_1540947, _1540949)), _1540951))), -(c_Map_Oran(_1540947, _1540949, hAPP(c_Map_Omap__of(_1540947, _1540949), _1540951)) = hAPP(c_Set_Oimage(tc_prod(_1540947, _1540949), _1540949, c_Product__Type_Osnd(_1540947, _1540949)), hAPP(c_List_Oset(tc_prod(_1540947, _1540949)), _1540951)))], (13083 ^ _777959) ^ [_1016438, _1016440, _1016442] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1016438, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1016438, tc_HOL_Obool)), _1016440), _1016442)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016438, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1016438, tc_HOL_Obool)), _1016440)), _1016442))], (14239 ^ _777959) ^ [_1043086, _1043088, _1043090, _1043092] : [class_Rings_Ocomm__semiring__1(_1043086), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043086), _1043088), _1043090)), _1043092) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043086), _1043088), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043086), _1043090), _1043092)))], (28830 ^ _777959) ^ [_1321336, _1321338, _1321340] : [class_Orderings_Olinorder(_1321336), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321336), _1321338), _1321340)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321336, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1321336), _1321338), c_Orderings_Obot__class_Obot(tc_fun(_1321336, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_1321336, _1321338, _1321340)) = c_SetInterval_Oord__class_OatLeastAtMost(_1321336, _1321338, _1321340))], (30872 ^ _777959) ^ [_1361248, _1361250] : [class_Rings_Olinordered__idom(_1361248), 30875 ^ _777959 : [(30882 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361248), c_Groups_Ozero__class_Ozero(_1361248)), _1361250)), -(c_Groups_Osgn__class_Osgn(_1361248, _1361250) = c_Groups_Oone__class_Oone(_1361248))], (30876 ^ _777959) ^ [] : [c_Groups_Osgn__class_Osgn(_1361248, _1361250) = c_Groups_Oone__class_Oone(_1361248), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361248), c_Groups_Ozero__class_Ozero(_1361248)), _1361250)))]]], (41439 ^ _777959) ^ [_1590167, _1590169, _1590171, _1590173, _1590175, _1590177] : [-(c_List_Olistrelp(_1590167, _1590169, hAPP(hAPP(c_List_Olist_OCons(_1590167), _1590171), _1590173), hAPP(hAPP(c_List_Olist_OCons(_1590167), _1590175), _1590177))), hBOOL(hAPP(hAPP(_1590169, _1590171), _1590175)), c_List_Olistrelp(_1590167, _1590169, _1590173, _1590177)], (42373 ^ _777959) ^ [_1614171, _1614173, _1614175, _1614177, _1614179, _1614181, _1614183, _1614185] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1614171, _1614173), tc_fun(tc_prod(_1614175, _1614177), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1614171, _1614173), _1614179), hAPP(c_COMBK(tc_fun(_1614173, tc_HOL_Obool), _1614171), _1614181))), hAPP(c_Product__Type_Oprod_Oprod__case(_1614171, _1614173, tc_fun(tc_prod(_1614175, _1614177), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1614171, tc_fun(_1614173, tc_fun(_1614175, tc_fun(_1614177, tc_HOL_Obool))), tc_fun(_1614173, tc_fun(tc_prod(_1614175, _1614177), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1614175, tc_fun(_1614177, tc_HOL_Obool)), tc_fun(tc_prod(_1614175, _1614177), tc_HOL_Obool)), tc_fun(tc_fun(_1614173, tc_fun(_1614175, tc_fun(_1614177, tc_HOL_Obool))), tc_fun(_1614173, tc_fun(tc_prod(_1614175, _1614177), tc_HOL_Obool))), _1614171), c_COMBB(tc_fun(_1614175, tc_fun(_1614177, tc_HOL_Obool)), tc_fun(tc_prod(_1614175, _1614177), tc_HOL_Obool), _1614173)), hAPP(hAPP(c_COMBB(tc_fun(_1614175, tc_HOL_Obool), tc_fun(tc_fun(_1614175, tc_fun(_1614177, tc_HOL_Obool)), tc_fun(tc_prod(_1614175, _1614177), tc_HOL_Obool)), _1614171), c_Product__Type_OSigma(_1614175, _1614177)), _1614183))), hAPP(hAPP(c_COMBB(tc_fun(_1614177, tc_HOL_Obool), tc_fun(_1614175, tc_fun(_1614177, tc_HOL_Obool)), _1614173), c_COMBK(tc_fun(_1614177, tc_HOL_Obool), _1614175)), _1614185)))) = hAPP(hAPP(c_Product__Type_OSigma(_1614175, _1614177), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1614171, tc_fun(_1614175, tc_HOL_Obool)), _1614179), _1614183)), hAPP(c_COMBK(tc_fun(_1614177, tc_HOL_Obool), _1614175), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1614173, tc_fun(_1614177, tc_HOL_Obool)), _1614181), _1614185))))], (45445 ^ _777959) ^ [_1683757, _1683759, _1683761] : [-(c_List_OdropWhile(_1683757, _1683759, _1683761) = c_List_Olist_ONil(_1683757)), hBOOL(hAPP(_1683759, hAPP(c_List_Ohd(_1683757), c_List_OdropWhile(_1683757, _1683759, _1683761))))], (12678 ^ _777959) ^ [_1008018, _1008020, _1008022, _1008024] : [class_Groups_Ouminus(_1008018), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1008020, _1008018)), _1008022), _1008024) = hAPP(c_Groups_Ouminus__class_Ouminus(_1008018), hAPP(_1008022, _1008024)))], (19504 ^ _777959) ^ [_1151236] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151236)), _1151236 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31136 ^ _777959) ^ [_1366083, _1366085] : [class_Groups_Oordered__ab__group__add__abs(_1366083), 31139 ^ _777959 : [(31146 ^ _777959) ^ [] : [-(_1366085 = c_Groups_Ozero__class_Ozero(_1366083)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366083), c_Groups_Ozero__class_Ozero(_1366083)), hAPP(c_Groups_Oabs__class_Oabs(_1366083), _1366085))))], (31140 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366083), c_Groups_Ozero__class_Ozero(_1366083)), hAPP(c_Groups_Oabs__class_Oabs(_1366083), _1366085))), _1366085 = c_Groups_Ozero__class_Ozero(_1366083)]]], (30313 ^ _777959) ^ [_1351203, _1351205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1351203)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1351203), _1351205)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1351203, _1351205) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1351203), _1351205))], (41886 ^ _777959) ^ [_1602595, _1602597, _1602599, _1602601, _1602603] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1602595, _1602597), _1602599), hAPP(hAPP(c_COMBS(_1602595, tc_fun(_1602597, tc_HOL_Obool), tc_fun(_1602597, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1602597, tc_HOL_Obool), tc_fun(tc_fun(_1602597, tc_HOL_Obool), tc_fun(_1602597, tc_HOL_Obool)), _1602595), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602597, tc_HOL_Obool))), _1602601)), _1602603)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1602595, _1602597), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1602595, _1602597), _1602599), _1602601)), hAPP(hAPP(c_Product__Type_OSigma(_1602595, _1602597), _1602599), _1602603)))], (43586 ^ _777959) ^ [_1644285, _1644287, _1644289] : [-(_1644285 = c_List_Olist_ONil(_1644287)), -(hAPP(hAPP(c_List_Otake(_1644287), hAPP(c_Nat_OSuc, _1644289)), _1644285) = hAPP(hAPP(c_List_Olist_OCons(_1644287), hAPP(c_List_Ohd(_1644287), _1644285)), hAPP(hAPP(c_List_Otake(_1644287), _1644289), hAPP(c_List_Otl(_1644287), _1644285))))], (50388 ^ _777959) ^ [_1799815, _1799817, _1799819, _1799821, _1799823, _1799825] : [-(c_New__Random__Sequence_Oneg__union(_1799815, _1799817, _1799819, _1799821, _1799823, _1799825) = c_New__DSequence_Oneg__union(_1799815, hAPP(hAPP(hAPP(_1799817, _1799821), _1799823), _1799825), hAPP(hAPP(hAPP(_1799819, _1799821), _1799823), _1799825)))], (8426 ^ _777959) ^ [_924172, _924174, _924176] : [class_Orderings_Olinorder(_924172), 8429 ^ _777959 : [(8430 ^ _777959) ^ [] : [-(_924174 = _924176), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924172), _924174), _924176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924172), _924176), _924174)))], (8440 ^ _777959) ^ [] : [8441 ^ _777959 : [(8444 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924172), _924176), _924174))], (8442 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_924172), _924174), _924176))]], _924174 = _924176]]], (3850 ^ _777959) ^ [_836237, _836239, _836241, _836243, _836245, _836247] : [-(c_List_OtakeWhile(_836247, _836243, _836239) = c_List_OtakeWhile(_836245, _836241, _836237)), _836247 = _836245, _836243 = _836241, _836239 = _836237], (38674 ^ _777959) ^ [_1520129, _1520131, _1520133, _1520135] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1520129, _1520131, _1520133, c_Code__Numeral_OSuc__code__numeral(_1520135)) = hAPP(_1520133, _1520135))], (46625 ^ _777959) ^ [_1709511, _1709513] : [-(c_List_Oinsert(_1709511, _1709513, c_List_Olist_ONil(_1709511)) = hAPP(hAPP(c_List_Olist_OCons(_1709511), _1709513), c_List_Olist_ONil(_1709511)))], (43582 ^ _777959) ^ [_1644180, _1644182] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644180)), hAPP(c_List_Otl(_1644180), _1644182)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1644180)), _1644182)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (36550 ^ _777959) ^ [_1471273, _1471275] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1471273, _1471275) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1471273, _1471275)))], (13823 ^ _777959) ^ [_1033526, _1033528, _1033530, _1033532, _1033534] : [-(hAPP(c_Map_Omap__add(_1033526, _1033528, _1033530, _1033532), _1033534) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1033528), _1033528, hAPP(_1033530, _1033534), c_Option_Ooption_OSome(_1033528)), hAPP(_1033532, _1033534)))], (9710 ^ _777959) ^ [_946270, _946272, _946274, _946276] : [class_Lattices_Olattice(_946270), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946270), _946272), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946270), _946274), _946276)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946270), _946274), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_946270), _946272), _946276)))], (41045 ^ _777959) ^ [_1580353, _1580355, _1580357] : [_1580353 = _1580355, 41048 ^ _777959 : [(41051 ^ _777959) ^ [_1580509] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1580357, _1580357)), _1580509), hAPP(c_List_Oset(tc_prod(_1580357, _1580357)), hAPP(hAPP(c_List_Ozip(_1580357, _1580357), _1580353), _1580355)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1580357, _1580357, tc_HOL_Obool), c_fequal), _1580509)))], (41049 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1580357)), _1580353) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1580357)), _1580355))]]], (36266 ^ _777959) ^ [_1465554, _1465556, _1465558] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1465554, _1465556), _1465558)), 36269 ^ _777959 : [(36270 ^ _777959) ^ [_1465639] : [hBOOL(hAPP(hAPP(_1465556, _1465639), _1465558)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1465554, _1465556), _1465639)))]]], (37227 ^ _777959) ^ [_1487551, _1487553, _1487555, _1487557] : [-(hAPP(c_Relation_OImage(_1487551, _1487553, _1487555), _1487557) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1487551, tc_fun(_1487553, tc_HOL_Obool)), _1487557), hAPP(hAPP(c_COMBB(tc_fun(_1487551, tc_HOL_Obool), tc_fun(_1487553, tc_HOL_Obool), _1487551), c_Relation_OImage(_1487551, _1487553, _1487555)), hAPP(hAPP(c_COMBC(_1487551, tc_fun(_1487551, tc_HOL_Obool), tc_fun(_1487551, tc_HOL_Obool)), c_Set_Oinsert(_1487551)), c_Orderings_Obot__class_Obot(tc_fun(_1487551, tc_HOL_Obool))))))], (41723 ^ _777959) ^ [_1598057, _1598059, _1598061, _1598063, _1598065, _1598067, _1598069] : [-(hAPP(c_Product__Type_Ofst(_1598057, _1598059), hAPP(c_Product__Type_Omap__pair(_1598061, _1598057, _1598063, _1598059, _1598065, _1598067), _1598069)) = hAPP(_1598065, hAPP(c_Product__Type_Ofst(_1598061, _1598063), _1598069)))], (49572 ^ _777959) ^ [_1782498, _1782500, _1782502] : [hBOOL(hAPP(hAPP(c_member(_1782498), _1782500), hAPP(c_List_Oset(_1782498), _1782502))), 49577 ^ _777959 : [(49580 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1782498), _1782500), hAPP(c_List_Oset(_1782498), 49576 ^ [_1782498, _1782500, _1782502])))], (49578 ^ _777959) ^ [] : [-(_1782502 = hAPP(hAPP(c_List_Oappend(_1782498), 49575 ^ [_1782498, _1782500, _1782502]), hAPP(hAPP(c_List_Olist_OCons(_1782498), _1782500), 49576 ^ [_1782498, _1782500, _1782502])))]]], (51072 ^ _777959) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (10154 ^ _777959) ^ [_955600, _955602, _955604, _955606, _955608] : [class_Groups_Oab__group__add(_955600), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_955602, _955600), hAPP(hAPP(c_COMBS(_955602, _955600, _955600), hAPP(hAPP(c_COMBB(_955600, tc_fun(_955600, _955600), _955602), c_Groups_Ominus__class_Ominus(_955600)), _955604)), _955606)), _955608) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_955600), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_955602, _955600), _955604), _955608)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_955602, _955600), _955606), _955608)))], (33465 ^ _777959) ^ [_1408778, _1408780] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1408778), _1408780), hAPP(c_Int_Onumber__class_Onumber__of(_1408778), c_Int_OBit1(c_Int_OPls))) = _1408780), class_Fields_Ofield(_1408778), class_Int_Onumber__ring(_1408778)], (39862 ^ _777959) ^ [_1549013, _1549015, _1549017, _1549019, _1549021, _1549023] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1549013, _1549015)), hAPP(hAPP(c_Product__Type_OPair(_1549013, _1549015), _1549017), _1549019)), hAPP(c_List_Oset(tc_prod(_1549013, _1549015)), hAPP(hAPP(c_List_Ozip(_1549013, _1549015), _1549021), _1549023)))), 39865 ^ _777959 : [(39868 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1549015), _1549019), hAPP(c_List_Oset(_1549015), _1549023))))], (39866 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1549013), _1549017), hAPP(c_List_Oset(_1549013), _1549021))))]]], (27680 ^ _777959) ^ [_1300844, _1300846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1300844)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1300844), _1300846)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1300846), _1300844)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1300846)), hAPP(c_Int_Onat, _1300844)))], (47750 ^ _777959) ^ [_1738332, _1738334, _1738336, _1738338, _1738340] : [hAPP(c_List_Ofilter(_1738332, _1738334), _1738336) = hAPP(hAPP(c_List_Olist_OCons(_1738332), _1738338), _1738340), 47755 ^ _777959 : [(47764 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1738334, _1738338)))], (47766 ^ _777959) ^ [] : [-(_1738340 = hAPP(c_List_Ofilter(_1738332, _1738334), 47754 ^ [_1738332, _1738334, _1738336, _1738338, _1738340]))], (47758 ^ _777959) ^ [_1738646] : [hBOOL(hAPP(hAPP(c_member(_1738332), _1738646), hAPP(c_List_Oset(_1738332), 47753 ^ [_1738332, _1738334, _1738336, _1738338, _1738340]))), hBOOL(hAPP(_1738334, _1738646))], (47756 ^ _777959) ^ [] : [-(_1738336 = hAPP(hAPP(c_List_Oappend(_1738332), 47753 ^ [_1738332, _1738334, _1738336, _1738338, _1738340]), hAPP(hAPP(c_List_Olist_OCons(_1738332), _1738338), 47754 ^ [_1738332, _1738334, _1738336, _1738338, _1738340])))]]], (38802 ^ _777959) ^ [_1523042, _1523044, _1523046, _1523048] : [hAPP(c_Set_Oimage(_1523042, _1523044, _1523046), c_Orderings_Otop__class_Otop(tc_fun(_1523042, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1523044, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1523042, _1523044, _1523046), hAPP(c_Set_Ovimage(_1523042, _1523044, _1523046), _1523048)) = _1523048)], (51148 ^ _777959) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (41129 ^ _777959) ^ [_1582696, _1582698] : [-(c_Relation_Orefl__on(_1582696, _1582698, c_Relation_OId__on(_1582696, _1582698)))], (14043 ^ _777959) ^ [_1038814, _1038816, _1038818, _1038820] : [class_Complete__Lattice_Ocomplete__lattice(_1038814), hBOOL(hAPP(c_Finite__Set_Ofinite(_1038816), _1038818)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1038816, _1038814), _1038818), _1038820) = hAPP(hAPP(c_Finite__Set_Ofold(_1038816, _1038814, hAPP(hAPP(c_COMBB(_1038814, tc_fun(_1038814, _1038814), _1038816), c_Lattices_Osemilattice__inf__class_Oinf(_1038814)), _1038820)), c_Orderings_Otop__class_Otop(_1038814)), _1038818))], (23655 ^ _777959) ^ [_1228016, _1228018] : [class_Groups_Omonoid__mult(_1228016), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1228016), _1228018), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1228018)], (34493 ^ _777959) ^ [_1427230] : [-(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)))), _1427230) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1427230), _1427230))], (50690 ^ _777959) ^ [_1806099, _1806101, _1806103] : [class_Fields_Olinordered__field(_1806099), 50696 ^ _777959 : [(50699 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1806099), _1806101), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1806099), _1806103), 50695 ^ [_1806099, _1806101, _1806103])))], (50697 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1806099), c_Groups_Ozero__class_Ozero(_1806099)), 50695 ^ [_1806099, _1806101, _1806103])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1806099), _1806101), _1806103)))], (44676 ^ _777959) ^ [_1665785, _1665787] : [class_Orderings_Olinorder(_1665785), 44679 ^ _777959 : [(44680 ^ _777959) ^ [] : [c_List_Olinorder__class_Osorted(_1665785, _1665787), 44683 ^ _777959 : [(44684 ^ _777959) ^ [_1665956] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1665956), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665785)), _1665787))), 44687 ^ _777959 : [(44688 ^ _777959) ^ [_1666073] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1666073), _1665956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1665785), hAPP(hAPP(c_List_Onth(_1665785), _1665787), _1666073)), hAPP(hAPP(c_List_Onth(_1665785), _1665787), _1665956))))]]]]], (44694 ^ _777959) ^ [] : [44696 ^ _777959 : [(44702 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1665785), hAPP(hAPP(c_List_Onth(_1665785), _1665787), 44698 ^ [_1665785, _1665787])), hAPP(hAPP(c_List_Onth(_1665785), _1665787), 44695 ^ [_1665785, _1665787])))], (44700 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 44698 ^ [_1665785, _1665787]), 44695 ^ [_1665785, _1665787])))], (44697 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44695 ^ [_1665785, _1665787]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1665785)), _1665787))))]], -(c_List_Olinorder__class_Osorted(_1665785, _1665787))]]], (21089 ^ _777959) ^ [_1178643, _1178645, _1178647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1178643), _1178645)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1178647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1178647), _1178643)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1178647), _1178645))))], (39244 ^ _777959) ^ [_1534264, _1534266, _1534268, _1534270, _1534272, _1534274, _1534276] : [c_Fun_Oinj__on(_1534264, _1534266, _1534268, hAPP(c_Set_Oimage(_1534270, _1534264, _1534272), _1534274)), c_Fun_Oinj__on(_1534270, _1534264, _1534272, _1534274), hBOOL(hAPP(hAPP(c_member(_1534266), _1534276), hAPP(c_Set_Oimage(_1534264, _1534266, _1534268), hAPP(c_Set_Oimage(_1534270, _1534264, _1534272), _1534274)))), -(hAPP(c_Fun_Othe__inv__into(_1534270, _1534266, _1534274, hAPP(c_Fun_Ocomp(_1534264, _1534266, _1534270, _1534268), _1534272)), _1534276) = hAPP(hAPP(c_Fun_Ocomp(_1534264, _1534270, _1534266, c_Fun_Othe__inv__into(_1534270, _1534264, _1534274, _1534272)), c_Fun_Othe__inv__into(_1534264, _1534266, hAPP(c_Set_Oimage(_1534270, _1534264, _1534272), _1534274), _1534268)), _1534276))], (28125 ^ _777959) ^ [_1308573] : [c_Nat__Transfer_Onat__set(_1308573), -(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), _1308573)) = _1308573)], (51130 ^ _777959) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (31833 ^ _777959) ^ [_1379200, _1379202, _1379204, _1379206, _1379208, _1379210] : [c_Com_Ocom_OCond(_1379200, _1379202, _1379204) = c_Com_Ocom_OLocal(_1379206, _1379208, _1379210)], (38758 ^ _777959) ^ [_1522024, _1522026] : [-(hAPP(hAPP(c_List_Omap(_1522024, _1522024), c_COMBI(_1522024)), _1522026) = _1522026)], (32963 ^ _777959) ^ [_1400565, _1400567] : [_1400565 = _1400567, -(c_Int_OBit1(_1400565) = c_Int_OBit1(_1400567))], (34903 ^ _777959) ^ [_1434876] : [-(_1434876 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 34906 ^ _777959 : [(34913 ^ _777959) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1434876, 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, _1434876) = 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), _1434876), 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)))], (34907 ^ _777959) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1434876, 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, _1434876) = 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), _1434876), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (25944 ^ _777959) ^ [_1269747, _1269749, _1269751, _1269753] : [class_Orderings_Oorder(_1269747), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1269747, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1269747, _1269749, _1269751)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1269747, _1269751), _1269753)) = c_Orderings_Obot__class_Obot(tc_fun(_1269747, tc_HOL_Obool)))], (39685 ^ _777959) ^ [_1544862, _1544864, _1544866, _1544868, _1544870, _1544872] : [c_Finite__Set_Ofolding__idem(_1544862, _1544864, _1544866, _1544868), hBOOL(hAPP(c_Finite__Set_Ofinite(_1544862), _1544870)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1544862, tc_HOL_Obool)), _1544872), _1544870)), -(hAPP(c_Fun_Ocomp(_1544864, _1544864, _1544864, hAPP(_1544868, _1544870)), hAPP(_1544868, _1544872)) = hAPP(_1544868, _1544870))], (36129 ^ _777959) ^ [_1463083] : [-(c_Divides_Odivmod__nat(_1463083, 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)), _1463083))], (49030 ^ _777959) ^ [_1768427, _1768429, _1768431] : [-(hAPP(c_Relation_Oconverse(_1768427, _1768429), hAPP(c_Relation_Oconverse(_1768429, _1768427), _1768431)) = _1768431)], (40614 ^ _777959) ^ [_1566854, _1566856, _1566858, _1566860] : [class_Groups_Ocomm__monoid__add(_1566854), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1566854), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1566854), _1566856), c_List_Oupto(_1566858, _1566860))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1566854), _1566856), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1566858, _1566860))))], (25344 ^ _777959) ^ [_1258224, _1258226] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258224), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1258226)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1258224), _1258226)))], (47230 ^ _777959) ^ [_1725416, _1725418, _1725420, _1725422] : [-(hAPP(c_Relation_ORange(_1725416, _1725418), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1725416, _1725418), tc_HOL_Obool)), _1725420), _1725422)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1725418, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1725416, _1725418), _1725420)), hAPP(c_Relation_ORange(_1725416, _1725418), _1725422)))], (35293 ^ _777959) ^ [_1441419, _1441421] : [-(_1441419 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1441419, _1441421) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1441419), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1441421)))], (49320 ^ _777959) ^ [_1775561, _1775563, _1775565, _1775567, _1775569, _1775571] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775561, _1775561)), hAPP(hAPP(c_Product__Type_OPair(_1775561, _1775561), _1775563), _1775565)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775561, _1775561), tc_HOL_Obool), _1775567), _1775569))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775561, _1775561)), hAPP(hAPP(c_Product__Type_OPair(_1775561, _1775561), _1775565), _1775571)), _1775569)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775561, _1775561)), hAPP(hAPP(c_Product__Type_OPair(_1775561, _1775561), _1775563), _1775571)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775561, _1775561), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1775567)), _1775569))))], (19694 ^ _777959) ^ [_1154209, _1154211, _1154213, _1154215] : [class_Groups_Ocomm__monoid__mult(_1154209), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1154211), _1154213))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1154211, _1154209), _1154215), _1154213) = c_Groups_Oone__class_Oone(_1154209))], (33409 ^ _777959) ^ [_1407847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1407847), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407847) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (38826 ^ _777959) ^ [_1523710, _1523712, _1523714, _1523716] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1523710), hAPP(c_Set_Ovimage(_1523710, _1523712, _1523714), _1523716))), hAPP(c_Set_Oimage(_1523710, _1523712, _1523714), c_Orderings_Otop__class_Otop(tc_fun(_1523710, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1523712, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523712), _1523716)))], (35009 ^ _777959) ^ [_1436982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1436982))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1436982)))], (19917 ^ _777959) ^ [_1158248, _1158250, _1158252, _1158254, _1158256] : [class_Rings_Oordered__semiring(_1158248), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158248), _1158250), _1158252)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158248), _1158254), _1158256)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158248), c_Groups_Ozero__class_Ozero(_1158248)), _1158250)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158248), c_Groups_Ozero__class_Ozero(_1158248)), _1158254)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158248), _1158250), _1158254)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158248), _1158252), _1158256))))], (13317 ^ _777959) ^ [_1021478, _1021480, _1021482, _1021484, _1021486, _1021488] : [hBOOL(hAPP(hAPP(c_member(_1021478), _1021480), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1021482, tc_fun(_1021478, tc_HOL_Obool)), _1021484), _1021486))), hBOOL(hAPP(hAPP(c_member(_1021482), _1021488), _1021484)), -(hBOOL(hAPP(hAPP(c_member(_1021478), _1021480), hAPP(_1021486, _1021488))))], (11652 ^ _777959) ^ [_987197, _987199, _987201, _987203, _987205] : [hAPP(_987197, _987199) = hAPP(c_Option_Ooption_OSome(_987201), _987203), -(hBOOL(hAPP(hAPP(c_member(_987201), _987203), c_Map_Oran(_987205, _987201, _987197))))], (3622 ^ _777959) ^ [_832641, _832643, _832645, _832647] : [-(c_Wellfounded_Omin__ext(_832647, _832643) = c_Wellfounded_Omin__ext(_832645, _832641)), _832647 = _832645, _832643 = _832641], (6657 ^ _777959) ^ [_885918, _885920] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_885918, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_885918, tc_HOL_Obool))), _885920) = _885920)], (42845 ^ _777959) ^ [_1626975, _1626977, _1626979, _1626981] : [-(hAPP(c_Map_Omap__of(_1626975, _1626977), hAPP(hAPP(c_List_Oappend(tc_prod(_1626975, _1626977)), _1626979), _1626981)) = c_Map_Omap__add(_1626975, _1626977, hAPP(c_Map_Omap__of(_1626975, _1626977), _1626981), hAPP(c_Map_Omap__of(_1626975, _1626977), _1626979)))], (50150 ^ _777959) ^ [_1794463] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1794463)))], (25432 ^ _777959) ^ [_1260190, _1260192] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260190), _1260192)), _1260190)))], (49862 ^ _777959) ^ [_1789147, _1789149, _1789151] : [c_List_Olist__all(_1789147, _1789149, _1789151), 49865 ^ _777959 : [(49866 ^ _777959) ^ [_1789228] : [hBOOL(hAPP(hAPP(c_member(_1789147), _1789228), hAPP(c_List_Oset(_1789147), _1789151))), -(hBOOL(hAPP(_1789149, _1789228)))]]], (37934 ^ _777959) ^ [_1504735, _1504737, _1504739, _1504741] : [37936 ^ _777959 : [(37940 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504735), 37938 ^ [_1504735, _1504737, _1504739, _1504741]), _1504741)))], (37942 ^ _777959) ^ [] : [-(hAPP(_1504739, 37935 ^ [_1504735, _1504737, _1504739, _1504741]) = hAPP(_1504739, 37938 ^ [_1504735, _1504737, _1504739, _1504741]))], (37944 ^ _777959) ^ [] : [37935 ^ [_1504735, _1504737, _1504739, _1504741] = 37938 ^ [_1504735, _1504737, _1504739, _1504741]], (37937 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1504735), 37935 ^ [_1504735, _1504737, _1504739, _1504741]), _1504741)))]], -(c_Fun_Oinj__on(_1504735, _1504737, _1504739, _1504741))], (21210 ^ _777959) ^ [_1181054, _1181056, _1181058] : [class_Groups_Oordered__comm__monoid__add(_1181054), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181054), c_Groups_Ozero__class_Ozero(_1181054)), _1181056)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181054), c_Groups_Ozero__class_Ozero(_1181054)), _1181058)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181054), c_Groups_Ozero__class_Ozero(_1181054)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181054), _1181056), _1181058))))], (21252 ^ _777959) ^ [_1181815, _1181817, _1181819] : [class_Groups_Oordered__comm__monoid__add(_1181815), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181815), _1181817), c_Groups_Ozero__class_Ozero(_1181815))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1181815), _1181819), c_Groups_Ozero__class_Ozero(_1181815))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1181815), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1181815), _1181817), _1181819)), c_Groups_Ozero__class_Ozero(_1181815))))], (44150 ^ _777959) ^ [_1656474, _1656476] : [class_Orderings_Olinorder(_1656474), c_List_Olinorder__class_Osorted(_1656474, _1656476), -(c_List_Olinorder__class_Osorted(_1656474, hAPP(c_List_Otl(_1656474), _1656476)))], (50990 ^ _777959) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (15546 ^ _777959) ^ [_1073468] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073468), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1073468)], (46227 ^ _777959) ^ [_1700825, _1700827, _1700829, _1700831] : [-(hBOOL(hAPP(c_List_Olistsp(_1700825, _1700827), hAPP(hAPP(c_List_Oappend(_1700825), _1700829), _1700831)))), hBOOL(hAPP(c_List_Olistsp(_1700825, _1700827), _1700829)), hBOOL(hAPP(c_List_Olistsp(_1700825, _1700827), _1700831))], (49755 ^ _777959) ^ [_1787079, _1787081, _1787083] : [c_List_Olist__all(_1787079, _1787081, _1787083), 49758 ^ _777959 : [(49759 ^ _777959) ^ [_1787168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1787168), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1787079)), _1787083))), -(hBOOL(hAPP(_1787081, hAPP(hAPP(c_List_Onth(_1787079), _1787083), _1787168))))]]], (6206 ^ _777959) ^ [_877770, _877772, _877774, _877776] : [6208 ^ _777959 : [(6211 ^ _777959) ^ [] : [hBOOL(hAPP(_877776, 6207 ^ [_877770, _877772, _877774, _877776]))], (6209 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_877770), 6207 ^ [_877770, _877772, _877774, _877776]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_877770, tc_HOL_Obool)), _877772), _877774))))]], 6212 ^ _777959 : [(6219 ^ _777959) ^ [_878087] : [hBOOL(hAPP(hAPP(c_member(_877770), _878087), _877774)), -(hBOOL(hAPP(_877776, _878087)))], (6213 ^ _777959) ^ [_877990] : [hBOOL(hAPP(hAPP(c_member(_877770), _877990), _877772)), -(hBOOL(hAPP(_877776, _877990)))]]], (12195 ^ _777959) ^ [_999358, _999360, _999362, _999364] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999358), _999360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999362), _999364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999358), _999362)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999360), _999364))))], (28642 ^ _777959) ^ [_1317564, _1317566] : [c_Nat__Transfer_Onat__set(_1317564), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1317566), _1317564)), -(c_Nat__Transfer_Ois__nat(_1317566))], (8274 ^ _777959) ^ [_920721, _920723, _920725, _920727, _920729, _920731] : [hBOOL(hAPP(hAPP(c_member(_920721), _920723), _920725)), -(hAPP(c_Set_Oimage(_920721, _920727, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_920721, _920727), _920729), _920723), _920731)), _920725) = hAPP(hAPP(c_Set_Oinsert(_920727), _920731), hAPP(c_Set_Oimage(_920721, _920727, _920729), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_920721, tc_HOL_Obool)), _920725), hAPP(hAPP(c_Set_Oinsert(_920721), _920723), c_Orderings_Obot__class_Obot(tc_fun(_920721, tc_HOL_Obool)))))))], (14616 ^ _777959) ^ [_1052559, _1052561, _1052563, _1052565, _1052567, _1052569] : [hBOOL(hAPP(hAPP(c_member(_1052559), _1052561), _1052563)), -(hAPP(c_Fun_Ooverride__on(_1052559, _1052565, _1052567, _1052569, _1052563), _1052561) = hAPP(_1052569, _1052561))], (3536 ^ _777959) ^ [_831286, _831288, _831290, _831292, _831294, _831296] : [-(c_List_Oinsert(_831296, _831292, _831288) = c_List_Oinsert(_831294, _831290, _831286)), _831296 = _831294, _831292 = _831290, _831288 = _831286], (31775 ^ _777959) ^ [_1378114, _1378116, _1378118] : [class_Orderings_Olinorder(_1378114), hBOOL(hAPP(c_Finite__Set_Ofinite(_1378114), _1378116)), 31785 ^ _777959 : [(31788 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1378114), _1378118), 31784 ^ [_1378114, _1378116, _1378118]))], (31786 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1378114), 31784 ^ [_1378114, _1378116, _1378118]), _1378116)))]], hBOOL(hAPP(hAPP(c_member(_1378114), _1378118), _1378116)), -(c_Big__Operators_Olinorder__class_OMin(_1378114, _1378116) = _1378118)], (30766 ^ _777959) ^ [_1359189, _1359191] : [class_Rings_Olinordered__idom(_1359189), 30769 ^ _777959 : [(30776 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359189), c_Groups_Ozero__class_Ozero(_1359189)), _1359191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359189), c_Groups_Ozero__class_Ozero(_1359189)), c_Groups_Osgn__class_Osgn(_1359189, _1359191))))], (30770 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359189), c_Groups_Ozero__class_Ozero(_1359189)), c_Groups_Osgn__class_Osgn(_1359189, _1359191))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359189), c_Groups_Ozero__class_Ozero(_1359189)), _1359191)))]]], (14464 ^ _777959) ^ [_1049315, _1049317, _1049319, _1049321] : [c_Orderings_Otop__class_Otop(tc_fun(_1049315, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1049317, tc_fun(_1049315, tc_HOL_Obool)), _1049319), _1049321), 14467 ^ _777959 : [(14468 ^ _777959) ^ [_1049431] : [hBOOL(hAPP(hAPP(c_member(_1049317), _1049431), _1049319)), -(hAPP(_1049321, _1049431) = c_Orderings_Otop__class_Otop(tc_fun(_1049315, tc_HOL_Obool)))]]], (41739 ^ _777959) ^ [_1598732, _1598734, _1598736, _1598738, _1598740, _1598742] : [hAPP(c_Set_Oimage(_1598732, _1598734, _1598736), c_Orderings_Otop__class_Otop(tc_fun(_1598732, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1598734, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1598738, _1598740, _1598742), c_Orderings_Otop__class_Otop(tc_fun(_1598738, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1598740, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1598732, _1598738), tc_prod(_1598734, _1598740), c_Product__Type_Omap__pair(_1598732, _1598734, _1598738, _1598740, _1598736, _1598742)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1598732, _1598738), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1598734, _1598740), tc_HOL_Obool)))], (40799 ^ _777959) ^ [_1571180, _1571182, _1571184, _1571186] : [hBOOL(hAPP(hAPP(c_member(_1571180), _1571182), hAPP(c_List_Oset(_1571180), hAPP(hAPP(c_List_Otake(_1571180), _1571184), _1571186)))), -(hBOOL(hAPP(hAPP(c_member(_1571180), _1571182), hAPP(c_List_Oset(_1571180), _1571186))))], (48685 ^ _777959) ^ [_1759522, _1759524, _1759526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1759522, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1759522, _1759522, _1759524), _1759526)), _1759526)), -(hAPP(c_Relation_OImage(_1759522, _1759522, c_Transitive__Closure_Ortrancl(_1759522, _1759524)), _1759526) = _1759526)], (49698 ^ _777959) ^ [_1785843, _1785845, _1785847] : [-(c_Nitpick_Otimes__frac(_1785843, _1785845, _1785847) = hAPP(hAPP(c_Nitpick_Ofrac(_1785843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1785843), _1785845)), hAPP(c_Nitpick_Onum(_1785843), _1785847))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1785843), _1785845)), hAPP(c_Nitpick_Odenom(_1785843), _1785847))))], (41411 ^ _777959) ^ [_1589547, _1589549, _1589551, _1589553] : [hBOOL(hAPP(hAPP(c_member(_1589547), _1589549), c_Wellfounded_Oacc(_1589547, _1589551))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1589547)), _1589553), c_Wellfounded_Oacc(tc_List_Olist(_1589547), c_List_Olistrel1(_1589547, _1589551)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1589547)), hAPP(hAPP(c_List_Olist_OCons(_1589547), _1589549), _1589553)), c_Wellfounded_Oacc(tc_List_Olist(_1589547), c_List_Olistrel1(_1589547, _1589551)))))], (39640 ^ _777959) ^ [_1544003, _1544005] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1544003, _1544005) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1544003), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1544005), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (40383 ^ _777959) ^ [_1561791, _1561793, _1561795, _1561797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1561791)), _1561793)), _1561795)), -(hAPP(hAPP(c_List_Olist__update(_1561791, _1561793), _1561795), _1561797) = _1561793)], (20301 ^ _777959) ^ [_1165231, _1165233, _1165235, _1165237] : [class_Rings_Olinordered__ring__strict(_1165231), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165231), c_Groups_Ozero__class_Ozero(_1165231)), _1165233)), 20308 ^ _777959 : [(20315 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165231), _1165235), _1165237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165231), _1165233), _1165235)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165231), _1165233), _1165237))))], (20309 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165231), _1165233), _1165235)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165231), _1165233), _1165237))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165231), _1165235), _1165237)))]]], (24437 ^ _777959) ^ [_1242135, _1242137, _1242139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1242135), _1242137)), -(c_Smallcheck_Osmall_H(_1242139, _1242135, _1242137) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))], (31018 ^ _777959) ^ [_1363937, _1363939] : [class_Rings_Olinordered__idom(_1363937), -(hAPP(c_Groups_Oabs__class_Oabs(_1363937), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1363937), _1363939)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1363937), _1363939))], (20669 ^ _777959) ^ [_1171868, _1171870] : [class_Groups_Oordered__ab__group__add(_1171868), 20672 ^ _777959 : [(20679 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171868), _1171870), c_Groups_Ozero__class_Ozero(_1171868))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171868), c_Groups_Ozero__class_Ozero(_1171868)), hAPP(c_Groups_Ouminus__class_Ouminus(_1171868), _1171870))))], (20673 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171868), c_Groups_Ozero__class_Ozero(_1171868)), hAPP(c_Groups_Ouminus__class_Ouminus(_1171868), _1171870))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171868), _1171870), c_Groups_Ozero__class_Ozero(_1171868))))]]], (4510 ^ _777959) ^ [_846179, _846181] : [_846181 = _846179, -(c_Int_OBit1(_846181) = c_Int_OBit1(_846179))], (3612 ^ _777959) ^ [_832492, _832494, _832496, _832498] : [-(c_List_Olexn(_832498, _832494) = c_List_Olexn(_832496, _832492)), _832498 = _832496, _832494 = _832492], (8028 ^ _777959) ^ [_915046, _915048] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OSemi(_915046, _915048)))), hBOOL(hAPP(c_Com_OWT, _915046)), hBOOL(hAPP(c_Com_OWT, _915048))], (33779 ^ _777959) ^ [_1413813] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1413813)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413813) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44334 ^ _777959) ^ [_1659515, _1659517, _1659519] : [class_Orderings_Olinorder(_1659515), c_List_Olinorder__class_Osorted(_1659515, _1659517), -(c_List_Olinorder__class_Osorted(_1659515, c_List_Olinorder__class_Oinsort__insert__key(_1659515, _1659515, c_COMBI(_1659515), _1659519, _1659517)))], (13389 ^ _777959) ^ [_1023204, _1023206, _1023208, _1023210] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023204, tc_fun(_1023206, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1023204, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1023206, tc_HOL_Obool), tc_fun(_1023206, tc_HOL_Obool), _1023204), hAPP(c_COMBC(_1023206, tc_fun(_1023206, tc_HOL_Obool), tc_HOL_Obool), c_member(_1023206))), _1023208)), _1023210)), -(hBOOL(hAPP(hAPP(c_member(_1023206), _1023210), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023204, tc_fun(_1023206, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1023204, tc_HOL_Obool))), _1023208))))], (51022 ^ _777959) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (50904 ^ _777959) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (25438 ^ _777959) ^ [_1260306, _1260308] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1260306), _1260308)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1260306), _1260308) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23359 ^ _777959) ^ [_1222938, _1222940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1222938), _1222940)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222938), _1222940)))], (34431 ^ _777959) ^ [_1426236] : [class_Int_Onumber__ring(_1426236), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1426236), c_Groups_Oone__class_Oone(_1426236)), c_Groups_Oone__class_Oone(_1426236)) = hAPP(c_Int_Onumber__class_Onumber__of(_1426236), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (35771 ^ _777959) ^ [_1456265, _1456267, _1456269, _1456271, _1456273, _1456275] : [hAPP(hAPP(c_Product__Type_OPair(_1456265, _1456267), _1456269), _1456271) = hAPP(hAPP(c_Product__Type_OPair(_1456265, _1456267), _1456273), _1456275), 35774 ^ _777959 : [(35777 ^ _777959) ^ [] : [-(_1456271 = _1456275)], (35775 ^ _777959) ^ [] : [-(_1456269 = _1456273)]]], (24449 ^ _777959) ^ [_1242296, _1242298, _1242300, _1242302, _1242304] : [class_Groups_Oordered__ab__semigroup__add(_1242296), class_Rings_Osemiring__1(_1242296), 24459 ^ _777959 : [(24462 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242296), hAPP(_1242302, 24458 ^ [_1242296, _1242298, _1242300, _1242302, _1242304])), _1242304))], (24460 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1242298), 24458 ^ [_1242296, _1242298, _1242300, _1242302, _1242304]), _1242300)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1242296), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1242298, _1242296), _1242302), _1242300)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1242296), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1242296), hAPP(c_Finite__Set_Ocard(_1242298), _1242300))), _1242304))))], (51180 ^ _777959) ^ [_1811748, _1811750] : [-(class_Enum_Oenum(tc_sum(_1811748, _1811750))), class_Enum_Oenum(_1811748), class_Enum_Oenum(_1811750)], (44738 ^ _777959) ^ [_1667297, _1667299, _1667301] : [44739 ^ _777959 : [(44742 ^ _777959) ^ [] : [_1667301 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44740 ^ _777959) ^ [] : [-(_1667297 = c_List_Olist_ONil(tc_List_Olist(_1667299)))]], 44746 ^ _777959 : [(44749 ^ _777959) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667299)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1667299)), _1667297), 44745 ^ [_1667297, _1667299, _1667301])) = _1667301], (44747 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44745 ^ [_1667297, _1667299, _1667301]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1667299))), _1667297))))]], -(c_List_Otranspose(_1667299, _1667297) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1667299)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1667299)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1667299), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1667299)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1667299)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1667299), hAPP(hAPP(c_COMBB(tc_List_Olist(_1667299), tc_fun(tc_Nat_Onat, _1667299), tc_Nat_Onat), c_List_Onth(_1667299)), hAPP(c_List_Onth(tc_List_Olist(_1667299)), _1667297))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1667299))), _1667297)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1667301)))], (14462 ^ _777959) ^ [_1049262, _1049264] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_1049262, tc_HOL_Obool)), _1049264)))], (12870 ^ _777959) ^ [_1011586, _1011588, _1011590] : [-(hBOOL(hAPP(hAPP(c_member(_1011586), _1011588), _1011590))), -(hBOOL(hAPP(hAPP(c_member(_1011586), _1011588), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1011586, tc_HOL_Obool)), _1011590))))], (18229 ^ _777959) ^ [_1126090, _1126092, _1126094] : [class_Orderings_Olinorder(_1126090), hBOOL(hAPP(c_Finite__Set_Ofinite(_1126090), _1126092)), hBOOL(hAPP(hAPP(c_member(_1126090), _1126094), _1126092)), 18240 ^ _777959 : [(18247 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1126090, tc_HOL_Obool)), _1126092), hAPP(hAPP(c_Set_Oinsert(_1126090), _1126094), c_Orderings_Obot__class_Obot(tc_fun(_1126090, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1126090, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1126090, c_Orderings_Oord__class_Omin(_1126090), _1126092) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1126090), _1126094), c_Big__Operators_Olattice_OInf__fin(_1126090, c_Orderings_Oord__class_Omin(_1126090), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1126090, tc_HOL_Obool)), _1126092), hAPP(hAPP(c_Set_Oinsert(_1126090), _1126094), c_Orderings_Obot__class_Obot(tc_fun(_1126090, tc_HOL_Obool)))))))], (18241 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1126090, tc_HOL_Obool)), _1126092), hAPP(hAPP(c_Set_Oinsert(_1126090), _1126094), c_Orderings_Obot__class_Obot(tc_fun(_1126090, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1126090, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1126090, c_Orderings_Oord__class_Omin(_1126090), _1126092) = _1126094)]]], (13935 ^ _777959) ^ [_1035969, _1035971, _1035973, _1035975, _1035977] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1035969, tc_fun(_1035971, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1035969), _1035973), _1035975)), _1035977) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1035971, tc_HOL_Obool)), hAPP(_1035977, _1035973)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1035969, tc_fun(_1035971, tc_HOL_Obool)), _1035975), _1035977)))], (19554 ^ _777959) ^ [_1151973, _1151975, _1151977, _1151979, _1151981] : [class_Groups_Ocomm__monoid__mult(_1151973), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1151975, _1151973), hAPP(hAPP(c_COMBS(_1151975, _1151973, _1151973), hAPP(hAPP(c_COMBB(_1151973, tc_fun(_1151973, _1151973), _1151975), c_Groups_Otimes__class_Otimes(_1151973)), _1151977)), _1151979)), _1151981) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1151973), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1151975, _1151973), _1151977), _1151981)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1151975, _1151973), _1151979), _1151981)))], (35723 ^ _777959) ^ [_1455243, _1455245, _1455247, _1455249, _1455251, _1455253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1455243, tc_fun(_1455245, tc_HOL_Obool))), _1455247), _1455249)), hBOOL(hAPP(hAPP(_1455247, _1455251), _1455253)), -(hBOOL(hAPP(hAPP(_1455249, _1455251), _1455253)))], (41942 ^ _777959) ^ [_1604058, _1604060, _1604062, _1604064, _1604066] : [class_Orderings_Olinorder(_1604058), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1604060, _1604058, _1604062), _1604064), _1604066) = c_List_Olist_ONil(_1604060)], (48535 ^ _777959) ^ [_1755783, _1755785, _1755787, _1755789] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1755783, _1755783)), hAPP(hAPP(c_Product__Type_OPair(_1755783, _1755783), _1755785), _1755787)), c_Transitive__Closure_Otrancl(_1755783, _1755789))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1755783, _1755783)), hAPP(hAPP(c_Product__Type_OPair(_1755783, _1755783), _1755785), _1755787)), c_Transitive__Closure_Ortrancl(_1755783, _1755789))))], (25720 ^ _777959) ^ [_1265825, _1265827, _1265829, _1265831] : [class_Rings_Odivision__ring(_1265825), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265825), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1265825), _1265827), _1265829)), _1265831) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1265825), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265825), _1265827), _1265831)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1265825), _1265829), _1265831)))], (15184 ^ _777959) ^ [_1067260, _1067262, _1067264, _1067266] : [class_Rings_Ocomm__semiring__1(_1067260), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067260), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067260), _1067262), _1067264)), _1067266) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067260), _1067262), _1067266)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067260), _1067264), _1067266)))], (25200 ^ _777959) ^ [_1255481, _1255483, _1255485, _1255487] : [class_Groups_Ocomm__monoid__add(_1255481), 25203 ^ _777959 : [(25210 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1255483), _1255485))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1255481), _1255487), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1255485), hAPP(c_Nat_OSuc, _1255483))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255481), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1255481), _1255487), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1255485), _1255483))), hAPP(_1255487, _1255483)))], (25204 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1255483), _1255485)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1255481), _1255487), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1255485), hAPP(c_Nat_OSuc, _1255483))) = c_Groups_Ozero__class_Ozero(_1255481))]]], (16563 ^ _777959) ^ [_1095446, _1095448, _1095450, _1095452] : [class_Orderings_Olinorder(_1095446), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095446), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095446), _1095448), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095446), _1095450), _1095452))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095446), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095446), _1095448), _1095450)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095446), _1095448), _1095452)))))], (47576 ^ _777959) ^ [_1733844, _1733846, _1733848, _1733850, _1733852, _1733854] : [-(_1733844 = c_Orderings_Obot__class_Obot(tc_fun(_1733846, tc_HOL_Obool))), 47582 ^ _777959 : [(47585 ^ _777959) ^ [] : [c_Fun_Oinj__on(_1733848, _1733850, _1733852, hAPP(_1733854, 47581 ^ [_1733844, _1733846, _1733848, _1733850, _1733852, _1733854]))], (47583 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1733846), 47581 ^ [_1733844, _1733846, _1733848, _1733850, _1733852, _1733854]), _1733844)))]], -(c_Fun_Oinj__on(_1733848, _1733850, _1733852, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1733846, tc_fun(_1733848, tc_HOL_Obool)), _1733844), _1733854)))], (20605 ^ _777959) ^ [_1170784, _1170786] : [class_Groups_Oordered__ab__group__add(_1170784), 20608 ^ _777959 : [(20615 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170784), _1170786), c_Groups_Ozero__class_Ozero(_1170784))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170784), c_Groups_Ozero__class_Ozero(_1170784)), hAPP(c_Groups_Ouminus__class_Ouminus(_1170784), _1170786))))], (20609 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170784), c_Groups_Ozero__class_Ozero(_1170784)), hAPP(c_Groups_Ouminus__class_Ouminus(_1170784), _1170786))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1170784), _1170786), c_Groups_Ozero__class_Ozero(_1170784))))]]], (48298 ^ _777959) ^ [_1750044, _1750046] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1750044)), hAPP(c_Code__Numeral_Onat__of, _1750046))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1750044), _1750046)))], (41557 ^ _777959) ^ [_1592762, _1592764, _1592766] : [hBOOL(hAPP(c_List_Odistinct(_1592762), hAPP(hAPP(c_List_Olist_OCons(_1592762), _1592764), _1592766))), 41560 ^ _777959 : [(41563 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1592762), _1592766)))], (41561 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1592762), _1592764), hAPP(c_List_Oset(_1592762), _1592766)))]]], (36762 ^ _777959) ^ [_1475569, _1475571] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1475569), _1475571) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1475569, _1475571)))], (51106 ^ _777959) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (49510 ^ _777959) ^ [_1780961, _1780963, _1780965, _1780967] : [49512 ^ _777959 : [(49517 ^ _777959) ^ [] : [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(_1780965, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 49511 ^ [_1780961, _1780963, _1780965, _1780967]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1780965, 49511 ^ [_1780961, _1780963, _1780965, _1780967])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (49515 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49511 ^ [_1780961, _1780963, _1780965, _1780967]), _1780963)))], (49513 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1780961), 49511 ^ [_1780961, _1780963, _1780965, _1780967])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1780961), _1780963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1780965, _1780961)), _1780967)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1780967), hAPP(_1780965, _1780963))), 49531 ^ _777959 : [(49536 ^ _777959) ^ [] : [-(hAPP(_1780965, 49530 ^ [_1780961, _1780963, _1780965, _1780967]) = _1780967)], (49534 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 49530 ^ [_1780961, _1780963, _1780965, _1780967]), _1780963)))], (49532 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1780961), 49530 ^ [_1780961, _1780963, _1780965, _1780967])))]]], (47949 ^ _777959) ^ [_1743450, _1743452, _1743454] : [-(c_List_Olist__ex(_1743450, _1743452, _1743454)), 47950 ^ _777959 : [(47951 ^ _777959) ^ [_1743515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1743515), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1743450)), _1743454))), hBOOL(hAPP(_1743452, hAPP(hAPP(c_List_Onth(_1743450), _1743454), _1743515)))]]], (33553 ^ _777959) ^ [_1410108, _1410110] : [class_Int_Onumber__ring(_1410108), class_Rings_Olinordered__idom(_1410108), 33560 ^ _777959 : [(33567 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410110), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410108), hAPP(c_Int_Onumber__class_Onumber__of(_1410108), _1410110)), c_Groups_Ozero__class_Ozero(_1410108))))], (33561 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410108), hAPP(c_Int_Onumber__class_Onumber__of(_1410108), _1410110)), c_Groups_Ozero__class_Ozero(_1410108))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410110), c_Int_OPls)))]]], (50144 ^ _777959) ^ [_1794349] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1794349)), c_Int_OMin))], (28382 ^ _777959) ^ [_1313133, _1313135] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1313133, _1313135))))], (29729 ^ _777959) ^ [_1338952, _1338954, _1338956] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1338952, tc_HOL_Obool)), _1338954), hAPP(c_Set_OPow(_1338952), _1338956))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1338952, tc_HOL_Obool)), _1338954), _1338956)))], (11766 ^ _777959) ^ [_990409, _990411, _990413, _990415, _990417] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990409, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990411, tc_fun(_990409, tc_HOL_Obool)), _990413), _990415)), _990417) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990411, tc_fun(_990409, tc_HOL_Obool)), _990413), hAPP(hAPP(c_COMBC(_990411, tc_fun(_990409, tc_HOL_Obool), tc_fun(_990409, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_990409, tc_HOL_Obool), tc_fun(tc_fun(_990409, tc_HOL_Obool), tc_fun(_990409, tc_HOL_Obool)), _990411), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990409, tc_HOL_Obool))), _990415)), _990417)))], (47185 ^ _777959) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (34395 ^ _777959) ^ [_1425464, _1425466] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1425464), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1425466))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1425464), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425466))), 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))))], (42680 ^ _777959) ^ [_1623276, _1623278, _1623280, _1623282, _1623284] : [hAPP(hAPP(c_List_Olist_OCons(_1623276), _1623278), _1623280) = hAPP(hAPP(c_List_Oappend(_1623276), _1623282), _1623284), 42685 ^ _777959 : [(42688 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1623276), _1623278), _1623280) = _1623284)], (42686 ^ _777959) ^ [] : [-(_1623282 = c_List_Olist_ONil(_1623276))]], 42690 ^ _777959 : [(42693 ^ _777959) ^ [] : [-(_1623280 = hAPP(hAPP(c_List_Oappend(_1623276), 42689 ^ [_1623276, _1623278, _1623280, _1623282, _1623284]), _1623284))], (42691 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1623276), _1623278), 42689 ^ [_1623276, _1623278, _1623280, _1623282, _1623284]) = _1623282)]]], (17087 ^ _777959) ^ [_1104753, _1104755] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1104753)), hAPP(c_Nat_OSuc, _1104755)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1104753), _1104755)))], (48059 ^ _777959) ^ [_1745622, _1745624, _1745626, _1745628, _1745630, _1745632, _1745634, _1745636, _1745638] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1745622, _1745624, _1745626, _1745628), hAPP(hAPP(c_Product__Type_Oscomp(_1745622, _1745630, _1745632, tc_prod(_1745624, _1745626)), _1745634), _1745636)), _1745638) = hAPP(hAPP(c_Product__Type_Oscomp(_1745622, _1745630, _1745632, _1745628), _1745634), hAPP(hAPP(c_COMBC(_1745630, tc_fun(_1745624, tc_fun(_1745626, _1745628)), tc_fun(_1745632, _1745628)), hAPP(hAPP(c_COMBB(tc_fun(_1745632, tc_prod(_1745624, _1745626)), tc_fun(tc_fun(_1745624, tc_fun(_1745626, _1745628)), tc_fun(_1745632, _1745628)), _1745630), c_Product__Type_Oscomp(_1745632, _1745624, _1745626, _1745628)), _1745636)), _1745638)))], (14976 ^ _777959) ^ [_1062703, _1062705, _1062707, _1062709, _1062711, _1062713] : [-(c_Map_Omap__comp(_1062703, _1062705, _1062707, _1062709, _1062711, _1062713) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1062705), _1062703, c_Option_Ooption_ONone(_1062705), _1062709), hAPP(_1062711, _1062713)))], (35463 ^ _777959) ^ [_1449571, _1449573, _1449575, _1449577, _1449579, _1449581] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449571, tc_fun(_1449573, tc_fun(_1449575, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1449571, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1449573, _1449575), tc_HOL_Obool), tc_fun(_1449573, tc_fun(_1449575, tc_HOL_Obool)), _1449571), hAPP(c_COMBC(_1449573, tc_fun(tc_prod(_1449573, _1449575), tc_HOL_Obool), tc_fun(_1449575, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449575, tc_fun(tc_fun(tc_prod(_1449573, _1449575), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1449573, _1449575), tc_HOL_Obool), tc_fun(_1449575, tc_HOL_Obool)), _1449573), c_COMBC(_1449575, tc_fun(tc_prod(_1449573, _1449575), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449575, tc_prod(_1449573, _1449575)), tc_fun(_1449575, tc_fun(tc_fun(tc_prod(_1449573, _1449575), tc_HOL_Obool), tc_HOL_Obool)), _1449573), hAPP(c_COMBB(tc_prod(_1449573, _1449575), tc_fun(tc_fun(tc_prod(_1449573, _1449575), tc_HOL_Obool), tc_HOL_Obool), _1449575), c_member(tc_prod(_1449573, _1449575)))), c_Product__Type_OPair(_1449573, _1449575))))), _1449577)), _1449579), _1449581)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1449573, _1449575)), hAPP(hAPP(c_Product__Type_OPair(_1449573, _1449575), _1449579), _1449581)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1449571, tc_fun(tc_prod(_1449573, _1449575), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1449571, tc_HOL_Obool))), _1449577))))], (13759 ^ _777959) ^ [_1032468, _1032470, _1032472, _1032474, _1032476] : [-(_1032468 = c_Orderings_Obot__class_Obot(tc_fun(_1032470, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1032470, tc_fun(_1032472, tc_HOL_Obool)), _1032468), hAPP(hAPP(c_COMBB(tc_fun(_1032472, tc_HOL_Obool), tc_fun(_1032472, tc_HOL_Obool), _1032470), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1032472, tc_HOL_Obool)), _1032474)), _1032476)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1032472, tc_HOL_Obool)), _1032474), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1032470, tc_fun(_1032472, tc_HOL_Obool)), _1032468), _1032476)))], (15404 ^ _777959) ^ [_1070904, _1070906, _1070908] : [class_Rings_Oring(_1070904), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070904), hAPP(c_Groups_Ouminus__class_Ouminus(_1070904), _1070906)), _1070908) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1070904), _1070906), hAPP(c_Groups_Ouminus__class_Ouminus(_1070904), _1070908)))], (32591 ^ _777959) ^ [_1393383, _1393385, _1393387, _1393389] : [class_Int_Onumber__ring(_1393383), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1393383), hAPP(c_Int_Onumber__class_Onumber__of(_1393383), _1393385)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1393383), _1393387), hAPP(c_Int_Onumber__class_Onumber__of(_1393383), _1393389))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1393383), hAPP(c_Int_Onumber__class_Onumber__of(_1393383), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393385), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1393389)))), _1393387))], (14207 ^ _777959) ^ [_1042300, _1042302, _1042304, _1042306, _1042308] : [-(_1042300 = c_Orderings_Obot__class_Obot(tc_fun(_1042302, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042304, tc_HOL_Obool)), _1042306), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1042302, tc_fun(_1042304, tc_HOL_Obool)), _1042300), _1042308)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1042302, tc_fun(_1042304, tc_HOL_Obool)), _1042300), hAPP(hAPP(c_COMBB(tc_fun(_1042304, tc_HOL_Obool), tc_fun(_1042304, tc_HOL_Obool), _1042302), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1042304, tc_HOL_Obool)), _1042306)), _1042308)))], (45504 ^ _777959) ^ [_1685149, _1685151] : [class_Orderings_Olinorder(_1685149), 45511 ^ _777959 : [(45516 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1685149), hAPP(hAPP(c_List_Onth(_1685149), _1685151), 45509 ^ [_1685149, _1685151])), hAPP(hAPP(c_List_Onth(_1685149), _1685151), 45510 ^ [_1685149, _1685151])))], (45514 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 45510 ^ [_1685149, _1685151]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685149)), _1685151))))], (45512 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 45509 ^ [_1685149, _1685151]), 45510 ^ [_1685149, _1685151])))]], -(c_List_Olinorder__class_Osorted(_1685149, _1685151))], (7896 ^ _777959) ^ [_912302, _912304, _912306, _912308] : [hBOOL(hAPP(hAPP(c_member(_912302), _912304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_912302, tc_HOL_Obool)), _912306), _912308))), hBOOL(hAPP(hAPP(c_member(_912302), _912304), _912308))], (19402 ^ _777959) ^ [_1149824, _1149826] : [class_Groups_Olinordered__ab__group__add(_1149824), 19405 ^ _777959 : [(19412 ^ _777959) ^ [] : [_1149826 = c_Groups_Ozero__class_Ozero(_1149824), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1149824), _1149826) = _1149826)], (19406 ^ _777959) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1149824), _1149826) = _1149826, -(_1149826 = c_Groups_Ozero__class_Ozero(_1149824))]]], (48783 ^ _777959) ^ [] : [-(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))))], (16907 ^ _777959) ^ [_1101532, _1101534, _1101536] : [class_Orderings_Olinorder(_1101532), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101532), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1101532), _1101534), _1101536)), _1101534)))], (33259 ^ _777959) ^ [_1405557, _1405559] : [class_Int_Onumber__ring(_1405557), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1405557), _1405559), hAPP(c_Int_Onumber__class_Onumber__of(_1405557), c_Int_OPls)) = _1405559)], (3888 ^ _777959) ^ [_836828, _836830, _836832, _836834, _836836, _836838, _836840, _836842] : [-(c_Random_Oiterate(_836842, _836838, _836834, _836830) = c_Random_Oiterate(_836840, _836836, _836832, _836828)), _836842 = _836840, _836838 = _836836, _836834 = _836832, _836830 = _836828], (12466 ^ _777959) ^ [_1004456, _1004458] : [class_Complete__Lattice_Ocomplete__lattice(_1004456), hBOOL(hAPP(c_Finite__Set_Ofinite(_1004456), _1004458)), -(c_Complete__Lattice_OSup__class_OSup(_1004456, _1004458) = hAPP(hAPP(c_Finite__Set_Ofold(_1004456, _1004456, c_Lattices_Osemilattice__sup__class_Osup(_1004456)), c_Orderings_Obot__class_Obot(_1004456)), _1004458))], (20927 ^ _777959) ^ [_1175961, _1175963] : [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), _1175961), _1175963))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1175963)))], (23174 ^ _777959) ^ [_1219639, _1219641] : [class_Int_Oring__char__0(_1219639), hBOOL(hAPP(hAPP(c_member(_1219639), _1219641), c_Int_Oring__1__class_OInts(_1219639))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219639), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1219639), c_Groups_Oone__class_Oone(_1219639)), _1219641)), _1219641) = c_Groups_Ozero__class_Ozero(_1219639)], (50998 ^ _777959) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (42377 ^ _777959) ^ [_1614725, _1614727, _1614729] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1614725), _1614727)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1614725, _1614725), tc_HOL_Obool)), _1614729), hAPP(hAPP(c_Product__Type_OSigma(_1614725, _1614725), _1614727), hAPP(c_COMBK(tc_fun(_1614725, tc_HOL_Obool), _1614725), _1614727)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1614725, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1614725), _1614727), _1614729))))], (13651 ^ _777959) ^ [_1029272, _1029274, _1029276, _1029278, _1029280, _1029282] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029272, tc_fun(_1029274, tc_HOL_Obool)), _1029276), hAPP(hAPP(c_COMBB(_1029278, tc_fun(_1029274, tc_HOL_Obool), _1029272), _1029280), _1029282)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029278, tc_fun(_1029274, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1029272, _1029278, _1029282), _1029276)), _1029280))], (34819 ^ _777959) ^ [_1433167] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1433167, 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, _1433167, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (47469 ^ _777959) ^ [_1731831, _1731833, _1731835] : [c_Wellfounded_OwfP(_1731831, _1731833), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1731831, _1731833), _1731835)))], (44983 ^ _777959) ^ [_1672903, _1672905, _1672907] : [-(hAPP(c_List_Orev(_1672903), hAPP(hAPP(c_List_Odrop(_1672903), _1672905), _1672907)) = hAPP(hAPP(c_List_Otake(_1672903), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672903)), _1672907)), _1672905)), hAPP(c_List_Orev(_1672903), _1672907)))], (50846 ^ _777959) ^ [_1808583, _1808585] : [-(class_HOL_Oequal(tc_fun(_1808583, _1808585))), class_Enum_Oenum(_1808583), class_HOL_Oequal(_1808585)], (25417 ^ _777959) ^ [_1259754, _1259756, _1259758, _1259760] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1259754, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25418 ^ [_1259754, _1259756, _1259758, _1259760])), _1259756) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1259754, 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), 25418 ^ [_1259754, _1259756, _1259758, _1259760]), _1259758))), _1259760), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1259754, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1259756) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1259754, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1259760))], (5877 ^ _777959) ^ [_871354] : [c_Hoare__Mirabelle_Ostate__not__singleton, c_Com_OWT__bodies, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), _871354), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), hAPP(hAPP(c_COMBB(tc_Com_Ocom, tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_Com_Opname), c_Hoare__Mirabelle_OMGT), c_Com_Ocom_OBODY)), c_Map_Odom(tc_Com_Opname, tc_Com_Ocom, c_Com_Obody)), _871354))], (17365 ^ _777959) ^ [_1110029, _1110031, _1110033] : [class_Orderings_Olinorder(_1110029), hBOOL(hAPP(c_Finite__Set_Ofinite(_1110029), _1110031)), -(_1110031 = c_Orderings_Obot__class_Obot(tc_fun(_1110029, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1110029, hAPP(hAPP(c_Set_Oinsert(_1110029), _1110033), _1110031)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1110029), _1110033), c_Big__Operators_Olinorder__class_OMax(_1110029, _1110031)))], (21614 ^ _777959) ^ [_1188625, _1188627] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1188625)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1188625), hAPP(c_Nat_OSuc, _1188627))), _1188625)))], (51138 ^ _777959) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (40337 ^ _777959) ^ [_1560725, _1560727] : [-(hAPP(c_List_Oset(_1560725), _1560727) = hAPP(c_Set_OCollect(_1560725), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1560725), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1560725, 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)), _1560725), 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)), _1560725), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1560725, tc_fun(tc_Nat_Onat, _1560725), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1560725, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1560725), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1560725), c_COMBB(_1560725, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1560725), _1560727))))), 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(_1560725)), _1560727))))))], (12610 ^ _777959) ^ [_1006921, _1006923, _1006925] : [class_Groups_Ogroup__add(_1006921), 12613 ^ _777959 : [(12620 ^ _777959) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1006921), _1006925) = _1006923, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1006921), _1006923) = _1006925)], (12614 ^ _777959) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1006921), _1006923) = _1006925, -(hAPP(c_Groups_Ouminus__class_Ouminus(_1006921), _1006925) = _1006923)]]], (14525 ^ _777959) ^ [_1050791, _1050793, _1050795, _1050797, _1050799, _1050801, _1050803] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1050791, tc_fun(_1050793, tc_fun(_1050795, tc_HOL_Obool))), _1050797), _1050799), _1050801), _1050803)), 14528 ^ _777959 : [(14529 ^ _777959) ^ [_1050919] : [hBOOL(hAPP(hAPP(c_member(_1050791), _1050919), _1050797)), -(hBOOL(hAPP(hAPP(hAPP(_1050799, _1050919), _1050801), _1050803)))]]], (24712 ^ _777959) ^ [_1246767, _1246769, _1246771] : [class_Divides_Osemiring__div(_1246767), -(_1246769 = c_Groups_Ozero__class_Ozero(_1246767)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1246767), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1246767), _1246769), _1246771)), _1246769) = _1246771)], (28313 ^ _777959) ^ [_1311655, _1311657] : [c_Nat__Transfer_Onat__set(_1311655), c_Nat__Transfer_Onat__set(_1311657), 28320 ^ _777959 : [(28327 ^ _777959) ^ [] : [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), _1311655)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311657))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1311655), _1311657)))], (28321 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint, tc_HOL_Obool)), _1311655), _1311657)), -(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), _1311655)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1311657))))]]], (48713 ^ _777959) ^ [_1760243] : [-(c_Transitive__Closure_Ortrancl(_1760243, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1760243, _1760243), tc_HOL_Obool))) = c_Relation_OId(_1760243))], (50236 ^ _777959) ^ [_1796204] : [-(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1796204), _1796204)))], (24814 ^ _777959) ^ [_1248317, _1248319, _1248321, _1248323] : [class_Groups_Ocomm__monoid__add(_1248317), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1248317), _1248319), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1248321)), hAPP(c_Nat_OSuc, _1248323))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1248317), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1248317, tc_Nat_Onat), _1248319), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1248321), _1248323)))], (18984 ^ _777959) ^ [_1142485, _1142487, _1142489] : [-(hAPP(c_Option_Omap(_1142485, _1142487), _1142489) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(_1142487), _1142485, c_Option_Ooption_ONone(_1142487), hAPP(hAPP(c_COMBB(_1142487, tc_Option_Ooption(_1142487), _1142485), c_Option_Ooption_OSome(_1142487)), _1142489)))], (16667 ^ _777959) ^ [_1097399, _1097401, _1097403] : [class_Orderings_Olinorder(_1097399), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1097399), _1097401), _1097403)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1097399), _1097401), _1097403) = _1097403)], (45766 ^ _777959) ^ [_1691320, _1691322] : [class_Orderings_Olinorder(_1691320), -(c_List_Olinorder__class_Osorted__list__of__set(_1691320, hAPP(c_List_Oset(_1691320), _1691322)) = c_List_Olinorder__class_Osort__key(_1691320, _1691320, c_COMBI(_1691320), c_List_Oremdups(_1691320, _1691322)))], (7756 ^ _777959) ^ [_909567, _909569] : [-(c_HOL_OThe(_909567, hAPP(c_fequal, _909569)) = _909569)], (35281 ^ _777959) ^ [_1441113] : [-(c_Int_Oint__ge__less__than(_1441113) = 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), _1441113)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (10344 ^ _777959) ^ [_960225, _960227, _960229, _960231, _960233] : [c_Finite__Set_Ofolding__one__idem(_960225, _960227, _960229), hBOOL(hAPP(c_Finite__Set_Ofinite(_960225), _960231)), -(hAPP(_960229, hAPP(hAPP(c_Set_Oinsert(_960225), _960233), _960231)) = hAPP(hAPP(c_Finite__Set_Ofold(_960225, _960225, _960227), _960233), _960231))], (50414 ^ _777959) ^ [_1800485, _1800487, _1800489, _1800491] : [-(c_Predicate_Oconversep(_1800485, _1800487, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1800485, tc_fun(_1800487, tc_HOL_Obool))), _1800489), _1800491)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1800487, tc_fun(_1800485, tc_HOL_Obool))), c_Predicate_Oconversep(_1800485, _1800487, _1800489)), c_Predicate_Oconversep(_1800485, _1800487, _1800491)))], (44883 ^ _777959) ^ [_1670686, _1670688] : [class_Groups_Ocomm__monoid__add(_1670686), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1670686), hAPP(c_List_Orev(_1670686), _1670688)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1670686), _1670688))], (27225 ^ _777959) ^ [_1293545, _1293547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293545)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293547)), 27232 ^ _777959 : [(27239 ^ _777959) ^ [] : [_1293545 = _1293547, -(hAPP(c_Int_Onat, _1293545) = hAPP(c_Int_Onat, _1293547))], (27233 ^ _777959) ^ [] : [hAPP(c_Int_Onat, _1293545) = hAPP(c_Int_Onat, _1293547), -(_1293545 = _1293547)]]], (50932 ^ _777959) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (16057 ^ _777959) ^ [_1083850, _1083852, _1083854, _1083856, _1083858, _1083860] : [-(c_Map_Omap__comp(_1083850, _1083852, _1083854, _1083856, _1083858, _1083860) = c_Option_Ooption_ONone(_1083852)), 16058 ^ _777959 : [(16061 ^ _777959) ^ [_1083962] : [hAPP(_1083858, _1083860) = hAPP(c_Option_Ooption_OSome(_1083850), _1083962), hAPP(_1083856, _1083962) = c_Option_Ooption_ONone(_1083852)], (16059 ^ _777959) ^ [] : [hAPP(_1083858, _1083860) = c_Option_Ooption_ONone(_1083850)]]], (7448 ^ _777959) ^ [_902907, _902909, _902911] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_902907, tc_HOL_Obool)), _902909), _902911)), hBOOL(hAPP(c_Finite__Set_Ofinite(_902907), _902911)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_902907), _902909)))], (39536 ^ _777959) ^ [_1541439, _1541441, _1541443, _1541445, _1541447] : [hBOOL(hAPP(c_List_Odistinct(_1541439), hAPP(hAPP(c_List_Omap(tc_prod(_1541439, _1541441), _1541439), c_Product__Type_Ofst(_1541439, _1541441)), _1541443))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1541439, _1541441)), hAPP(hAPP(c_Product__Type_OPair(_1541439, _1541441), _1541445), _1541447)), hAPP(c_List_Oset(tc_prod(_1541439, _1541441)), _1541443))), -(hAPP(hAPP(c_Map_Omap__of(_1541439, _1541441), _1541443), _1541445) = hAPP(c_Option_Ooption_OSome(_1541441), _1541447))], (48182 ^ _777959) ^ [_1747978, _1747980] : [-(c_Random_Opick(_1747978, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1747978), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1747978, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1747978, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1747978)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1747980)) = c_Random_Opick(_1747978, _1747980))], (35161 ^ _777959) ^ [_1439310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1439310), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1439310)), c_Int_OMin)))], (48246 ^ _777959) ^ [_1749150, _1749152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1749150)), hAPP(c_Code__Numeral_Oof__nat, _1749152))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1749150), _1749152)))], (6691 ^ _777959) ^ [_886668, _886670] : [-(hBOOL(hAPP(hAPP(c_member(_886668), 6692 ^ [_886668, _886670]), _886670))), -(_886670 = c_Orderings_Obot__class_Obot(tc_fun(_886668, tc_HOL_Obool)))], (36548 ^ _777959) ^ [_1471219, _1471221, _1471223] : [-(hAPP(c_Product__Type_Osnd(_1471219, _1471221), _1471223) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1471219, _1471221, _1471221), hAPP(c_COMBK(tc_fun(_1471221, _1471221), _1471219), c_COMBI(_1471221))), _1471223))], (48978 ^ _777959) ^ [_1767354, _1767356] : [c_Wellfounded_Oacyclic(_1767354, hAPP(c_Relation_Oconverse(_1767354, _1767354), _1767356)), -(c_Wellfounded_Oacyclic(_1767354, _1767356))], (40755 ^ _777959) ^ [_1569897, _1569899, _1569901, _1569903] : [-(c_Hilbert__Choice_OEps(tc_prod(_1569897, _1569899), hAPP(c_Product__Type_Oprod_Oprod__case(_1569897, _1569899, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1569897, tc_fun(_1569899, tc_HOL_Obool), tc_fun(_1569899, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1569899, tc_HOL_Obool), tc_fun(_1569899, tc_HOL_Obool)), _1569897), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1569899)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1569897), c_fconj), hAPP(c_fequal, _1569901)))), hAPP(c_fequal, _1569903)))) = hAPP(hAPP(c_Product__Type_OPair(_1569897, _1569899), _1569901), _1569903))], (37000 ^ _777959) ^ [_1481774, _1481776, _1481778, _1481780] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1481774), _1481776)), 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)), _1481774), _1481778)), 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)), _1481776), _1481780)), 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)), _1481776), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1481778), _1481780))), c_FunDef_Omin__strict)))], (36019 ^ _777959) ^ [_1461180, _1461182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461180)), 36022 ^ _777959 : [(36029 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1461182), _1461180))), -(c_Divides_OposDivAlg(_1461182, _1461180) = hAPP(c_Divides_Oadjust(_1461180), c_Divides_OposDivAlg(_1461182, 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)))), _1461180))))], (36023 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1461182), _1461180)), -(c_Divides_OposDivAlg(_1461182, _1461180) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461182))]]], (38997 ^ _777959) ^ [_1528653, _1528655, _1528657, _1528659, _1528661, _1528663, _1528665] : [-(hAPP(c_Fun_Ocomp(_1528653, _1528655, _1528657, _1528659), hAPP(c_Fun_Ocomp(_1528661, _1528653, _1528657, _1528663), _1528665)) = hAPP(c_Fun_Ocomp(_1528661, _1528655, _1528657, hAPP(c_Fun_Ocomp(_1528653, _1528655, _1528661, _1528659), _1528663)), _1528665))], (42527 ^ _777959) ^ [_1619453] : [-(hAPP(c_Option_Omap(_1619453, _1619453), c_Fun_Oid(_1619453)) = c_Fun_Oid(tc_Option_Ooption(_1619453)))], (20065 ^ _777959) ^ [_1161036, _1161038, _1161040] : [class_Rings_Oordered__cancel__semiring(_1161036), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161036), c_Groups_Ozero__class_Ozero(_1161036)), _1161038)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161036), c_Groups_Ozero__class_Ozero(_1161036)), _1161040)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161036), c_Groups_Ozero__class_Ozero(_1161036)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161036), _1161038), _1161040))))], (49146 ^ _777959) ^ [_1771225, _1771227, _1771229, _1771231, _1771233] : [c_Relation_Osingle__valued(_1771225, _1771227, _1771229), c_Relation_Osingle__valued(_1771227, _1771231, _1771233), -(c_Relation_Osingle__valued(_1771225, _1771231, hAPP(hAPP(c_Relation_Orel__comp(_1771225, _1771227, _1771231), _1771229), _1771233)))], (47130 ^ _777959) ^ [_1723070, _1723072, _1723074, _1723076] : [c_Wellfounded_Owf(_1723070, _1723072), c_Fun_Oinj__on(_1723070, _1723074, _1723076, c_Orderings_Otop__class_Otop(tc_fun(_1723070, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1723074, hAPP(c_Set_Oimage(tc_prod(_1723070, _1723070), tc_prod(_1723074, _1723074), c_Product__Type_Omap__pair(_1723070, _1723074, _1723070, _1723074, _1723076, _1723076)), _1723072)))], (36716 ^ _777959) ^ [_1474601] : [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), _1474601))), -(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), _1474601)) = 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), _1474601))))], (15016 ^ _777959) ^ [_1063558, _1063560, _1063562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1063560), _1063562)), -(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, _1063558)), _1063560)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1063558)), _1063562))))], (5737 ^ _777959) ^ [_868580, _868582, _868584, _868586] : [_868580 = c_Orderings_Obot__class_Obot(tc_fun(_868582, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_868582, _868584, hAPP(c_COMBK(_868584, _868582), _868586)), _868580) = c_Orderings_Obot__class_Obot(tc_fun(_868584, tc_HOL_Obool)))], (38062 ^ _777959) ^ [_1507100, _1507102, _1507104, _1507106] : [c_Fun_Oinj__on(_1507100, _1507102, _1507104, _1507106), -(hAPP(c_Finite__Set_Ocard(_1507102), hAPP(c_Set_Oimage(_1507100, _1507102, _1507104), _1507106)) = hAPP(c_Finite__Set_Ocard(_1507100), _1507106))], (48049 ^ _777959) ^ [_1745328, _1745330, _1745332, _1745334, _1745336, _1745338, _1745340] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1745328, _1745330, _1745332, _1745334), _1745336), _1745338), _1745340) = hAPP(hAPP(_1745338, hAPP(c_Product__Type_Ofst(_1745330, _1745332), hAPP(_1745336, _1745340))), hAPP(c_Product__Type_Osnd(_1745330, _1745332), hAPP(_1745336, _1745340))))], (49742 ^ _777959) ^ [_1786765, _1786767, _1786769, _1786771] : [class_Rings_Olinordered__semidom(_1786765), 49748 ^ _777959 : [(49751 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1786765), c_Groups_Ozero__class_Ozero(_1786765)), hAPP(_1786771, 49747 ^ [_1786765, _1786767, _1786769, _1786771])))], (49749 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786767), 49747 ^ [_1786765, _1786767, _1786769, _1786771]), _1786769)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1786765), c_Groups_Ozero__class_Ozero(_1786765)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1786767, _1786765), _1786771), _1786769))))], (16207 ^ _777959) ^ [_1087330, _1087332, _1087334, _1087336, _1087338] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1087330), _1087332)), -(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), _1087330), _1087334)), _1087336)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1087332), _1087334)), _1087338)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1087336), 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), _1087332), _1087330)), _1087334)), _1087338)))], (27086 ^ _777959) ^ [_1290854, _1290856, _1290858, _1290860, _1290862] : [class_Fields_Ofield(_1290854), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290856), _1290858)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1290856), _1290860)), 27100 ^ _777959 : [(27103 ^ _777959) ^ [] : [-(hAPP(_1290862, 27099 ^ [_1290854, _1290856, _1290858, _1290860, _1290862]) = c_Groups_Ozero__class_Ozero(_1290854))], (27101 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1290856), 27099 ^ [_1290854, _1290856, _1290858, _1290860, _1290862]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290856, tc_HOL_Obool)), _1290858), _1290860))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1290856, _1290854), _1290862), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1290856, tc_HOL_Obool)), _1290858), _1290860)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1290854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1290854), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1290856, _1290854), _1290862), _1290858)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1290856, _1290854), _1290862), _1290860))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1290856, _1290854), _1290862), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1290856, tc_HOL_Obool)), _1290858), _1290860))))], (39792 ^ _777959) ^ [_1547173, _1547175, _1547177, _1547179] : [-(c_List_Oremove1(_1547173, _1547175, c_List_Oremove1(_1547173, _1547177, _1547179)) = c_List_Oremove1(_1547173, _1547177, c_List_Oremove1(_1547173, _1547175, _1547179)))], (29140 ^ _777959) ^ [_1327213, _1327215, _1327217] : [class_Orderings_Oorder(_1327213), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1327213, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1327213), _1327215)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1327213, _1327215, _1327217)) = c_Orderings_Obot__class_Obot(tc_fun(_1327213, tc_HOL_Obool)))], (43219 ^ _777959) ^ [_1636022, _1636024, _1636026, _1636028] : [-(hAPP(c_List_Orotate1(_1636022), c_List_Olist_ONil(_1636022)) = c_List_Olist_ONil(_1636022))], (3750 ^ _777959) ^ [_834669, _834671, _834673, _834675] : [-(c_Nitpick_Onorm__frac(_834675, _834671) = c_Nitpick_Onorm__frac(_834673, _834669)), _834675 = _834673, _834671 = _834669], (33023 ^ _777959) ^ [_1401649, _1401651] : [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), _1401649))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1401651), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1401649))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1401651), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1401649))), 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), _1401651))), c_COMBI(tc_Int_Oint))))], (39651 ^ _777959) ^ [_1544263, _1544265] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1544263, _1544265) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1544263, _1544265)))], (10440 ^ _777959) ^ [_962401, _962403, _962405, _962407, _962409, _962411, _962413, _962415] : [c_Finite__Set_Ofolding__image__simple(_962401, _962403, _962405, _962407, _962409, _962411), hBOOL(hAPP(c_Finite__Set_Ofinite(_962403), _962413)), hBOOL(hAPP(c_Finite__Set_Ofinite(_962403), _962415)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962403, tc_HOL_Obool)), _962413), _962415) = c_Orderings_Obot__class_Obot(tc_fun(_962403, tc_HOL_Obool)), -(hAPP(_962411, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_962403, tc_HOL_Obool)), _962413), _962415)) = hAPP(hAPP(_962405, hAPP(_962411, _962413)), hAPP(_962411, _962415)))], (22629 ^ _777959) ^ [_1209724, _1209726, _1209728] : [class_Nat_Osemiring__char__0(_1209724), 22632 ^ _777959 : [(22639 ^ _777959) ^ [] : [_1209726 = _1209728, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209724), _1209726) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209724), _1209728))], (22633 ^ _777959) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209724), _1209726) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1209724), _1209728), -(_1209726 = _1209728)]]], (34783 ^ _777959) ^ [_1432404, _1432406, _1432408] : [class_Rings_Ocomm__semiring__1(_1432404), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1432404), _1432406), 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)))), _1432408))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432404), _1432406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1432404), hAPP(hAPP(c_Power_Opower__class_Opower(_1432404), _1432406), _1432408)), hAPP(hAPP(c_Power_Opower__class_Opower(_1432404), _1432406), _1432408))))], (11198 ^ _777959) ^ [_977301, _977303, _977305, _977307, _977309] : [class_Groups_Ocomm__monoid__add(_977301), hBOOL(hAPP(c_Finite__Set_Ofinite(_977303), _977305)), -(hBOOL(hAPP(hAPP(c_member(_977303), _977307), _977305))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977303, _977301), _977309), hAPP(hAPP(c_Set_Oinsert(_977303), _977307), _977305)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977301), hAPP(_977309, _977307)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977303, _977301), _977309), _977305)))], (24752 ^ _777959) ^ [_1247333, _1247335] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1247333), _1247335)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1247335), _1247333))], (41144 ^ _777959) ^ [_1583005, _1583007] : [-(hAPP(c_List_Olexn(_1583005, _1583007), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1583005), tc_List_Olist(_1583005)), tc_HOL_Obool)))], (11258 ^ _777959) ^ [_978434, _978436, _978438, _978440, _978442, _978444, _978446] : [c_Big__Operators_Ocomm__monoid__big(_978434, _978436, _978438, _978440, _978442), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_978436), _978444))), -(hAPP(hAPP(_978442, _978446), _978444) = _978440)], (31196 ^ _777959) ^ [_1367335, _1367337] : [class_Groups_Oordered__ab__group__add__abs(_1367335), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1367335), hAPP(c_Groups_Ouminus__class_Ouminus(_1367335), _1367337)), hAPP(c_Groups_Oabs__class_Oabs(_1367335), _1367337))))], (43813 ^ _777959) ^ [_1649292, _1649294, _1649296, _1649298] : [-(_1649292 = c_List_Olist_ONil(_1649294)), -(c_List_Olast(_1649296, hAPP(hAPP(c_List_Omap(_1649294, _1649296), _1649298), _1649292)) = hAPP(_1649298, c_List_Olast(_1649294, _1649292)))], (39616 ^ _777959) ^ [_1543266, _1543268, _1543270, _1543272, _1543274, _1543276] : [class_Groups_Ocomm__monoid__add(_1543266), hBOOL(hAPP(c_Finite__Set_Ofinite(_1543268), _1543270)), 39626 ^ _777959 : [(39627 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543268), 39625 ^ [_1543266, _1543268, _1543270, _1543272, _1543274, _1543276]), _1543270)))], (39632 ^ _777959) ^ [] : [39625 ^ [_1543266, _1543268, _1543270, _1543272, _1543274, _1543276] = 39628 ^ [_1543266, _1543268, _1543270, _1543272, _1543274, _1543276]], (39636 ^ _777959) ^ [] : [hAPP(_1543274, hAPP(_1543272, 39625 ^ [_1543266, _1543268, _1543270, _1543272, _1543274, _1543276])) = c_Groups_Ozero__class_Ozero(_1543266)], (39634 ^ _777959) ^ [] : [-(hAPP(_1543272, 39625 ^ [_1543266, _1543268, _1543270, _1543272, _1543274, _1543276]) = hAPP(_1543272, 39628 ^ [_1543266, _1543268, _1543270, _1543272, _1543274, _1543276]))], (39630 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1543268), 39628 ^ [_1543266, _1543268, _1543270, _1543272, _1543274, _1543276]), _1543270)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543276, _1543266), _1543274), hAPP(c_Set_Oimage(_1543268, _1543276, _1543272), _1543270)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1543268, _1543266), hAPP(c_Fun_Ocomp(_1543276, _1543266, _1543268, _1543274), _1543272)), _1543270))], (6749 ^ _777959) ^ [_887613, _887615, _887617, _887619] : [6750 ^ _777959 : [(6753 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_887613), _887615), _887619))], (6751 ^ _777959) ^ [] : [_887615 = _887617]], -(hBOOL(hAPP(hAPP(c_member(_887613), _887615), hAPP(hAPP(c_Set_Oinsert(_887613), _887617), _887619))))], (43252 ^ _777959) ^ [_1636802, _1636804, _1636806, _1636808] : [hBOOL(hAPP(hAPP(c_member(_1636802), _1636804), hAPP(c_List_Oset(_1636802), hAPP(hAPP(c_List_Odrop(_1636802), _1636806), _1636808)))), -(hBOOL(hAPP(hAPP(c_member(_1636802), _1636804), hAPP(c_List_Oset(_1636802), _1636808))))], (22950 ^ _777959) ^ [_1215623] : [class_Rings_Osemiring__1(_1215623), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1215623), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1215623))], (39017 ^ _777959) ^ [_1529192, _1529194, _1529196, _1529198, _1529200, _1529202] : [-(hAPP(hAPP(c_Fun_Ocomp(_1529192, _1529194, _1529196, hAPP(c_COMBK(_1529194, _1529192), _1529198)), _1529200), _1529202) = _1529198)], (51044 ^ _777959) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (35659 ^ _777959) ^ [_1453878, _1453880, _1453882, _1453884, _1453886, _1453888] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1453878, tc_fun(_1453880, tc_HOL_Obool))), _1453882), _1453884), _1453886), _1453888)), -(hBOOL(hAPP(hAPP(_1453882, _1453886), _1453888))), -(hBOOL(hAPP(hAPP(_1453884, _1453886), _1453888)))], (48018 ^ _777959) ^ [_1744653, _1744655, _1744657, _1744659] : [48019 ^ _777959 : [(48022 ^ _777959) ^ [] : [c_List_Olist__ex(_1744653, _1744655, _1744659)], (48020 ^ _777959) ^ [] : [c_List_Olist__ex(_1744653, _1744655, _1744657)]], -(c_List_Olist__ex(_1744653, _1744655, hAPP(hAPP(c_List_Oappend(_1744653), _1744657), _1744659)))], (46972 ^ _777959) ^ [_1719825, _1719827] : [c_Wellfounded_Owf(_1719825, _1719827), -(c_Wellfounded_Owf(tc_fun(_1719825, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1719825, _1719827)))], (50952 ^ _777959) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (12369 ^ _777959) ^ [_1002585, _1002587, _1002589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1002585), _1002587)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1002589), _1002587)), _1002585) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1002589), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1002587), _1002585)))], (21770 ^ _777959) ^ [_1191443, _1191445, _1191447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1191443), _1191445)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1191443), _1191447))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1191443)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1191445), _1191447)))], (13642 ^ _777959) ^ [_1029009, _1029011, _1029013, _1029015, _1029017] : [13644 ^ _777959 : [(13647 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1029009, tc_HOL_Obool)), _1029011), hAPP(_1029017, 13643 ^ [_1029009, _1029011, _1029013, _1029015, _1029017])))], (13645 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1029013), 13643 ^ [_1029009, _1029011, _1029013, _1029015, _1029017]), _1029015)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1029009, tc_HOL_Obool)), _1029011), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1029013, tc_fun(_1029009, tc_HOL_Obool)), _1029015), _1029017))))], (1440 ^ _777959) ^ [_798683, _798685] : [-(class_Rings_Olinordered__comm__semiring__strict(_798683)), _798685 = _798683, class_Rings_Olinordered__comm__semiring__strict(_798685)], (44224 ^ _777959) ^ [_1657733, _1657735, _1657737, _1657739] : [class_Orderings_Olinorder(_1657733), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1657733), _1657735), _1657737)), c_List_Olinorder__class_Osorted(_1657733, hAPP(hAPP(c_List_Olist_OCons(_1657733), _1657737), _1657739)), -(c_List_Olinorder__class_Osorted(_1657733, hAPP(hAPP(c_List_Olist_OCons(_1657733), _1657735), hAPP(hAPP(c_List_Olist_OCons(_1657733), _1657737), _1657739))))], (10810 ^ _777959) ^ [_969904, _969906, _969908, _969910, _969912] : [class_Groups_Oordered__ab__semigroup__add(_969904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969904), _969906), _969908)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969904), _969910), _969912)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_969904), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969904), _969906), _969910)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_969904), _969908), _969912))))], (34089 ^ _777959) ^ [_1420022] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1420022)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1420022)))], (932 ^ _777959) ^ [_792175, _792177, _792179, _792181] : [-(c_FunDef_Ois__measure(_792179, _792175)), c_FunDef_Ois__measure(_792181, _792177), _792181 = _792179, _792177 = _792175], (30078 ^ _777959) ^ [_1346797, _1346799, _1346801, _1346803] : [class_Divides_Oring__div(_1346797), -(c_Divides_Odiv__class_Omod(_1346797, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346797), _1346799), _1346801), _1346803) = c_Divides_Odiv__class_Omod(_1346797, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1346797), c_Divides_Odiv__class_Omod(_1346797, _1346799, _1346803)), c_Divides_Odiv__class_Omod(_1346797, _1346801, _1346803)), _1346803))], (50242 ^ _777959) ^ [_1796329, _1796331] : [-(hAPP(c_New__DSequence_Opos__empty(_1796329), _1796331) = c_Lazy__Sequence_Oempty(_1796329))], (39312 ^ _777959) ^ [_1535895, _1535897, _1535899, _1535901, _1535903, _1535905, _1535907, _1535909] : [c_Finite__Set_Ofolding__image(_1535895, _1535897, _1535899, _1535901, _1535903), hBOOL(hAPP(c_Finite__Set_Ofinite(_1535897), _1535905)), c_Fun_Oinj__on(_1535897, _1535897, _1535907, _1535905), -(hAPP(hAPP(_1535903, _1535909), hAPP(c_Set_Oimage(_1535897, _1535897, _1535907), _1535905)) = hAPP(hAPP(_1535903, hAPP(c_Fun_Ocomp(_1535897, _1535895, _1535897, _1535909), _1535907)), _1535905))], (9658 ^ _777959) ^ [_945064, _945066, _945068, _945070, _945072] : [-(c_Map_Orestrict__map(_945064, _945066, c_Map_Orestrict__map(_945064, _945066, _945068, _945070), _945072) = c_Map_Orestrict__map(_945064, _945066, _945068, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945064, tc_HOL_Obool)), _945070), _945072)))], (8740 ^ _777959) ^ [_928760, _928762, _928764, _928766, _928768, _928770] : [-(_928760 = _928762), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928764, _928766), _928768), _928762), _928770), _928760) = hAPP(_928768, _928760))], (33853 ^ _777959) ^ [_1415475, _1415477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1415475)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415477))), -(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(_1415477))), 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), _1415475)), c_Int_Onat))))))], (33227 ^ _777959) ^ [_1405122] : [-(c_Int_Osucc(c_Int_Opred(_1405122)) = _1405122)], (12058 ^ _777959) ^ [_996681, _996683, _996685] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996681), _996683)), _996685) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996681), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996683), _996685)))], (50484 ^ _777959) ^ [_1802450, _1802452, _1802454] : [-(_1802450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1802452), c_List_Oreplicate(_1802452, _1802450, _1802454)) = c_List_Oreplicate(_1802452, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1802450), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1802454))], (30303 ^ _777959) ^ [_1350914, _1350916, _1350918] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1350914), _1350916)), _1350918) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1350914), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1350916), _1350918))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1350914), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350916, _1350918))), _1350918)))], (25138 ^ _777959) ^ [_1254131, _1254133] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1254131, 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(_1254131, tc_HOL_Obool)), tc_fun(_1254131, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1254131, tc_HOL_Obool)), tc_fun(_1254131, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1254131, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1254133)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1254131, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1254133))], (40668 ^ _777959) ^ [_1568136, _1568138, _1568140, _1568142, _1568144] : [class_Groups_Omonoid__add(_1568136), class_Groups_Oordered__ab__semigroup__add(_1568136), 40678 ^ _777959 : [(40681 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1568136), hAPP(_1568142, 40677 ^ [_1568136, _1568138, _1568140, _1568142, _1568144])), hAPP(_1568144, 40677 ^ [_1568136, _1568138, _1568140, _1568142, _1568144])))], (40679 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1568138), 40677 ^ [_1568136, _1568138, _1568140, _1568142, _1568144]), hAPP(c_List_Oset(_1568138), _1568140))))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1568136), hAPP(c_List_Omonoid__add__class_Olistsum(_1568136), hAPP(hAPP(c_List_Omap(_1568138, _1568136), _1568142), _1568140))), hAPP(c_List_Omonoid__add__class_Olistsum(_1568136), hAPP(hAPP(c_List_Omap(_1568138, _1568136), _1568144), _1568140)))))], (36598 ^ _777959) ^ [_1472113, _1472115, _1472117] : [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), _1472113), _1472115))), -(hBOOL(hAPP(hAPP(_1472117, _1472113), _1472115))), 36605 ^ _777959 : [(36608 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 36604 ^ [_1472113, _1472115, _1472117]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1472117, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 36603 ^ [_1472113, _1472115, _1472117])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 36604 ^ [_1472113, _1472115, _1472117]))))], (36614 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1472117, 36603 ^ [_1472113, _1472115, _1472117]), 36604 ^ [_1472113, _1472115, _1472117]))], (36606 ^ _777959) ^ [] : [-(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), 36603 ^ [_1472113, _1472115, _1472117]), 36604 ^ [_1472113, _1472115, _1472117]))))]]], (34291 ^ _777959) ^ [_1423550] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1423550))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1423550)))))], (5442 ^ _777959) ^ [_861171, _861173] : [_861173 = _861171, -(c_Orderings_Oord__class_Oless__eq(_861173) = c_Orderings_Oord__class_Oless__eq(_861171))], (5755 ^ _777959) ^ [_868905, _868907] : [c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, _868905))), _868907), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _868905)))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))), -(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, _868907, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, _868905))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)))))], (50822 ^ _777959) ^ [_1808267, _1808269] : [class_Orderings_Oord(_1808267), -(class_Orderings_Oord(tc_fun(_1808269, _1808267)))], (14027 ^ _777959) ^ [_1038396, _1038398] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1038396, tc_HOL_Obool)), _1038398), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038396, tc_HOL_Obool)), _1038398)) = c_Orderings_Otop__class_Otop(tc_fun(_1038396, tc_HOL_Obool)))], (48811 ^ _777959) ^ [_1762552, _1762554, _1762556, _1762558] : [hBOOL(hAPP(hAPP(c_member(_1762552), _1762554), c_Wellfounded_Oacc(_1762552, _1762556))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1762552, _1762552)), hAPP(hAPP(c_Product__Type_OPair(_1762552, _1762552), _1762558), _1762554)), c_Transitive__Closure_Ortrancl(_1762552, _1762556))), -(hBOOL(hAPP(hAPP(c_member(_1762552), _1762558), c_Wellfounded_Oacc(_1762552, _1762556))))], (18027 ^ _777959) ^ [_1122251, _1122253, _1122255] : [class_Orderings_Olinorder(_1122251), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122251), _1122253)), -(c_Big__Operators_Olattice_OSup__fin(_1122251, c_Orderings_Oord__class_Omax(_1122251), hAPP(hAPP(c_Set_Oinsert(_1122251), _1122255), _1122253)) = hAPP(hAPP(c_Finite__Set_Ofold(_1122251, _1122251, c_Orderings_Oord__class_Omax(_1122251)), _1122255), _1122253))], (19855 ^ _777959) ^ [_1157073, _1157075, _1157077] : [class_Rings_Oordered__cancel__semiring(_1157073), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157073), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157073), _1157075), _1157077)), c_Groups_Ozero__class_Ozero(_1157073)))), 19860 ^ _777959 : [(19867 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157073), _1157075), c_Groups_Ozero__class_Ozero(_1157073))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157073), c_Groups_Ozero__class_Ozero(_1157073)), _1157077))], (19861 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157073), c_Groups_Ozero__class_Ozero(_1157073)), _1157075)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157073), _1157077), c_Groups_Ozero__class_Ozero(_1157073)))]]], (50208 ^ _777959) ^ [_1795518] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit0(_1795518)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), _1795518), c_Int_OPls)))], (22627 ^ _777959) ^ [_1209682, _1209684] : [-(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, _1209682)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1209684))))], (13901 ^ _777959) ^ [_1035298, _1035300, _1035302, _1035304] : [class_Complete__Lattice_Ocomplete__lattice(_1035298), -(_1035300 = c_Orderings_Obot__class_Obot(tc_fun(_1035302, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1035302, _1035298), _1035300), hAPP(c_COMBK(_1035298, _1035302), _1035304)) = _1035304)], (15819 ^ _777959) ^ [_1078735, _1078737] : [class_Orderings_Olinorder(_1078735), -(c_Big__Operators_Olinorder__class_OMin(_1078735, hAPP(hAPP(c_Set_Oinsert(_1078735), _1078737), c_Orderings_Obot__class_Obot(tc_fun(_1078735, tc_HOL_Obool)))) = _1078737)], (47206 ^ _777959) ^ [_1724859, _1724861, _1724863] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1724859), _1724861), _1724863) = c_Nitpick_OAbs__Frac(_1724859, c_Nitpick_Onorm__frac(_1724861, _1724863)))], (27611 ^ _777959) ^ [_1299612, _1299614] : [hBOOL(hAPP(_1299612, hAPP(c_Int_Onat, _1299614))), 27614 ^ _777959 : [(27621 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1299614), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1299612, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (27615 ^ _777959) ^ [_1299712] : [_1299614 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1299712), -(hBOOL(hAPP(_1299612, _1299712)))]]], (48743 ^ _777959) ^ [_1761036] : [-(hAPP(c_Relation_ODomain(_1761036, _1761036), c_Relation_OId(_1761036)) = c_Orderings_Otop__class_Otop(tc_fun(_1761036, tc_HOL_Obool)))], (46898 ^ _777959) ^ [_1718238, _1718240] : [c_Wellfounded_Owf(_1718238, _1718240), -(c_Wellfounded_Owf(_1718238, hAPP(hAPP(c_Relation_Orel__comp(_1718238, _1718238, _1718238), _1718240), _1718240)))], (45736 ^ _777959) ^ [_1690499, _1690501, _1690503, _1690505, _1690507] : [class_Orderings_Olinorder(_1690499), -(c_List_Olinorder__class_Osort__key(_1690501, _1690499, _1690503, hAPP(hAPP(c_List_Olist_OCons(_1690501), _1690505), _1690507)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1690501, _1690499, _1690503), _1690505), c_List_Olinorder__class_Osort__key(_1690501, _1690499, _1690503, _1690507)))], (3158 ^ _777959) ^ [_825383, _825385] : [_825385 = _825383, -(c_SetInterval_Oord__class_OlessThan(_825385) = c_SetInterval_Oord__class_OlessThan(_825383))], (34667 ^ _777959) ^ [_1430166, _1430168] : [class_Rings_Oring__1__no__zero__divisors(_1430166), 34670 ^ _777959 : [(34671 ^ _777959) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1430166), _1430168), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1430166), -(_1430168 = c_Groups_Oone__class_Oone(_1430166)), -(_1430168 = hAPP(c_Groups_Ouminus__class_Ouminus(_1430166), c_Groups_Oone__class_Oone(_1430166)))], (34681 ^ _777959) ^ [] : [34682 ^ _777959 : [(34685 ^ _777959) ^ [] : [_1430168 = hAPP(c_Groups_Ouminus__class_Ouminus(_1430166), c_Groups_Oone__class_Oone(_1430166))], (34683 ^ _777959) ^ [] : [_1430168 = c_Groups_Oone__class_Oone(_1430166)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1430166), _1430168), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1430166))]]], (38790 ^ _777959) ^ [_1522782, _1522784, _1522786, _1522788, _1522790] : [hBOOL(hAPP(hAPP(c_member(_1522782), _1522784), hAPP(c_Set_Ovimage(_1522782, _1522786, _1522788), _1522790))), -(hBOOL(hAPP(hAPP(c_member(_1522786), hAPP(_1522788, _1522784)), _1522790)))], (21408 ^ _777959) ^ [_1184785, _1184787, _1184789, _1184791, _1184793] : [class_Rings_Olinordered__semiring__strict(_1184785), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184785), _1184787), _1184789)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184785), _1184791), _1184793)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184785), c_Groups_Ozero__class_Ozero(_1184785)), _1184787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1184785), c_Groups_Ozero__class_Ozero(_1184785)), _1184791)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1184785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184785), _1184787), _1184791)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1184785), _1184789), _1184793))))], (45208 ^ _777959) ^ [_1679044, _1679046, _1679048, _1679050, _1679052] : [-(c_List_OtakeWhile(_1679044, _1679046, hAPP(hAPP(c_List_Omap(_1679048, _1679044), _1679050), _1679052)) = hAPP(hAPP(c_List_Omap(_1679048, _1679044), _1679050), c_List_OtakeWhile(_1679048, hAPP(c_Fun_Ocomp(_1679044, tc_HOL_Obool, _1679048, _1679046), _1679050), _1679052)))], (27469 ^ _777959) ^ [_1297368, _1297370] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1297368, _1297370)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1297370), _1297368))], (4638 ^ _777959) ^ [_848317, _848319, _848321, _848323] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_848323, _848319) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_848321, _848317)), _848323 = _848321, _848319 = _848317], (36427 ^ _777959) ^ [_1468492, _1468494, _1468496] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), c_Smallcheck_Osmall_H__rel), hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_Int_Oint, tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))), tc_prod(tc_Int_Oint, tc_Int_Oint)), _1468492), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1468494), _1468496)))), 36430 ^ _777959 : [(36437 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1468494), _1468496))), -(c_Smallcheck_Osmall_H(_1468492, _1468494, _1468496) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)), tc_List_Olist(tc_Code__Evaluation_Oterm), c_Smallcheck_Osmall_H(_1468492, _1468494, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1468496), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))), hAPP(_1468492, _1468496)))], (36431 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1468494), _1468496)), -(c_Smallcheck_Osmall_H(_1468492, _1468494, _1468496) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)))]]], (41257 ^ _777959) ^ [_1585515, _1585517, _1585519] : [c_Predicate_Oreflp(_1585515, _1585517), -(hBOOL(hAPP(hAPP(_1585517, _1585519), _1585519)))], (50232 ^ _777959) ^ [_1795898, _1795900, _1795902] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1795898, _1795900), _1795902) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1795898, tc_Lazy__Sequence_Olazy__sequence(_1795898)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1795898, tc_Lazy__Sequence_Olazy__sequence(_1795898), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1795898, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1795898), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1795898), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1795898), tc_Nat_Onat)), _1795898), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1795898), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1795898), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1795898), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1795898), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1795898)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1795898, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1795898), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1795898), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1795898), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1795898), tc_Nat_Onat)), _1795898), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1795898))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1795898), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1795900))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1795898, _1795900))))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1795898), _1795902)))], (46421 ^ _777959) ^ [_1705247, _1705249, _1705251, _1705253, _1705255] : [c_List_Olist__all2(_1705247, _1705249, _1705251, _1705253, _1705255), -(c_List_Olist__all2(_1705247, _1705249, _1705251, hAPP(c_List_Orev(_1705247), _1705253), hAPP(c_List_Orev(_1705249), _1705255)))], (13347 ^ _777959) ^ [_1022145, _1022147, _1022149, _1022151] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1022149), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1022145, tc_fun(_1022149, tc_HOL_Obool)), _1022147), _1022151)))), 13348 ^ _777959 : [(13349 ^ _777959) ^ [_1022219] : [hBOOL(hAPP(hAPP(c_member(_1022145), _1022219), _1022147)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1022149), hAPP(_1022151, _1022219)))]]], (47648 ^ _777959) ^ [_1735831, _1735833, _1735835, _1735837] : [47650 ^ _777959 : [(47653 ^ _777959) ^ [] : [hBOOL(hAPP(_1735835, 47649 ^ [_1735831, _1735833, _1735835, _1735837]))], (47651 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1735831), 47649 ^ [_1735831, _1735833, _1735835, _1735837]), hAPP(c_List_Oset(_1735831), _1735833))))]], -(c_List_OdropWhile(_1735831, _1735835, hAPP(hAPP(c_List_Oappend(_1735831), _1735833), _1735837)) = c_List_OdropWhile(_1735831, _1735835, _1735837))], (22619 ^ _777959) ^ [_1209582, _1209584, _1209586, _1209588] : [22620 ^ _777959 : [(22623 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1209586), _1209588)))], (22621 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1209582), _1209584)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1209582, _1209586)), c_Sum__Type_OPlus(_1209582, _1209586, _1209584, _1209588)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (21788 ^ _777959) ^ [_1191782, _1191784, _1191786, _1191788, _1191790] : [class_Groups_Ocomm__monoid__mult(_1191782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1191784), _1191786)), -(hBOOL(hAPP(hAPP(c_member(_1191784), _1191788), _1191786))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1191784, _1191782), _1191790), hAPP(hAPP(c_Set_Oinsert(_1191784), _1191788), _1191786)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1191782), hAPP(_1191790, _1191788)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1191784, _1191782), _1191790), _1191786)))], (19542 ^ _777959) ^ [_1151805] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1151805), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1151805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3760 ^ _777959) ^ [_834818, _834820, _834822, _834824, _834826, _834828, _834830, _834832] : [-(c_List_Ofoldl(_834832, _834828, _834824, _834820) = c_List_Ofoldl(_834830, _834826, _834822, _834818)), _834832 = _834830, _834828 = _834826, _834824 = _834822, _834820 = _834818], (14630 ^ _777959) ^ [_1052783, _1052785, _1052787] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052783), _1052785)), -(hBOOL(hAPP(hAPP(c_member(_1052783), _1052787), _1052785))), -(hAPP(c_Finite__Set_Ocard(_1052783), hAPP(hAPP(c_Set_Oinsert(_1052783), _1052787), _1052785)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1052783), _1052785)))], (10844 ^ _777959) ^ [_970565, _970567, _970569, _970571] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_970565), 10847 ^ _777959 : [(10854 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970565), _970569), _970571)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970565), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970565), _970567), _970569)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970565), _970567), _970571))))], (10848 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970565), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970565), _970567), _970569)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_970565), _970567), _970571))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_970565), _970569), _970571)))]]], (51168 ^ _777959) ^ [_1811592, _1811594] : [-(class_Finite__Set_Ofinite(tc_sum(_1811592, _1811594))), class_Finite__Set_Ofinite(_1811592), class_Finite__Set_Ofinite(_1811594)], (39029 ^ _777959) ^ [_1529504, _1529506, _1529508, _1529510, _1529512, _1529514, _1529516] : [-(hAPP(c_Product__Type_Oapfst(_1529504, _1529506, _1529508, _1529510), hAPP(c_Product__Type_Oapfst(_1529512, _1529504, _1529508, _1529514), _1529516)) = hAPP(c_Product__Type_Oapfst(_1529512, _1529506, _1529508, hAPP(c_Fun_Ocomp(_1529504, _1529506, _1529512, _1529510), _1529514)), _1529516))], (50029 ^ _777959) ^ [_1792424, _1792426, _1792428] : [c_FunDef_Ois__measure(_1792424, _1792426), -(c_FunDef_Ois__measure(tc_prod(_1792424, _1792428), hAPP(hAPP(c_COMBB(_1792424, tc_Nat_Onat, tc_prod(_1792424, _1792428)), _1792426), c_Product__Type_Ofst(_1792424, _1792428))))], (13121 ^ _777959) ^ [_1017330, _1017332, _1017334] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1017330, tc_HOL_Obool)), _1017332), _1017334) = c_Orderings_Obot__class_Obot(tc_fun(_1017330, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1017330, tc_HOL_Obool)), _1017332), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1017330, tc_HOL_Obool)), _1017334))))], (27194 ^ _777959) ^ [_1293003] : [-(hBOOL(hAPP(_1293003, 27201 ^ [_1293003]))), 27195 ^ _777959 : [(27196 ^ _777959) ^ [_1293055] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1293055)), hBOOL(hAPP(_1293003, hAPP(c_Int_Onat, _1293055)))]]], (9752 ^ _777959) ^ [_947149, _947151, _947153] : [class_Lattices_Osemilattice__inf(_947149), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_947149), _947151), _947153) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_947149), _947153), _947151))], (23218 ^ _777959) ^ [_1220433, _1220435, _1220437, _1220439] : [class_Rings_Olinordered__semidom(_1220433), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1220433), c_Groups_Oone__class_Oone(_1220433)), _1220435)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1220433), hAPP(hAPP(c_Power_Opower__class_Opower(_1220433), _1220435), _1220437)), hAPP(hAPP(c_Power_Opower__class_Opower(_1220433), _1220435), _1220439))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1220437), _1220439)))], (15286 ^ _777959) ^ [_1069031, _1069033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069031), _1069033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069031), hAPP(c_Nat_OSuc, _1069033))))], (47620 ^ _777959) ^ [_1735153] : [-(_1735153 = hAPP(c_Int_OAbs__Integ, 47618 ^ [_1735153]))], (16245 ^ _777959) ^ [_1088307, _1088309, _1088311, _1088313, _1088315] : [c_Hoare__Mirabelle_Otriple__valid(_1088307, _1088309, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1088307), _1088311), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1088313))), _1088315)), -(c_Hoare__Mirabelle_Otriple__valid(_1088307, hAPP(c_Nat_OSuc, _1088309), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1088307), _1088311), hAPP(c_Com_Ocom_OBODY, _1088313)), _1088315)))], (7620 ^ _777959) ^ [_906396, _906398, _906400] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_906396, _906398, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_906396)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_906396), _906400), c_Com_Ocom_OSKIP), _906400)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_906396), tc_HOL_Obool)))))], (38864 ^ _777959) ^ [_1524539, _1524541, _1524543, _1524545] : [hBOOL(hAPP(hAPP(c_member(_1524539), _1524541), _1524543)), -(hAPP(c_Set_Ovimage(_1524545, _1524539, hAPP(c_COMBK(_1524539, _1524545), _1524541)), _1524543) = c_Orderings_Otop__class_Otop(tc_fun(_1524545, tc_HOL_Obool)))], (10374 ^ _777959) ^ [_960957, _960959, _960961, _960963] : [-(hBOOL(hAPP(hAPP(c_member(_960957), _960959), _960961))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_960957, tc_Nat_Onat), _960963), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_960957, tc_HOL_Obool)), _960961), hAPP(hAPP(c_Set_Oinsert(_960957), _960959), c_Orderings_Obot__class_Obot(tc_fun(_960957, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_960957, tc_Nat_Onat), _960963), _960961))], (11268 ^ _777959) ^ [_978562, _978564, _978566] : [class_Lattices_Olattice(_978562), hBOOL(hAPP(c_Finite__Set_Ofinite(_978562), _978564)), -(_978564 = c_Orderings_Obot__class_Obot(tc_fun(_978562, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_978562), _978566)), -(_978566 = c_Orderings_Obot__class_Obot(tc_fun(_978562, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_978562, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978562, tc_HOL_Obool)), _978564), _978566)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978562), c_Big__Operators_Olattice__class_OInf__fin(_978562, _978564)), c_Big__Operators_Olattice__class_OInf__fin(_978562, _978566)))], (21033 ^ _777959) ^ [_1177607, _1177609] : [-(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), _1177607), _1177609)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1177607)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1177609))], (12574 ^ _777959) ^ [_1006456, _1006458] : [-(_1006456 = _1006458), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006456), _1006458))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006458), _1006456)))], (31514 ^ _777959) ^ [_1373186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373186)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1373186))], (36508 ^ _777959) ^ [_1470221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1470221)), 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), _1470221)) = 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), _1470221))))))], (43691 ^ _777959) ^ [_1646526, _1646528] : [class_Complete__Lattice_Ocomplete__lattice(_1646526), -(c_Complete__Lattice_OSup__class_OSup(_1646526, hAPP(c_List_Oset(_1646526), _1646528)) = hAPP(c_List_Ofoldl(_1646526, _1646526, c_Lattices_Osemilattice__sup__class_Osup(_1646526), c_Orderings_Obot__class_Obot(_1646526)), _1646528))], (43518 ^ _777959) ^ [_1642848] : [-(hAPP(c_List_Otl(_1642848), c_List_Olist_ONil(_1642848)) = c_List_Olist_ONil(_1642848))], (22693 ^ _777959) ^ [_1210843, _1210845] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210843)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210845)), _1210843 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1210845 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (33841 ^ _777959) ^ [_1415200, _1415202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415200)), hAPP(c_Nat_OSuc, _1415202))), -(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(_1415200))), 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)), _1415202)))))], (8706 ^ _777959) ^ [_928141, _928143, _928145, _928147, _928149] : [hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928141, _928143), _928145), _928147), _928149) = _928145, -(hAPP(_928145, _928147) = _928149)], (18277 ^ _777959) ^ [_1127138, _1127140, _1127142] : [class_Orderings_Olinorder(_1127138), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127138), _1127140)), -(_1127140 = c_Orderings_Obot__class_Obot(tc_fun(_1127138, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1127138), _1127142)), -(_1127142 = c_Orderings_Obot__class_Obot(tc_fun(_1127138, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1127138), c_Big__Operators_Olattice_OSup__fin(_1127138, c_Orderings_Oord__class_Omax(_1127138), _1127140)), c_Big__Operators_Olattice_OSup__fin(_1127138, c_Orderings_Oord__class_Omax(_1127138), _1127142)) = c_Big__Operators_Olattice_OSup__fin(_1127138, c_Orderings_Oord__class_Omax(_1127138), hAPP(c_Set_OCollect(_1127138), hAPP(hAPP(c_COMBB(tc_fun(_1127138, tc_HOL_Obool), tc_HOL_Obool, _1127138), c_HOL_OEx(_1127138)), hAPP(hAPP(c_COMBB(tc_fun(_1127138, tc_fun(_1127138, tc_HOL_Obool)), tc_fun(_1127138, tc_HOL_Obool), _1127138), hAPP(c_COMBB(tc_fun(_1127138, tc_HOL_Obool), tc_HOL_Obool, _1127138), c_HOL_OEx(_1127138))), hAPP(hAPP(c_COMBC(_1127138, tc_fun(_1127138, tc_fun(_1127138, tc_HOL_Obool)), tc_fun(_1127138, tc_fun(_1127138, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1127138, tc_fun(tc_fun(_1127138, tc_HOL_Obool), tc_fun(_1127138, tc_HOL_Obool))), tc_fun(tc_fun(_1127138, tc_fun(_1127138, tc_HOL_Obool)), tc_fun(_1127138, tc_fun(_1127138, tc_HOL_Obool))), _1127138), c_COMBS(_1127138, tc_fun(_1127138, tc_HOL_Obool), tc_fun(_1127138, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1127138, tc_fun(_1127138, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1127138, tc_fun(tc_fun(_1127138, tc_HOL_Obool), tc_fun(_1127138, tc_HOL_Obool))), _1127138), hAPP(c_COMBB(tc_fun(_1127138, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1127138, tc_HOL_Obool), tc_fun(_1127138, tc_HOL_Obool)), _1127138), c_COMBS(_1127138, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1127138, tc_fun(_1127138, tc_HOL_Obool)), tc_fun(_1127138, tc_fun(_1127138, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1127138), hAPP(c_COMBB(tc_fun(_1127138, tc_HOL_Obool), tc_fun(_1127138, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1127138), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1127138), c_fconj))), hAPP(hAPP(c_COMBC(_1127138, tc_fun(_1127138, tc_fun(_1127138, _1127138)), tc_fun(_1127138, tc_fun(_1127138, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1127138, _1127138), tc_fun(_1127138, tc_HOL_Obool)), tc_fun(tc_fun(_1127138, tc_fun(_1127138, _1127138)), tc_fun(_1127138, tc_fun(_1127138, tc_HOL_Obool))), _1127138), c_COMBB(tc_fun(_1127138, _1127138), tc_fun(_1127138, tc_HOL_Obool), _1127138)), hAPP(hAPP(c_COMBB(tc_fun(_1127138, tc_HOL_Obool), tc_fun(tc_fun(_1127138, _1127138), tc_fun(_1127138, tc_HOL_Obool)), _1127138), c_COMBB(_1127138, tc_HOL_Obool, _1127138)), c_fequal))), c_Orderings_Oord__class_Omin(_1127138)))))), hAPP(hAPP(c_COMBC(_1127138, tc_fun(_1127138, tc_HOL_Obool), tc_fun(_1127138, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1127138, tc_HOL_Obool), tc_fun(_1127138, tc_HOL_Obool)), _1127138), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1127138)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1127138), c_fconj), hAPP(hAPP(c_COMBC(_1127138, tc_fun(_1127138, tc_HOL_Obool), tc_HOL_Obool), c_member(_1127138)), _1127140)))), hAPP(hAPP(c_COMBC(_1127138, tc_fun(_1127138, tc_HOL_Obool), tc_HOL_Obool), c_member(_1127138)), _1127142))))))))], (17803 ^ _777959) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (44134 ^ _777959) ^ [_1656172, _1656174, _1656176] : [class_Orderings_Olinorder(_1656172), -(c_List_Olinorder__class_Osorted(_1656172, hAPP(c_List_Ofilter(_1656172, hAPP(hAPP(c_COMBC(_1656172, _1656172, tc_HOL_Obool), c_fequal), hAPP(_1656174, _1656176))), _1656176)))], (44565 ^ _777959) ^ [_1663657, _1663659] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1663657), hAPP(c_List_Onth(_1663657), _1663659)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1663657)), _1663659))) = _1663659)], (39774 ^ _777959) ^ [_1546828, _1546830, _1546832, _1546834] : [hBOOL(hAPP(c_List_Odistinct(_1546828), _1546830)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1546828, _1546832)), hAPP(hAPP(c_List_Ozip(_1546828, _1546832), _1546830), _1546834))))], (4192 ^ _777959) ^ [_841404, _841406, _841408, _841410, _841412, _841414, _841416, _841418] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_841418, _841414, _841410, _841406) = c_New__Random__Sequence_Opos__not__random__dseq(_841416, _841412, _841408, _841404)), _841418 = _841416, _841414 = _841412, _841410 = _841408, _841406 = _841404], (44509 ^ _777959) ^ [_1662611, _1662613] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662611)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662613))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662611), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662613)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662611)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662611)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1662613))))], (31532 ^ _777959) ^ [_1373460] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1373460)), -(hAPP(c_Int_Onat, _1373460) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (51200 ^ _777959) ^ [_1812003] : [class_Enum_Oenum(_1812003), -(class_Enum_Oenum(tc_Option_Ooption(_1812003)))], (29446 ^ _777959) ^ [_1333172, _1333174] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1333172)), 29455 ^ _777959 : [(29458 ^ _777959) ^ [] : [hBOOL(hAPP(_1333174, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 29451 ^ [_1333172, _1333174]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 29452 ^ [_1333172, _1333174]), _1333172))))], (29456 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1333174, 29451 ^ [_1333172, _1333174])))]], 29459 ^ _777959 : [(29462 ^ _777959) ^ [] : [hBOOL(hAPP(_1333174, 29451 ^ [_1333172, _1333174]))], (29460 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1333174, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 29451 ^ [_1333172, _1333174]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 29452 ^ [_1333172, _1333174]), _1333172)))))]], 29463 ^ _777959 : [(29473 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1333174, 29480 ^ [_1333172, _1333174]))), 29474 ^ _777959 : [(29475 ^ _777959) ^ [_1333719] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1333719), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1333172))), hBOOL(hAPP(_1333174, _1333719))]]], (29464 ^ _777959) ^ [] : [29465 ^ _777959 : [(29466 ^ _777959) ^ [_1333604] : [hBOOL(hAPP(_1333174, _1333604))]], 29468 ^ _777959 : [(29471 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1333174, 29467 ^ [_1333172, _1333174])))], (29469 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29467 ^ [_1333172, _1333174]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1333172))))]]]]], (33907 ^ _777959) ^ [_1416762, _1416764, _1416766, _1416768, _1416770] : [-(hAPP(c_Nat_Onat_Onat__rec(_1416762, _1416764, _1416766), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416768)), _1416770)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1416762), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1416768))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1416762, _1416762), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1416762, tc_fun(_1416762, _1416762)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1416762, tc_fun(_1416762, _1416762)), tc_Int_Oint), c_If(_1416762)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1416762, _1416764, _1416766), _1416770))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1416762, _1416762), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1416762, _1416762), tc_Int_Oint), _1416766), 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)), _1416770))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1416762, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1416762, _1416764, _1416766)), 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)), _1416770))))))], (39506 ^ _777959) ^ [_1540635, _1540637, _1540639, _1540641, _1540643] : [hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(_1540635, _1540637, _1540639), _1540641), _1540643)), 39509 ^ _777959 : [(39512 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1540639, _1540643)))], (39510 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1540637, _1540641), _1540643)))]]], (22497 ^ _777959) ^ [_1206751] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206751)) = 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), _1206751))))], (34453 ^ _777959) ^ [_1426584] : [class_Rings_Osemiring__1(_1426584), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1426584), c_Groups_Ozero__class_Ozero(_1426584)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1426584))], (26928 ^ _777959) ^ [_1287917, _1287919, _1287921, _1287923] : [class_Fields_Olinordered__field__inverse__zero(_1287917), 26931 ^ _777959 : [(26932 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287917), _1287919), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287917), _1287921), _1287923))), 26935 ^ _777959 : [(26942 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287917), c_Groups_Ozero__class_Ozero(_1287917)), _1287923))), 26945 ^ _777959 : [(26952 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287917), _1287923), c_Groups_Ozero__class_Ozero(_1287917)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287917), _1287919), c_Groups_Ozero__class_Ozero(_1287917))))], (26946 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287917), _1287923), c_Groups_Ozero__class_Ozero(_1287917))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287917), _1287921), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287917), _1287919), _1287923))))]]], (26936 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287917), c_Groups_Ozero__class_Ozero(_1287917)), _1287923)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287917), _1287919), _1287923)), _1287921)))]]], (26958 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287917), _1287919), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1287917), _1287921), _1287923)))), 26961 ^ _777959 : [(26964 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287917), _1287919), _1287923)), _1287921))], (26962 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287917), c_Groups_Ozero__class_Ozero(_1287917)), _1287923)))]], 26965 ^ _777959 : [(26968 ^ _777959) ^ [] : [26969 ^ _777959 : [(26972 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287917), _1287921), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1287917), _1287919), _1287923)))], (26970 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287917), _1287923), c_Groups_Ozero__class_Ozero(_1287917))))]], 26973 ^ _777959 : [(26976 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1287917), _1287919), 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hAPP(hAPP(c_COMBC(_1512633, tc_fun(_1512633, tc_HOL_Obool), tc_fun(_1512633, tc_HOL_Obool)), c_Set_Oinsert(_1512633)), c_Orderings_Obot__class_Obot(tc_fun(_1512633, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1512633, tc_HOL_Obool))))], (44045 ^ _777959) ^ [_1653734, _1653736, _1653738] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653734)), hAPP(c_List_Ofilter(_1653734, _1653736), _1653738)) = 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(_1653734)), _1653738)))), hAPP(hAPP(c_COMBB(_1653734, tc_HOL_Obool, tc_Nat_Onat), _1653736), hAPP(c_List_Onth(_1653734), _1653738))))))], (41994 ^ _777959) ^ [_1605523] : [class_Groups_Omonoid__add(_1605523), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1605523), c_List_Olist_ONil(_1605523)) = c_Groups_Ozero__class_Ozero(_1605523))], (40552 ^ _777959) ^ [_1565251, _1565253, _1565255, _1565257, _1565259] : [class_Rings_Osemiring__0(_1565251), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1565251), hAPP(hAPP(c_List_Omap(_1565253, _1565251), hAPP(hAPP(c_COMBB(_1565251, _1565251, _1565253), hAPP(c_Groups_Otimes__class_Otimes(_1565251), _1565255)), _1565257)), _1565259)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1565251), _1565255), hAPP(c_List_Omonoid__add__class_Olistsum(_1565251), hAPP(hAPP(c_List_Omap(_1565253, _1565251), _1565257), _1565259))))], (17301 ^ _777959) ^ [_1108789, _1108791, _1108793] : [class_Orderings_Olinorder(_1108789), hBOOL(hAPP(c_Finite__Set_Ofinite(_1108789), _1108791)), hBOOL(hAPP(hAPP(c_member(_1108789), _1108793), _1108791)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1108789), _1108793), c_Big__Operators_Olinorder__class_OMin(_1108789, _1108791)) = c_Big__Operators_Olinorder__class_OMin(_1108789, _1108791))], (46176 ^ _777959) ^ [_1699759, _1699761, _1699763, _1699765] : [-(hBOOL(hAPP(c_List_Olistsp(_1699759, hAPP(hAPP(c_COMBS(_1699759, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1699759), c_fconj), _1699761)), _1699763)), _1699765))), hBOOL(hAPP(c_List_Olistsp(_1699759, _1699761), _1699765)), hBOOL(hAPP(c_List_Olistsp(_1699759, _1699763), _1699765))], (2350 ^ _777959) ^ [_812707, _812709, _812711, _812713] : [-(c_Com_Ocom_OSemi(_812713, _812709) = c_Com_Ocom_OSemi(_812711, _812707)), _812713 = _812711, _812709 = _812707], (22675 ^ _777959) ^ [_1210552, _1210554] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210552)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1210554))))), _1210552 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1210554 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12550 ^ _777959) ^ [_1006185, _1006187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006185), _1006187)), _1006185 = _1006187], (6989 ^ _777959) ^ [_893614] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_893614), c_Orderings_Obot__class_Obot(tc_fun(_893614, tc_HOL_Obool)))))], (43594 ^ _777959) ^ [_1644441, _1644443] : [class_Lattices_Oab__semigroup__idem__mult(_1644441), -(_1644443 = c_List_Olist_ONil(_1644441)), -(hAPP(c_Finite__Set_Ofold1(_1644441, c_Groups_Otimes__class_Otimes(_1644441)), hAPP(c_List_Oset(_1644441), _1644443)) = hAPP(c_List_Ofoldl(_1644441, _1644441, c_Groups_Otimes__class_Otimes(_1644441), hAPP(c_List_Ohd(_1644441), _1644443)), hAPP(c_List_Otl(_1644441), _1644443)))], (44061 ^ _777959) ^ [_1654238, _1654240] : [44063 ^ _777959 : [(44066 ^ _777959) ^ [] : [44062 ^ [_1654238, _1654240] = c_List_Olist_ONil(_1654238)], (44064 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1654238)), 44062 ^ [_1654238, _1654240]), hAPP(c_List_Oset(tc_List_Olist(_1654238)), _1654240))))]], -(c_List_Otranspose(_1654238, _1654240) = c_List_Olist_ONil(tc_List_Olist(_1654238)))], (30513 ^ _777959) ^ [_1354919, _1354921] : [-(_1354919 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 30516 ^ _777959 : [(30523 ^ _777959) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1354921, _1354919) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1354921), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1354919)) = 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), _1354921), _1354919))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (30517 ^ _777959) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1354921, _1354919) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1354921), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1354919)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1354921), _1354919)))]]], (45342 ^ _777959) ^ [_1681609, _1681611, _1681613] : [hBOOL(hAPP(c_List_Odistinct(_1681609), _1681611)), -(c_List_Oremove1(_1681609, _1681613, c_List_Oremdups(_1681609, _1681611)) = c_List_Oremdups(_1681609, c_List_Oremove1(_1681609, _1681613, _1681611)))], (6828 ^ _777959) ^ [_889248, _889250, _889252, _889254, _889256, _889258] : [hBOOL(hAPP(hAPP(c_member(_889248), _889250), _889252)), _889254 = hAPP(_889256, _889250), -(hBOOL(hAPP(hAPP(c_member(_889258), _889254), hAPP(c_Set_Oimage(_889248, _889258, _889256), _889252))))], (48715 ^ _777959) ^ [_1760279, _1760281, _1760283, _1760285] : [48716 ^ _777959 : [(48719 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1760279, _1760279)), _1760281), c_Transitive__Closure_Ortrancl(_1760279, _1760285)))], (48717 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1760279, _1760279)), _1760281), c_Transitive__Closure_Ortrancl(_1760279, _1760283)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1760279, _1760279)), _1760281), c_Transitive__Closure_Ortrancl(_1760279, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1760279, _1760279), tc_HOL_Obool)), _1760283), _1760285)))))], (37259 ^ _777959) ^ [_1488504, _1488506, _1488508, _1488510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1488504), _1488510)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1488508), _1488506))), -(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), _1488504), _1488506)), 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), _1488508), _1488510)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (36540 ^ _777959) ^ [_1471010, _1471012, _1471014, _1471016, _1471018, _1471020] : [hAPP(_1471016, hAPP(c_Product__Type_Osnd(_1471014, _1471010), _1471018)) = hAPP(_1471020, hAPP(c_Product__Type_Osnd(_1471014, _1471010), _1471018)), -(hAPP(c_Product__Type_Oapsnd(_1471010, _1471012, _1471014, _1471016), _1471018) = hAPP(c_Product__Type_Oapsnd(_1471010, _1471012, _1471014, _1471020), _1471018))], (23287 ^ _777959) ^ [_1221750, _1221752] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1221750), _1221752)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1221750)), _1221752))], (12592 ^ _777959) ^ [_1006652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1006652), _1006652))], (50636 ^ _777959) ^ [_1805032, _1805034, _1805036, _1805038] : [-(hAPP(hAPP(c_List_Oappend(_1805032), c_List_Oreplicate(_1805032, _1805034, _1805036)), hAPP(hAPP(c_List_Olist_OCons(_1805032), _1805036), _1805038)) = hAPP(hAPP(c_List_Olist_OCons(_1805032), _1805036), hAPP(hAPP(c_List_Oappend(_1805032), c_List_Oreplicate(_1805032, _1805034, _1805036)), _1805038)))], (45434 ^ _777959) ^ [_1683523, _1683525, _1683527] : [45436 ^ _777959 : [(45439 ^ _777959) ^ [] : [hBOOL(hAPP(_1683525, 45435 ^ [_1683523, _1683525, _1683527]))], (45437 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1683523), 45435 ^ [_1683523, _1683525, _1683527]), hAPP(c_List_Oset(_1683523), _1683527))))]], -(c_List_OdropWhile(_1683523, _1683525, _1683527) = c_List_Olist_ONil(_1683523))], (37632 ^ _777959) ^ [_1497262, _1497264, _1497266, _1497268, _1497270, _1497272] : [c_Equiv__Relations_Oequiv(_1497262, _1497264, _1497266), c_Equiv__Relations_Ocongruent(_1497262, tc_fun(_1497268, tc_HOL_Obool), _1497266, _1497270), hBOOL(hAPP(hAPP(c_member(_1497262), _1497272), _1497264)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1497262, tc_fun(_1497268, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1497262, _1497262, _1497266), hAPP(hAPP(c_Set_Oinsert(_1497262), _1497272), c_Orderings_Obot__class_Obot(tc_fun(_1497262, tc_HOL_Obool))))), _1497270) = hAPP(_1497270, _1497272))], (8854 ^ _777959) ^ [_930604, _930606, _930608] : [class_Orderings_Olinorder(_930604), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930604), _930606), _930608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930604), _930608), _930606)))], (1500 ^ _777959) ^ [_799433, _799435] : [-(class_Rings_Oordered__cancel__semiring(_799433)), _799435 = _799433, class_Rings_Oordered__cancel__semiring(_799435)], (18113 ^ _777959) ^ [_1123916, _1123918, _1123920] : [class_Orderings_Olinorder(_1123916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123916), _1123918)), -(_1123918 = c_Orderings_Obot__class_Obot(tc_fun(_1123916, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123916), _1123920)), -(_1123920 = c_Orderings_Obot__class_Obot(tc_fun(_1123916, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1123916, tc_HOL_Obool)), _1123918), _1123920) = c_Orderings_Obot__class_Obot(tc_fun(_1123916, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1123916, c_Orderings_Oord__class_Omin(_1123916), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1123916, tc_HOL_Obool)), _1123918), _1123920)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1123916), c_Big__Operators_Olattice_OInf__fin(_1123916, c_Orderings_Oord__class_Omin(_1123916), _1123918)), c_Big__Operators_Olattice_OInf__fin(_1123916, c_Orderings_Oord__class_Omin(_1123916), _1123920)))], (36137 ^ _777959) ^ [_1463211, _1463213] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1463211), _1463213)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1463211), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1463213)))], (18157 ^ _777959) ^ [_1124783, _1124785, _1124787] : [class_Orderings_Olinorder(_1124783), hBOOL(hAPP(c_Finite__Set_Ofinite(_1124783), _1124785)), -(_1124785 = c_Orderings_Obot__class_Obot(tc_fun(_1124783, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1124783), _1124787)), -(_1124787 = c_Orderings_Obot__class_Obot(tc_fun(_1124783, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1124783, tc_HOL_Obool)), _1124785), _1124787) = c_Orderings_Obot__class_Obot(tc_fun(_1124783, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1124783, c_Orderings_Oord__class_Omax(_1124783), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1124783, tc_HOL_Obool)), _1124785), _1124787)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1124783), c_Big__Operators_Olattice_OSup__fin(_1124783, c_Orderings_Oord__class_Omax(_1124783), _1124785)), c_Big__Operators_Olattice_OSup__fin(_1124783, c_Orderings_Oord__class_Omax(_1124783), _1124787)))], (22742 ^ _777959) ^ [_1211623, _1211625] : [22743 ^ _777959 : [(22744 ^ _777959) ^ [_1211679] : [_1211625 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1211623), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1211679)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211623), _1211625)))], (48954 ^ _777959) ^ [_1766633, _1766635, _1766637, _1766639, _1766641] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1766633, _1766635)), hAPP(hAPP(c_Product__Type_OPair(_1766633, _1766635), _1766637), _1766639)), hAPP(c_Relation_Oconverse(_1766635, _1766633), _1766641))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1766635, _1766633)), hAPP(hAPP(c_Product__Type_OPair(_1766635, _1766633), _1766639), _1766637)), _1766641)))], (7710 ^ _777959) ^ [_908521, _908523, _908525, _908527, _908529] : [c_Finite__Set_Ofolding__one__idem(_908521, _908523, _908525), hAPP(_908527, hAPP(hAPP(_908523, 7715 ^ [_908521, _908523, _908525, _908527, _908529]), 7716 ^ [_908521, _908523, _908525, _908527, _908529])) = hAPP(hAPP(_908523, hAPP(_908527, 7715 ^ [_908521, _908523, _908525, _908527, _908529])), hAPP(_908527, 7716 ^ [_908521, _908523, _908525, _908527, _908529])), hBOOL(hAPP(c_Finite__Set_Ofinite(_908521), _908529)), -(_908529 = c_Orderings_Obot__class_Obot(tc_fun(_908521, tc_HOL_Obool))), -(hAPP(_908527, hAPP(_908525, _908529)) = hAPP(_908525, hAPP(c_Set_Oimage(_908521, _908521, _908527), _908529)))], (6863 ^ _777959) ^ [_890065, _890067, _890069] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_890065), tc_HOL_Obool)), _890067), _890069)), -(c_Hoare__Mirabelle_Ohoare__derivs(_890065, _890069, _890067))], (36327 ^ _777959) ^ [_1466660, _1466662, _1466664, _1466666] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1466660, _1466662), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1466664), _1466666))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1466660), _1466662) = _1466664)], (50738 ^ _777959) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (46812 ^ _777959) ^ [_1715009, _1715011, _1715013, _1715015, _1715017, _1715019, _1715021] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1715009, _1715011, _1715013), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1715015, tc_fun(tc_prod(_1715009, _1715011), tc_HOL_Obool)), _1715017), _1715019)), _1715021) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1715015, tc_fun(tc_prod(_1715009, _1715013), tc_HOL_Obool)), _1715017), hAPP(hAPP(c_COMBC(_1715015, tc_fun(tc_prod(_1715011, _1715013), tc_HOL_Obool), tc_fun(tc_prod(_1715009, _1715013), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1715009, _1715011), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1715011, _1715013), tc_HOL_Obool), tc_fun(tc_prod(_1715009, _1715013), tc_HOL_Obool)), _1715015), c_Relation_Orel__comp(_1715009, _1715011, _1715013)), _1715019)), _1715021)))], (42272 ^ _777959) ^ [_1611431, _1611433, _1611435, _1611437] : [_1611431 = c_Orderings_Obot__class_Obot(tc_fun(_1611433, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1611435, _1611433), _1611435, c_Product__Type_Ofst(_1611435, _1611433)), hAPP(hAPP(c_Product__Type_OSigma(_1611435, _1611433), _1611437), hAPP(c_COMBK(tc_fun(_1611433, tc_HOL_Obool), _1611435), _1611431))) = c_Orderings_Obot__class_Obot(tc_fun(_1611435, tc_HOL_Obool)))], (31544 ^ _777959) ^ [_1373583] : [-(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, _1373583))))))], (13993 ^ _777959) ^ [_1037514, _1037516] : [-(hAPP(c_Set_OCollect(_1037514), hAPP(hAPP(c_COMBC(_1037514, _1037514, tc_HOL_Obool), c_fequal), _1037516)) = hAPP(hAPP(c_Set_Oinsert(_1037514), _1037516), c_Orderings_Obot__class_Obot(tc_fun(_1037514, tc_HOL_Obool))))], (19765 ^ _777959) ^ [_1155528, _1155530, _1155532, _1155534] : [class_Groups_Oordered__comm__monoid__add(_1155528), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155528), c_Groups_Ozero__class_Ozero(_1155528)), _1155530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155528), _1155532), _1155534)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155528), _1155532), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155528), _1155530), _1155534))))], (39872 ^ _777959) ^ [_1549419, _1549421, _1549423, _1549425, _1549427, _1549429] : [-(hAPP(hAPP(c_List_Ozip(_1549419, _1549421), hAPP(hAPP(c_List_Omap(_1549423, _1549419), _1549425), _1549427)), _1549429) = hAPP(hAPP(c_List_Omap(tc_prod(_1549423, _1549421), tc_prod(_1549419, _1549421)), hAPP(c_Product__Type_Oprod_Oprod__case(_1549423, _1549421, tc_prod(_1549419, _1549421)), hAPP(hAPP(c_COMBB(_1549419, tc_fun(_1549421, tc_prod(_1549419, _1549421)), _1549423), c_Product__Type_OPair(_1549419, _1549421)), _1549425))), hAPP(hAPP(c_List_Ozip(_1549423, _1549421), _1549427), _1549429)))], (50936 ^ _777959) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (11184 ^ _777959) ^ [_977051, _977053, _977055, _977057, _977059] : [class_Groups_Ocomm__monoid__add(_977051), hBOOL(hAPP(c_Finite__Set_Ofinite(_977053), _977055)), -(hBOOL(hAPP(hAPP(c_member(_977053), _977057), _977055))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977053, _977051), _977059), hAPP(hAPP(c_Set_Oinsert(_977053), _977057), _977055)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_977051), hAPP(_977059, _977057)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_977053, _977051), _977059), _977055)))], (27579 ^ _777959) ^ [_1299072, _1299074] : [-(hAPP(c_Int_Onat, _1299072) = _1299074), 27582 ^ _777959 : [(27585 ^ _777959) ^ [] : [_1299072 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1299074)], (27583 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299072)))]], 27586 ^ _777959 : [(27589 ^ _777959) ^ [] : [_1299074 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (27587 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1299072))]]], (39292 ^ _777959) ^ [_1535501, _1535503, _1535505, _1535507] : [-(hBOOL(hAPP(hAPP(c_member(_1535501), _1535507), hAPP(c_Set_Oimage(tc_prod(_1535501, _1535503), _1535501, c_Product__Type_Ofst(_1535501, _1535503)), hAPP(c_List_Oset(tc_prod(_1535501, _1535503)), _1535505))))), -(hAPP(hAPP(c_Map_Omap__of(_1535501, _1535503), _1535505), _1535507) = c_Option_Ooption_ONone(_1535503))], (35830 ^ _777959) ^ [_1457607, _1457609, _1457611, _1457613, _1457615, _1457617] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1457607, _1457609, _1457611), _1457613), hAPP(hAPP(c_Product__Type_OPair(_1457607, _1457609), _1457615), _1457617)) = hAPP(hAPP(_1457613, _1457615), _1457617))], (6963 ^ _777959) ^ [_892332, _892334, _892336, _892338, _892340] : [c_Hoare__Mirabelle_Ohoare__derivs(_892332, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(_892332), tc_HOL_Obool)), _892334), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_892332), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892332)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892332))), hAPP(hAPP(c_COMBB(tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892332))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_892332)), _892336)), c_Com_Ocom_OBODY)), _892338)), _892340)), hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_892332), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892332)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892332))), hAPP(hAPP(c_COMBB(tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892332))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_892332)), _892336)), hAPP(hAPP(c_COMBB(tc_Option_Ooption(tc_Com_Ocom), tc_Com_Ocom, tc_Com_Opname), c_Option_Othe(tc_Com_Ocom)), c_Com_Obody))), _892338)), _892340)), -(c_Hoare__Mirabelle_Ohoare__derivs(_892332, _892334, hAPP(c_Set_Oimage(tc_Com_Opname, tc_Hoare__Mirabelle_Otriple(_892332), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892332)), hAPP(hAPP(c_COMBS(tc_Com_Opname, tc_Com_Ocom, tc_fun(tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892332))), hAPP(hAPP(c_COMBB(tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_fun(tc_Com_Ocom, tc_fun(tc_fun(_892332, tc_fun(tc_Com_Ostate, tc_HOL_Obool)), tc_Hoare__Mirabelle_Otriple(_892332))), tc_Com_Opname), c_Hoare__Mirabelle_Otriple_Otriple(_892332)), _892336)), c_Com_Ocom_OBODY)), _892338)), _892340)))], (42485 ^ _777959) ^ [_1617473, _1617475, _1617477, _1617479, _1617481, _1617483, _1617485] : [class_Rings_Osemiring__0(_1617473), c_Fun_Oinj__on(tc_prod(_1617475, _1617477), _1617473, hAPP(c_Product__Type_Oprod_Oprod__case(_1617475, _1617477, _1617473), hAPP(hAPP(c_COMBC(_1617475, tc_fun(_1617477, _1617473), tc_fun(_1617477, _1617473)), hAPP(hAPP(c_COMBB(tc_fun(_1617473, _1617473), tc_fun(tc_fun(_1617477, _1617473), tc_fun(_1617477, _1617473)), _1617475), c_COMBB(_1617473, _1617473, _1617477)), hAPP(hAPP(c_COMBB(_1617473, tc_fun(_1617473, _1617473), _1617475), c_Groups_Otimes__class_Otimes(_1617473)), _1617479))), _1617481)), hAPP(hAPP(c_Product__Type_OSigma(_1617475, _1617477), _1617483), hAPP(c_COMBK(tc_fun(_1617477, tc_HOL_Obool), _1617475), _1617485))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1617473), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1617475, _1617473), _1617479), _1617483)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1617477, _1617473), _1617481), _1617485)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1617473, _1617473), c_Fun_Oid(_1617473)), hAPP(c_Set_OCollect(_1617473), hAPP(hAPP(c_COMBB(tc_fun(_1617475, tc_HOL_Obool), tc_HOL_Obool, _1617473), c_HOL_OEx(_1617475)), hAPP(hAPP(c_COMBB(tc_fun(_1617475, tc_fun(_1617477, tc_HOL_Obool)), tc_fun(_1617475, tc_HOL_Obool), _1617473), hAPP(c_COMBB(tc_fun(_1617477, tc_HOL_Obool), tc_HOL_Obool, _1617475), c_HOL_OEx(_1617477))), hAPP(hAPP(c_COMBC(_1617473, tc_fun(_1617475, tc_fun(_1617477, tc_HOL_Obool)), tc_fun(_1617475, tc_fun(_1617477, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1617475, tc_fun(tc_fun(_1617477, tc_HOL_Obool), tc_fun(_1617477, tc_HOL_Obool))), tc_fun(tc_fun(_1617475, tc_fun(_1617477, tc_HOL_Obool)), tc_fun(_1617475, tc_fun(_1617477, tc_HOL_Obool))), _1617473), c_COMBS(_1617475, tc_fun(_1617477, tc_HOL_Obool), tc_fun(_1617477, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1617475, tc_fun(_1617477, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1617475, tc_fun(tc_fun(_1617477, tc_HOL_Obool), tc_fun(_1617477, tc_HOL_Obool))), _1617473), hAPP(c_COMBB(tc_fun(_1617477, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1617477, tc_HOL_Obool), tc_fun(_1617477, tc_HOL_Obool)), _1617475), c_COMBS(_1617477, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1617475, tc_fun(_1617477, tc_HOL_Obool)), tc_fun(_1617475, tc_fun(_1617477, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1617473), hAPP(c_COMBB(tc_fun(_1617477, tc_HOL_Obool), tc_fun(_1617477, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1617475), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1617477), c_fconj))), hAPP(hAPP(c_COMBC(_1617473, tc_fun(_1617475, tc_fun(_1617477, _1617473)), tc_fun(_1617475, tc_fun(_1617477, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1617477, _1617473), tc_fun(_1617477, tc_HOL_Obool)), tc_fun(tc_fun(_1617475, tc_fun(_1617477, _1617473)), tc_fun(_1617475, tc_fun(_1617477, tc_HOL_Obool))), _1617473), c_COMBB(tc_fun(_1617477, _1617473), tc_fun(_1617477, tc_HOL_Obool), _1617475)), hAPP(hAPP(c_COMBB(tc_fun(_1617473, tc_HOL_Obool), tc_fun(tc_fun(_1617477, _1617473), tc_fun(_1617477, tc_HOL_Obool)), _1617473), c_COMBB(_1617473, tc_HOL_Obool, _1617477)), c_fequal))), hAPP(hAPP(c_COMBC(_1617475, tc_fun(_1617477, _1617473), tc_fun(_1617477, _1617473)), hAPP(hAPP(c_COMBB(tc_fun(_1617473, _1617473), tc_fun(tc_fun(_1617477, _1617473), tc_fun(_1617477, _1617473)), _1617475), c_COMBB(_1617473, _1617473, _1617477)), hAPP(hAPP(c_COMBB(_1617473, tc_fun(_1617473, _1617473), _1617475), c_Groups_Otimes__class_Otimes(_1617473)), _1617479))), _1617481)))))), hAPP(hAPP(c_COMBC(_1617475, tc_fun(_1617477, tc_HOL_Obool), tc_fun(_1617477, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1617477, tc_HOL_Obool), tc_fun(_1617477, tc_HOL_Obool)), _1617475), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1617477)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1617475), c_fconj), hAPP(hAPP(c_COMBC(_1617475, tc_fun(_1617475, tc_HOL_Obool), tc_HOL_Obool), c_member(_1617475)), _1617483)))), hAPP(hAPP(c_COMBC(_1617477, tc_fun(_1617477, tc_HOL_Obool), tc_HOL_Obool), c_member(_1617477)), _1617485))))))))], (13957 ^ _777959) ^ [_1036820, _1036822, _1036824, _1036826] : [hBOOL(hAPP(hAPP(c_member(_1036820), _1036822), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1036820, tc_HOL_Obool)), _1036824), hAPP(c_Set_OCollect(_1036820), _1036826)))), 13960 ^ _777959 : [(13963 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1036826, _1036822)))], (13961 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1036820), _1036822), _1036824)))]]], (49300 ^ _777959) ^ [_1774933, _1774935, _1774937, _1774939] : [-(hAPP(hAPP(c_Nat_Ocompow(_1774933, _1774933), _1774935), hAPP(hAPP(c_Nat_Ocompow(_1774933, _1774933), _1774937), _1774939)) = hAPP(hAPP(c_Nat_Ocompow(_1774933, _1774933), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1774937), _1774935)), _1774939))], (45795 ^ _777959) ^ [_1691850, _1691852, _1691854] : [class_Enum_Oenum(_1691850), 45798 ^ _777959 : [(45799 ^ _777959) ^ [] : [c_Enum_Oall__n__lists(_1691850, _1691852, _1691854), 45802 ^ _777959 : [(45803 ^ _777959) ^ [_1692000] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1691850)), _1692000), hAPP(c_List_Oset(tc_List_Olist(_1691850)), c_Enum_On__lists(_1691850, _1691854, c_Enum_Oenum__class_Oenum(_1691850))))), -(hBOOL(hAPP(_1691852, _1692000)))]]], (45809 ^ _777959) ^ [] : [45811 ^ _777959 : [(45814 ^ _777959) ^ [] : [hBOOL(hAPP(_1691852, 45810 ^ [_1691850, _1691852, _1691854]))], (45812 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1691850)), 45810 ^ [_1691850, _1691852, _1691854]), hAPP(c_List_Oset(tc_List_Olist(_1691850)), c_Enum_On__lists(_1691850, _1691854, c_Enum_Oenum__class_Oenum(_1691850))))))]], -(c_Enum_Oall__n__lists(_1691850, _1691852, _1691854))]]], (43073 ^ _777959) ^ [_1632090, _1632092, _1632094, _1632096] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1632090), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632092)), _1632094)))), -(hAPP(hAPP(c_List_Onth(_1632092), hAPP(hAPP(c_List_Oappend(_1632092), _1632094), _1632096)), _1632090) = hAPP(hAPP(c_List_Onth(_1632092), _1632096), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1632090), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1632092)), _1632094))))], (34519 ^ _777959) ^ [] : [-(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))))], (26834 ^ _777959) ^ [_1286172, _1286174, _1286176, _1286178] : [class_Fields_Ofield(_1286172), -(_1286174 = c_Groups_Ozero__class_Ozero(_1286172)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1286172), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286172), _1286176), _1286174)), _1286178) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286172), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1286172), _1286176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286172), _1286174), _1286178))), _1286174))], (22868 ^ _777959) ^ [_1214129, _1214131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1214129), _1214131)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1214131)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1214129)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1214131), _1214129)))], (51342 ^ _777959) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (43250 ^ _777959) ^ [_1636747, _1636749, _1636751] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1636747, tc_HOL_Obool)), hAPP(c_List_Oset(_1636747), hAPP(hAPP(c_List_Odrop(_1636747), _1636749), _1636751))), hAPP(c_List_Oset(_1636747), _1636751))))], (14189 ^ _777959) ^ [_1041967] : [class_Lattices_Oboolean__algebra(_1041967), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1041967), c_Orderings_Otop__class_Otop(_1041967)) = c_Orderings_Obot__class_Obot(_1041967))], (44172 ^ _777959) ^ [_1656792, _1656794] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656792), _1656794)), -(c_List_Oupt(_1656792, hAPP(c_Nat_OSuc, _1656794)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1656792, _1656794)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1656794), c_List_Olist_ONil(tc_Nat_Onat))))], (51136 ^ _777959) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (16295 ^ _777959) ^ [_1089848, _1089850, _1089852, _1089854, _1089856] : [class_Groups_Oab__semigroup__mult(_1089848), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1089848, _1089848, c_Groups_Otimes__class_Otimes(_1089848), _1089850, _1089852), _1089854)), hBOOL(hAPP(hAPP(c_member(_1089848), _1089856), _1089852)), -(hBOOL(hAPP(hAPP(c_member(_1089848), _1089850), _1089852))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1089848, _1089848, c_Groups_Otimes__class_Otimes(_1089848), _1089856, hAPP(hAPP(c_Set_Oinsert(_1089848), _1089850), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1089848, tc_HOL_Obool)), _1089852), hAPP(hAPP(c_Set_Oinsert(_1089848), _1089856), c_Orderings_Obot__class_Obot(tc_fun(_1089848, tc_HOL_Obool)))))), _1089854)))], (24403 ^ _777959) ^ [_1241504, _1241506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1241504), _1241506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241504)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241506))))], (30970 ^ _777959) ^ [_1362942, _1362944, _1362946, _1362948] : [class_Groups_Oordered__ab__group__add__abs(_1362942), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1362942), hAPP(c_Groups_Oabs__class_Oabs(_1362942), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362944, _1362942), _1362946), _1362948))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1362944, _1362942), hAPP(hAPP(c_COMBB(_1362942, _1362942, _1362944), c_Groups_Oabs__class_Oabs(_1362942)), _1362946)), _1362948))))], (32909 ^ _777959) ^ [_1399592, _1399594] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1399592)), c_Int_OBit1(_1399594))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1399592), _1399594)))], (8784 ^ _777959) ^ [_929541, _929543, _929545, _929547, _929549, _929551] : [-(_929541 = _929543), -(hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_929545, _929547), _929549), _929543), _929551), _929541) = hAPP(_929549, _929541))], (8184 ^ _777959) ^ [_918840, _918842, _918844, _918846, _918848] : [c_Finite__Set_Ofolding__one(_918840, _918842, _918844), hBOOL(hAPP(c_Finite__Set_Ofinite(_918840), _918846)), 8191 ^ _777959 : [(8198 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918840, tc_HOL_Obool)), _918846), hAPP(hAPP(c_Set_Oinsert(_918840), _918848), c_Orderings_Obot__class_Obot(tc_fun(_918840, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_918840, tc_HOL_Obool))), -(hAPP(_918844, hAPP(hAPP(c_Set_Oinsert(_918840), _918848), _918846)) = hAPP(hAPP(_918842, _918848), hAPP(_918844, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918840, tc_HOL_Obool)), _918846), hAPP(hAPP(c_Set_Oinsert(_918840), _918848), c_Orderings_Obot__class_Obot(tc_fun(_918840, tc_HOL_Obool)))))))], (8192 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_918840, tc_HOL_Obool)), _918846), hAPP(hAPP(c_Set_Oinsert(_918840), _918848), c_Orderings_Obot__class_Obot(tc_fun(_918840, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_918840, tc_HOL_Obool)), -(hAPP(_918844, hAPP(hAPP(c_Set_Oinsert(_918840), _918848), _918846)) = _918848)]]], (23577 ^ _777959) ^ [_1226661, _1226663] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1226661), _1226663) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1226663 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1226661 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (49794 ^ _777959) ^ [_1787861, _1787863, _1787865, _1787867] : [c_List_Olist__all(_1787861, _1787863, hAPP(hAPP(c_List_Oappend(_1787861), _1787865), _1787867)), 49797 ^ _777959 : [(49800 ^ _777959) ^ [] : [-(c_List_Olist__all(_1787861, _1787863, _1787867))], (49798 ^ _777959) ^ [] : [-(c_List_Olist__all(_1787861, _1787863, _1787865))]]], (21978 ^ _777959) ^ [_1195915, _1195917, _1195919, _1195921] : [class_Groups_Ocomm__monoid__mult(_1195915), 21981 ^ _777959 : [(21988 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1195917), _1195919))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1195917, _1195915), _1195921), _1195919) = c_Groups_Oone__class_Oone(_1195915))], (21982 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1195917), _1195919)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1195917, _1195915), _1195921), _1195919) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1195915, _1195917, c_Groups_Otimes__class_Otimes(_1195915)), _1195921), c_Groups_Oone__class_Oone(_1195915)), _1195919))]]], (7088 ^ _777959) ^ [_896360, _896362, _896364] : [_896362 = _896364, -(hBOOL(hAPP(hAPP(c_member(_896360), _896362), hAPP(c_fequal, _896364))))], (19480 ^ _777959) ^ [_1150980] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1150980)], (33827 ^ _777959) ^ [_1414831, _1414833] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1414831) = hAPP(c_Nat_OSuc, _1414833), -(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(_1414831))), 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)), _1414833))))))], (44979 ^ _777959) ^ [_1672791, _1672793] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1672791), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1672791))), c_List_Otranspose(_1672791, _1672793)))))], (42042 ^ _777959) ^ [_1606433, _1606435] : [-(c_List_Olistrelp(_1606433, _1606435, c_List_Olist_ONil(_1606433), c_List_Olist_ONil(_1606433)))], (51324 ^ _777959) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (36578 ^ _777959) ^ [_1471745, _1471747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1471745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1471747), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1471745, _1471747) = 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), _1471745), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1471747)))))], (8734 ^ _777959) ^ [_928670, _928672, _928674, _928676, _928678, _928680, _928682] : [-(_928670 = _928672), -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928674, _928676), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928674, _928676), _928678), _928670), _928680)), _928672), _928682) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928674, _928676), hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928674, _928676), _928678), _928672), _928682)), _928670), _928680))], (17185 ^ _777959) ^ [_1106498, _1106500, _1106502] : [c_Hoare__Mirabelle_Otriple__valid(_1106498, hAPP(c_Nat_OSuc, _1106500), _1106502), -(c_Hoare__Mirabelle_Otriple__valid(_1106498, _1106500, _1106502))], (28376 ^ _777959) ^ [_1312932, _1312934] : [class_Rings_Ocomm__semiring__1(_1312932), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1312932), c_Groups_Oone__class_Oone(_1312932)), c_Groups_Oone__class_Oone(_1312932))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1312932), c_Nat_Osemiring__1__class_Oof__nat(_1312932)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1312934))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1312932), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1312932), _1312934)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1312932), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1312932), _1312934)), c_Groups_Oone__class_Oone(_1312932))))], (30862 ^ _777959) ^ [_1361077, _1361079] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1361077)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1361079)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1361077, _1361079)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1361077), hAPP(c_Int_Onat, _1361079)))], (38818 ^ _777959) ^ [_1523481, _1523483, _1523485, _1523487, _1523489] : [hAPP(_1523487, _1523483) = _1523489, -(hBOOL(hAPP(hAPP(c_member(_1523481), _1523483), hAPP(c_Set_Ovimage(_1523481, _1523485, _1523487), hAPP(hAPP(c_Set_Oinsert(_1523485), _1523489), c_Orderings_Obot__class_Obot(tc_fun(_1523485, tc_HOL_Obool)))))))], (21025 ^ _777959) ^ [_1177484, _1177486] : [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), _1177484), _1177486))), 21028 ^ _777959 : [(21031 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1177486)))], (21029 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1177484)))]]], (7682 ^ _777959) ^ [_907663, _907665, _907667, _907669, _907671, _907673] : [c_Hoare__Mirabelle_Ohoare__derivs(_907663, _907665, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_907663)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_907663), _907667), _907669), _907671)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_907663), tc_HOL_Obool)))), 7689 ^ _777959 : [(7692 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_907673, 7687 ^ [_907663, _907665, _907667, _907669, _907671, _907673]), 7688 ^ [_907663, _907665, _907667, _907669, _907671, _907673]))], (7690 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_907671, 7687 ^ [_907663, _907665, _907667, _907669, _907671, _907673]), 7688 ^ [_907663, _907665, _907667, _907669, _907671, _907673])))]], -(c_Hoare__Mirabelle_Ohoare__derivs(_907663, _907665, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_907663)), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_907663), _907667), _907669), _907673)), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_907663), tc_HOL_Obool)))))], (19040 ^ _777959) ^ [_1143682, _1143684, _1143686, _1143688] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1143682), _1143684))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1143686), hAPP(c_Set_Oimage(_1143682, _1143686, _1143688), _1143684))), 19048 ^ _777959 : [(19051 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1143682), hAPP(c_Set_OCollect(_1143682), hAPP(hAPP(c_COMBS(_1143682, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1143682), c_fconj), hAPP(hAPP(c_COMBC(_1143682, tc_fun(_1143682, tc_HOL_Obool), tc_HOL_Obool), c_member(_1143682)), _1143684))), hAPP(hAPP(c_COMBC(_1143682, _1143686, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1143686, tc_fun(_1143686, tc_HOL_Obool), _1143682), c_fequal), _1143688)), hAPP(_1143688, 19047 ^ [_1143682, _1143684, _1143686, _1143688]))))))], (19049 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1143682), 19047 ^ [_1143682, _1143684, _1143686, _1143688]), _1143684)))]]], (30289 ^ _777959) ^ [_1350715, _1350717] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350715, _1350717) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350715, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1350717)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (17101 ^ _777959) ^ [_1105049, _1105051, _1105053, _1105055, _1105057, _1105059] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1105049, _1105051, _1105053, _1105055, _1105057), _1105059)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1105049), _1105057)))], (21079 ^ _777959) ^ [_1178462, _1178464, _1178466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1178462), _1178464)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1178466)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1178462), _1178466)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1178464), _1178466))))], (5749 ^ _777959) ^ [_868774, _868776, _868778, _868780, _868782] : [hAPP(_868774, _868776) = hAPP(c_Option_Ooption_OSome(_868778), _868780), -(hAPP(hAPP(c_Set_Oinsert(_868782), _868776), c_Map_Odom(_868782, _868778, _868774)) = c_Map_Odom(_868782, _868778, _868774))], (30802 ^ _777959) ^ [_1359957, _1359959, _1359961] : [hBOOL(hAPP(_1359957, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1359959, _1359961))), 30805 ^ _777959 : [(30812 ^ _777959) ^ [] : [-(_1359961 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 30815 ^ _777959 : [(30816 ^ _777959) ^ [_1360205, _1360207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1360205), _1359961)), _1359959 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1359961), _1360207)), _1360205), -(hBOOL(hAPP(_1359957, _1360205)))]]], (30806 ^ _777959) ^ [] : [_1359961 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1359957, _1359959)))]]], (14245 ^ _777959) ^ [_1043229, _1043231, _1043233, _1043235] : [class_Rings_Ocomm__semiring__1(_1043229), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043229), _1043231), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043229), _1043233), _1043235)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043229), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043229), _1043231), _1043233)), _1043235))], (49310 ^ _777959) ^ [_1775248, _1775250, _1775252, _1775254, _1775256, _1775258] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1775248, _1775248)), hAPP(hAPP(c_Product__Type_OPair(_1775248, _1775248), _1775250), _1775252)), _1775254)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1775248, _1775248)), hAPP(hAPP(c_Product__Type_OPair(_1775248, _1775248), _1775252), _1775256)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775248, _1775248), tc_HOL_Obool), _1775258), _1775254))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1775248, _1775248)), hAPP(hAPP(c_Product__Type_OPair(_1775248, _1775248), _1775250), _1775256)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1775248, _1775248), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1775258)), _1775254))))], (2866 ^ _777959) ^ [_820753, _820755, _820757, _820759, _820761, _820763] : [-(c_List_Oset__Cons(_820763, _820759, _820755) = c_List_Oset__Cons(_820761, _820757, _820753)), _820763 = _820761, _820759 = _820757, _820755 = _820753], (33363 ^ _777959) ^ [_1407126, _1407128] : [class_Int_Onumber__ring(_1407126), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1407126), hAPP(c_Int_Onumber__class_Onumber__of(_1407126), c_Int_OBit1(c_Int_OPls))), _1407128) = _1407128)], (6857 ^ _777959) ^ [_889914, _889916, _889918, _889920, _889922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889914, tc_HOL_Obool)), _889916), _889918)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889920, tc_HOL_Obool)), hAPP(c_Set_Oimage(_889914, _889920, _889922), _889916)), hAPP(c_Set_Oimage(_889914, _889920, _889922), _889918))))], (25146 ^ _777959) ^ [_1254398, _1254400, _1254402] : [class_Orderings_Olinorder(_1254398), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254398), _1254400), _1254402)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1254398, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1254398), _1254400)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1254398, _1254400), _1254402)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1254398), _1254402))], (48553 ^ _777959) ^ [_1756215, _1756217] : [-(c_Transitive__Closure_Otrancl(_1756215, _1756217) = hAPP(hAPP(c_Relation_Orel__comp(_1756215, _1756215, _1756215), c_Transitive__Closure_Ortrancl(_1756215, _1756217)), _1756217))], (13467 ^ _777959) ^ [_1025013] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1025013, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1025013), hAPP(c_COMBK(tc_HOL_Obool, _1025013), c_fTrue)))], (5314 ^ _777959) ^ [_859291, _859293] : [_859293 = _859291, -(c_List_Orev(_859293) = c_List_Orev(_859291))], (39918 ^ _777959) ^ [_1550770, _1550772, _1550774, _1550776, _1550778, _1550780, _1550782] : [hAPP(hAPP(c_List_Omap(_1550770, _1550772), _1550774), _1550776) = hAPP(hAPP(c_List_Omap(_1550778, _1550772), _1550780), _1550782), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550770)), _1550776) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550778)), _1550782))], (16141 ^ _777959) ^ [_1085720, _1085722, _1085724, _1085726, _1085728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085720), _1085722)), 16144 ^ _777959 : [(16151 ^ _777959) ^ [] : [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), _1085722), _1085720)), _1085724)), _1085726)), _1085728)), -(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), _1085722), _1085724)), _1085726)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1085720), _1085724)), _1085728))))], (16145 ^ _777959) ^ [] : [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), _1085722), _1085724)), _1085726)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1085720), _1085724)), _1085728))), -(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), _1085722), _1085720)), _1085724)), _1085726)), _1085728)))]]], (31600 ^ _777959) ^ [_1374619, _1374621, _1374623] : [hBOOL(hAPP(c_Com_OWT, _1374619)), hBOOL(hAPP(c_Com_OWT, _1374621)), -(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1374623, _1374619, _1374621))))], (28894 ^ _777959) ^ [_1322714, _1322716, _1322718] : [class_Orderings_Olinorder(_1322714), 28897 ^ _777959 : [(28904 ^ _777959) ^ [] : [_1322716 = _1322718, -(hAPP(c_SetInterval_Oord__class_OatMost(_1322714), _1322716) = hAPP(c_SetInterval_Oord__class_OatMost(_1322714), _1322718))], (28898 ^ _777959) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_1322714), _1322716) = hAPP(c_SetInterval_Oord__class_OatMost(_1322714), _1322718), -(_1322716 = _1322718)]]], (19450 ^ _777959) ^ [_1150508, _1150510] : [class_Groups_Ogroup__add(_1150508), 19453 ^ _777959 : [(19460 ^ _777959) ^ [] : [c_Groups_Ozero__class_Ozero(_1150508) = _1150510, -(c_Groups_Ozero__class_Ozero(_1150508) = hAPP(c_Groups_Ouminus__class_Ouminus(_1150508), _1150510))], (19454 ^ _777959) ^ [] : [c_Groups_Ozero__class_Ozero(_1150508) = hAPP(c_Groups_Ouminus__class_Ouminus(_1150508), _1150510), -(c_Groups_Ozero__class_Ozero(_1150508) = _1150510)]]], (8336 ^ _777959) ^ [_922175, _922177, _922179, _922181] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_922175, tc_HOL_Obool)), _922177), hAPP(hAPP(c_Set_Oinsert(_922175), _922179), _922181)))), 8339 ^ _777959 : [(8342 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_922175, tc_HOL_Obool)), _922177), _922181))], (8340 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_922175), _922179), _922181)))]], 8343 ^ _777959 : [(8346 ^ _777959) ^ [] : [8347 ^ _777959 : [(8350 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_922175, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_922175, tc_HOL_Obool)), _922177), hAPP(hAPP(c_Set_Oinsert(_922175), _922179), c_Orderings_Obot__class_Obot(tc_fun(_922175, tc_HOL_Obool))))), _922181))], (8348 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_922175), _922179), _922177)))]], 8351 ^ _777959 : [(8354 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922175, tc_HOL_Obool)), _922177), _922181))], (8352 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_922175), _922179), _922177))]]], (8344 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_922175), _922179), _922181))]]], (1780 ^ _777959) ^ [_802933, _802935] : [-(class_Power_Opower(_802933)), _802935 = _802933, class_Power_Opower(_802935)], (47074 ^ _777959) ^ [_1721676, _1721678, _1721680] : [c_Wellfounded_Owf(_1721676, _1721678), c_Wellfounded_Owf(_1721676, _1721680), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1721676, _1721676), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1721676, _1721676, _1721676), _1721678), _1721680)), _1721678)), -(c_Wellfounded_Owf(_1721676, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1721676, _1721676), tc_HOL_Obool)), _1721678), _1721680)))], (8970 ^ _777959) ^ [_932256, _932258, _932260] : [class_Orderings_Oorder(_932256), -(_932258 = _932260), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_932256), _932258), _932260)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_932256), _932258), _932260)))], (30784 ^ _777959) ^ [_1359520, _1359522, _1359524] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1359520), _1359522)), _1359524) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1359520), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1359522), _1359524))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1359520), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1359522, _1359524))), _1359524)))], (11708 ^ _777959) ^ [_988499, _988501, _988503] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_988499, tc_fun(_988501, tc_HOL_Obool)), _988503), hAPP(c_COMBK(tc_fun(_988501, tc_HOL_Obool), _988499), c_Orderings_Obot__class_Obot(tc_fun(_988501, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_988501, tc_HOL_Obool)))], (23999 ^ _777959) ^ [_1234263, _1234265, _1234267] : [class_Rings_Olinordered__semidom(_1234263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234263), c_Groups_Ozero__class_Ozero(_1234263)), _1234265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234263), _1234265), c_Groups_Oone__class_Oone(_1234263))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1234263), hAPP(hAPP(c_Power_Opower__class_Opower(_1234263), _1234265), hAPP(c_Nat_OSuc, _1234267))), c_Groups_Oone__class_Oone(_1234263))))], (22174 ^ _777959) ^ [_1199663, _1199665, _1199667, _1199669, _1199671] : [class_Groups_Ocomm__monoid__add(_1199663), hBOOL(hAPP(c_Finite__Set_Ofinite(_1199665), _1199667)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1199665, _1199663), _1199669), hAPP(c_Set_OCollect(_1199665), hAPP(hAPP(c_COMBS(_1199665, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1199665), c_fconj), hAPP(hAPP(c_COMBC(_1199665, tc_fun(_1199665, tc_HOL_Obool), tc_HOL_Obool), c_member(_1199665)), _1199667))), hAPP(hAPP(c_COMBC(_1199665, tc_fun(_1199665, tc_HOL_Obool), tc_HOL_Obool), c_member(_1199665)), _1199671)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1199665, _1199663), hAPP(hAPP(c_COMBC(_1199665, _1199663, _1199663), hAPP(hAPP(c_COMBS(_1199665, _1199663, tc_fun(_1199663, _1199663)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1199663, tc_fun(_1199663, _1199663)), _1199665), c_If(_1199663)), hAPP(hAPP(c_COMBC(_1199665, tc_fun(_1199665, tc_HOL_Obool), tc_HOL_Obool), c_member(_1199665)), _1199671))), _1199669)), c_Groups_Ozero__class_Ozero(_1199663))), _1199667))], (818 ^ _777959) ^ [_790512, _790514, _790516, _790518, _790520, _790522] : [-(c_Relation_Osingle__valued(_790520, _790516, _790512)), c_Relation_Osingle__valued(_790522, _790518, _790514), _790522 = _790520, _790518 = _790516, _790514 = _790512], (28289 ^ _777959) ^ [_1311277] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1311277)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1311277)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1311277)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (24343 ^ _777959) ^ [_1240506] : [24345 ^ _777959 : [(24348 ^ _777959) ^ [] : [hBOOL(hAPP(_1240506, 24344 ^ [_1240506]))], (24346 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 24344 ^ [_1240506])))]], 24349 ^ _777959 : [(24350 ^ _777959) ^ [_1240633] : [-(hBOOL(hAPP(_1240506, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1240633))))]]], (23154 ^ _777959) ^ [_1219249, _1219251, _1219253, _1219255] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1219249, _1219251)), c_Sum__Type_OPlus(_1219249, _1219251, _1219253, _1219255)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219249), _1219253)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219251), _1219255))], (43887 ^ _777959) ^ [_1650428, _1650430] : [-(_1650428 = c_List_Olist_ONil(_1650430)), -(c_List_Olast(_1650430, _1650428) = hAPP(hAPP(c_List_Onth(_1650430), _1650428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650430)), _1650428)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (50412 ^ _777959) ^ [_1800454, _1800456] : [-(c_List_Osplice(_1800454, c_List_Olist_ONil(_1800454), _1800456) = _1800456)], (30197 ^ _777959) ^ [_1348937, _1348939, _1348941] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1348937), _1348939)), _1348941) = 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), _1348937), _1348941)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1348939), _1348941))), 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, _1348937, _1348941)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1348939, _1348941))), _1348941)))], (31104 ^ _777959) ^ [_1365572, _1365574] : [class_Groups_Oordered__ab__group__add__abs(_1365572), 31107 ^ _777959 : [(31114 ^ _777959) ^ [] : [_1365574 = c_Groups_Ozero__class_Ozero(_1365572), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365572), hAPP(c_Groups_Oabs__class_Oabs(_1365572), _1365574)), c_Groups_Ozero__class_Ozero(_1365572))))], (31108 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365572), hAPP(c_Groups_Oabs__class_Oabs(_1365572), _1365574)), c_Groups_Ozero__class_Ozero(_1365572))), -(_1365574 = c_Groups_Ozero__class_Ozero(_1365572))]]], (968 ^ _777959) ^ [_792721, _792723, _792725, _792727] : [-(c_Wellfounded_Oacyclic(_792725, _792721)), c_Wellfounded_Oacyclic(_792727, _792723), _792727 = _792725, _792723 = _792721], (22537 ^ _777959) ^ [_1207502, _1207504, _1207506] : [class_Orderings_Olinorder(_1207502), 22540 ^ _777959 : [(22547 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207502), _1207504), _1207506)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1207502, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1207502), _1207504)), hAPP(c_SetInterval_Oord__class_OlessThan(_1207502), _1207506))))], (22541 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1207502, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1207502), _1207504)), hAPP(c_SetInterval_Oord__class_OlessThan(_1207502), _1207506))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1207502), _1207504), _1207506)))]]], (46166 ^ _777959) ^ [_1699533, _1699535] : [-(hBOOL(hAPP(c_List_Olistsp(_1699533, _1699535), c_List_Olist_ONil(_1699533))))], (44849 ^ _777959) ^ [_1670015, _1670017, _1670019] : [-(hAPP(c_List_Orev(_1670015), hAPP(hAPP(c_List_Oappend(_1670015), _1670017), _1670019)) = hAPP(hAPP(c_List_Oappend(_1670015), hAPP(c_List_Orev(_1670015), _1670019)), hAPP(c_List_Orev(_1670015), _1670017)))], (48142 ^ _777959) ^ [_1747106, _1747108, _1747110] : [-(_1747106 = c_List_Olist_ONil(_1747108)), -(hBOOL(hAPP(hAPP(c_member(_1747108), hAPP(c_Product__Type_Ofst(_1747108, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1747108, _1747106), _1747110))), hAPP(c_List_Oset(_1747108), _1747106))))], (28750 ^ _777959) ^ [_1319544, _1319546, _1319548, _1319550] : [class_Orderings_Oorder(_1319544), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1319544, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1319544, _1319546, _1319548)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1319544, _1319548, _1319550)) = c_Orderings_Obot__class_Obot(tc_fun(_1319544, tc_HOL_Obool)))], (48845 ^ _777959) ^ [_1763470, _1763472, _1763474, _1763476] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1763470), tc_List_Olist(_1763470))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1763470), tc_List_Olist(_1763470)), _1763472), _1763474)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1763470), c_List_Olistrel1(_1763470, _1763476)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763470)), _1763472) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1763470)), _1763474))], (36938 ^ _777959) ^ [_1479615, _1479617, _1479619, _1479621, _1479623] : [-(hAPP(c_Product__Type_Ofst(_1479615, _1479617), hAPP(c_Product__Type_Oapfst(_1479619, _1479615, _1479617, _1479621), _1479623)) = hAPP(_1479621, hAPP(c_Product__Type_Ofst(_1479619, _1479617), _1479623)))], (31893 ^ _777959) ^ [_1380243, _1380245, _1380247] : [class_Int_Onumber(_1380243), 31896 ^ _777959 : [(31903 ^ _777959) ^ [] : [_1380247 = hAPP(c_Int_Onumber__class_Onumber__of(_1380243), _1380245), -(hAPP(c_Int_Onumber__class_Onumber__of(_1380243), _1380245) = _1380247)], (31897 ^ _777959) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1380243), _1380245) = _1380247, -(_1380247 = hAPP(c_Int_Onumber__class_Onumber__of(_1380243), _1380245))]]], (30736 ^ _777959) ^ [_1358602, _1358604] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1358602, _1358604)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1358602), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1358604)))], (35457 ^ _777959) ^ [_1449055, _1449057, _1449059, _1449061, _1449063, _1449065] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1449057, _1449059)), hAPP(hAPP(c_Product__Type_OPair(_1449057, _1449059), _1449063), _1449065)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1449055, tc_fun(tc_prod(_1449057, _1449059), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1449055, tc_HOL_Obool))), _1449061))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1449055, tc_fun(_1449057, tc_fun(_1449059, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1449055, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1449057, _1449059), tc_HOL_Obool), tc_fun(_1449057, tc_fun(_1449059, tc_HOL_Obool)), _1449055), hAPP(c_COMBC(_1449057, tc_fun(tc_prod(_1449057, _1449059), tc_HOL_Obool), tc_fun(_1449059, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449059, tc_fun(tc_fun(tc_prod(_1449057, _1449059), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1449057, _1449059), tc_HOL_Obool), tc_fun(_1449059, tc_HOL_Obool)), _1449057), c_COMBC(_1449059, tc_fun(tc_prod(_1449057, _1449059), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1449059, tc_prod(_1449057, _1449059)), tc_fun(_1449059, tc_fun(tc_fun(tc_prod(_1449057, _1449059), tc_HOL_Obool), tc_HOL_Obool)), _1449057), hAPP(c_COMBB(tc_prod(_1449057, _1449059), tc_fun(tc_fun(tc_prod(_1449057, _1449059), tc_HOL_Obool), tc_HOL_Obool), _1449059), c_member(tc_prod(_1449057, _1449059)))), c_Product__Type_OPair(_1449057, _1449059))))), _1449061)), _1449063), _1449065)))], (13081 ^ _777959) ^ [_1016365, _1016367, _1016369] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1016365, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1016365, tc_HOL_Obool)), _1016367), _1016369)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016365, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1016365, tc_HOL_Obool)), _1016367)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1016365, tc_HOL_Obool)), _1016369)))], (21294 ^ _777959) ^ [_1182594, _1182596, _1182598, _1182600] : [class_Rings_Olinordered__semiring__strict(_1182594), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182594), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182594), _1182596), _1182598)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1182594), _1182600), _1182598))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1182594), c_Groups_Ozero__class_Ozero(_1182594)), _1182598)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1182594), _1182596), _1182600)))], (6639 ^ _777959) ^ [_885536, _885538, _885540, _885542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885536, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_885536), _885538), _885540)), _885542)), 6642 ^ _777959 : [(6645 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885536, tc_HOL_Obool)), _885540), _885542)))], (6643 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885536), _885538), _885542)))]]], (24878 ^ _777959) ^ [_1249727, _1249729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249727), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1249729), _1249727)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1249727), _1249729) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (22088 ^ _777959) ^ [_1198273, _1198275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1198273), _1198275))), 22091 ^ _777959 : [(22094 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1198273), _1198275)))], (22092 ^ _777959) ^ [] : [_1198275 = c_Orderings_Obot__class_Obot(tc_fun(_1198273, tc_HOL_Obool))]]], (13681 ^ _777959) ^ [_1030642, _1030644, _1030646] : [hBOOL(hAPP(_1030646, _1030644)), -(hBOOL(hAPP(hAPP(c_member(_1030642), _1030644), hAPP(c_Set_OCollect(_1030642), _1030646))))], (24331 ^ _777959) ^ [] : [-(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)))], (18550 ^ _777959) ^ [_1134573, _1134575, _1134577, _1134579] : [_1134573 = c_Finite__Set_Ofold1(_1134575, _1134577), -(hAPP(_1134573, hAPP(hAPP(c_Set_Oinsert(_1134575), _1134579), c_Orderings_Obot__class_Obot(tc_fun(_1134575, tc_HOL_Obool)))) = _1134579)], (27265 ^ _777959) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (42553 ^ _777959) ^ [_1619927] : [-(hAPP(c_Set_Oimage(_1619927, _1619927, c_Fun_Oid(_1619927)), c_Orderings_Otop__class_Otop(tc_fun(_1619927, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1619927, tc_HOL_Obool)))], (46475 ^ _777959) ^ [_1706292, _1706294, _1706296, _1706298, _1706300] : [c_List_Olist__all2(_1706292, _1706294, _1706296, _1706298, _1706300), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706292)), _1706298) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706294)), _1706300))], (26372 ^ _777959) ^ [_1277800, _1277802, _1277804, _1277806] : [class_Fields_Ofield__inverse__zero(_1277800), -(_1277802 = c_Groups_Ozero__class_Ozero(_1277800)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277800), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277800), _1277804), _1277802)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1277800), _1277806), _1277802)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1277800), _1277804), _1277806))], (46984 ^ _777959) ^ [_1720003, _1720005, _1720007] : [c_Wellfounded_Owf(_1720003, _1720005), -(c_Wellfounded_Owf(_1720003, c_Wellfounded_Omlex__prod(_1720003, _1720007, _1720005)))], (7011 ^ _777959) ^ [_894054, _894056, _894058, _894060] : [7012 ^ _777959 : [(7015 ^ _777959) ^ [] : [hBOOL(hAPP(_894058, _894056))], (7013 ^ _777959) ^ [] : [hBOOL(hAPP(_894054, _894056))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_894060, tc_HOL_Obool)), _894058), _894054), _894056)))], (12317 ^ _777959) ^ [_1001556, _1001558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1001556), _1001558)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001558), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1001558), _1001556)) = _1001556)], (29058 ^ _777959) ^ [_1325547, _1325549] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1325547), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1325549) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1325547, _1325549))], (28506 ^ _777959) ^ [_1315111, _1315113, _1315115] : [class_Orderings_Oorder(_1315111), 28509 ^ _777959 : [(28516 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315111), _1315113), _1315115))), -(c_Orderings_Obot__class_Obot(tc_fun(_1315111, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1315111, _1315113, _1315115))], (28510 ^ _777959) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1315111, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_1315111, _1315113, _1315115), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315111), _1315113), _1315115))]]], (35087 ^ _777959) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (46615 ^ _777959) ^ [_1709310, _1709312, _1709314] : [-(c_List_Oinsert(_1709310, _1709312, c_List_Oremdups(_1709310, _1709314)) = c_List_Oremdups(_1709310, c_List_Oinsert(_1709310, _1709312, _1709314)))], (19474 ^ _777959) ^ [_1150875] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1150875)], (25359 ^ _777959) ^ [_1258533, _1258535] : [25361 ^ _777959 : [(25364 ^ _777959) ^ [] : [hBOOL(hAPP(_1258535, 25360 ^ [_1258533, _1258535]))], (25362 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 25360 ^ [_1258533, _1258535]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258533))))]], 25365 ^ _777959 : [(25366 ^ _777959) ^ [_1258686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1258686), _1258533)), -(hBOOL(hAPP(_1258535, _1258686)))]]], (50302 ^ _777959) ^ [_1797862, _1797864, _1797866, _1797868] : [-(c_New__Random__Sequence_Oneg__map(_1797862, _1797864, _1797866, _1797868) = c_New__Random__Sequence_Oneg__bind(_1797862, _1797864, _1797868, hAPP(c_Fun_Ocomp(_1797864, 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(_1797864)))))), _1797862, c_New__Random__Sequence_Oneg__single(_1797864)), _1797866)))], (40620 ^ _777959) ^ [_1566997, _1566999, _1567001, _1567003, _1567005, _1567007, _1567009] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1566997)), _1566999)), _1567001)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1567001), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1567003)), _1567005))), -(c_Map_Omap__upds(_1566997, _1567003, _1567007, _1566999, hAPP(hAPP(c_List_Olist__update(_1567003, _1567005), _1567001), _1567009)) = c_Map_Omap__upds(_1566997, _1567003, _1567007, _1566999, _1567005))], (28532 ^ _777959) ^ [_1315493, _1315495, _1315497, _1315499, _1315501] : [class_Orderings_Oorder(_1315493), 28535 ^ _777959 : [(28548 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315493, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1315493, _1315495, _1315497)), c_SetInterval_Oord__class_OatLeastAtMost(_1315493, _1315499, _1315501)))), 28549 ^ _777959 : [(28552 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315493), _1315499), _1315495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315493), _1315497), _1315501))], (28550 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315493), _1315495), _1315497)))]]], (28536 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1315493, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1315493, _1315495, _1315497)), c_SetInterval_Oord__class_OatLeastAtMost(_1315493, _1315499, _1315501))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315493), _1315495), _1315497)), 28543 ^ _777959 : [(28546 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315493), _1315497), _1315501)))], (28544 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1315493), _1315499), _1315495)))]]]]], (43773 ^ _777959) ^ [_1648684, _1648686, _1648688, _1648690] : [-(_1648684 = c_List_Olist_ONil(_1648686)), 43776 ^ _777959 : [(43783 ^ _777959) ^ [] : [-(_1648688 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648686)), _1648684)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1648686, hAPP(hAPP(c_List_Olist__update(_1648686, _1648684), _1648688), _1648690)) = c_List_Olast(_1648686, _1648684))], (43777 ^ _777959) ^ [] : [_1648688 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648686)), _1648684)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1648686, hAPP(hAPP(c_List_Olist__update(_1648686, _1648684), _1648688), _1648690)) = _1648690)]]], (15428 ^ _777959) ^ [_1071394, _1071396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071394), hAPP(c_Nat_OSuc, _1071396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071394), _1071396))), -(_1071394 = hAPP(c_Nat_OSuc, _1071396))], (11082 ^ _777959) ^ [_975079, _975081, _975083] : [c_Map_Odom(_975079, _975081, _975083) = c_Orderings_Obot__class_Obot(tc_fun(_975079, tc_HOL_Obool)), -(_975083 = hAPP(c_COMBK(tc_Option_Ooption(_975081), _975079), c_Option_Ooption_ONone(_975081)))], (11598 ^ _777959) ^ [_985696, _985698, _985700, _985702, _985704] : [11600 ^ _777959 : [(11603 ^ _777959) ^ [] : [hBOOL(hAPP(_985704, 11599 ^ [_985696, _985698, _985700, _985702, _985704]))], (11601 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_985696), 11599 ^ [_985696, _985698, _985700, _985702, _985704]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985698, tc_fun(_985696, tc_HOL_Obool)), _985700), _985702))))]], 11604 ^ _777959 : [(11605 ^ _777959) ^ [_985918] : [hBOOL(hAPP(hAPP(c_member(_985698), _985918), _985700)), 11608 ^ _777959 : [(11609 ^ _777959) ^ [_986015] : [hBOOL(hAPP(hAPP(c_member(_985696), _986015), hAPP(_985702, _985918))), -(hBOOL(hAPP(_985704, _986015)))]]]]], (12215 ^ _777959) ^ [_999730, _999732, _999734] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _999730), _999732)), _999734)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _999730), _999734)))], (10420 ^ _777959) ^ [_961912, _961914, _961916] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_961912), _961914)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_961912, tc_HOL_Obool)), _961916), _961914) = hAPP(hAPP(c_Finite__Set_Ofold(_961912, tc_fun(_961912, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_961912, tc_HOL_Obool), tc_fun(tc_fun(_961912, tc_HOL_Obool), tc_fun(_961912, tc_HOL_Obool)), _961912), hAPP(c_COMBC(tc_fun(_961912, tc_HOL_Obool), tc_fun(_961912, tc_HOL_Obool), tc_fun(_961912, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_961912, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_961912, tc_fun(_961912, tc_HOL_Obool), tc_fun(_961912, tc_HOL_Obool)), c_Set_Oinsert(_961912)), c_Orderings_Obot__class_Obot(tc_fun(_961912, tc_HOL_Obool))))), _961916), _961914))], (496 ^ _777959) ^ [_785693, _785695] : [-(class_Lattices_Oab__semigroup__idem__mult(_785693)), _785695 = _785693, class_Lattices_Oab__semigroup__idem__mult(_785695)], (16491 ^ _777959) ^ [_1093740, _1093742, _1093744, _1093746] : [class_Orderings_Olinorder(_1093740), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093740), _1093742), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093740), _1093744), _1093746)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093740), _1093744), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093740), _1093742), _1093746)))], (36952 ^ _777959) ^ [_1480041, _1480043, _1480045, _1480047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1480041), _1480043)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1480045), _1480047)), -(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), _1480041), _1480045)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1480043), _1480047))), c_FunDef_Opair__less)))], (26000 ^ _777959) ^ [_1270908, _1270910, _1270912, _1270914] : [class_Fields_Olinordered__field(_1270908), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270908), _1270910), _1270912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270908), c_Groups_Ozero__class_Ozero(_1270908)), _1270914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270908), c_Groups_Ozero__class_Ozero(_1270908)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270908), _1270912), _1270910))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270908), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270908), _1270914), _1270912)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270908), _1270914), _1270910))))], (3036 ^ _777959) ^ [_823434, _823436, _823438, _823440, _823442, _823444] : [-(c_Big__Operators_Olattice_OSup__fin(_823444, _823440, _823436) = c_Big__Operators_Olattice_OSup__fin(_823442, _823438, _823434)), _823444 = _823442, _823440 = _823438, _823436 = _823434], (7246 ^ _777959) ^ [_899429, _899431, _899433] : [class_Lattices_Olattice(_899429), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899429), _899431), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_899429), _899433), _899431))))], (44644 ^ _777959) ^ [_1665217, _1665219, _1665221] : [class_Orderings_Olinorder(_1665217), hBOOL(hAPP(hAPP(c_member(_1665217), _1665219), hAPP(c_List_Oset(_1665217), _1665221))), c_List_Olinorder__class_Osorted(_1665217, _1665221), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1665217, _1665217, c_COMBI(_1665217)), _1665219), c_List_Oremove1(_1665217, _1665219, _1665221)) = _1665221)], (48284 ^ _777959) ^ [_1749791, _1749793] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1749791), _1749793) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1749791)), hAPP(c_Code__Numeral_Onat__of, _1749793))))], (20233 ^ _777959) ^ [_1164019, _1164021, _1164023, _1164025] : [class_Rings_Olinordered__ring__strict(_1164019), 20236 ^ _777959 : [(20251 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164019), _1164021), _1164023)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164019), _1164025), _1164023)))), 20252 ^ _777959 : [(20259 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164019), _1164023), c_Groups_Ozero__class_Ozero(_1164019))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164019), _1164025), _1164021))], (20253 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164019), c_Groups_Ozero__class_Ozero(_1164019)), _1164023)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164019), _1164021), _1164025))]]], (20237 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164019), _1164021), _1164023)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164019), _1164025), _1164023))), 20242 ^ _777959 : [(20245 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164019), _1164021), _1164025)))], (20243 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164019), c_Groups_Ozero__class_Ozero(_1164019)), _1164023)))]], 20246 ^ _777959 : [(20249 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164019), _1164025), _1164021)))], (20247 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1164019), _1164023), c_Groups_Ozero__class_Ozero(_1164019))))]]]]], (35547 ^ _777959) ^ [_1451659, _1451661] : [class_Rings_Osemiring__1(_1451659), -(hBOOL(hAPP(hAPP(c_member(_1451659), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1451659), _1451661)), c_Nat_Osemiring__1__class_ONats(_1451659))))], (36035 ^ _777959) ^ [_1461420, _1461422] : [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), _1461420))), 36038 ^ _777959 : [(36045 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1461422)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1461420)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1461422), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1461420)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1461420)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1461422), 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), _1461420)))))], (36039 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1461422)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1461420))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1461422), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1461420)) = 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), _1461422)))]]], (25924 ^ _777959) ^ [_1269382] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), hAPP(c_Com_Ocom_OBODY, _1269382)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2318 ^ _777959) ^ [_812239, _812241] : [_812241 = _812239, -(c_SetInterval_Oord__class_OatLeast(_812241) = c_SetInterval_Oord__class_OatLeast(_812239))], (39970 ^ _777959) ^ [_1551798, _1551800, _1551802, _1551804] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551798)), _1551800) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1551802)), _1551804), -(hAPP(hAPP(c_List_Omap(tc_prod(_1551798, _1551802), _1551798), c_Product__Type_Ofst(_1551798, _1551802)), hAPP(hAPP(c_List_Ozip(_1551798, _1551802), _1551800), _1551804)) = _1551800)], (11782 ^ _777959) ^ [_991081, _991083, _991085, _991087, _991089] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991081, tc_fun(_991083, tc_HOL_Obool)), _991085), hAPP(hAPP(c_COMBC(_991081, tc_fun(_991083, tc_HOL_Obool), tc_fun(_991083, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_991083, tc_HOL_Obool), tc_fun(tc_fun(_991083, tc_HOL_Obool), tc_fun(_991083, tc_HOL_Obool)), _991081), c_Groups_Ominus__class_Ominus(tc_fun(_991083, tc_HOL_Obool))), _991087)), _991089)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_991083, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991081, tc_fun(_991083, tc_HOL_Obool)), _991085), _991087)), _991089))], (41617 ^ _777959) ^ [_1594135, _1594137, _1594139, _1594141] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1594135) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1594137), hAPP(hAPP(c_List_Olist_OCons(_1594137), _1594139), _1594141)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1594135)) = hAPP(hAPP(c_List_Onth(_1594137), _1594141), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1594135)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (27756 ^ _777959) ^ [_1302422] : [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, _1302422))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1302422)))], (15190 ^ _777959) ^ [_1067419, _1067421, _1067423, _1067425] : [class_Rings_Ocomm__semiring__1(_1067419), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067419), _1067421), _1067423)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067419), _1067425), _1067423)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1067419), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1067419), _1067421), _1067425)), _1067423))], (50922 ^ _777959) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (7624 ^ _777959) ^ [_906522, _906524, _906526, _906528] : [c_Finite__Set_Ofolding__one__idem(_906522, _906524, _906526), -(hAPP(hAPP(_906524, _906528), _906528) = _906528)], (40089 ^ _777959) ^ [_1554694, _1554696, _1554698] : [-(hAPP(c_List_Oset(_1554694), hAPP(c_List_OremoveAll(_1554694, _1554696), _1554698)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1554694, tc_HOL_Obool)), hAPP(c_List_Oset(_1554694), _1554698)), hAPP(hAPP(c_Set_Oinsert(_1554694), _1554696), c_Orderings_Obot__class_Obot(tc_fun(_1554694, tc_HOL_Obool)))))], (34261 ^ _777959) ^ [_1422977, _1422979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1422977)), c_Int_OBit0(_1422979))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1422977), _1422979)))], (19482 ^ _777959) ^ [_1151015] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1151015)], (36682 ^ _777959) ^ [_1473842, _1473844, _1473846, _1473848, _1473850] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1473842, _1473844, _1473846), _1473848), _1473850) = hAPP(hAPP(_1473848, hAPP(c_Product__Type_Ofst(_1473842, _1473844), _1473850)), hAPP(c_Product__Type_Osnd(_1473842, _1473844), _1473850)))], (20621 ^ _777959) ^ [_1171058, _1171060] : [class_Groups_Olinordered__ab__group__add(_1171058), 20624 ^ _777959 : [(20631 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171058), _1171060), c_Groups_Ozero__class_Ozero(_1171058))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171058), _1171060), hAPP(c_Groups_Ouminus__class_Ouminus(_1171058), _1171060))))], (20625 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171058), _1171060), hAPP(c_Groups_Ouminus__class_Ouminus(_1171058), _1171060))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1171058), _1171060), c_Groups_Ozero__class_Ozero(_1171058))))]]], (33351 ^ _777959) ^ [_1406970] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406970), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406970)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1406970)))], (34979 ^ _777959) ^ [_1436546] : [c_Int_OBit1(_1436546) = c_Int_OMin, -(_1436546 = c_Int_OMin)], (41515 ^ _777959) ^ [_1591754, _1591756, _1591758, _1591760] : [-(hAPP(hAPP(c_List_Otake(_1591754), hAPP(c_Nat_OSuc, _1591756)), hAPP(hAPP(c_List_Olist_OCons(_1591754), _1591758), _1591760)) = hAPP(hAPP(c_List_Olist_OCons(_1591754), _1591758), hAPP(hAPP(c_List_Otake(_1591754), _1591756), _1591760)))], (45990 ^ _777959) ^ [_1695511, _1695513, _1695515] : [class_Enum_Oenum(_1695511), class_Enum_Oenum(_1695513), 45997 ^ _777959 : [(46004 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1695513), hAPP(hAPP(c_COMBB(tc_fun(_1695511, tc_HOL_Obool), tc_HOL_Obool, _1695513), c_Enum_Oenum__class_Oenum__ex(_1695511)), hAPP(hAPP(c_COMBB(tc_fun(_1695511, tc_prod(_1695513, _1695511)), tc_fun(_1695511, tc_HOL_Obool), _1695513), hAPP(c_COMBB(tc_prod(_1695513, _1695511), tc_HOL_Obool, _1695511), _1695515)), c_Product__Type_OPair(_1695513, _1695511))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1695513, _1695511)), _1695515)))], (45998 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1695513, _1695511)), _1695515)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1695513), hAPP(hAPP(c_COMBB(tc_fun(_1695511, tc_HOL_Obool), tc_HOL_Obool, _1695513), c_Enum_Oenum__class_Oenum__ex(_1695511)), hAPP(hAPP(c_COMBB(tc_fun(_1695511, tc_prod(_1695513, _1695511)), tc_fun(_1695511, tc_HOL_Obool), _1695513), hAPP(c_COMBB(tc_prod(_1695513, _1695511), tc_HOL_Obool, _1695511), _1695515)), c_Product__Type_OPair(_1695513, _1695511))))))]]], (36155 ^ _777959) ^ [_1463555, _1463557] : [-(c_Divides_Odivmod__nat(_1463557, _1463555) = 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), _1463557), _1463555), _1463555))), -(_1463555 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1463557), _1463555)))], (8094 ^ _777959) ^ [_916712, _916714, _916716] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_916712, tc_HOL_Obool)), _916714), _916716)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916712, tc_HOL_Obool)), _916714), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_916712, tc_HOL_Obool)), _916716), _916714)) = _916716)], (48589 ^ _777959) ^ [_1757068, _1757070, _1757072, _1757074] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1757068, _1757068)), hAPP(hAPP(c_Product__Type_OPair(_1757068, _1757068), _1757070), _1757072)), c_Transitive__Closure_Ortrancl(_1757068, _1757074))), -(_1757070 = _1757072), 48596 ^ _777959 : [(48599 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1757068, _1757068)), hAPP(hAPP(c_Product__Type_OPair(_1757068, _1757068), _1757070), _1757072)), c_Transitive__Closure_Otrancl(_1757068, _1757074))))], (48597 ^ _777959) ^ [] : [_1757070 = _1757072]]], (51178 ^ _777959) ^ [_1811721, _1811723] : [-(class_HOL_Oequal(tc_sum(_1811721, _1811723)))], (13060 ^ _777959) ^ [_1015761, _1015763, _1015765] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1015761, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1015761, tc_HOL_Obool), _1015763)), _1015765) = c_Orderings_Obot__class_Obot(tc_fun(_1015761, tc_HOL_Obool)), 13063 ^ _777959 : [(13064 ^ _777959) ^ [_1015896] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1015761, tc_HOL_Obool)), _1015896), _1015763)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1015761, tc_HOL_Obool)), _1015896), _1015765) = c_Orderings_Obot__class_Obot(tc_fun(_1015761, tc_HOL_Obool)))]]], (18073 ^ _777959) ^ [_1122940, _1122942, _1122944] : [class_Orderings_Olinorder(_1122940), hBOOL(hAPP(c_Finite__Set_Ofinite(_1122940), _1122942)), 18080 ^ _777959 : [(18087 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1122940, tc_HOL_Obool)), _1122942), hAPP(hAPP(c_Set_Oinsert(_1122940), _1122944), c_Orderings_Obot__class_Obot(tc_fun(_1122940, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1122940, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1122940, c_Orderings_Oord__class_Omin(_1122940), hAPP(hAPP(c_Set_Oinsert(_1122940), _1122944), _1122942)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1122940), _1122944), c_Big__Operators_Olattice_OInf__fin(_1122940, c_Orderings_Oord__class_Omin(_1122940), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1122940, tc_HOL_Obool)), _1122942), hAPP(hAPP(c_Set_Oinsert(_1122940), _1122944), c_Orderings_Obot__class_Obot(tc_fun(_1122940, tc_HOL_Obool)))))))], (18081 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1122940, tc_HOL_Obool)), _1122942), hAPP(hAPP(c_Set_Oinsert(_1122940), _1122944), c_Orderings_Obot__class_Obot(tc_fun(_1122940, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1122940, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1122940, c_Orderings_Oord__class_Omin(_1122940), hAPP(hAPP(c_Set_Oinsert(_1122940), _1122944), _1122942)) = _1122944)]]], (34825 ^ _777959) ^ [_1433264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1433264)), -(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), _1433264), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (15596 ^ _777959) ^ [_1074609, _1074611, _1074613] : [class_Rings_Olinordered__semidom(_1074609), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074609), c_Groups_Oone__class_Oone(_1074609)), _1074611)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074609), c_Groups_Oone__class_Oone(_1074609)), _1074613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1074609), c_Groups_Oone__class_Oone(_1074609)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1074609), _1074611), _1074613))))], (28123 ^ _777959) ^ [] : [-(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)))], (41463 ^ _777959) ^ [_1590780, _1590782, _1590784, _1590786] : [-(hAPP(hAPP(c_List_Onth(_1590780), hAPP(hAPP(c_List_Olist_OCons(_1590780), _1590782), _1590784)), hAPP(c_Nat_OSuc, _1590786)) = hAPP(hAPP(c_List_Onth(_1590780), _1590784), _1590786))], (46168 ^ _777959) ^ [_1699586, _1699588, _1699590, _1699592] : [hBOOL(hAPP(c_List_Olistsp(_1699586, hAPP(hAPP(c_COMBS(_1699586, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1699586), c_fconj), _1699588)), _1699590)), _1699592)), 46171 ^ _777959 : [(46174 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1699586, _1699590), _1699592)))], (46172 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1699586, _1699588), _1699592)))]]], (39665 ^ _777959) ^ [_1544502] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1544502)), -(c_List_Onat__list(_1544502))], (15068 ^ _777959) ^ [_1064535, _1064537, _1064539] : [_1064537 = _1064539, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1064535)), _1064537) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1064535)), _1064539))], (48216 ^ _777959) ^ [_1748631, _1748633] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1748631)), hAPP(c_Code__Numeral_Oof__nat, _1748633)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1748631), _1748633)))], (41449 ^ _777959) ^ [_1590364, _1590366, _1590368, _1590370, _1590372] : [-(hAPP(hAPP(c_List_Omap(_1590364, _1590366), _1590368), hAPP(hAPP(c_List_Olist_OCons(_1590364), _1590370), _1590372)) = hAPP(hAPP(c_List_Olist_OCons(_1590366), hAPP(_1590368, _1590370)), hAPP(hAPP(c_List_Omap(_1590364, _1590366), _1590368), _1590372)))], (50600 ^ _777959) ^ [_1804476, _1804478, _1804480] : [c_List_Olist_ONil(_1804476) = c_List_Oreplicate(_1804476, _1804478, _1804480), -(_1804478 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32117 ^ _777959) ^ [_1384462, _1384464, _1384466, _1384468] : [class_Int_Onumber__ring(_1384462), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384462), hAPP(c_Int_Onumber__class_Onumber__of(_1384462), _1384464)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384462), hAPP(c_Int_Onumber__class_Onumber__of(_1384462), _1384466)), _1384468)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1384462), hAPP(c_Int_Onumber__class_Onumber__of(_1384462), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1384464), _1384466))), _1384468))], (50866 ^ _777959) ^ [] : [-(class_HOL_Oequal(tc_Com_Ocom))], (8254 ^ _777959) ^ [_920345, _920347, _920349, _920351, _920353] : [class_Groups_Oordered__ab__group__add(_920345), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_920345), _920347), _920349) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_920345), _920351), _920353), 8261 ^ _777959 : [(8268 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920345), _920351), _920353)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920345), _920347), _920349)))], (8262 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920345), _920347), _920349)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920345), _920351), _920353)))]]], (12690 ^ _777959) ^ [_1008230, _1008232, _1008234, _1008236] : [class_Groups_Ouminus(_1008230), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1008232, _1008230)), _1008234), _1008236) = hAPP(c_Groups_Ouminus__class_Ouminus(_1008230), hAPP(_1008234, _1008236)))], (1060 ^ _777959) ^ [_793933, _793935] : [-(class_Rings_Olinordered__ring__strict(_793933)), _793935 = _793933, class_Rings_Olinordered__ring__strict(_793935)], (9802 ^ _777959) ^ [_948286, _948288, _948290] : [class_Lattices_Osemilattice__inf(_948286), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948286), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_948286), _948288), _948290)), _948288)))], (33183 ^ _777959) ^ [_1404418, _1404420] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404418)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1404418)), _1404420) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1404418)), _1404420)))], (41039 ^ _777959) ^ [_1580094, _1580096] : [class_Complete__Lattice_Ocomplete__lattice(_1580094), -(c_Complete__Lattice_OSup__class_OSup(_1580094, _1580096) = c_Complete__Lattice_OInf__class_OInf(_1580094, hAPP(c_Set_OCollect(_1580094), hAPP(hAPP(c_COMBB(tc_fun(_1580094, tc_HOL_Obool), tc_HOL_Obool, _1580094), c_HOL_OAll(_1580094)), hAPP(hAPP(c_COMBB(tc_fun(_1580094, tc_HOL_Obool), tc_fun(_1580094, tc_HOL_Obool), _1580094), hAPP(c_COMBS(_1580094, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1580094), c_fimplies), hAPP(hAPP(c_COMBC(_1580094, tc_fun(_1580094, tc_HOL_Obool), tc_HOL_Obool), c_member(_1580094)), _1580096)))), hAPP(c_COMBC(_1580094, _1580094, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1580094)))))))], (17429 ^ _777959) ^ [_1111073, _1111075, _1111077] : [class_Orderings_Olinorder(_1111073), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111073), _1111075)), -(_1111075 = c_Orderings_Obot__class_Obot(tc_fun(_1111073, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1111073), _1111077)), -(_1111077 = c_Orderings_Obot__class_Obot(tc_fun(_1111073, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1111073, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1111073, tc_HOL_Obool)), _1111075), _1111077)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1111073), c_Big__Operators_Olinorder__class_OMax(_1111073, _1111075)), c_Big__Operators_Olinorder__class_OMax(_1111073, _1111077)))], (19490 ^ _777959) ^ [_1151073, _1151075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151073), _1151075)), _1151075 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (48757 ^ _777959) ^ [_1761290, _1761292] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1761290), tc_List_Olist(_1761290)), tc_HOL_Obool)), c_List_Olistrel1(_1761290, c_Transitive__Closure_Ortrancl(_1761290, _1761292))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1761290), c_List_Olistrel1(_1761290, _1761292)))))], (45210 ^ _777959) ^ [_1679109] : [-(c_List_Oreturn__list(_1679109) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1679109))], (30571 ^ _777959) ^ [_1356024, _1356026] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1356024))), -(c_SMT_Oz3mod(_1356026, _1356024) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1356026, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1356024)))], (31590 ^ _777959) ^ [_1374464, _1374466, _1374468] : [-(hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1374464, _1374466, _1374468)))), hBOOL(hAPP(c_Com_OWT, _1374466)), hBOOL(hAPP(c_Com_OWT, _1374468))], (40775 ^ _777959) ^ [_1570564, _1570566, _1570568, _1570570, _1570572] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1570564, _1570566)), _1570568), hAPP(hAPP(c_List_Ozip(_1570564, _1570566), _1570570), _1570572)) = hAPP(hAPP(c_List_Ozip(_1570564, _1570566), hAPP(hAPP(c_List_Otake(_1570564), _1570568), _1570570)), hAPP(hAPP(c_List_Otake(_1570566), _1570568), _1570572)))], (26844 ^ _777959) ^ [_1286350, _1286352, _1286354, _1286356] : [class_Fields_Ofield__inverse__zero(_1286350), -(_1286352 = c_Groups_Ozero__class_Ozero(_1286350)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1286350), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286350), _1286354), _1286352)), _1286356) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1286350), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1286350), _1286354), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1286350), _1286356), _1286352))), _1286352))], (23331 ^ _777959) ^ [_1222471] : [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)), _1222471)), _1222471)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1222471), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (49852 ^ _777959) ^ [_1788933, _1788935, _1788937] : [c_List_Olist__all(_1788933, _1788937, _1788935), 49855 ^ _777959 : [(49856 ^ _777959) ^ [_1789014] : [hBOOL(hAPP(hAPP(c_member(_1788933), _1789014), hAPP(c_List_Oset(_1788933), _1788935))), -(hBOOL(hAPP(_1788937, _1789014)))]]], (7296 ^ _777959) ^ [_900279, _900281, _900283, _900285] : [class_Lattices_Osemilattice__sup(_900279), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900279), _900281), _900283)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900279), _900281), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_900279), _900283), _900285))))], (35705 ^ _777959) ^ [_1454859, _1454861, _1454863, _1454865] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1454859, tc_fun(_1454861, tc_HOL_Obool))), _1454863), _1454865))], (5578 ^ _777959) ^ [_863195, _863197, _863199, _863201, _863203, _863205] : [-(c_COMBB(_863205, _863201, _863197) = c_COMBB(_863203, _863199, _863195)), _863205 = _863203, _863201 = _863199, _863197 = _863195], (34189 ^ _777959) ^ [_1421705] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1421705)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1421705), c_Int_OPls)))], (1886 ^ _777959) ^ [_805115, _805117, _805119, _805121, _805123, _805125, _805127, _805129] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_805129, _805125, _805121, _805117) = c_Hoare__Mirabelle_Otriple_Otriple__case(_805127, _805123, _805119, _805115)), _805129 = _805127, _805125 = _805123, _805121 = _805119, _805117 = _805115], (44622 ^ _777959) ^ [_1664798, _1664800, _1664802, _1664804, _1664806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1664798), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1664800), _1664802))), -(hAPP(hAPP(c_List_Onth(_1664804), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1664804), _1664806), c_List_Oupt(_1664802, _1664800))), _1664798) = hAPP(_1664806, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1664802), _1664798)))], (15936 ^ _777959) ^ [_1081688, _1081690, _1081692, _1081694, _1081696] : [-(c_Map_Omap__comp(_1081688, _1081690, _1081692, hAPP(c_COMBK(tc_Option_Ooption(_1081690), _1081688), c_Option_Ooption_ONone(_1081690)), _1081694, _1081696) = c_Option_Ooption_ONone(_1081690))], (51032 ^ _777959) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (25490 ^ _777959) ^ [_1261232, _1261234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1261232)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1261234)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1261234), _1261232)), _1261234)))], (15090 ^ _777959) ^ [_1064982, _1064984, _1064986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1064984), _1064986)), -(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, _1064982)), _1064984)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1064982)), _1064986))))], (28410 ^ _777959) ^ [_1313495, _1313497] : [c_Nat__Transfer_Ois__nat(_1313495), c_Nat__Transfer_Ois__nat(_1313497), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1313495), _1313497)))], (16189 ^ _777959) ^ [_1086898, _1086900, _1086902, _1086904] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086898), _1086900)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086902), _1086900)), _1086904)) = 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), _1086898), _1086902)), _1086900)), _1086904))], (29765 ^ _777959) ^ [_1339850, _1339852, _1339854, _1339856, _1339858] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1339850, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1339852, _1339850, _1339854), _1339856)), _1339858)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1339850, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_1339852, tc_HOL_Obool), tc_fun(_1339850, tc_HOL_Obool), c_Set_Oimage(_1339852, _1339850, _1339854)), hAPP(c_Set_OPow(_1339852), _1339856))), hAPP(c_Set_OPow(_1339850), _1339858))))], (38985 ^ _777959) ^ [_1528369, _1528371, _1528373, _1528375, _1528377, _1528379, _1528381] : [hAPP(c_Fun_Ocomp(_1528369, _1528371, _1528373, _1528375), _1528377) = _1528379, -(hAPP(_1528375, hAPP(_1528377, _1528381)) = hAPP(_1528379, _1528381))], (13975 ^ _777959) ^ [_1037190, _1037192] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1037190), _1037192)), 13978 ^ _777959 : [(13985 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1037190), c_Orderings_Otop__class_Otop(tc_fun(_1037190, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1037190), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1037190, tc_HOL_Obool)), _1037192))))], (13979 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1037190), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1037190, tc_HOL_Obool)), _1037192))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1037190), c_Orderings_Otop__class_Otop(tc_fun(_1037190, tc_HOL_Obool)))))]]], (33343 ^ _777959) ^ [_1406836] : [-(c_Int_Opred(_1406836) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1406836), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (13825 ^ _777959) ^ [_1033583, _1033585, _1033587, _1033589, _1033591] : [class_Complete__Lattice_Ocomplete__lattice(_1033583), 13828 ^ _777959 : [(13829 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033583), _1033585), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1033587, _1033583), _1033589), _1033591))), 13832 ^ _777959 : [(13833 ^ _777959) ^ [_1033764] : [hBOOL(hAPP(hAPP(c_member(_1033587), _1033764), _1033589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033583), _1033585), hAPP(_1033591, _1033764))))]]], (13839 ^ _777959) ^ [] : [13841 ^ _777959 : [(13844 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033583), _1033585), hAPP(_1033591, 13840 ^ [_1033583, _1033585, _1033587, _1033589, _1033591])))], (13842 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1033587), 13840 ^ [_1033583, _1033585, _1033587, _1033589, _1033591]), _1033589)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1033583), _1033585), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1033587, _1033583), _1033589), _1033591))))]]], (18458 ^ _777959) ^ [_1132374, _1132376, _1132378] : [class_Orderings_Olinorder(_1132374), hAPP(_1132376, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1132374), 18463 ^ [_1132374, _1132376, _1132378]), 18464 ^ [_1132374, _1132376, _1132378])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1132374), hAPP(_1132376, 18463 ^ [_1132374, _1132376, _1132378])), hAPP(_1132376, 18464 ^ [_1132374, _1132376, _1132378])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1132374), _1132378)), -(_1132378 = c_Orderings_Obot__class_Obot(tc_fun(_1132374, tc_HOL_Obool))), -(hAPP(_1132376, c_Big__Operators_Olinorder__class_OMax(_1132374, _1132378)) = c_Big__Operators_Olinorder__class_OMax(_1132374, hAPP(c_Set_Oimage(_1132374, _1132374, _1132376), _1132378)))], (50682 ^ _777959) ^ [_1805987, _1805989, _1805991] : [-(_1805987 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1805989), c_List_Oreplicate(_1805989, _1805987, _1805991)) = hAPP(hAPP(c_Set_Oinsert(_1805989), _1805991), c_Orderings_Obot__class_Obot(tc_fun(_1805989, tc_HOL_Obool))))], (39087 ^ _777959) ^ [_1530738, _1530740, _1530742, _1530744, _1530746, _1530748] : [c_Fun_Oinj__on(_1530738, _1530740, hAPP(c_Fun_Ocomp(_1530742, _1530740, _1530738, _1530744), _1530746), _1530748), -(c_Fun_Oinj__on(_1530738, _1530742, _1530746, _1530748))], (15528 ^ _777959) ^ [_1073214, _1073216] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1073214), _1073216), 15531 ^ _777959 : [(15534 ^ _777959) ^ [] : [-(_1073216 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (15532 ^ _777959) ^ [] : [-(_1073214 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (16795 ^ _777959) ^ [_1099611, _1099613, _1099615, _1099617] : [class_Orderings_Olinorder(_1099611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099611), _1099613), _1099615)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099611), _1099613), _1099617)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099611), _1099613), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099611), _1099615), _1099617))))], (10310 ^ _777959) ^ [_959550, _959552, _959554] : [class_Lattices_Olattice(_959550), hBOOL(hAPP(c_Finite__Set_Ofinite(_959550), _959552)), hBOOL(hAPP(hAPP(c_member(_959550), _959554), _959552)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_959550), _959554), c_Big__Operators_Olattice__class_OSup__fin(_959550, _959552)) = _959554)], (30211 ^ _777959) ^ [_1349286, _1349288, _1349290] : [class_Divides_Osemiring__div(_1349286), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1349286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1349286), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1349286), _1349288), _1349290)), _1349290)), c_Divides_Odiv__class_Omod(_1349286, _1349288, _1349290)) = _1349288)], (41974 ^ _777959) ^ [_1604980, _1604982, _1604984, _1604986, _1604988] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1604980, _1604982), _1604984), hAPP(hAPP(c_COMBS(_1604980, tc_fun(_1604982, tc_HOL_Obool), tc_fun(_1604982, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1604982, tc_HOL_Obool), tc_fun(tc_fun(_1604982, tc_HOL_Obool), tc_fun(_1604982, tc_HOL_Obool)), _1604980), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1604982, tc_HOL_Obool))), _1604986)), _1604988)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1604980, _1604982), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1604980, _1604982), _1604984), _1604986)), hAPP(hAPP(c_Product__Type_OSigma(_1604980, _1604982), _1604984), _1604988)))], (48258 ^ _777959) ^ [_1749366, _1749368] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1749366)), hAPP(c_Code__Numeral_Oof__nat, _1749368)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1749366), _1749368)))], (10120 ^ _777959) ^ [_954484, _954486, _954488, _954490] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954484, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954484, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954484, tc_HOL_Obool)), _954486), _954488)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954484, tc_HOL_Obool)), _954488), _954490))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954484, tc_HOL_Obool)), _954490), _954486)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954484, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954484, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954484, tc_HOL_Obool)), _954486), _954488)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954484, tc_HOL_Obool)), _954488), _954490))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954484, tc_HOL_Obool)), _954490), _954486)))], (4868 ^ _777959) ^ [_852176, _852178, _852180, _852182, _852184, _852186, _852188, _852190] : [-(c_Lazy__Sequence_Oproduct(_852190, _852186, _852182, _852178) = c_Lazy__Sequence_Oproduct(_852188, _852184, _852180, _852176)), _852190 = _852188, _852186 = _852184, _852182 = _852180, _852178 = _852176], (26464 ^ _777959) ^ [_1279205, _1279207, _1279209] : [class_Fields_Olinordered__field(_1279205), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279205), c_Groups_Ozero__class_Ozero(_1279205)), _1279207)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1279205), _1279209), c_Groups_Ozero__class_Ozero(_1279205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1279205), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1279205), _1279207), _1279209)), c_Groups_Ozero__class_Ozero(_1279205))))], (35445 ^ _777959) ^ [_1448506] : [-(_1448506 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1448506), 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)))))], (24526 ^ _777959) ^ [_1243712, _1243714] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1243712), _1243714))))], (16431 ^ _777959) ^ [_1092484, _1092486, _1092488] : [class_Orderings_Olinorder(_1092484), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1092484), _1092486), _1092488) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1092484), _1092488), _1092486))], (18201 ^ _777959) ^ [_1125650, _1125652, _1125654] : [class_Orderings_Olinorder(_1125650), hBOOL(hAPP(c_Finite__Set_Ofinite(_1125650), _1125652)), -(hBOOL(hAPP(hAPP(c_member(_1125650), _1125654), _1125652))), -(c_Big__Operators_Olattice_OInf__fin(_1125650, c_Orderings_Oord__class_Omin(_1125650), hAPP(hAPP(c_Set_Oinsert(_1125650), _1125654), _1125652)) = hAPP(hAPP(c_Finite__Set_Ofold(_1125650, _1125650, c_Orderings_Oord__class_Omin(_1125650)), _1125654), _1125652))], (19244 ^ _777959) ^ [_1147471, _1147473, _1147475] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1147471), 19247 ^ _777959 : [(19254 ^ _777959) ^ [] : [_1147475 = c_Groups_Ozero__class_Ozero(_1147471), -(_1147473 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1147471), _1147473), _1147475))], (19248 ^ _777959) ^ [] : [_1147473 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1147471), _1147473), _1147475), -(_1147475 = c_Groups_Ozero__class_Ozero(_1147471))]]], (44795 ^ _777959) ^ [_1668987, _1668989, _1668991] : [hAPP(c_List_Orev(_1668987), _1668989) = hAPP(hAPP(c_List_Olist_OCons(_1668987), _1668991), c_List_Olist_ONil(_1668987)), -(_1668989 = hAPP(hAPP(c_List_Olist_OCons(_1668987), _1668991), c_List_Olist_ONil(_1668987)))], (16781 ^ _777959) ^ [_1099340, _1099342, _1099344, _1099346, _1099348] : [class_Orderings_Olinorder(_1099340), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099340), _1099342), _1099344)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099340), _1099346), _1099348)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099340), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099340), _1099342), _1099346)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1099340), _1099344), _1099348))))], (41609 ^ _777959) ^ [_1593941, _1593943, _1593945, _1593947] : [-(c_List_Olist_Olist__size(_1593941, _1593943, hAPP(hAPP(c_List_Olist_OCons(_1593941), _1593945), _1593947)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1593943, _1593945)), c_List_Olist_Olist__size(_1593941, _1593943, _1593947))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (34267 ^ _777959) ^ [_1423078, _1423080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1423078), _1423080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1423078)), c_Int_OBit0(_1423080))))], (11056 ^ _777959) ^ [_974551, _974553, _974555, _974557] : [-(c_Option_Ooption_Ooption__rec(_974551, _974553, _974555, _974557, c_Option_Ooption_ONone(_974553)) = _974555)], (31610 ^ _777959) ^ [_1374793, _1374795, _1374797, _1374799, _1374801] : [c_Com_Ocom_OWhile(_1374793, _1374795) = c_Com_Ocom_OCond(_1374797, _1374799, _1374801)], (26078 ^ _777959) ^ [_1272475, _1272477, _1272479] : [class_Fields_Ofield__inverse__zero(_1272475), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1272475), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272475), _1272477), _1272479)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1272475), _1272477), hAPP(c_Groups_Ouminus__class_Ouminus(_1272475), _1272479)))], (18358 ^ _777959) ^ [_1130206, _1130208] : [class_Orderings_Olinorder(_1130206), hBOOL(hAPP(c_Finite__Set_Ofinite(_1130206), _1130208)), -(_1130208 = c_Orderings_Obot__class_Obot(tc_fun(_1130206, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1130206), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1130206), 18371 ^ [_1130206, _1130208]), 18372 ^ [_1130206, _1130208])), hAPP(hAPP(c_Set_Oinsert(_1130206), 18371 ^ [_1130206, _1130208]), hAPP(hAPP(c_Set_Oinsert(_1130206), 18372 ^ [_1130206, _1130208]), c_Orderings_Obot__class_Obot(tc_fun(_1130206, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1130206), c_Big__Operators_Olattice_OInf__fin(_1130206, c_Orderings_Oord__class_Omin(_1130206), _1130208)), _1130208)))], (34479 ^ _777959) ^ [_1426981] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1426981), 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, _1426981)))], (47542 ^ _777959) ^ [_1733390, _1733392] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1733390, _1733390)), _1733392)), c_Wellfounded_Oacyclic(_1733390, _1733392), -(c_Wellfounded_Owf(_1733390, _1733392))], (7844 ^ _777959) ^ [_911317, _911319, _911321, _911323] : [-(c_Com_Ocom_OWhile(_911317, _911319) = c_Com_Ocom_OWhile(_911321, _911323)), _911317 = _911321, _911319 = _911323], (34897 ^ _777959) ^ [_1434800] : [_1434800 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1434800) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (42080 ^ _777959) ^ [_1607167, _1607169] : [c_Orderings_Obot__class_Obot(tc_fun(_1607167, tc_HOL_Obool)) = hAPP(c_List_Oset(_1607167), _1607169), -(_1607169 = c_List_Olist_ONil(_1607167))], (35687 ^ _777959) ^ [_1454412, _1454414, _1454416, _1454418, _1454420, _1454422, _1454424] : [hBOOL(hAPP(hAPP(c_member(_1454412), _1454414), hAPP(hAPP(_1454416, _1454418), _1454420))), -(hBOOL(hAPP(hAPP(c_member(_1454412), _1454414), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1454422, _1454424, tc_fun(_1454412, tc_HOL_Obool)), _1454416), hAPP(hAPP(c_Product__Type_OPair(_1454422, _1454424), _1454418), _1454420)))))], (46285 ^ _777959) ^ [_1702139, _1702141, _1702143, _1702145, _1702147] : [-(c_List_Olist__all2(_1702139, _1702141, _1702143, _1702145, _1702147)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702139)), _1702145) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1702141)), _1702147), 46291 ^ _777959 : [(46294 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1702139, _1702141, tc_HOL_Obool), _1702143), 46290 ^ [_1702139, _1702141, _1702143, _1702145, _1702147]))], (46292 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1702139, _1702141)), 46290 ^ [_1702139, _1702141, _1702143, _1702145, _1702147]), hAPP(c_List_Oset(tc_prod(_1702139, _1702141)), hAPP(hAPP(c_List_Ozip(_1702139, _1702141), _1702145), _1702147)))))]]], (15150 ^ _777959) ^ [_1066490, _1066492, _1066494, _1066496, _1066498] : [class_Rings_Osemiring(_1066490), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066490), _1066492), _1066494)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066490), _1066496), _1066494)), _1066498)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066490), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066490), _1066492), _1066496)), _1066494)), _1066498))], (49802 ^ _777959) ^ [_1787986, _1787988, _1787990, _1787992] : [-(c_List_Olist__all(_1787986, _1787988, hAPP(hAPP(c_List_Oappend(_1787986), _1787990), _1787992))), c_List_Olist__all(_1787986, _1787988, _1787990), c_List_Olist__all(_1787986, _1787988, _1787992)], (50982 ^ _777959) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (19216 ^ _777959) ^ [_1147040, _1147042] : [class_Groups_Olinordered__ab__group__add(_1147040), 19219 ^ _777959 : [(19226 ^ _777959) ^ [] : [_1147042 = c_Groups_Ozero__class_Ozero(_1147040), -(c_Groups_Ozero__class_Ozero(_1147040) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1147040), _1147042), _1147042))], (19220 ^ _777959) ^ [] : [c_Groups_Ozero__class_Ozero(_1147040) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1147040), _1147042), _1147042), -(_1147042 = c_Groups_Ozero__class_Ozero(_1147040))]]], (22703 ^ _777959) ^ [_1211004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1211004)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1211004 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (47444 ^ _777959) ^ [_1731409] : [-(c_Wellfounded_OwfP(_1731409, hAPP(c_COMBK(tc_fun(_1731409, tc_HOL_Obool), _1731409), hAPP(c_COMBK(tc_HOL_Obool, _1731409), c_fFalse))))], (50098 ^ _777959) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29046 ^ _777959) ^ [_1325325, _1325327] : [class_Orderings_Olinorder(_1325325), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1325325, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1325325), _1325327)) = hAPP(c_SetInterval_Oord__class_OatMost(_1325325), _1325327))], (24421 ^ _777959) ^ [_1241846, _1241848] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241846)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241848)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1241846), _1241848)))], (37306 ^ _777959) ^ [_1489715, _1489717, _1489719] : [-(hAPP(c_Relation_OField(_1489715), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1489715, _1489715), tc_HOL_Obool)), _1489717), _1489719)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1489715, tc_HOL_Obool)), hAPP(c_Relation_OField(_1489715), _1489717)), hAPP(c_Relation_OField(_1489715), _1489719)))], (51088 ^ _777959) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (21928 ^ _777959) ^ [_1194672, _1194674, _1194676, _1194678, _1194680] : [class_Groups_Ocomm__monoid__add(_1194672), hBOOL(hAPP(c_Finite__Set_Ofinite(_1194674), _1194676)), 21935 ^ _777959 : [(21942 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1194674), _1194678), _1194676))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1194674, _1194672), hAPP(hAPP(c_COMBC(_1194674, _1194672, _1194672), hAPP(hAPP(c_COMBS(_1194674, _1194672, tc_fun(_1194672, _1194672)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1194672, tc_fun(_1194672, _1194672)), _1194674), c_If(_1194672)), hAPP(c_fequal, _1194678))), _1194680)), c_Groups_Ozero__class_Ozero(_1194672))), _1194676) = c_Groups_Ozero__class_Ozero(_1194672))], (21936 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1194674), _1194678), _1194676)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1194674, _1194672), hAPP(hAPP(c_COMBC(_1194674, _1194672, _1194672), hAPP(hAPP(c_COMBS(_1194674, _1194672, tc_fun(_1194672, _1194672)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1194672, tc_fun(_1194672, _1194672)), _1194674), c_If(_1194672)), hAPP(c_fequal, _1194678))), _1194680)), c_Groups_Ozero__class_Ozero(_1194672))), _1194676) = hAPP(_1194680, _1194678))]]], (25000 ^ _777959) ^ [_1251691, _1251693] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251691)), 25003 ^ _777959 : [(25010 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251693)), -(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), _1251693), _1251691))))], (25004 ^ _777959) ^ [] : [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), _1251693), _1251691))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251693)))]]], (7458 ^ _777959) ^ [_903094, _903096, _903098] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_903094), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_903094, tc_HOL_Obool)), _903096), _903098))), 7461 ^ _777959 : [(7464 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_903094), _903098)))], (7462 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_903094), _903096)))]]], (29970 ^ _777959) ^ [_1344523, _1344525, _1344527, _1344529] : [class_Divides_Osemiring__div(_1344523), -(c_Divides_Odiv__class_Omod(_1344523, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344523), _1344525), c_Divides_Odiv__class_Omod(_1344523, _1344527, _1344529)), _1344529) = c_Divides_Odiv__class_Omod(_1344523, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344523), _1344525), _1344527), _1344529))], (22772 ^ _777959) ^ [_1212263, _1212265] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1212263), _1212265)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212263)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1212265))))], (7112 ^ _777959) ^ [_896718, _896720] : [class_Lattices_Osemilattice__sup(_896718), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_896718), _896720), _896720) = _896720)], (34655 ^ _777959) ^ [_1430050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1430050), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1430050 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1430050 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (48781 ^ _777959) ^ [_1761965, _1761967] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1761965), tc_List_Olist(_1761965)), tc_HOL_Obool)), c_List_Olistrel(_1761965, _1761967)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1761965), c_List_Olistrel1(_1761965, _1761967)))))], (2158 ^ _777959) ^ [_809683, _809685, _809687, _809689] : [-(c_Orderings_Oord_Omin(_809689, _809685) = c_Orderings_Oord_Omin(_809687, _809683)), _809689 = _809687, _809685 = _809683], (9836 ^ _777959) ^ [_948863, _948865, _948867, _948869] : [class_Lattices_Osemilattice__inf(_948863), 9839 ^ _777959 : [(9848 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948863), _948865), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_948863), _948867), _948869)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948863), _948865), _948867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948863), _948865), _948869))], (9840 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948863), _948865), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_948863), _948867), _948869))), 9843 ^ _777959 : [(9846 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948863), _948865), _948869)))], (9844 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948863), _948865), _948867)))]]]]], (47624 ^ _777959) ^ [_1735216, _1735218] : [47626 ^ _777959 : [(47629 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735218), 47625 ^ [_1735216, _1735218]))], (47627 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 47625 ^ [_1735216, _1735218]), _1735216)))]], -(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)), _1735218), _1735216))], (19540 ^ _777959) ^ [_1151768] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151768)))], (43566 ^ _777959) ^ [_1643866] : [-(c_List_Orotate(_1643866, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1643866)))], (44985 ^ _777959) ^ [_1672969, _1672971, _1672973] : [-(hAPP(c_List_Orotate(_1672969, _1672971), hAPP(c_List_Orev(_1672969), _1672973)) = hAPP(c_List_Orev(_1672969), hAPP(c_List_Orotate(_1672969, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672969)), _1672973)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1672971, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672969)), _1672973)))), _1672973)))], (48350 ^ _777959) ^ [_1750915] : [-(c_Code__Numeral_OSuc__code__numeral(_1750915) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1750915))))], (32057 ^ _777959) ^ [_1383347, _1383349, _1383351] : [class_Int_Onumber__ring(_1383347), class_Rings_Olinordered__idom(_1383347), 32064 ^ _777959 : [(32071 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1383349), _1383351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1383347), hAPP(c_Int_Onumber__class_Onumber__of(_1383347), _1383349)), hAPP(c_Int_Onumber__class_Onumber__of(_1383347), _1383351))))], (32065 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1383347), hAPP(c_Int_Onumber__class_Onumber__of(_1383347), _1383349)), hAPP(c_Int_Onumber__class_Onumber__of(_1383347), _1383351))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1383349), _1383351)))]]], (38564 ^ _777959) ^ [_1517750, _1517752, _1517754, _1517756] : [c_Fun_Oinj__on(_1517750, _1517752, _1517754, c_Orderings_Otop__class_Otop(tc_fun(_1517750, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1517750, _1517752, c_Orderings_Otop__class_Otop(tc_fun(_1517750, tc_HOL_Obool)), _1517754), hAPP(_1517754, _1517756)) = _1517756)], (33149 ^ _777959) ^ [_1403847, _1403849] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403847)))), 33152 ^ _777959 : [(33159 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403849)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403847), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403849)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403847), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403849))))], (33153 ^ _777959) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403849))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403847), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403849)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403847))]]], (11750 ^ _777959) ^ [_989659, _989661, _989663, _989665, _989667, _989669] : [-(hAPP(c_Set_Oimage(_989659, _989661, _989663), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989665, tc_fun(_989659, tc_HOL_Obool)), _989667), _989669)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_989665, tc_fun(_989661, tc_HOL_Obool)), _989667), hAPP(hAPP(c_COMBB(tc_fun(_989659, tc_HOL_Obool), tc_fun(_989661, tc_HOL_Obool), _989665), c_Set_Oimage(_989659, _989661, _989663)), _989669)))], (17191 ^ _777959) ^ [_1106587, _1106589, _1106591] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1106587, tc_HOL_Obool)), _1106589), _1106591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1106587, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1106587, tc_HOL_Obool), _1106591)), _1106589)))], (51006 ^ _777959) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (38942 ^ _777959) ^ [_1527138, _1527140] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1527138), hAPP(c_List_Oset(_1527138), _1527140))))], (41358 ^ _777959) ^ [_1588170, _1588172, _1588174, _1588176] : [-(_1588170 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588172)), _1588174)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1588172, hAPP(hAPP(c_List_Olist__update(_1588172, _1588174), _1588170), _1588176)) = hAPP(hAPP(c_List_Olist__update(_1588172, c_List_Obutlast(_1588172, _1588174)), _1588170), _1588176))], (42847 ^ _777959) ^ [_1627038, _1627040, _1627042] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627038)), hAPP(hAPP(c_List_Oappend(_1627038), _1627040), _1627042)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627038)), _1627040)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627038)), _1627042)))], (44128 ^ _777959) ^ [_1656077, _1656079] : [class_Orderings_Olinorder(_1656077), -(c_List_Olinorder__class_Osorted(_1656077, hAPP(hAPP(c_List_Olist_OCons(_1656077), _1656079), c_List_Olist_ONil(_1656077))))], (11658 ^ _777959) ^ [_987342, _987344, _987346, _987348, _987350] : [hBOOL(hAPP(hAPP(c_member(_987342), _987344), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_987346, tc_fun(_987342, tc_HOL_Obool)), _987348), _987350))), 11662 ^ _777959 : [(11665 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_987342), _987344), hAPP(_987350, 11661 ^ [_987342, _987344, _987346, _987348, _987350]))))], (11663 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_987346), 11661 ^ [_987342, _987344, _987346, _987348, _987350]), _987348)))]]], (30679 ^ _777959) ^ [_1357745, _1357747] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1357745, _1357747)) = _1357747, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1357745), _1357747) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29096 ^ _777959) ^ [_1326215, _1326217, _1326219] : [class_Orderings_Oorder(_1326215), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1326215, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1326215, _1326217), _1326219)), hAPP(c_SetInterval_Oord__class_OatLeast(_1326215), _1326219)) = c_Orderings_Obot__class_Obot(tc_fun(_1326215, tc_HOL_Obool)))], (44430 ^ _777959) ^ [_1661029, _1661031, _1661033, _1661035, _1661037] : [class_Orderings_Olinorder(_1661029), -(c_List_Olinorder__class_Osorted(_1661029, hAPP(hAPP(c_List_Omap(_1661031, _1661029), _1661033), hAPP(c_List_Ofilter(_1661031, hAPP(hAPP(c_COMBC(_1661031, _1661029, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1661029, tc_fun(_1661029, tc_HOL_Obool), _1661031), c_fequal), _1661033)), hAPP(_1661035, _1661037))), _1661037))))], (34461 ^ _777959) ^ [] : [-(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))))], (22735 ^ _777959) ^ [_1211504, _1211506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1211504), _1211506)), -(_1211506 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1211504), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 22738 ^ [_1211504, _1211506]))))], (29741 ^ _777959) ^ [_1339226, _1339228] : [-(hAPP(c_Set_OPow(_1339226), _1339228) = hAPP(c_Set_OCollect(tc_fun(_1339226, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1339226, tc_HOL_Obool), tc_fun(_1339226, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1339226, tc_HOL_Obool))), _1339228)))], (41553 ^ _777959) ^ [_1592636, _1592638, _1592640] : [-(hAPP(c_List_Oset(_1592636), hAPP(hAPP(c_List_Olist_OCons(_1592636), _1592638), _1592640)) = hAPP(hAPP(c_Set_Oinsert(_1592636), _1592638), hAPP(c_List_Oset(_1592636), _1592640)))], (19512 ^ _777959) ^ [_1151355, _1151357] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1151355), _1151357) = _1151355, -(_1151357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (13505 ^ _777959) ^ [_1025726] : [class_Complete__Lattice_Ocomplete__lattice(_1025726), -(c_Complete__Lattice_OSup__class_OSup(_1025726, c_Orderings_Otop__class_Otop(tc_fun(_1025726, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_1025726))], (44000 ^ _777959) ^ [_1652733, _1652735, _1652737] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1652733, tc_HOL_Obool)), hAPP(c_List_Oset(_1652733), hAPP(c_List_Ofilter(_1652733, _1652735), _1652737))), hAPP(c_List_Oset(_1652733), _1652737))))], (27818 ^ _777959) ^ [_1303509, _1303511] : [class_Rings_Oring__1(_1303509), 27821 ^ _777959 : [(27828 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303511), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1303509), _1303511) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1303509), hAPP(c_Int_Onat, _1303511)))], (27822 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1303511), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1303509), _1303511) = hAPP(c_Groups_Ouminus__class_Ouminus(_1303509), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1303509), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1303511)))))]]], (8712 ^ _777959) ^ [_928250, _928252, _928254, _928256, _928258] : [hAPP(_928254, _928256) = _928258, -(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_928250, _928252), _928254), _928256), _928258) = _928254)], (38762 ^ _777959) ^ [_1522118, _1522120, _1522122, _1522124, _1522126] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1522118, _1522120, _1522122), _1522124), _1522126)), -(hBOOL(hAPP(_1522124, hAPP(_1522122, _1522126))))], (25570 ^ _777959) ^ [_1262670, _1262672] : [-(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)), _1262670)), 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), _1262672), _1262670))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1262670), _1262672))], (15028 ^ _777959) ^ [_1063786, _1063788] : [class_Lattices_Oab__semigroup__idem__mult(_1063786), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1063786), _1063788), _1063788) = _1063788)], (10118 ^ _777959) ^ [_954436, _954438, _954440] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_954436, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954436, tc_HOL_Obool)), _954438), _954440)), _954438)))], (14313 ^ _777959) ^ [_1045029, _1045031, _1045033] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045029), _1045031)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1045029, tc_HOL_Obool)), _1045031), _1045033)), -(hAPP(c_Finite__Set_Ocard(_1045029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1045029, tc_HOL_Obool)), _1045033), _1045031)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1045029), _1045033)), hAPP(c_Finite__Set_Ocard(_1045029), _1045031)))], (9820 ^ _777959) ^ [_948607, _948609, _948611] : [class_Lattices_Osemilattice__inf(_948607), 9823 ^ _777959 : [(9830 ^ _777959) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_948607), _948609), _948611) = _948609, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948607), _948609), _948611)))], (9824 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948607), _948609), _948611)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_948607), _948609), _948611) = _948609)]]], (10128 ^ _777959) ^ [_954875, _954877, _954879, _954881] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954875, tc_HOL_Obool)), _954877), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954875, tc_HOL_Obool)), _954879), _954881)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954875, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954875, tc_HOL_Obool)), _954877), _954879)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954875, tc_HOL_Obool)), _954877), _954881)))], (48326 ^ _777959) ^ [_1750495, _1750497] : [_1750495 = _1750497, -(hAPP(c_Code__Numeral_Onat__of, _1750495) = hAPP(c_Code__Numeral_Onat__of, _1750497))], (28954 ^ _777959) ^ [_1323732] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1323732)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1323732))], (43935 ^ _777959) ^ [_1651539, _1651541, _1651543, _1651545] : [-(hBOOL(hAPP(_1651539, _1651541))), -(hAPP(c_List_Ofilter(_1651543, _1651539), hAPP(hAPP(c_List_Olist_OCons(_1651543), _1651541), _1651545)) = hAPP(c_List_Ofilter(_1651543, _1651539), _1651545))], (51064 ^ _777959) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (7172 ^ _777959) ^ [_897940, _897942, _897944, _897946] : [class_Lattices_Osemilattice__sup(_897940), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897940), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897940), _897942), _897944)), _897946) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897940), _897942), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897940), _897944), _897946)))], (15745 ^ _777959) ^ [_1077491, _1077493] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1077491), _1077493)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1077491)), _1077493)))], (25385 ^ _777959) ^ [_1259030, _1259032] : [25393 ^ _777959 : [(25396 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1259032, 25392 ^ [_1259030, _1259032])))], (25394 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25392 ^ [_1259030, _1259032]), _1259030)))]], 25386 ^ _777959 : [(25387 ^ _777959) ^ [_1259098] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1259098), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1259030))), hBOOL(hAPP(_1259032, _1259098))]]], (42879 ^ _777959) ^ [_1627940, _1627942, _1627944] : [_1627940 = c_List_Olist_ONil(_1627942), -(c_List_Obutlast(_1627942, hAPP(hAPP(c_List_Oappend(_1627942), _1627944), _1627940)) = c_List_Obutlast(_1627942, _1627944))], (42284 ^ _777959) ^ [_1611681, _1611683, _1611685, _1611687] : [_1611681 = c_Orderings_Obot__class_Obot(tc_fun(_1611683, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1611683, _1611685), _1611685, c_Product__Type_Osnd(_1611683, _1611685)), hAPP(hAPP(c_Product__Type_OSigma(_1611683, _1611685), _1611681), hAPP(c_COMBK(tc_fun(_1611685, tc_HOL_Obool), _1611683), _1611687))) = c_Orderings_Obot__class_Obot(tc_fun(_1611685, tc_HOL_Obool)))], (19823 ^ _777959) ^ [_1156507, _1156509] : [class_Groups_Olinordered__ab__group__add(_1156507), 19826 ^ _777959 : [(19833 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156507), _1156509), c_Groups_Ozero__class_Ozero(_1156507))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156507), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156507), _1156509), _1156509)), c_Groups_Ozero__class_Ozero(_1156507))))], (19827 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156507), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1156507), _1156509), _1156509)), c_Groups_Ozero__class_Ozero(_1156507))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156507), _1156509), c_Groups_Ozero__class_Ozero(_1156507))))]]], (33345 ^ _777959) ^ [_1406873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1406873), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406873)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11134 ^ _777959) ^ [_976161, _976163, _976165, _976167, _976169] : [hAPP(_976161, _976163) = c_Option_Ooption_ONone(_976165), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976167, tc_HOL_Obool)), c_Map_Odom(_976167, _976165, _976161)), hAPP(hAPP(c_Set_Oinsert(_976167), _976163), _976169)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976167, tc_HOL_Obool)), c_Map_Odom(_976167, _976165, _976161)), _976169))], (48160 ^ _777959) ^ [_1747425, _1747427, _1747429] : [-(c_Random_Oselect__weight(_1747425, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1747425)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1747425), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1747427)), _1747429)) = c_Random_Oselect__weight(_1747425, _1747429))], (28255 ^ _777959) ^ [_1310618] : [c_Nat__Transfer_Onat__set(_1310618), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1310618) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1310618)))], (49207 ^ _777959) ^ [_1772622, _1772624, _1772626] : [c_Relation_Ototal__on(_1772622, _1772624, _1772626), 49210 ^ _777959 : [(49211 ^ _777959) ^ [_1772766] : [hBOOL(hAPP(hAPP(c_member(_1772622), _1772766), _1772624)), 49214 ^ _777959 : [(49215 ^ _777959) ^ [_1772906] : [hBOOL(hAPP(hAPP(c_member(_1772622), _1772906), _1772624)), -(_1772766 = _1772906), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1772622, _1772622)), hAPP(hAPP(c_Product__Type_OPair(_1772622, _1772622), _1772766), _1772906)), _1772626))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1772622, _1772622)), hAPP(hAPP(c_Product__Type_OPair(_1772622, _1772622), _1772906), _1772766)), _1772626)))]]]]], (37068 ^ _777959) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (42726 ^ _777959) ^ [_1624233, _1624235, _1624237, _1624239, _1624241] : [-(hAPP(hAPP(c_List_Oappend(_1624233), _1624235), _1624237) = hAPP(hAPP(c_List_Olist_OCons(_1624233), _1624239), _1624241)), 42727 ^ _777959 : [(42734 ^ _777959) ^ [_1624416] : [_1624235 = hAPP(hAPP(c_List_Olist_OCons(_1624233), _1624239), _1624416), hAPP(hAPP(c_List_Oappend(_1624233), _1624416), _1624237) = _1624241], (42728 ^ _777959) ^ [] : [_1624235 = c_List_Olist_ONil(_1624233), _1624237 = hAPP(hAPP(c_List_Olist_OCons(_1624233), _1624239), _1624241)]]], (43440 ^ _777959) ^ [_1641710, _1641712, _1641714] : [-(_1641710 = c_List_Olist_ONil(_1641712)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641714), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641712)), _1641710))), -(hAPP(c_List_Ohd(_1641712), hAPP(hAPP(c_List_Odrop(_1641712), _1641714), _1641710)) = hAPP(hAPP(c_List_Onth(_1641712), _1641710), _1641714))], (18093 ^ _777959) ^ [_1123428, _1123430, _1123432] : [class_Orderings_Olinorder(_1123428), hBOOL(hAPP(c_Finite__Set_Ofinite(_1123428), _1123430)), 18100 ^ _777959 : [(18107 ^ _777959) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1123428, tc_HOL_Obool)), _1123430), hAPP(hAPP(c_Set_Oinsert(_1123428), _1123432), c_Orderings_Obot__class_Obot(tc_fun(_1123428, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1123428, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1123428, c_Orderings_Oord__class_Omax(_1123428), hAPP(hAPP(c_Set_Oinsert(_1123428), _1123432), _1123430)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1123428), _1123432), c_Big__Operators_Olattice_OSup__fin(_1123428, c_Orderings_Oord__class_Omax(_1123428), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1123428, tc_HOL_Obool)), _1123430), hAPP(hAPP(c_Set_Oinsert(_1123428), _1123432), c_Orderings_Obot__class_Obot(tc_fun(_1123428, tc_HOL_Obool)))))))], (18101 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1123428, tc_HOL_Obool)), _1123430), hAPP(hAPP(c_Set_Oinsert(_1123428), _1123432), c_Orderings_Obot__class_Obot(tc_fun(_1123428, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1123428, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1123428, c_Orderings_Oord__class_Omax(_1123428), hAPP(hAPP(c_Set_Oinsert(_1123428), _1123432), _1123430)) = _1123432)]]], (49302 ^ _777959) ^ [_1774995, _1774997] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1774995, _1774995), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1774997) = _1774997)], (13549 ^ _777959) ^ [_1026575, _1026577, _1026579, _1026581, _1026583] : [-(_1026575 = c_Orderings_Obot__class_Obot(tc_fun(_1026577, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026577, tc_fun(_1026579, tc_HOL_Obool)), _1026575), hAPP(hAPP(c_COMBB(tc_fun(_1026579, tc_HOL_Obool), tc_fun(_1026579, tc_HOL_Obool), _1026577), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026579, tc_HOL_Obool)), _1026581)), _1026583)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026579, tc_HOL_Obool)), _1026581), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026577, tc_fun(_1026579, tc_HOL_Obool)), _1026575), _1026583)))], (9196 ^ _777959) ^ [_935801, _935803, _935805] : [9197 ^ _777959 : [(9200 ^ _777959) ^ [] : [_935803 = _935805], (9198 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_935801, tc_HOL_Obool)), _935803), _935805))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_935801, tc_HOL_Obool)), _935803), _935805)))], (14379 ^ _777959) ^ [_1046750, _1046752, _1046754, _1046756, _1046758, _1046760, _1046762] : [class_Groups_Ocomm__monoid__add(_1046750), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046752), _1046754)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046756), _1046758)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046752, _1046750), hAPP(hAPP(c_COMBS(_1046752, tc_fun(_1046756, tc_HOL_Obool), _1046750), hAPP(hAPP(c_COMBB(tc_fun(_1046756, _1046750), tc_fun(tc_fun(_1046756, tc_HOL_Obool), _1046750), _1046752), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046756, _1046750)), _1046760)), hAPP(hAPP(c_COMBB(tc_fun(_1046756, tc_HOL_Obool), tc_fun(_1046756, tc_HOL_Obool), _1046752), c_Set_OCollect(_1046756)), hAPP(hAPP(c_COMBB(tc_fun(_1046756, tc_HOL_Obool), tc_fun(_1046756, tc_HOL_Obool), _1046752), hAPP(c_COMBS(_1046756, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1046756), c_fconj), hAPP(hAPP(c_COMBC(_1046756, tc_fun(_1046756, tc_HOL_Obool), tc_HOL_Obool), c_member(_1046756)), _1046758)))), _1046762)))), _1046754) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046756, _1046750), hAPP(hAPP(c_COMBS(_1046756, tc_fun(_1046752, tc_HOL_Obool), _1046750), hAPP(hAPP(c_COMBB(tc_fun(_1046752, _1046750), tc_fun(tc_fun(_1046752, tc_HOL_Obool), _1046750), _1046756), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046752, _1046750)), hAPP(c_COMBC(_1046752, _1046756, _1046750), _1046760))), hAPP(hAPP(c_COMBB(tc_fun(_1046752, tc_HOL_Obool), tc_fun(_1046752, tc_HOL_Obool), _1046756), c_Set_OCollect(_1046752)), hAPP(hAPP(c_COMBB(tc_fun(_1046752, tc_HOL_Obool), tc_fun(_1046752, tc_HOL_Obool), _1046756), hAPP(c_COMBS(_1046752, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1046752), c_fconj), hAPP(hAPP(c_COMBC(_1046752, tc_fun(_1046752, tc_HOL_Obool), tc_HOL_Obool), c_member(_1046752)), _1046754)))), hAPP(c_COMBC(_1046752, _1046756, tc_HOL_Obool), _1046762))))), _1046758))], (41898 ^ _777959) ^ [_1603148, _1603150, _1603152, _1603154, _1603156, _1603158] : [class_Groups_Ocomm__monoid__add(_1603148), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1603150, _1603148), hAPP(hAPP(c_COMBC(_1603150, tc_fun(_1603152, tc_HOL_Obool), _1603148), hAPP(hAPP(c_COMBB(tc_fun(_1603152, _1603148), tc_fun(tc_fun(_1603152, tc_HOL_Obool), _1603148), _1603150), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1603152, _1603148)), _1603154)), _1603156)), _1603158) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1603150, _1603152), _1603148), hAPP(c_Product__Type_Oprod_Oprod__case(_1603150, _1603152, _1603148), _1603154)), hAPP(hAPP(c_Product__Type_OSigma(_1603150, _1603152), _1603158), hAPP(c_COMBK(tc_fun(_1603152, tc_HOL_Obool), _1603150), _1603156))))], (24283 ^ _777959) ^ [] : [-(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))))], (40091 ^ _777959) ^ [_1554761, _1554763, _1554765] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1554761)), c_List_Osublist(_1554761, _1554763, _1554765)) = 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(_1554761)), _1554763)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1554765)))))], (51318 ^ _777959) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (27357 ^ _777959) ^ [_1295600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1295600), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1295600) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29773 ^ _777959) ^ [_1340327] : [-(hAPP(c_Set_OPow(_1340327), c_Orderings_Obot__class_Obot(tc_fun(_1340327, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1340327, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1340327, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1340327, tc_HOL_Obool), tc_HOL_Obool))))], (30750 ^ _777959) ^ [_1358921, _1358923] : [class_Rings_Olinordered__idom(_1358921), 30753 ^ _777959 : [(30760 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358921), _1358923), c_Groups_Ozero__class_Ozero(_1358921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358921), c_Groups_Osgn__class_Osgn(_1358921, _1358923)), c_Groups_Ozero__class_Ozero(_1358921))))], (30754 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358921), c_Groups_Osgn__class_Osgn(_1358921, _1358923)), c_Groups_Ozero__class_Ozero(_1358921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358921), _1358923), c_Groups_Ozero__class_Ozero(_1358921))))]]], (25982 ^ _777959) ^ [_1270549, _1270551, _1270553, _1270555] : [class_Fields_Olinordered__field__inverse__zero(_1270549), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270549), _1270551), _1270553)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270549), _1270555), c_Groups_Ozero__class_Ozero(_1270549))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1270549), c_Groups_Ozero__class_Ozero(_1270549)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1270549), _1270551), _1270553))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1270549), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270549), _1270555), _1270551)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1270549), _1270555), _1270553))))], (48148 ^ _777959) ^ [_1747170, _1747172, _1747174] : [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, _1747170), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1747170)), _1747172)))), -(hBOOL(hAPP(hAPP(c_member(_1747170), hAPP(c_Product__Type_Ofst(_1747170, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1747170, _1747172), _1747174))), hAPP(c_List_Oset(_1747170), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1747170), _1747170), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1747170)), _1747172)))))], (39007 ^ _777959) ^ [_1528917, _1528919, _1528921, _1528923, _1528925, _1528927, _1528929, _1528931] : [hAPP(c_Fun_Ocomp(_1528917, _1528919, _1528921, _1528923), _1528925) = hAPP(c_Fun_Ocomp(_1528927, _1528919, _1528921, _1528929), _1528931), 39010 ^ _777959 : [(39011 ^ _777959) ^ [_1529032] : [-(hAPP(_1528923, hAPP(_1528925, _1529032)) = hAPP(_1528929, hAPP(_1528931, _1529032)))]]], (19472 ^ _777959) ^ [_1150840] : [hAPP(c_Nat_OSuc, _1150840) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29128 ^ _777959) ^ [_1326936, _1326938, _1326940] : [class_Orderings_Olinorder(_1326936), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1326936), _1326938), _1326940)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1326936, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1326936), _1326938)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1326936, _1326938, _1326940)) = hAPP(c_SetInterval_Oord__class_OatMost(_1326936), _1326940))], (50234 ^ _777959) ^ [_1796093, _1796095, _1796097, _1796099, _1796101, _1796103, _1796105] : [-(c_New__Random__Sequence_Opos__decr__bind(_1796093, _1796095, _1796097, _1796099, _1796101, _1796103, _1796105) = c_New__DSequence_Opos__decr__bind(_1796093, _1796095, hAPP(hAPP(hAPP(_1796097, _1796101), _1796103), _1796105), hAPP(hAPP(c_COMBC(_1796093, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1796095))), hAPP(hAPP(c_COMBC(_1796093, 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(_1796095)))), hAPP(hAPP(c_COMBC(_1796093, 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(_1796095))))), _1796099), _1796101)), _1796103)), _1796105)))], (9662 ^ _777959) ^ [_945194, _945196, _945198] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945194, tc_HOL_Obool)), _945196), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945194, tc_HOL_Obool)), _945196), _945198)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945194, tc_HOL_Obool)), _945196), _945198))], (49382 ^ _777959) ^ [_1777178, _1777180] : [-(c_Transitive__Closure_Ortrancl(_1777178, _1777180) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1777178, _1777178), 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(_1777178, _1777178), tc_HOL_Obool), tc_fun(tc_prod(_1777178, _1777178), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1777178, _1777178), tc_HOL_Obool)), _1777180)))], (37104 ^ _777959) ^ [_1483543, _1483545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1483543), _1483545)), -(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), _1483543), _1483545)), c_Wellfounded_Oless__than)))], (27812 ^ _777959) ^ [_1303407, _1303409] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1303407, _1303409)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1303409), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1303407), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (4794 ^ _777959) ^ [_850967, _850969, _850971, _850973, _850975, _850977, _850979, _850981] : [-(c_New__Random__Sequence_Oneg__map(_850981, _850977, _850973, _850969) = c_New__Random__Sequence_Oneg__map(_850979, _850975, _850971, _850967)), _850981 = _850979, _850977 = _850975, _850973 = _850971, _850969 = _850967], (7222 ^ _777959) ^ [_898939, _898941, _898943] : [hAPP(hAPP(c_COMBC(_898939, tc_fun(_898939, tc_HOL_Obool), tc_HOL_Obool), c_member(_898939)), _898941) = hAPP(hAPP(c_COMBC(_898939, tc_fun(_898939, tc_HOL_Obool), tc_HOL_Obool), c_member(_898939)), _898943), -(_898941 = _898943)], (5795 ^ _777959) ^ [_869782, _869784, _869786] : [c_Orderings_Obot__class_Obot(tc_fun(_869782, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_869782), _869784), _869786)], (13133 ^ _777959) ^ [_1017622, _1017624, _1017626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017622), _1017624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1017622), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1017626), _1017624))))], (42961 ^ _777959) ^ [_1629340, _1629342, _1629344] : [_1629344 = c_List_Olist_ONil(_1629340), -(hAPP(hAPP(c_List_Oappend(_1629340), _1629342), _1629344) = _1629342)], (11760 ^ _777959) ^ [_990120, _990122, _990124, _990126, _990128] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990120, tc_fun(_990122, tc_HOL_Obool)), _990124), hAPP(hAPP(c_COMBC(_990120, tc_fun(_990122, tc_HOL_Obool), tc_fun(_990122, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_990122, tc_HOL_Obool), tc_fun(tc_fun(_990122, tc_HOL_Obool), tc_fun(_990122, tc_HOL_Obool)), _990120), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990122, tc_HOL_Obool))), _990126)), _990128)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_990122, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_990120, tc_fun(_990122, tc_HOL_Obool)), _990124), _990126)), _990128))], (29592 ^ _777959) ^ [_1336008, _1336010, _1336012, _1336014, _1336016] : [class_Groups_Ocomm__monoid__mult(_1336008), hBOOL(hAPP(c_Finite__Set_Ofinite(_1336010), _1336012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1336010, tc_HOL_Obool)), _1336014), _1336012)), 29606 ^ _777959 : [(29609 ^ _777959) ^ [] : [hAPP(_1336016, 29605 ^ [_1336008, _1336010, _1336012, _1336014, _1336016]) = c_Groups_Oone__class_Oone(_1336008)], (29607 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1336010), 29605 ^ [_1336008, _1336010, _1336012, _1336014, _1336016]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1336010, tc_HOL_Obool)), _1336012), _1336014))))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336010, _1336008), _1336016), _1336012) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1336010, _1336008), _1336016), _1336014))], (4154 ^ _777959) ^ [_840851, _840853, _840855, _840857] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_840857, _840853) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_840855, _840851)), _840857 = _840855, _840853 = _840851], (8310 ^ _777959) ^ [_921648, _921650, _921652, _921654] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_921648, tc_HOL_Obool)), _921650), hAPP(hAPP(c_Set_Oinsert(_921648), _921652), _921654))), 8313 ^ _777959 : [(8320 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_921648), _921652), _921654))), 8323 ^ _777959 : [(8330 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_921648), _921652), _921650))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921648, tc_HOL_Obool)), _921650), _921654)))], (8324 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_921648), _921652), _921650)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_921648, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_921648, tc_HOL_Obool)), _921650), hAPP(hAPP(c_Set_Oinsert(_921648), _921652), c_Orderings_Obot__class_Obot(tc_fun(_921648, tc_HOL_Obool))))), _921654)))]]], (8314 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_921648), _921652), _921654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_921648, tc_HOL_Obool)), _921650), _921654)))]]], (9528 ^ _777959) ^ [_942458, _942460, _942462, _942464, _942466] : [class_Rings_Oring(_942458), hBOOL(hAPP(c_Finite__Set_Ofinite(_942460), _942462)), hBOOL(hAPP(hAPP(c_member(_942460), _942464), _942462)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_942460, _942458), _942466), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_942460, tc_HOL_Obool)), _942462), hAPP(hAPP(c_Set_Oinsert(_942460), _942464), c_Orderings_Obot__class_Obot(tc_fun(_942460, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_942458), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_942460, _942458), _942466), _942462)), hAPP(_942466, _942464)))], (10110 ^ _777959) ^ [_954267, _954269, _954271] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_954267, tc_HOL_Obool)), _954269), _954271)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954267, tc_HOL_Obool)), _954269), _954271) = _954269)], (15980 ^ _777959) ^ [_1082372, _1082374] : [class_Orderings_Olinorder(_1082372), hBOOL(hAPP(c_Finite__Set_Ofinite(_1082372), _1082374)), -(_1082374 = c_Orderings_Obot__class_Obot(tc_fun(_1082372, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1082372), c_Big__Operators_Olinorder__class_OMin(_1082372, _1082374)), _1082374)))], (28992 ^ _777959) ^ [_1324373, _1324375, _1324377] : [class_Orderings_Oorder(_1324373), 28995 ^ _777959 : [(29002 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324373), _1324377), _1324375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1324373, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1324373), _1324375)), hAPP(c_SetInterval_Oord__class_OatLeast(_1324373), _1324377))))], (28996 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1324373, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1324373), _1324375)), hAPP(c_SetInterval_Oord__class_OatLeast(_1324373), _1324377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1324373), _1324377), _1324375)))]]], (40296 ^ _777959) ^ [_1559899, _1559901, _1559903] : [hBOOL(hAPP(hAPP(c_member(_1559899), _1559901), hAPP(c_List_Oset(_1559899), _1559903))), 40300 ^ _777959 : [(40303 ^ _777959) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1559899), _1559903), 40299 ^ [_1559899, _1559901, _1559903]) = _1559901)], (40301 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40299 ^ [_1559899, _1559901, _1559903]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1559899)), _1559903))))]]], (34411 ^ _777959) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (37150 ^ _777959) ^ [_1485128, _1485130, _1485132, _1485134, _1485136] : [hBOOL(hAPP(hAPP(c_member(_1485128), _1485130), hAPP(c_Relation_OImage(_1485132, _1485128, _1485134), hAPP(hAPP(c_Set_Oinsert(_1485132), _1485136), c_Orderings_Obot__class_Obot(tc_fun(_1485132, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1485132, _1485128)), hAPP(hAPP(c_Product__Type_OPair(_1485132, _1485128), _1485136), _1485130)), _1485134)))], (17789 ^ _777959) ^ [_1117886, _1117888, _1117890] : [class_Orderings_Olinorder(_1117886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1117886), _1117888)), -(_1117888 = c_Orderings_Obot__class_Obot(tc_fun(_1117886, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1117886), _1117890), c_Big__Operators_Olattice_OSup__fin(_1117886, c_Orderings_Oord__class_Omax(_1117886), _1117888)) = c_Big__Operators_Olattice_OSup__fin(_1117886, c_Orderings_Oord__class_Omax(_1117886), hAPP(c_Set_OCollect(_1117886), hAPP(hAPP(c_COMBB(tc_fun(_1117886, tc_HOL_Obool), tc_HOL_Obool, _1117886), c_HOL_OEx(_1117886)), hAPP(hAPP(c_COMBC(_1117886, tc_fun(_1117886, tc_HOL_Obool), tc_fun(_1117886, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1117886, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1117886, tc_HOL_Obool), tc_fun(_1117886, tc_HOL_Obool)), _1117886), c_COMBS(_1117886, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1117886, tc_HOL_Obool), tc_fun(_1117886, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1117886), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1117886), c_fconj)), hAPP(hAPP(c_COMBC(_1117886, tc_fun(_1117886, _1117886), tc_fun(_1117886, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1117886, tc_HOL_Obool), tc_fun(tc_fun(_1117886, _1117886), tc_fun(_1117886, tc_HOL_Obool)), _1117886), c_COMBB(_1117886, tc_HOL_Obool, _1117886)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1117886), _1117890))))), hAPP(hAPP(c_COMBC(_1117886, tc_fun(_1117886, tc_HOL_Obool), tc_HOL_Obool), c_member(_1117886)), _1117888))))))], (18536 ^ _777959) ^ [_1134349, _1134351, _1134353] : [class_Groups_Oab__semigroup__mult(_1134349), hBOOL(hAPP(c_Finite__Set_Ofinite(_1134349), _1134351)), -(hBOOL(hAPP(hAPP(c_member(_1134349), _1134353), _1134351))), -(hAPP(c_Finite__Set_Ofold1(_1134349, c_Groups_Otimes__class_Otimes(_1134349)), hAPP(hAPP(c_Set_Oinsert(_1134349), _1134353), _1134351)) = hAPP(hAPP(c_Finite__Set_Ofold(_1134349, _1134349, c_Groups_Otimes__class_Otimes(_1134349)), _1134353), _1134351))], (29426 ^ _777959) ^ [_1332764, _1332766, _1332768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332764)), 29429 ^ _777959 : [(29430 ^ _777959) ^ [_1332898] : [29432 ^ _777959 : [(29438 ^ _777959) ^ [] : [-(_1332898 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 29434 ^ [_1332764, _1332766, _1332768, _1332898]), 29431 ^ [_1332764, _1332766, _1332768, _1332898]))], (29436 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29434 ^ [_1332764, _1332766, _1332768, _1332898]), _1332766)))], (29433 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 29431 ^ [_1332764, _1332766, _1332768, _1332898]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1332764))))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1332768), _1332898)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1332768), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1332898), _1332764))))]]], (28886 ^ _777959) ^ [_1322539] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1322539)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1322539)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1322539), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (37436 ^ _777959) ^ [_1492979, _1492981, _1492983, _1492985] : [c_Equiv__Relations_Oequiv(_1492979, _1492981, _1492983), hBOOL(hAPP(hAPP(c_member(_1492979), _1492985), _1492981)), -(hBOOL(hAPP(hAPP(c_member(_1492979), _1492985), hAPP(c_Relation_OImage(_1492979, _1492979, _1492983), hAPP(hAPP(c_Set_Oinsert(_1492979), _1492985), c_Orderings_Obot__class_Obot(tc_fun(_1492979, tc_HOL_Obool)))))))], (7258 ^ _777959) ^ [_899643, _899645, _899647] : [class_Lattices_Osemilattice__sup(_899643), 7261 ^ _777959 : [(7268 ^ _777959) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_899643), _899645), _899647) = _899647, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899643), _899645), _899647)))], (7262 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899643), _899645), _899647)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_899643), _899645), _899647) = _899647)]]], (40821 ^ _777959) ^ [_1571725, _1571727, _1571729, _1571731, _1571733] : [hBOOL(hAPP(hAPP(c_member(_1571725), _1571727), hAPP(c_List_Oset(_1571725), _1571729))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1571731), hAPP(_1571733, _1571727))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1571731), c_List_Olist_Olist__size(_1571725, _1571733, _1571729))))], (48829 ^ _777959) ^ [_1762989, _1762991, _1762993, _1762995] : [-(c_Wellfounded_Owf(_1762989, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1762989, _1762989)), hAPP(hAPP(c_Product__Type_OPair(_1762989, _1762989), _1762991), _1762993)), _1762995))), c_Wellfounded_Owf(_1762989, _1762995), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1762989, _1762989)), hAPP(hAPP(c_Product__Type_OPair(_1762989, _1762989), _1762993), _1762991)), c_Transitive__Closure_Ortrancl(_1762989, _1762995))))], (33311 ^ _777959) ^ [_1406382] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1406382), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1406382)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1406382)))], (22327 ^ _777959) ^ [_1203170, _1203172] : [class_Groups_Olinordered__ab__group__add(_1203170), 22330 ^ _777959 : [(22337 ^ _777959) ^ [] : [_1203172 = c_Groups_Ozero__class_Ozero(_1203170), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1203170), _1203172), _1203172) = c_Groups_Ozero__class_Ozero(_1203170))], (22331 ^ _777959) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1203170), _1203172), _1203172) = c_Groups_Ozero__class_Ozero(_1203170), -(_1203172 = c_Groups_Ozero__class_Ozero(_1203170))]]], (47381 ^ _777959) ^ [_1729640, _1729642] : [-(hAPP(c_Relation_OField(_1729640), _1729642) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1729640, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1729640, _1729640), _1729642)), hAPP(c_Relation_ORange(_1729640, _1729640), _1729642)))], (42549 ^ _777959) ^ [_1619856, _1619858, _1619860] : [-(hAPP(c_Fun_Ocomp(_1619856, _1619858, _1619856, _1619860), c_Fun_Oid(_1619856)) = _1619860)], (30114 ^ _777959) ^ [_1347535, _1347537, _1347539, _1347541] : [class_Divides_Osemiring__div(_1347535), -(c_Divides_Odiv__class_Omod(_1347535, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1347535), _1347537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347535), _1347539), _1347541)), _1347539) = c_Divides_Odiv__class_Omod(_1347535, _1347537, _1347539))], (24397 ^ _777959) ^ [_1241399, _1241401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241399)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241401))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1241399), _1241401)))], (20987 ^ _777959) ^ [_1176828, _1176830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1176830), _1176828)), -(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), _1176828), _1176830))))], (17605 ^ _777959) ^ [_1114308, _1114310, _1114312] : [class_Orderings_Olinorder(_1114308), hBOOL(hAPP(c_Finite__Set_Ofinite(_1114308), _1114310)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1114308), _1114312)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1114308, tc_HOL_Obool)), _1114310), _1114312) = c_Orderings_Obot__class_Obot(tc_fun(_1114308, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1114308), c_Big__Operators_Olinorder__class_OMax(_1114308, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1114308, tc_HOL_Obool)), _1114310), _1114312))), c_Big__Operators_Olinorder__class_OMax(_1114308, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1114308, tc_HOL_Obool)), _1114310), _1114312))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1114308), c_Big__Operators_Olinorder__class_OMax(_1114308, _1114310)), c_Big__Operators_Olinorder__class_OMax(_1114308, _1114312)))], (19181 ^ _777959) ^ [_1146414, _1146416, _1146418] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1146414), _1146416)), 19184 ^ _777959 : [(19185 ^ _777959) ^ [] : [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(_1146414, tc_Nat_Onat), _1146418), _1146416))), 19188 ^ _777959 : [(19189 ^ _777959) ^ [_1146582] : [hBOOL(hAPP(hAPP(c_member(_1146414), _1146582), _1146416)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1146418, _1146582))))]]], (19195 ^ _777959) ^ [] : [19197 ^ _777959 : [(19200 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1146418, 19196 ^ [_1146414, _1146416, _1146418])))], (19198 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1146414), 19196 ^ [_1146414, _1146416, _1146418]), _1146416)))]], -(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(_1146414, tc_Nat_Onat), _1146418), _1146416))))]]], (13991 ^ _777959) ^ [_1037468, _1037470] : [-(hAPP(c_Set_OCollect(_1037468), hAPP(c_fequal, _1037470)) = hAPP(hAPP(c_Set_Oinsert(_1037468), _1037470), c_Orderings_Obot__class_Obot(tc_fun(_1037468, tc_HOL_Obool))))], (20961 ^ _777959) ^ [_1176412, _1176414] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1176412), _1176414) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1176412 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1176414 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42316 ^ _777959) ^ [_1612593, _1612595, _1612597] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1612593), tc_List_Olist(_1612593))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1612593), tc_List_Olist(_1612593)), _1612595), c_List_Olist_ONil(_1612593))), c_List_Olexord(_1612593, _1612597)))], (49038 ^ _777959) ^ [_1768670, _1768672, _1768674, _1768676] : [-(hAPP(c_Relation_Oconverse(_1768670, _1768670), hAPP(hAPP(c_Relation_Oinv__image(_1768672, _1768670), _1768674), _1768676)) = hAPP(hAPP(c_Relation_Oinv__image(_1768672, _1768670), hAPP(c_Relation_Oconverse(_1768672, _1768672), _1768674)), _1768676))], (50666 ^ _777959) ^ [_1805695, _1805697, _1805699, _1805701, _1805703, _1805705] : [-(hAPP(hAPP(c_List_Ozip(_1805695, _1805697), c_List_Oreplicate(_1805695, _1805699, _1805701)), c_List_Oreplicate(_1805697, _1805703, _1805705)) = c_List_Oreplicate(tc_prod(_1805695, _1805697), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1805699), _1805703), hAPP(hAPP(c_Product__Type_OPair(_1805695, _1805697), _1805701), _1805705)))], (34087 ^ _777959) ^ [_1419991] : [-(c_Int_OBit0(_1419991) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1419991), _1419991))], (40920 ^ _777959) ^ [_1574740, _1574742, _1574744, _1574746] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1574740), tc_List_Olist(_1574740))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1574740), tc_List_Olist(_1574740)), _1574742), _1574744)), c_List_Olex(_1574740, _1574746)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1574740), tc_List_Olist(_1574740))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1574740), tc_List_Olist(_1574740)), _1574742), _1574744)), c_List_Olexord(_1574740, _1574746))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1574740)), _1574742) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1574740)), _1574744)], (28093 ^ _777959) ^ [_1307958, _1307960, _1307962] : [class_Groups_Ocomm__monoid__add(_1307958), class_Groups_Ocomm__monoid__mult(_1307958), c_Nat__Transfer_Onat__set(_1307960), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1307958), _1307962), _1307960) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1307958), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1307958, tc_Nat_Onat), _1307962), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1307960)))], (30728 ^ _777959) ^ [_1358440, _1358442, _1358444] : [-(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), _1358440), _1358442)), _1358444), _1358442) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1358444, _1358442))], (36514 ^ _777959) ^ [_1470377, _1470379, _1470381, _1470383] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1470377, _1470377)), hAPP(hAPP(c_Product__Type_OPair(_1470377, _1470377), _1470379), _1470381)), hAPP(c_Wellfounded_Omeasure(_1470377), _1470383))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1470383, _1470379)), hAPP(_1470383, _1470381))))], (38836 ^ _777959) ^ [_1523911, _1523913, _1523915, _1523917, _1523919] : [hAPP(c_Set_Oimage(_1523911, _1523913, _1523915), c_Orderings_Otop__class_Otop(tc_fun(_1523911, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1523913, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1523911, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1523911, _1523913, _1523915), _1523917)), _1523919)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1523913, tc_HOL_Obool)), _1523917), hAPP(c_Set_Oimage(_1523911, _1523913, _1523915), _1523919))))], (15302 ^ _777959) ^ [_1069258, _1069260, _1069262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069258), _1069260)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069260), _1069262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1069258)), _1069262)))], (11930 ^ _777959) ^ [_994551, _994553, _994555] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994551), _994553)), _994555) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994551), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994553), _994555)))], (38618 ^ _777959) ^ [_1518890, _1518892, _1518894, _1518896, _1518898, _1518900] : [c_Typedef_Otype__definition(_1518890, _1518892, _1518894, _1518896, _1518898), -(hAPP(_1518896, hAPP(_1518894, _1518900)) = _1518900)], (16185 ^ _777959) ^ [_1086810, _1086812] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086810), _1086812) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1086812), _1086810))], (42236 ^ _777959) ^ [_1610612, _1610614] : [-(_1610614 = c_List_Olist_ONil(_1610612)), -(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(_1610612)), _1610614))))], (24297 ^ _777959) ^ [] : [-(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))))], (25410 ^ _777959) ^ [_1259424, _1259426, _1259428, _1259430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1259424, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1259424, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 25411 ^ [_1259424, _1259426, _1259428, _1259430])), _1259426)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1259424, 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), 25411 ^ [_1259424, _1259426, _1259428, _1259430]), _1259428))), _1259430))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1259424, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1259424, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1259426)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1259424, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1259430))))], (14041 ^ _777959) ^ [_1038733, _1038735, _1038737] : [-(hAPP(c_Set_OCollect(_1038733), hAPP(hAPP(c_COMBS(_1038733, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1038733), c_fimplies), _1038735)), _1038737)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1038733, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1038733, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1038733), _1038735))), hAPP(c_Set_OCollect(_1038733), _1038737)))], (45588 ^ _777959) ^ [_1687591, _1687593] : [hBOOL(hAPP(c_List_Odistinct(_1687591), _1687593)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1687591, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1687591), tc_fun(_1687591, tc_HOL_Obool)), c_List_Oset(_1687591)), c_Enum_Osublists(_1687591, _1687593)))))], (39747 ^ _777959) ^ [_1546235, _1546237, _1546239, _1546241, _1546243] : [-(hBOOL(hAPP(hAPP(c_member(_1546235), _1546237), hAPP(c_List_Oset(_1546235), _1546239)))), -(hAPP(hAPP(c_Map_Omap__of(_1546235, _1546241), hAPP(hAPP(c_List_Ozip(_1546235, _1546241), _1546239), hAPP(hAPP(c_List_Omap(_1546235, _1546241), _1546243), _1546239))), _1546237) = c_Option_Ooption_ONone(_1546241))], (720 ^ _777959) ^ [_788983, _788985, _788987, _788989, _788991, _788993, _788995, _788997] : [-(c_Fun_Oinj__on(_788995, _788991, _788987, _788983)), c_Fun_Oinj__on(_788997, _788993, _788989, _788985), _788997 = _788995, _788993 = _788991, _788989 = _788987, _788985 = _788983], (34345 ^ _777959) ^ [_1424484, _1424486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1424484)), c_Int_OBit0(_1424486))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1424484), _1424486)))], (14654 ^ _777959) ^ [_1053221, _1053223, _1053225] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1053221), _1053223)), -(hAPP(c_Finite__Set_Ocard(_1053221), hAPP(hAPP(c_Set_Oinsert(_1053221), _1053225), _1053223)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1053221), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053221, tc_HOL_Obool)), _1053223), hAPP(hAPP(c_Set_Oinsert(_1053221), _1053225), c_Orderings_Obot__class_Obot(tc_fun(_1053221, tc_HOL_Obool)))))))], (33903 ^ _777959) ^ [_1416572, _1416574] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1416572)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1416574)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1416574))), 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, _1416572))), 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), _1416572)), c_Int_Onat)))))], (27690 ^ _777959) ^ [_1301029, _1301031, _1301033] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1301029, tc_Nat_Onat), _1301031), _1301033) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1301029, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1301029), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1301031)), _1301033)))], (42911 ^ _777959) ^ [_1628454, _1628456] : [-(hAPP(hAPP(c_List_Oappend(_1628454), _1628456), c_List_Olist_ONil(_1628454)) = _1628456)], (38648 ^ _777959) ^ [_1519406, _1519408, _1519410, _1519412, _1519414, _1519416] : [c_Typedef_Otype__definition(_1519406, _1519408, _1519410, _1519412, _1519414), hBOOL(hAPP(hAPP(c_member(_1519408), _1519416), _1519414)), -(hAPP(_1519410, hAPP(_1519412, _1519416)) = _1519416)], (12890 ^ _777959) ^ [_1011920, _1011922, _1011924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1011920, tc_HOL_Obool)), _1011922), _1011924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1011920, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1011920, tc_HOL_Obool)), _1011924)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1011920, tc_HOL_Obool)), _1011922))))], (4430 ^ _777959) ^ [_845001, _845003, _845005, _845007, _845009, _845011] : [-(c_Product__Type_Ointernal__split(_845011, _845007, _845003) = c_Product__Type_Ointernal__split(_845009, _845005, _845001)), _845011 = _845009, _845007 = _845005, _845003 = _845001], (32915 ^ _777959) ^ [_1399693, _1399695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1399693), _1399695)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1399693)), c_Int_OBit1(_1399695))))], (9278 ^ _777959) ^ [_937505] : [-(c_Finite__Set_Ofun__left__comm__idem(_937505, tc_fun(_937505, tc_HOL_Obool), c_Set_Oinsert(_937505)))], (25136 ^ _777959) ^ [_1254093] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1254093), hAPP(c_Nat_OSuc, _1254093)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1254093), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (16913 ^ _777959) ^ [_1101639, _1101641, _1101643, _1101645] : [class_Orderings_Olinorder(_1101639), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101639), _1101641), _1101643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101639), _1101641), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1101639), _1101643), _1101645))))], (35123 ^ _777959) ^ [_1438713] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1438713), hAPP(c_Int_Onumber__class_Onumber__of(_1438713), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1438713)), class_Int_Onumber__ring(_1438713), class_Rings_Olinordered__idom(_1438713)], (13511 ^ _777959) ^ [_1025819, _1025821, _1025823, _1025825, _1025827, _1025829] : [class_Complete__Lattice_Ocomplete__lattice(_1025819), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1025821, _1025819), _1025823), hAPP(hAPP(c_COMBB(tc_fun(_1025825, _1025819), _1025819, _1025821), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1025825, _1025819), _1025827)), _1025829)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1025825, _1025819), _1025827), hAPP(hAPP(c_COMBB(tc_fun(_1025821, _1025819), _1025819, _1025825), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1025821, _1025819), _1025823)), hAPP(c_COMBC(_1025821, _1025825, _1025819), _1025829))))], (29158 ^ _777959) ^ [_1327594, _1327596] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1327594, _1327596)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1327596), _1327594)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (21762 ^ _777959) ^ [_1191263, _1191265, _1191267] : [21763 ^ _777959 : [(21766 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1191263), _1191267))], (21764 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1191265)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1191263), _1191265)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1191267), _1191265))))], (51126 ^ _777959) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (3220 ^ _777959) ^ [_826384, _826386] : [_826386 = _826384, -(c_Orderings_Oord__class_Omax(_826386) = c_Orderings_Oord__class_Omax(_826384))], (10920 ^ _777959) ^ [_972035, _972037, _972039, _972041] : [class_Groups_Oordered__cancel__ab__semigroup__add(_972035), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972035), _972037), _972039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_972035), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972035), _972037), _972041)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_972035), _972039), _972041))))], (22645 ^ _777959) ^ [_1209965, _1209967, _1209969] : [class_Rings_Oring__1(_1209965), hBOOL(hAPP(hAPP(c_member(_1209965), _1209967), c_Int_Oring__1__class_OInts(_1209965))), -(hBOOL(hAPP(hAPP(c_member(_1209965), hAPP(hAPP(c_Power_Opower__class_Opower(_1209965), _1209967), _1209969)), c_Int_Oring__1__class_OInts(_1209965))))], (45650 ^ _777959) ^ [_1689016, _1689018, _1689020, _1689022] : [class_Orderings_Olinorder(_1689016), 45653 ^ _777959 : [(45660 ^ _777959) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1689018), _1689022)), -(hBOOL(hAPP(c_List_Odistinct(_1689018), c_List_Olinorder__class_Osort__key(_1689018, _1689016, _1689020, _1689022))))], (45654 ^ _777959) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1689018), c_List_Olinorder__class_Osort__key(_1689018, _1689016, _1689020, _1689022))), -(hBOOL(hAPP(c_List_Odistinct(_1689018), _1689022)))]]], (28618 ^ _777959) ^ [_1317133, _1317135] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1317133), _1317135) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1317133, _1317135))], (20439 ^ _777959) ^ [_1167778, _1167780, _1167782, _1167784] : [class_Rings_Olinordered__semiring__strict(_1167778), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167778), _1167780), _1167782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167778), c_Groups_Ozero__class_Ozero(_1167778)), _1167784)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167778), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167778), _1167780), _1167784)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167778), _1167782), _1167784))))], (14506 ^ _777959) ^ [_1050320, _1050322, _1050324, _1050326, _1050328] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1050320, tc_fun(_1050322, tc_HOL_Obool)), _1050324), _1050326), _1050328)), 14509 ^ _777959 : [(14510 ^ _777959) ^ [_1050429] : [hBOOL(hAPP(hAPP(c_member(_1050320), _1050429), _1050324)), -(hBOOL(hAPP(hAPP(_1050326, _1050429), _1050328)))]]], (47202 ^ _777959) ^ [_1724794] : [-(c_Nitpick_Oone__frac(_1724794) = c_Nitpick_OAbs__Frac(_1724794, 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))))], (35269 ^ _777959) ^ [] : [-(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)))], (12852 ^ _777959) ^ [_1011202, _1011204, _1011206] : [hBOOL(hAPP(hAPP(c_member(_1011202), _1011204), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1011202, tc_HOL_Obool)), _1011206))), hBOOL(hAPP(hAPP(c_member(_1011202), _1011204), _1011206))], (44973 ^ _777959) ^ [_1672740, _1672742] : [-(_1672740 = c_List_Olist_ONil(_1672742)), -(hAPP(c_List_Ohd(_1672742), hAPP(c_List_Orev(_1672742), _1672740)) = c_List_Olast(_1672742, _1672740))], (10294 ^ _777959) ^ [_959188, _959190, _959192] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_959188), _959190)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959188, tc_HOL_Obool)), _959190), _959192) = hAPP(hAPP(c_Finite__Set_Ofold(_959188, tc_fun(_959188, tc_HOL_Obool), c_Set_Oinsert(_959188)), _959192), _959190))], (16087 ^ _777959) ^ [_1084421, _1084423, _1084425] : [class_Orderings_Olinorder(_1084421), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084421, tc_HOL_Obool)), _1084423), _1084425)), -(_1084423 = c_Orderings_Obot__class_Obot(tc_fun(_1084421, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084421), _1084425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1084421), c_Big__Operators_Olinorder__class_OMin(_1084421, _1084425)), c_Big__Operators_Olinorder__class_OMin(_1084421, _1084423))))], (35763 ^ _777959) ^ [_1456087, _1456089, _1456091, _1456093, _1456095, _1456097] : [hAPP(hAPP(c_Product__Type_OPair(_1456087, _1456089), _1456091), _1456093) = hAPP(hAPP(c_Product__Type_OPair(_1456087, _1456089), _1456095), _1456097), 35766 ^ _777959 : [(35769 ^ _777959) ^ [] : [-(_1456093 = _1456097)], (35767 ^ _777959) ^ [] : [-(_1456091 = _1456095)]]], (44591 ^ _777959) ^ [_1664234, _1664236, _1664238] : [class_Orderings_Olinorder(_1664234), 44594 ^ _777959 : [(44607 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1664234, hAPP(hAPP(c_List_Olist_OCons(_1664234), _1664236), _1664238))), 44611 ^ _777959 : [(44614 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664234), _1664236), 44610 ^ [_1664234, _1664236, _1664238]))], (44612 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1664234), 44610 ^ [_1664234, _1664236, _1664238]), hAPP(c_List_Oset(_1664234), _1664238))))]], c_List_Olinorder__class_Osorted(_1664234, _1664238)], (44595 ^ _777959) ^ [] : [c_List_Olinorder__class_Osorted(_1664234, hAPP(hAPP(c_List_Olist_OCons(_1664234), _1664236), _1664238)), 44598 ^ _777959 : [(44599 ^ _777959) ^ [_1664402] : [hBOOL(hAPP(hAPP(c_member(_1664234), _1664402), hAPP(c_List_Oset(_1664234), _1664238))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1664234), _1664236), _1664402)))], (44605 ^ _777959) ^ [] : [-(c_List_Olinorder__class_Osorted(_1664234, _1664238))]]]]], (36173 ^ _777959) ^ [_1463774, _1463776] : [-(_1463774 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1463776, _1463774) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1463776), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1463774)))], (40718 ^ _777959) ^ [_1569100, _1569102] : [40719 ^ _777959 : [(40720 ^ _777959) ^ [_1569146] : [hBOOL(hAPP(_1569100, _1569146))]], -(hBOOL(hAPP(_1569100, c_Hilbert__Choice_OEps(_1569102, _1569100))))], (33503 ^ _777959) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (11124 ^ _777959) ^ [_975868, _975870, _975872, _975874] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_975868), _975870)), hBOOL(hAPP(c_Finite__Set_Ofinite(_975868), _975872)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_975868, tc_Nat_Onat), _975874), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_975868, tc_HOL_Obool)), _975870), _975872)) = 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(_975868, tc_Nat_Onat), _975874), _975870)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_975868, tc_Nat_Onat), _975874), _975872))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_975868, tc_Nat_Onat), _975874), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975868, tc_HOL_Obool)), _975870), _975872))))], (37088 ^ _777959) ^ [] : [-(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)))))], (46680 ^ _777959) ^ [_1711095, _1711097, _1711099, _1711101, _1711103] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1711095, _1711095)), hAPP(hAPP(c_Product__Type_OPair(_1711095, _1711095), _1711097), _1711099)), c_List_Omeasures(_1711095, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1711095, tc_Nat_Onat)), _1711101), _1711103)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1711101, _1711097)), hAPP(_1711101, _1711099)))), 46687 ^ _777959 : [(46690 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1711095, _1711095)), hAPP(hAPP(c_Product__Type_OPair(_1711095, _1711095), _1711097), _1711099)), c_List_Omeasures(_1711095, _1711103))))], (46688 ^ _777959) ^ [] : [-(hAPP(_1711101, _1711097) = hAPP(_1711101, _1711099))]]], (49116 ^ _777959) ^ [_1770705, _1770707, _1770709] : [c_Relation_Ototal__on(_1770705, _1770707, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1770705, _1770705), tc_HOL_Obool)), _1770709), c_Relation_OId(_1770705))), -(c_Relation_Ototal__on(_1770705, _1770707, _1770709))], (35421 ^ _777959) ^ [_1448190, _1448192, _1448194, _1448196, _1448198, _1448200] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1448190, _1448192), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1448194), _1448196))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1448190, _1448192), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1448198), _1448200))), -(_1448192 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1448194 = _1448198)], (31730 ^ _777959) ^ [_1377131, _1377133, _1377135] : [31732 ^ _777959 : [(31737 ^ _777959) ^ [] : [hBOOL(hAPP(_1377133, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 31731 ^ [_1377131, _1377133, _1377135]), _1377131)))], (31735 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1377133, 31731 ^ [_1377131, _1377133, _1377135])))], (31733 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31731 ^ [_1377131, _1377133, _1377135]), _1377131)))]], hBOOL(hAPP(_1377133, _1377135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1377135), _1377131)), -(hBOOL(hAPP(_1377133, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (29898 ^ _777959) ^ [_1343180, _1343182] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1343180), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1343182)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1343180, _1343182)))], (14502 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (30988 ^ _777959) ^ [_1363393, _1363395, _1363397] : [class_Fields_Olinordered__field__inverse__zero(_1363393), -(hAPP(c_Groups_Oabs__class_Oabs(_1363393), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363393), _1363395), _1363397)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363393), hAPP(c_Groups_Oabs__class_Oabs(_1363393), _1363395)), hAPP(c_Groups_Oabs__class_Oabs(_1363393), _1363397)))], (29685 ^ _777959) ^ [_1337942, _1337944] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1337942), _1337944)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1337942, tc_HOL_Obool)), hAPP(c_Set_OPow(_1337942), _1337944)) = 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(_1337942), _1337944)))], (44926 ^ _777959) ^ [_1671685, _1671687] : [c_List_Olist_ONil(_1671685) = c_List_Oconcat(_1671685, _1671687), 44929 ^ _777959 : [(44930 ^ _777959) ^ [_1671776] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1671685)), _1671776), hAPP(c_List_Oset(tc_List_Olist(_1671685)), _1671687))), -(_1671776 = c_List_Olist_ONil(_1671685))]]], (50406 ^ _777959) ^ [_1800283, _1800285, _1800287, _1800289] : [-(c_Predicate_Oconversep(_1800283, _1800285, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1800283, tc_fun(_1800285, tc_HOL_Obool))), _1800287), _1800289)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1800285, tc_fun(_1800283, tc_HOL_Obool))), c_Predicate_Oconversep(_1800283, _1800285, _1800287)), c_Predicate_Oconversep(_1800283, _1800285, _1800289)))], (50434 ^ _777959) ^ [_1800893, _1800895, _1800897, _1800899, _1800901] : [hBOOL(hAPP(hAPP(_1800893, _1800895), _1800897)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1800899, _1800901, _1800893), _1800897), _1800895)))], (46672 ^ _777959) ^ [_1710803, _1710805] : [-(c_List_Omeasures(_1710803, _1710805) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1710803), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1710803, tc_List_Olist(tc_fun(_1710803, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1710803, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1710803, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1710803), c_List_Omap(tc_fun(_1710803, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1710803, tc_Nat_Onat), _1710803, tc_Nat_Onat), c_COMBI(tc_fun(_1710803, tc_Nat_Onat))))), _1710805)))], (35089 ^ _777959) ^ [_1438164] : [class_Int_Onumber__ring(_1438164), c_Int_Oiszero(_1438164, hAPP(c_Int_Onumber__class_Onumber__of(_1438164), c_Int_OMin))], (28004 ^ _777959) ^ [_1306394] : [class_Rings_Oring__1(_1306394), -(hAPP(c_Int_Oring__1__class_Oof__int(_1306394), c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(_1306394))], (24984 ^ _777959) ^ [_1251441, _1251443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1251441)), 24987 ^ _777959 : [(24994 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1251441), _1251443)), -(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), _1251443), _1251441))))], (24988 ^ _777959) ^ [] : [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), _1251443), _1251441))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1251441), _1251443)))]]], (31823 ^ _777959) ^ [_1378973, _1378975, _1378977] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), c_Com_Ocom_OLocal(_1378973, _1378975, _1378977)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom), _1378977)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (39910 ^ _777959) ^ [_1550611, _1550613, _1550615, _1550617] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1550611, _1550613))), hAPP(hAPP(c_List_Ozip(_1550611, _1550613), _1550615), _1550617)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550611)), _1550615)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1550613)), _1550617)))], (50132 ^ _777959) ^ [_1794168] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1794168))), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1794168)))], (50526 ^ _777959) ^ [_1803124, _1803126, _1803128, _1803130] : [-(hAPP(hAPP(c_List_Otake(_1803124), _1803126), c_List_Oreplicate(_1803124, _1803128, _1803130)) = c_List_Oreplicate(_1803124, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1803126), _1803128), _1803130))], (47315 ^ _777959) ^ [_1727841, _1727843, _1727845, _1727847, _1727849, _1727851, _1727853, _1727855] : [47317 ^ _777959 : [(47320 ^ _777959) ^ [] : [hAPP(c_Fun_Ocomp(_1727845, _1727845, _1727847, hAPP(_1727849, 47316 ^ [_1727841, _1727843, _1727845, _1727847, _1727849, _1727851, _1727853, _1727855])), _1727851) = hAPP(c_Fun_Ocomp(_1727847, _1727845, _1727847, _1727851), hAPP(_1727853, 47316 ^ [_1727841, _1727843, _1727845, _1727847, _1727849, _1727851, _1727853, _1727855]))], (47318 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1727841), 47316 ^ [_1727841, _1727843, _1727845, _1727847, _1727849, _1727851, _1727853, _1727855]), hAPP(c_List_Oset(_1727841), _1727843))))]], -(hAPP(c_List_Ofoldl(_1727845, _1727841, hAPP(c_COMBC(_1727841, _1727845, _1727845), _1727849), hAPP(_1727851, _1727855)), _1727843) = hAPP(_1727851, hAPP(c_List_Ofoldl(_1727847, _1727841, hAPP(c_COMBC(_1727841, _1727847, _1727847), _1727853), _1727855), _1727843)))], (10180 ^ _777959) ^ [_956285, _956287, _956289, _956291] : [hBOOL(hAPP(hAPP(c_member(_956285), _956291), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956285, tc_HOL_Obool)), _956287), _956289))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_956285, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_956285, tc_fun(_956285, tc_HOL_Obool), tc_HOL_Obool), c_member(_956285)), _956287)), hAPP(hAPP(c_COMBC(_956285, tc_fun(_956285, tc_HOL_Obool), tc_HOL_Obool), c_member(_956285)), _956289)), _956291)))], (27181 ^ _777959) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (1770 ^ _777959) ^ [_802808, _802810] : [-(class_Groups_Ominus(_802808)), _802810 = _802808, class_Groups_Ominus(_802810)], (42991 ^ _777959) ^ [_1629962, _1629964, _1629966, _1629968, _1629970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1629962), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629964)), _1629966))), -(hAPP(hAPP(c_List_Olist__update(_1629964, hAPP(hAPP(c_List_Oappend(_1629964), _1629966), _1629968)), _1629962), _1629970) = hAPP(hAPP(c_List_Oappend(_1629964), hAPP(hAPP(c_List_Olist__update(_1629964, _1629966), _1629962), _1629970)), _1629968))], (45196 ^ _777959) ^ [_1678922, _1678924, _1678926, _1678928] : [-(hBOOL(hAPP(_1678922, _1678924))), -(c_List_OtakeWhile(_1678926, _1678922, hAPP(hAPP(c_List_Olist_OCons(_1678926), _1678924), _1678928)) = c_List_Olist_ONil(_1678926))], (9306 ^ _777959) ^ [_937932, _937934, _937936] : [class_Lattices_Olattice(_937932), hBOOL(hAPP(c_Finite__Set_Ofinite(_937932), _937934)), -(_937934 = c_Orderings_Obot__class_Obot(tc_fun(_937932, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_937932, hAPP(hAPP(c_Set_Oinsert(_937932), _937936), _937934)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_937932), _937936), c_Big__Operators_Olattice__class_OSup__fin(_937932, _937934)))], (32329 ^ _777959) ^ [_1388210, _1388212, _1388214, _1388216] : [class_Int_Onumber__ring(_1388210), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1388210), hAPP(c_Int_Onumber__class_Onumber__of(_1388210), _1388212)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388210), hAPP(c_Int_Onumber__class_Onumber__of(_1388210), _1388214)), _1388216)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388210), hAPP(c_Int_Onumber__class_Onumber__of(_1388210), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1388212), _1388214))), _1388216))], (11710 ^ _777959) ^ [_988578, _988580, _988582, _988584] : [c_Orderings_Obot__class_Obot(tc_fun(_988578, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_988580, tc_fun(_988578, tc_HOL_Obool)), _988582), _988584), 11713 ^ _777959 : [(11714 ^ _777959) ^ [_988694] : [hBOOL(hAPP(hAPP(c_member(_988580), _988694), _988582)), -(hAPP(_988584, _988694) = c_Orderings_Obot__class_Obot(tc_fun(_988578, tc_HOL_Obool)))]]], (50890 ^ _777959) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (51150 ^ _777959) ^ [] : [-(class_HOL_Oequal(tc_Com_Ostate))], (23413 ^ _777959) ^ [_1223919] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1223919) = _1223919)], (48453 ^ _777959) ^ [_1752902, _1752904, _1752906, _1752908, _1752910] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1752902, _1752902)), hAPP(hAPP(c_Product__Type_OPair(_1752902, _1752902), _1752904), _1752906)), c_Transitive__Closure_Otrancl(_1752902, _1752908))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1752902, _1752902)), hAPP(hAPP(c_Product__Type_OPair(_1752902, _1752902), _1752906), _1752910)), _1752908)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1752902, _1752902)), hAPP(hAPP(c_Product__Type_OPair(_1752902, _1752902), _1752904), _1752910)), c_Transitive__Closure_Otrancl(_1752902, _1752908))))], (32165 ^ _777959) ^ [_1385586, _1385588] : [class_Int_Onumber__ring(_1385586), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1385586), hAPP(c_Int_Onumber__class_Onumber__of(_1385586), _1385588)) = hAPP(c_Int_Onumber__class_Onumber__of(_1385586), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385588)))], (26018 ^ _777959) ^ [_1271267, _1271269, _1271271, _1271273] : [class_Fields_Olinordered__field(_1271267), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1271267), _1271269), c_Groups_Ozero__class_Ozero(_1271267))), 26025 ^ _777959 : [(26032 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1271267), _1271273), _1271269)), _1271271)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271267), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271267), _1271271), _1271269)), _1271273)))], (26026 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271267), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1271267), _1271271), _1271269)), _1271273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1271267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1271267), _1271273), _1271269)), _1271271)))]]], (21646 ^ _777959) ^ [_1189149, _1189151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1189149)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1189151)), -(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), _1189151), _1189149))))], (36103 ^ _777959) ^ [_1462565, _1462567] : [_1462565 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1462565, _1462567) = 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)))], (35391 ^ _777959) ^ [_1447538, _1447540, _1447542, _1447544] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1447538, _1447540)), hAPP(hAPP(c_Product__Type_OPair(_1447538, _1447540), _1447542), _1447544)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1447538, _1447540), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1447538, tc_fun(_1447540, tc_HOL_Obool))), _1447542), _1447544)))], (11960 ^ _777959) ^ [_995226, _995228] : [11961 ^ _777959 : [(11964 ^ _777959) ^ [] : [_995226 = _995228], (11962 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995226), _995228))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995226), _995228)))], (15813 ^ _777959) ^ [_1078628, _1078630] : [class_Orderings_Olinorder(_1078628), -(c_Big__Operators_Olinorder__class_OMax(_1078628, hAPP(hAPP(c_Set_Oinsert(_1078628), _1078630), c_Orderings_Obot__class_Obot(tc_fun(_1078628, tc_HOL_Obool)))) = _1078630)], (24363 ^ _777959) ^ [_1240866] : [-(hBOOL(hAPP(_1240866, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 24370 ^ [_1240866])))), 24364 ^ _777959 : [(24365 ^ _777959) ^ [_1240918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240918)), hBOOL(hAPP(_1240866, _1240918))]]], (40636 ^ _777959) ^ [_1567391, _1567393, _1567395, _1567397, _1567399, _1567401, _1567403] : [-(hBOOL(hAPP(hAPP(c_member(_1567391), _1567393), hAPP(c_List_Oset(_1567391), _1567395)))), -(c_Map_Omap__upds(_1567391, _1567397, hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1567391, tc_Option_Ooption(_1567397)), _1567399), _1567393), hAPP(c_Option_Ooption_OSome(_1567397), _1567401)), _1567395, _1567403) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_1567391, tc_Option_Ooption(_1567397)), c_Map_Omap__upds(_1567391, _1567397, _1567399, _1567395, _1567403)), _1567393), hAPP(c_Option_Ooption_OSome(_1567397), _1567401)))], (36131 ^ _777959) ^ [_1463112, _1463114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1463112), _1463114)), -(c_Divides_Odivmod__nat(_1463112, _1463114) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1463112))], (49632 ^ _777959) ^ [_1784168, _1784170] : [-(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)))), _1784168)) = 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)))), _1784170))), 49634 ^ _777959 : [(49637 ^ _777959) ^ [] : [49638 ^ _777959 : [(49641 ^ _777959) ^ [] : [hBOOL(hAPP(_1784170, 49633 ^ [_1784168, _1784170]))], (49639 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1784168, 49633 ^ [_1784168, _1784170])))]], 49642 ^ _777959 : [(49645 ^ _777959) ^ [] : [hBOOL(hAPP(_1784168, 49633 ^ [_1784168, _1784170]))], (49643 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1784170, 49633 ^ [_1784168, _1784170])))]]], (49635 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 49633 ^ [_1784168, _1784170])))]]], (41731 ^ _777959) ^ [_1598378, _1598380, _1598382, _1598384, _1598386, _1598388, _1598390, _1598392, _1598394, _1598396, _1598398] : [-(hAPP(c_Product__Type_Omap__pair(_1598378, _1598380, _1598382, _1598384, _1598386, _1598388), hAPP(c_Product__Type_Omap__pair(_1598390, _1598378, _1598392, _1598382, _1598394, _1598396), _1598398)) = hAPP(c_Product__Type_Omap__pair(_1598390, _1598380, _1598392, _1598384, hAPP(c_Fun_Ocomp(_1598378, _1598380, _1598390, _1598386), _1598394), hAPP(c_Fun_Ocomp(_1598382, _1598384, _1598392, _1598388), _1598396)), _1598398))], (40199 ^ _777959) ^ [_1557459, _1557461, _1557463] : [40201 ^ _777959 : [(40204 ^ _777959) ^ [] : [hBOOL(hAPP(_1557463, hAPP(hAPP(c_List_Onth(_1557459), _1557461), 40200 ^ [_1557459, _1557461, _1557463])))], (40202 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40200 ^ [_1557459, _1557461, _1557463]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1557459)), _1557461))))]], 40205 ^ _777959 : [(40206 ^ _777959) ^ [_1557661] : [hBOOL(hAPP(hAPP(c_member(_1557459), _1557661), hAPP(c_List_Oset(_1557459), _1557461))), -(hBOOL(hAPP(_1557463, _1557661)))]]], (3350 ^ _777959) ^ [_828455, _828457] : [_828457 = _828455, -(c_List_Oembed__list(_828457) = c_List_Oembed__list(_828455))], (19286 ^ _777959) ^ [_1148074, _1148076, _1148078] : [class_Rings_Ono__zero__divisors(_1148074), -(_1148076 = c_Groups_Ozero__class_Ozero(_1148074)), -(_1148078 = c_Groups_Ozero__class_Ozero(_1148074)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1148074), _1148076), _1148078) = c_Groups_Ozero__class_Ozero(_1148074)], (15777 ^ _777959) ^ [_1078073, _1078075] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1078073), _1078075)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078075)), _1078073) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1078075), _1078073)))], (27485 ^ _777959) ^ [_1297684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1297684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1297684)))], (50944 ^ _777959) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (15322 ^ _777959) ^ [_1069545, _1069547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1069545)), _1069547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1069545), _1069547)))], (43229 ^ _777959) ^ [_1636230, _1636232, _1636234, _1636236] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1636230), _1636232)), 43235 ^ _777959 : [(43238 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1636234), hAPP(_1636236, 43234 ^ [_1636230, _1636232, _1636234, _1636236])))], (43236 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1636230), 43234 ^ [_1636230, _1636232, _1636234, _1636236]), _1636232)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1636230, _1636234)), hAPP(hAPP(c_Product__Type_OSigma(_1636230, _1636234), _1636232), _1636236))))], (11948 ^ _777959) ^ [_994978, _994980, _994982] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994978), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994982), _994980))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994978), _994980)), _994982)))], (40831 ^ _777959) ^ [_1571924, _1571926, _1571928, _1571930, _1571932] : [hBOOL(hAPP(hAPP(c_member(_1571924), _1571926), hAPP(c_List_Oset(_1571924), _1571928))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1571930), hAPP(_1571932, _1571926))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1571930), c_List_Olist_Olist__size(_1571924, _1571932, _1571928))))], (28439 ^ _777959) ^ [_1313960, _1313962] : [28447 ^ _777959 : [(28450 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1313962, 28446 ^ [_1313960, _1313962])))], (28448 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 28446 ^ [_1313960, _1313962]), _1313960)))]], 28440 ^ _777959 : [(28441 ^ _777959) ^ [_1314029] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1314029), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1313960))), hBOOL(hAPP(_1313962, _1314029))]]], (40315 ^ _777959) ^ [_1560323, _1560325, _1560327, _1560329, _1560331] : [class_Orderings_Olinorder(_1560323), 40318 ^ _777959 : [(40327 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1560325), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1560325, _1560323, _1560327), _1560329), _1560331)))), -(hBOOL(hAPP(hAPP(c_member(_1560325), _1560329), hAPP(c_List_Oset(_1560325), _1560331)))), hBOOL(hAPP(c_List_Odistinct(_1560325), _1560331))], (40319 ^ _777959) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1560325), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1560325, _1560323, _1560327), _1560329), _1560331))), 40322 ^ _777959 : [(40325 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1560325), _1560331)))], (40323 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1560325), _1560329), hAPP(c_List_Oset(_1560325), _1560331)))]]]]], (24618 ^ _777959) ^ [_1245245, _1245247] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245247)), -(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), _1245245), _1245247))))], (12072 ^ _777959) ^ [_996972, _996974, _996976] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996972), _996974) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _996976), _996974), -(_996972 = _996976)], (3370 ^ _777959) ^ [_828761, _828763] : [_828763 = _828761, -(c_Set_OPow(_828763) = c_Set_OPow(_828761))], (35579 ^ _777959) ^ [_1452352, _1452354, _1452356, _1452358] : [_1452352 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1452354), _1452356)), _1452358), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1452352, _1452354), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1452356), _1452358)))), 35586 ^ _777959 : [(35589 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452358)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1452358), _1452354))], (35587 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452354)))]], 35594 ^ _777959 : [(35597 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1452354), _1452358)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1452358), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35595 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1452354))]]], (6044 ^ _777959) ^ [_874586, _874588, _874590] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874586, tc_HOL_Obool)), _874588), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_874586, tc_HOL_Obool)), _874588), _874590))))], (43863 ^ _777959) ^ [_1649993, _1649995, _1649997, _1649999] : [hAPP(hAPP(c_List_Oappend(_1649993), _1649995), hAPP(hAPP(c_List_Olist_OCons(_1649993), _1649997), c_List_Olist_ONil(_1649993))) = _1649999, 43866 ^ _777959 : [(43871 ^ _777959) ^ [] : [-(c_List_Olast(_1649993, _1649999) = _1649997)], (43869 ^ _777959) ^ [] : [-(c_List_Obutlast(_1649993, _1649999) = _1649995)], (43867 ^ _777959) ^ [] : [_1649999 = c_List_Olist_ONil(_1649993)]]], (18818 ^ _777959) ^ [_1139304, _1139306, _1139308] : [class_Orderings_Olinorder(_1139304), hBOOL(hAPP(c_Finite__Set_Ofinite(_1139304), _1139306)), -(_1139306 = c_Orderings_Obot__class_Obot(tc_fun(_1139304, tc_HOL_Obool))), 18829 ^ _777959 : [(18839 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139304), hAPP(c_Finite__Set_Ofold1(_1139304, c_Orderings_Oord__class_Omin(_1139304)), _1139306)), _1139308))), 18840 ^ _777959 : [(18841 ^ _777959) ^ [_1139693] : [hBOOL(hAPP(hAPP(c_member(_1139304), _1139693), _1139306)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139304), _1139693), _1139308))]]], (18830 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139304), hAPP(c_Finite__Set_Ofold1(_1139304, c_Orderings_Oord__class_Omin(_1139304)), _1139306)), _1139308)), 18834 ^ _777959 : [(18837 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139304), 18833 ^ [_1139304, _1139306, _1139308]), _1139308)))], (18835 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1139304), 18833 ^ [_1139304, _1139306, _1139308]), _1139306)))]]]]], (37956 ^ _777959) ^ [_1505269, _1505271, _1505273, _1505275, _1505277] : [c_Fun_Oinj__on(_1505269, _1505271, _1505273, _1505275), c_Fun_Oinj__on(_1505269, _1505271, _1505273, _1505277), -(c_Fun_Oinj__on(_1505269, _1505271, _1505273, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1505269, tc_HOL_Obool)), _1505275), _1505277)))], (37184 ^ _777959) ^ [_1486346, _1486348, _1486350, _1486352, _1486354, _1486356] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486346, _1486346)), hAPP(hAPP(c_Product__Type_OPair(_1486346, _1486346), _1486348), _1486350)), hAPP(hAPP(c_Relation_Oinv__image(_1486352, _1486346), _1486354), _1486356))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486352, _1486352)), hAPP(hAPP(c_Product__Type_OPair(_1486352, _1486352), hAPP(_1486356, _1486348)), hAPP(_1486356, _1486350))), _1486354)))], (33809 ^ _777959) ^ [_1414422, _1414424] : [class_Int_Onumber__ring(_1414422), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1414422), hAPP(c_Int_Onumber__class_Onumber__of(_1414422), _1414424)), c_Groups_Oone__class_Oone(_1414422)) = hAPP(c_Int_Onumber__class_Onumber__of(_1414422), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1414424), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (14504 ^ _777959) ^ [] : [-(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))], (14323 ^ _777959) ^ [_1045254, _1045256, _1045258] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045254), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1045254, tc_HOL_Obool)), _1045256), _1045258))), -(hAPP(c_Finite__Set_Ocard(_1045254), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1045254, tc_HOL_Obool)), _1045256), _1045258)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1045254), _1045256)), hAPP(c_Finite__Set_Ocard(_1045254), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1045254, tc_HOL_Obool)), _1045256), _1045258))))], (31664 ^ _777959) ^ [_1375813, _1375815] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1375813), _1375815) = 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), _1375813)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1375815)))))], (48859 ^ _777959) ^ [_1763865, _1763867, _1763869, _1763871] : [-(c_Wellfounded_Oacyclic(_1763865, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1763865, _1763865)), hAPP(hAPP(c_Product__Type_OPair(_1763865, _1763865), _1763867), _1763869)), _1763871))), c_Wellfounded_Oacyclic(_1763865, _1763871), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1763865, _1763865)), hAPP(hAPP(c_Product__Type_OPair(_1763865, _1763865), _1763869), _1763867)), c_Transitive__Closure_Ortrancl(_1763865, _1763871))))], (11030 ^ _777959) ^ [_974093, _974095, _974097, _974099, _974101] : [class_Groups_Oordered__cancel__ab__semigroup__add(_974093), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974093), _974095), _974097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_974093), _974099), _974101)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_974093), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974093), _974095), _974099)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_974093), _974097), _974101))))], (20945 ^ _777959) ^ [_1176212] : [-(hAPP(c_Finite__Set_Ocard(_1176212), c_Orderings_Obot__class_Obot(tc_fun(_1176212, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15074 ^ _777959) ^ [_1064652, _1064654] : [hAPP(c_Nat_OSuc, _1064652) = hAPP(c_Nat_OSuc, _1064654), -(_1064652 = _1064654)], (49881 ^ _777959) ^ [_1789540, _1789542, _1789544, _1789546] : [c_List_Olist__ex1(_1789540, _1789542, hAPP(hAPP(c_List_Olist_OCons(_1789540), _1789544), _1789546)), 49884 ^ _777959 : [(49891 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1789542, _1789544))), -(c_List_Olist__ex1(_1789540, _1789542, _1789546))], (49885 ^ _777959) ^ [] : [hBOOL(hAPP(_1789542, _1789544)), -(c_List_Olist__all(_1789540, hAPP(hAPP(c_COMBS(_1789540, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1789540), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1789540), c_fNot), _1789542))), hAPP(c_fequal, _1789544)), _1789546))]]], (41031 ^ _777959) ^ [_1579702, _1579704, _1579706, _1579708] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1579702, tc_fun(_1579704, tc_HOL_Obool)), _1579706), _1579708) = hAPP(c_Set_OCollect(_1579704), hAPP(hAPP(c_COMBB(tc_fun(_1579702, tc_HOL_Obool), tc_HOL_Obool, _1579704), c_HOL_OAll(_1579702)), hAPP(hAPP(c_COMBB(tc_fun(_1579702, tc_HOL_Obool), tc_fun(_1579702, tc_HOL_Obool), _1579704), hAPP(c_COMBS(_1579702, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1579702), c_fimplies), hAPP(hAPP(c_COMBC(_1579702, tc_fun(_1579702, tc_HOL_Obool), tc_HOL_Obool), c_member(_1579702)), _1579706)))), hAPP(hAPP(c_COMBC(_1579704, tc_fun(_1579702, tc_fun(_1579704, tc_HOL_Obool)), tc_fun(_1579702, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1579704, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1579702, tc_fun(_1579704, tc_HOL_Obool)), tc_fun(_1579702, tc_HOL_Obool)), _1579704), c_COMBB(tc_fun(_1579704, tc_HOL_Obool), tc_HOL_Obool, _1579702)), c_member(_1579704))), _1579708)))))], (45594 ^ _777959) ^ [_1687728] : [-(c_Enum_Osublists(_1687728, c_List_Olist_ONil(_1687728)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1687728)), c_List_Olist_ONil(_1687728)), c_List_Olist_ONil(tc_List_Olist(_1687728))))], (7336 ^ _777959) ^ [_900959, _900961, _900963, _900965] : [class_Lattices_Osemilattice__sup(_900959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900959), _900961), _900963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900959), _900965), _900963)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_900959), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_900959), _900961), _900965)), _900963)))], (16533 ^ _777959) ^ [_1094773, _1094775, _1094777, _1094779] : [class_Orderings_Olinorder(_1094773), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094773), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094773), _1094775), _1094777)), _1094779) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1094773), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094773), _1094775), _1094779)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094773), _1094777), _1094779)))], (47789 ^ _777959) ^ [_1739400, _1739402, _1739404, _1739406, _1739408] : [hAPP(hAPP(c_List_Olist_OCons(_1739400), _1739402), _1739404) = hAPP(c_List_Ofilter(_1739400, _1739406), _1739408), 47794 ^ _777959 : [(47803 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1739406, _1739402)))], (47805 ^ _777959) ^ [] : [-(_1739404 = hAPP(c_List_Ofilter(_1739400, _1739406), 47793 ^ [_1739400, _1739402, _1739404, _1739406, _1739408]))], (47797 ^ _777959) ^ [_1739714] : [hBOOL(hAPP(hAPP(c_member(_1739400), _1739714), hAPP(c_List_Oset(_1739400), 47792 ^ [_1739400, _1739402, _1739404, _1739406, _1739408]))), hBOOL(hAPP(_1739406, _1739714))], (47795 ^ _777959) ^ [] : [-(_1739408 = hAPP(hAPP(c_List_Oappend(_1739400), 47792 ^ [_1739400, _1739402, _1739404, _1739406, _1739408]), hAPP(hAPP(c_List_Olist_OCons(_1739400), _1739402), 47793 ^ [_1739400, _1739402, _1739404, _1739406, _1739408])))]]], (13435 ^ _777959) ^ [_1024373, _1024375] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1024373, _1024375)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1024373, _1024375), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024373), c_Orderings_Otop__class_Otop(tc_fun(_1024373, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1024375), c_Orderings_Otop__class_Otop(tc_fun(_1024375, tc_HOL_Obool))))], (10172 ^ _777959) ^ [_955999, _956001, _956003, _956005, _956007] : [-(c_Map_Orestrict__map(_955999, _956001, _956003, hAPP(hAPP(c_Set_Oinsert(_955999), _956005), _956007)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(_955999, tc_Option_Ooption(_956001)), c_Map_Orestrict__map(_955999, _956001, _956003, _956007)), _956005), hAPP(_956003, _956005)))], (39474 ^ _777959) ^ [_1539549, _1539551, _1539553, _1539555, _1539557, _1539559] : [c_Finite__Set_Ofolding(_1539549, _1539551, _1539553, _1539555), hBOOL(hAPP(c_Finite__Set_Ofinite(_1539549), _1539557)), -(hAPP(_1539555, hAPP(hAPP(c_Set_Oinsert(_1539549), _1539559), _1539557)) = hAPP(c_Fun_Ocomp(_1539551, _1539551, _1539551, hAPP(_1539555, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1539549, tc_HOL_Obool)), _1539557), hAPP(hAPP(c_Set_Oinsert(_1539549), _1539559), c_Orderings_Obot__class_Obot(tc_fun(_1539549, tc_HOL_Obool)))))), hAPP(_1539553, _1539559)))], (13745 ^ _777959) ^ [_1032010, _1032012, _1032014] : [-(hAPP(c_Set_OCollect(_1032010), hAPP(hAPP(c_COMBS(_1032010, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1032010), c_fdisj), _1032012)), _1032014)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1032010, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1032010), _1032012)), hAPP(c_Set_OCollect(_1032010), _1032014)))], (35271 ^ _777959) ^ [_1440940, _1440942] : [class_Int_Onumber__ring(_1440940), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1440940), hAPP(c_Int_Onumber__class_Onumber__of(_1440940), 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)))), _1440942)) = c_Groups_Oone__class_Oone(_1440940))], (1330 ^ _777959) ^ [_797308, _797310] : [-(class_Lattices_Oboolean__algebra(_797308)), _797310 = _797308, class_Lattices_Oboolean__algebra(_797310)], (43248 ^ _777959) ^ [_1636710, _1636712] : [-(hAPP(hAPP(c_List_Odrop(_1636710), _1636712), c_List_Olist_ONil(_1636710)) = c_List_Olist_ONil(_1636710))], (50900 ^ _777959) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (31036 ^ _777959) ^ [_1364238, _1364240] : [class_Rings_Olinordered__idom(_1364238), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364238), hAPP(c_Groups_Oabs__class_Oabs(_1364238), _1364240)), hAPP(c_Groups_Oabs__class_Oabs(_1364238), _1364240)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364238), _1364240), _1364240))], (13381 ^ _777959) ^ [_1022910, _1022912] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1022910, tc_HOL_Obool), _1022912) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1022910, tc_HOL_Obool), tc_fun(_1022910, tc_HOL_Obool)), _1022912), c_COMBI(tc_fun(_1022910, tc_HOL_Obool))))], (30655 ^ _777959) ^ [_1357356, _1357358] : [class_Rings_Olinordered__idom(_1357356), 30658 ^ _777959 : [(30665 ^ _777959) ^ [] : [_1357358 = c_Groups_Ozero__class_Ozero(_1357356), -(c_Groups_Osgn__class_Osgn(_1357356, _1357358) = c_Groups_Ozero__class_Ozero(_1357356))], (30659 ^ _777959) ^ [] : [c_Groups_Osgn__class_Osgn(_1357356, _1357358) = c_Groups_Ozero__class_Ozero(_1357356), -(_1357358 = c_Groups_Ozero__class_Ozero(_1357356))]]], (33755 ^ _777959) ^ [_1413426, _1413428, _1413430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1413426), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413426)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1413428)), _1413430)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2724 ^ _777959) ^ [_818552, _818554] : [_818554 = _818552, -(c_Hoare__Mirabelle_Otriple_Otriple(_818554) = c_Hoare__Mirabelle_Otriple_Otriple(_818552))], (1760 ^ _777959) ^ [_802683, _802685] : [-(class_Orderings_Oord(_802683)), _802685 = _802683, class_Orderings_Oord(_802685)], (42537 ^ _777959) ^ [_1619615, _1619617] : [-(c_Fun_Oinj__on(_1619615, _1619615, c_Fun_Oid(_1619615), _1619617))], (30529 ^ _777959) ^ [_1355193, _1355195, _1355197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1355193), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30532 ^ _777959 : [(30533 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1355195, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1355197), _1355193)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1355197, _1355193))), 30536 ^ _777959 : [(30537 ^ _777959) ^ [_1355403, _1355405] : [-(hBOOL(hAPP(hAPP(_1355195, _1355405), _1355403))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1355193), _1355403)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1355403), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1355197 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1355193), _1355405)), _1355403)]]], (30551 ^ _777959) ^ [] : [30554 ^ _777959 : [(30557 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 30553 ^ [_1355193, _1355195, _1355197]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30559 ^ _777959) ^ [] : [-(_1355197 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1355193), 30552 ^ [_1355193, _1355195, _1355197])), 30553 ^ [_1355193, _1355195, _1355197]))], (30561 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1355195, 30552 ^ [_1355193, _1355195, _1355197]), 30553 ^ [_1355193, _1355195, _1355197]))], (30555 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1355193), 30553 ^ [_1355193, _1355195, _1355197])))]], -(hBOOL(hAPP(hAPP(_1355195, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1355197), _1355193)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1355197, _1355193))))]]], (48053 ^ _777959) ^ [_1745463, _1745465, _1745467, _1745469, _1745471, _1745473, _1745475] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1745463, _1745465, _1745467, _1745469), _1745471), _1745473), _1745475) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1745465, _1745467, _1745469), _1745473), hAPP(_1745471, _1745475)))], (36984 ^ _777959) ^ [_1481180, _1481182, _1481184, _1481186] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1481180, tc_HOL_Obool), tc_fun(_1481180, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1481180, tc_HOL_Obool), tc_fun(_1481180, tc_HOL_Obool)), _1481184), _1481186)), c_Wellfounded_Omax__ext(_1481180, _1481182))), -(c_Wellfounded_Omax__extp(_1481180, hAPP(hAPP(c_COMBC(_1481180, tc_fun(tc_prod(_1481180, _1481180), tc_HOL_Obool), tc_fun(_1481180, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1481180, tc_fun(tc_fun(tc_prod(_1481180, _1481180), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1481180, _1481180), tc_HOL_Obool), tc_fun(_1481180, tc_HOL_Obool)), _1481180), c_COMBC(_1481180, tc_fun(tc_prod(_1481180, _1481180), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1481180, tc_prod(_1481180, _1481180)), tc_fun(_1481180, tc_fun(tc_fun(tc_prod(_1481180, _1481180), tc_HOL_Obool), tc_HOL_Obool)), _1481180), hAPP(c_COMBB(tc_prod(_1481180, _1481180), tc_fun(tc_fun(tc_prod(_1481180, _1481180), tc_HOL_Obool), tc_HOL_Obool), _1481180), c_member(tc_prod(_1481180, _1481180)))), c_Product__Type_OPair(_1481180, _1481180)))), _1481182), _1481184, _1481186))], (34527 ^ _777959) ^ [_1427849] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1427849), _1427849)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1427849)], (49166 ^ _777959) ^ [_1771577, _1771579, _1771581] : [c_Relation_Osingle__valued(_1771577, _1771579, _1771581), 49169 ^ _777959 : [(49170 ^ _777959) ^ [_1771698, _1771700] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1771577, _1771579)), hAPP(hAPP(c_Product__Type_OPair(_1771577, _1771579), _1771700), _1771698)), _1771581)), 49173 ^ _777959 : [(49174 ^ _777959) ^ [_1771824] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1771577, _1771579)), hAPP(hAPP(c_Product__Type_OPair(_1771577, _1771579), _1771700), _1771824)), _1771581)), -(_1771698 = _1771824)]]]]], (18765 ^ _777959) ^ [_1138347, _1138349, _1138351] : [class_Lattices_Oab__semigroup__idem__mult(_1138347), hBOOL(hAPP(c_Finite__Set_Ofinite(_1138347), _1138349)), -(_1138349 = c_Orderings_Obot__class_Obot(tc_fun(_1138347, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1138347), _1138351)), -(_1138351 = c_Orderings_Obot__class_Obot(tc_fun(_1138347, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1138347, c_Groups_Otimes__class_Otimes(_1138347)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1138347, tc_HOL_Obool)), _1138349), _1138351)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138347), hAPP(c_Finite__Set_Ofold1(_1138347, c_Groups_Otimes__class_Otimes(_1138347)), _1138349)), hAPP(c_Finite__Set_Ofold1(_1138347, c_Groups_Otimes__class_Otimes(_1138347)), _1138351)))], (10528 ^ _777959) ^ [_964291, _964293, _964295, _964297, _964299, _964301, _964303] : [c_Big__Operators_Ocomm__monoid__big(_964291, _964293, _964295, _964297, _964299), 10531 ^ _777959 : [(10538 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_964293), _964301))), -(hAPP(hAPP(_964299, _964303), _964301) = _964297)], (10532 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_964293), _964301)), -(hAPP(hAPP(_964299, _964303), _964301) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_964291, _964293, _964295), _964303), _964297), _964301))]]], (44074 ^ _777959) ^ [_1654540, _1654542] : [-(c_List_Otranspose(_1654540, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1654540)), c_List_Olist_ONil(_1654540)), _1654542)) = c_List_Otranspose(_1654540, _1654542))], (35079 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (44706 ^ _777959) ^ [_1666509, _1666511, _1666513, _1666515, _1666517] : [class_Orderings_Olinorder(_1666509), c_Fun_Oinj__on(_1666511, _1666509, _1666513, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1666511, tc_HOL_Obool)), hAPP(c_List_Oset(_1666511), _1666515)), hAPP(c_List_Oset(_1666511), _1666517))), c_List_Olinorder__class_Osorted(_1666509, hAPP(hAPP(c_List_Omap(_1666511, _1666509), _1666513), _1666515)), hBOOL(hAPP(c_List_Odistinct(_1666509), hAPP(hAPP(c_List_Omap(_1666511, _1666509), _1666513), _1666515))), c_List_Olinorder__class_Osorted(_1666509, hAPP(hAPP(c_List_Omap(_1666511, _1666509), _1666513), _1666517)), hBOOL(hAPP(c_List_Odistinct(_1666509), hAPP(hAPP(c_List_Omap(_1666511, _1666509), _1666513), _1666517))), hAPP(c_List_Oset(_1666511), _1666515) = hAPP(c_List_Oset(_1666511), _1666517), -(_1666515 = _1666517)], (43807 ^ _777959) ^ [_1649191, _1649193, _1649195] : [_1649191 = c_List_Olist_ONil(_1649193), -(c_List_Olast(_1649193, hAPP(hAPP(c_List_Olist_OCons(_1649193), _1649195), _1649191)) = _1649195)], (19484 ^ _777959) ^ [_1151037] : [-(_1151037 = 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)), _1151037)))], (22856 ^ _777959) ^ [_1213923, _1213925] : [class_Rings_Olinordered__semidom(_1213923), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1213923), c_Groups_Ozero__class_Ozero(_1213923)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1213923), _1213925))))], (38572 ^ _777959) ^ [_1517997, _1517999, _1518001, _1518003, _1518005] : [-(hAPP(c_Fun_Othe__inv__into(_1517997, _1517999, _1518001, _1518003), _1518005) = c_HOL_OThe(_1517997, hAPP(hAPP(c_COMBS(_1517997, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1517997), c_fconj), hAPP(hAPP(c_COMBC(_1517997, tc_fun(_1517997, tc_HOL_Obool), tc_HOL_Obool), c_member(_1517997)), _1518001))), hAPP(hAPP(c_COMBC(_1517997, _1517999, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1517999, tc_fun(_1517999, tc_HOL_Obool), _1517997), c_fequal), _1518003)), _1518005))))], (27117 ^ _777959) ^ [_1291559] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291559)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1291559) = 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, _1291559))))], (19390 ^ _777959) ^ [_1149660] : [class_Rings_Ozero__neq__one(_1149660), c_Groups_Ozero__class_Ozero(_1149660) = c_Groups_Oone__class_Oone(_1149660)], (51290 ^ _777959) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (6757 ^ _777959) ^ [_887777, _887779, _887781, _887783] : [-(hBOOL(hAPP(hAPP(c_member(_887777), _887779), _887781))), -(hBOOL(hAPP(hAPP(c_member(_887777), _887779), _887783))), 6764 ^ _777959 : [(6771 ^ _777959) ^ [] : [_887781 = _887783, -(hAPP(hAPP(c_Set_Oinsert(_887777), _887779), _887781) = hAPP(hAPP(c_Set_Oinsert(_887777), _887779), _887783))], (6765 ^ _777959) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_887777), _887779), _887781) = hAPP(hAPP(c_Set_Oinsert(_887777), _887779), _887783), -(_887781 = _887783)]]], (4068 ^ _777959) ^ [_839566, _839568, _839570, _839572] : [-(c_Product__Type_OSigma(_839572, _839568) = c_Product__Type_OSigma(_839570, _839566)), _839572 = _839570, _839568 = _839566], (10082 ^ _777959) ^ [_953607, _953609, _953611, _953613] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953607, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_953607), _953609), _953611)), hAPP(hAPP(c_Set_Oinsert(_953607), _953609), _953613)) = hAPP(hAPP(c_Set_Oinsert(_953607), _953609), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_953607, tc_HOL_Obool)), _953611), _953613)))], (49824 ^ _777959) ^ [_1788367, _1788369, _1788371] : [c_List_Olist__all(_1788367, _1788369, _1788371), 49827 ^ _777959 : [(49828 ^ _777959) ^ [_1788448] : [hBOOL(hAPP(hAPP(c_member(_1788367), _1788448), hAPP(c_List_Oset(_1788367), _1788371))), -(hBOOL(hAPP(_1788369, _1788448)))]]], (19063 ^ _777959) ^ [_1144307, _1144309, _1144311, _1144313] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1144307)), hAPP(c_Set_Oimage(_1144309, tc_Option_Ooption(_1144307), _1144311), c_Orderings_Otop__class_Otop(tc_fun(_1144309, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1144307)), hAPP(c_Set_Oimage(_1144309, tc_Option_Ooption(_1144307), c_Map_Omap__add(_1144309, _1144307, _1144311, hAPP(c_Map_Omap__of(_1144309, _1144307), _1144313))), c_Orderings_Otop__class_Otop(tc_fun(_1144309, tc_HOL_Obool))))))], (46890 ^ _777959) ^ [_1718080, _1718082] : [-(c_Wellfounded_Owf(_1718080, hAPP(c_Wellfounded_Omeasure(_1718080), _1718082)))], (15699 ^ _777959) ^ [_1076712, _1076714] : [class_Rings_Ocomm__ring__1(_1076712), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1076712), _1076714) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1076712), hAPP(c_Groups_Ouminus__class_Ouminus(_1076712), c_Groups_Oone__class_Oone(_1076712))), _1076714))], (39097 ^ _777959) ^ [_1530996, _1530998, _1531000, _1531002, _1531004, _1531006] : [class_Groups_Ocomm__monoid__add(_1530996), c_Fun_Oinj__on(_1530998, _1531000, _1531002, _1531004), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1531000, _1530996), _1531006), hAPP(c_Set_Oimage(_1530998, _1531000, _1531002), _1531004)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1530998, _1530996), hAPP(c_Fun_Ocomp(_1531000, _1530996, _1530998, _1531006), _1531002)), _1531004))], (31088 ^ _777959) ^ [_1365244, _1365246, _1365248, _1365250] : [class_Groups_Oordered__ab__group__add__abs(_1365244), -(hAPP(c_Groups_Oabs__class_Oabs(_1365244), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365246, _1365244), hAPP(hAPP(c_COMBB(_1365244, _1365244, _1365246), c_Groups_Oabs__class_Oabs(_1365244)), _1365248)), _1365250)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1365246, _1365244), hAPP(hAPP(c_COMBB(_1365244, _1365244, _1365246), c_Groups_Oabs__class_Oabs(_1365244)), _1365248)), _1365250))], (25858 ^ _777959) ^ [_1268119, _1268121, _1268123] : [class_Rings_Odivision__ring(_1268119), -(_1268121 = c_Groups_Ozero__class_Ozero(_1268119)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268119), hAPP(c_Groups_Ouminus__class_Ouminus(_1268119), _1268123)), hAPP(c_Groups_Ouminus__class_Ouminus(_1268119), _1268121)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1268119), _1268123), _1268121))], (9784 ^ _777959) ^ [_947903, _947905, _947907, _947909] : [-(c_Map_Odom(_947903, _947905, c_Map_Orestrict__map(_947903, _947905, _947907, _947909)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947903, tc_HOL_Obool)), c_Map_Odom(_947903, _947905, _947907)), _947909))], (48541 ^ _777959) ^ [_1755952, _1755954, _1755956] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1755952), tc_List_Olist(_1755952))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1755952), tc_List_Olist(_1755952)), _1755954), _1755954)), c_List_Olistrel(_1755952, c_Transitive__Closure_Ortrancl(_1755952, _1755956)))))], (40685 ^ _777959) ^ [_1568560, _1568562, _1568564] : [40686 ^ _777959 : [(40687 ^ _777959) ^ [_1568614] : [hBOOL(hAPP(_1568560, _1568614))]], _1568562 = c_Hilbert__Choice_OEps(_1568564, _1568560), -(hBOOL(hAPP(_1568560, _1568562)))], (22982 ^ _777959) ^ [_1216209, _1216211, _1216213] : [class_Rings_Oring__1(_1216209), hBOOL(hAPP(hAPP(c_member(_1216209), _1216211), c_Int_Oring__1__class_OInts(_1216209))), hBOOL(hAPP(hAPP(c_member(_1216209), _1216213), c_Int_Oring__1__class_OInts(_1216209))), -(hBOOL(hAPP(hAPP(c_member(_1216209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1216209), _1216211), _1216213)), c_Int_Oring__1__class_OInts(_1216209))))], (2426 ^ _777959) ^ [_813859, _813861, _813863, _813865, _813867, _813869, _813871, _813873] : [-(c_Nitpick_Oprod(_813873, _813869, _813865, _813861) = c_Nitpick_Oprod(_813871, _813867, _813863, _813859)), _813873 = _813871, _813869 = _813867, _813865 = _813863, _813861 = _813859], (44891 ^ _777959) ^ [_1670831, _1670833, _1670835, _1670837] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670831)), _1670833) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1670835)), _1670837), -(hAPP(hAPP(c_List_Ozip(_1670831, _1670835), hAPP(c_List_Orev(_1670831), _1670833)), hAPP(c_List_Orev(_1670835), _1670837)) = hAPP(c_List_Orev(tc_prod(_1670831, _1670835)), hAPP(hAPP(c_List_Ozip(_1670831, _1670835), _1670833), _1670837)))], (50920 ^ _777959) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (1600 ^ _777959) ^ [_800683, _800685] : [-(class_Groups_Ocomm__monoid__add(_800683)), _800685 = _800683, class_Groups_Ocomm__monoid__add(_800685)], (4516 ^ _777959) ^ [_846264, _846266] : [_846266 = _846264, -(c_Int_OBit0(_846266) = c_Int_OBit0(_846264))], (51062 ^ _777959) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (36127 ^ _777959) ^ [_1463021, _1463023, _1463025, _1463027, _1463029, _1463031] : [-(hAPP(c_Product__Type_Oapsnd(_1463021, _1463023, _1463025, _1463027), hAPP(hAPP(c_Product__Type_OPair(_1463025, _1463021), _1463029), _1463031)) = hAPP(hAPP(c_Product__Type_OPair(_1463025, _1463023), _1463029), hAPP(_1463027, _1463031)))], (28820 ^ _777959) ^ [_1321123, _1321125, _1321127] : [class_Orderings_Olinorder(_1321123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1321123), _1321125), _1321127)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321123, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1321123, _1321125), _1321127)), hAPP(hAPP(c_Set_Oinsert(_1321123), _1321127), c_Orderings_Obot__class_Obot(tc_fun(_1321123, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_1321123, _1321125, _1321127))], (27467 ^ _777959) ^ [_1297336] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1297336))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34297 ^ _777959) ^ [_1423651] : [-(c_Int_Opred(c_Int_OBit0(_1423651)) = c_Int_OBit1(c_Int_Opred(_1423651)))], (41681 ^ _777959) ^ [_1595943, _1595945, _1595947, _1595949, _1595951, _1595953] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595943), tc_List_Olist(_1595943))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595943), tc_List_Olist(_1595943)), hAPP(hAPP(c_List_Olist_OCons(_1595943), _1595945), _1595947)), hAPP(hAPP(c_List_Olist_OCons(_1595943), _1595949), _1595951))), c_List_Olexord(_1595943, _1595953)))), 41682 ^ _777959 : [(41685 ^ _777959) ^ [] : [_1595945 = _1595949, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1595943), tc_List_Olist(_1595943))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1595943), tc_List_Olist(_1595943)), _1595947), _1595951)), c_List_Olexord(_1595943, _1595953)))], (41683 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595943, _1595943)), hAPP(hAPP(c_Product__Type_OPair(_1595943, _1595943), _1595945), _1595949)), _1595953))]]], (50984 ^ _777959) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (41906 ^ _777959) ^ [_1603436, _1603438, _1603440, _1603442] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1603436), _1603438)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1603440), _1603442)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1603436, _1603440)), hAPP(hAPP(c_Product__Type_OSigma(_1603436, _1603440), _1603438), hAPP(c_COMBK(tc_fun(_1603440, tc_HOL_Obool), _1603436), _1603442)))))], (23957 ^ _777959) ^ [_1233440, _1233442, _1233444] : [class_Rings_Oring__1(_1233440), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1233440), hAPP(c_Groups_Ouminus__class_Ouminus(_1233440), _1233442)), _1233444) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1233440), hAPP(hAPP(c_Power_Opower__class_Opower(_1233440), hAPP(c_Groups_Ouminus__class_Ouminus(_1233440), c_Groups_Oone__class_Oone(_1233440))), _1233444)), hAPP(hAPP(c_Power_Opower__class_Opower(_1233440), _1233442), _1233444)))], (49040 ^ _777959) ^ [_1768729, _1768731, _1768733] : [-(hAPP(c_Relation_ORange(_1768729, _1768731), hAPP(c_Relation_Oconverse(_1768731, _1768729), _1768733)) = hAPP(c_Relation_ODomain(_1768731, _1768729), _1768733))], (23543 ^ _777959) ^ [_1226036, _1226038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226036), _1226038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1226036), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1226038), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (30629 ^ _777959) ^ [_1356898, _1356900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1356898), _1356900)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1356898, _1356900) = _1356898)], (21176 ^ _777959) ^ [_1180261, _1180263, _1180265, _1180267, _1180269] : [class_Groups_Ocomm__monoid__mult(_1180261), hBOOL(hAPP(c_Finite__Set_Ofinite(_1180263), _1180265)), 21183 ^ _777959 : [(21190 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1180263), _1180267), _1180265))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1180263, _1180261), hAPP(hAPP(c_COMBC(_1180263, _1180261, _1180261), hAPP(hAPP(c_COMBS(_1180263, _1180261, tc_fun(_1180261, _1180261)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1180261, tc_fun(_1180261, _1180261)), _1180263), c_If(_1180261)), hAPP(hAPP(c_COMBC(_1180263, _1180263, tc_HOL_Obool), c_fequal), _1180267))), _1180269)), c_Groups_Oone__class_Oone(_1180261))), _1180265) = c_Groups_Oone__class_Oone(_1180261))], (21184 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1180263), _1180267), _1180265)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1180263, _1180261), hAPP(hAPP(c_COMBC(_1180263, _1180261, _1180261), hAPP(hAPP(c_COMBS(_1180263, _1180261, tc_fun(_1180261, _1180261)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1180261, tc_fun(_1180261, _1180261)), _1180263), c_If(_1180261)), hAPP(hAPP(c_COMBC(_1180263, _1180263, tc_HOL_Obool), c_fequal), _1180267))), _1180269)), c_Groups_Oone__class_Oone(_1180261))), _1180265) = hAPP(_1180269, _1180267))]]], (9424 ^ _777959) ^ [_939914, _939916] : [class_Lattices_Olattice(_939914), hBOOL(hAPP(c_Finite__Set_Ofinite(_939914), _939916)), -(_939916 = c_Orderings_Obot__class_Obot(tc_fun(_939914, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_939914), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939914), 9437 ^ [_939914, _939916]), 9438 ^ [_939914, _939916])), hAPP(hAPP(c_Set_Oinsert(_939914), 9437 ^ [_939914, _939916]), hAPP(hAPP(c_Set_Oinsert(_939914), 9438 ^ [_939914, _939916]), c_Orderings_Obot__class_Obot(tc_fun(_939914, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_939914), c_Big__Operators_Olattice__class_OSup__fin(_939914, _939916)), _939916)))], (6397 ^ _777959) ^ [_881257, _881259, _881261, _881263] : [class_Orderings_Oord(_881257), _881259 = _881261, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881257), _881261), _881263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881257), _881259), _881263)))], (25034 ^ _777959) ^ [_1252178, _1252180] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1252178), _1252180) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25035 ^ _777959 : [(25044 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1252178), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1252180), _1252178))], (25038 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1252178)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1252178), _1252180))], (25036 ^ _777959) ^ [] : [_1252180 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]]], (45818 ^ _777959) ^ [_1692291, _1692293, _1692295] : [class_Enum_Oenum(_1692291), class_Enum_Oenum(_1692293), 45825 ^ _777959 : [(45832 ^ _777959) ^ [] : [c_Enum_Oall__n__lists(_1692291, hAPP(hAPP(c_COMBB(tc_fun(_1692293, _1692291), tc_HOL_Obool, tc_List_Olist(_1692291)), _1692295), hAPP(hAPP(c_COMBB(tc_fun(_1692293, tc_Option_Ooption(_1692291)), tc_fun(_1692293, _1692291), tc_List_Olist(_1692291)), c_Fun_Ocomp(tc_Option_Ooption(_1692291), _1692291, _1692293, c_Option_Othe(_1692291))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1692293, _1692291)), tc_fun(_1692293, tc_Option_Ooption(_1692291)), tc_List_Olist(_1692291)), c_Map_Omap__of(_1692293, _1692291)), hAPP(c_List_Ozip(_1692293, _1692291), c_Enum_Oenum__class_Oenum(_1692293))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692293)), c_Enum_Oenum__class_Oenum(_1692293))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1692293, _1692291)), _1692295)))], (45826 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(_1692293, _1692291)), _1692295)), -(c_Enum_Oall__n__lists(_1692291, hAPP(hAPP(c_COMBB(tc_fun(_1692293, _1692291), tc_HOL_Obool, tc_List_Olist(_1692291)), _1692295), hAPP(hAPP(c_COMBB(tc_fun(_1692293, tc_Option_Ooption(_1692291)), tc_fun(_1692293, _1692291), tc_List_Olist(_1692291)), c_Fun_Ocomp(tc_Option_Ooption(_1692291), _1692291, _1692293, c_Option_Othe(_1692291))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1692293, _1692291)), tc_fun(_1692293, tc_Option_Ooption(_1692291)), tc_List_Olist(_1692291)), c_Map_Omap__of(_1692293, _1692291)), hAPP(c_List_Ozip(_1692293, _1692291), c_Enum_Oenum__class_Oenum(_1692293))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692293)), c_Enum_Oenum__class_Oenum(_1692293))))]]], (43464 ^ _777959) ^ [_1642134, _1642136, _1642138] : [-(_1642134 = c_List_Olist_ONil(_1642136)), -(hAPP(c_List_Ohd(_1642136), hAPP(hAPP(c_List_Oappend(_1642136), _1642134), _1642138)) = hAPP(c_List_Ohd(_1642136), _1642134))], (506 ^ _777959) ^ [_785818, _785820, _785822, _785824, _785826, _785828] : [-(c_Finite__Set_Ofun__left__comm__idem(_785826, _785822, _785818)), c_Finite__Set_Ofun__left__comm__idem(_785828, _785824, _785820), _785828 = _785826, _785824 = _785822, _785820 = _785818], (8068 ^ _777959) ^ [_915907, _915909, _915911, _915913] : [hBOOL(hAPP(hAPP(c_member(_915907), _915909), _915911)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915907, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_915907), _915909), _915913)), _915911) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_915907, tc_HOL_Obool)), _915913), _915911))], (39157 ^ _777959) ^ [_1532233, _1532235, _1532237, _1532239, _1532241] : [hAPP(hAPP(c_List_Omap(_1532233, _1532235), _1532237), _1532239) = hAPP(hAPP(c_List_Omap(_1532233, _1532235), _1532237), _1532241), c_Fun_Oinj__on(_1532233, _1532235, _1532237, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1532233, tc_HOL_Obool)), hAPP(c_List_Oset(_1532233), _1532239)), hAPP(c_List_Oset(_1532233), _1532241))), -(_1532239 = _1532241)], (39711 ^ _777959) ^ [_1545411, _1545413, _1545415, _1545417, _1545419, _1545421] : [c_Finite__Set_Ofolding__idem(_1545411, _1545413, _1545415, _1545417), hBOOL(hAPP(c_Finite__Set_Ofinite(_1545411), _1545419)), hBOOL(hAPP(hAPP(c_member(_1545411), _1545421), _1545419)), -(hAPP(c_Fun_Ocomp(_1545413, _1545413, _1545413, hAPP(_1545417, _1545419)), hAPP(_1545415, _1545421)) = hAPP(_1545417, _1545419))], (37070 ^ _777959) ^ [_1483094] : [-(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)), _1483094), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (47807 ^ _777959) ^ [_1739918, _1739920, _1739922, _1739924, _1739926] : [-(hAPP(hAPP(c_List_Olist_OCons(_1739918), _1739920), _1739922) = hAPP(c_List_Ofilter(_1739918, _1739924), _1739926)), 47808 ^ _777959 : [(47809 ^ _777959) ^ [_1740046, _1740048] : [_1739926 = hAPP(hAPP(c_List_Oappend(_1739918), _1740048), hAPP(hAPP(c_List_Olist_OCons(_1739918), _1739920), _1740046)), 47815 ^ _777959 : [(47818 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1739924, 47814 ^ [_1739918, _1739920, _1739922, _1739924, _1739926, _1740046, _1740048])))], (47816 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1739918), 47814 ^ [_1739918, _1739920, _1739922, _1739924, _1739926, _1740046, _1740048]), hAPP(c_List_Oset(_1739918), _1740048))))]], hBOOL(hAPP(_1739924, _1739920)), _1739922 = hAPP(c_List_Ofilter(_1739918, _1739924), _1740046)]]], (13693 ^ _777959) ^ [_1030858, _1030860, _1030862] : [hBOOL(hAPP(hAPP(c_member(_1030858), _1030860), hAPP(c_Set_OCollect(_1030858), _1030862))), -(hBOOL(hAPP(_1030862, _1030860)))], (18398 ^ _777959) ^ [_1131100, _1131102] : [class_Orderings_Olinorder(_1131100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131100), _1131102)), -(_1131102 = c_Orderings_Obot__class_Obot(tc_fun(_1131100, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1131100), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1131100), 18411 ^ [_1131100, _1131102]), 18412 ^ [_1131100, _1131102])), hAPP(hAPP(c_Set_Oinsert(_1131100), 18411 ^ [_1131100, _1131102]), hAPP(hAPP(c_Set_Oinsert(_1131100), 18412 ^ [_1131100, _1131102]), c_Orderings_Obot__class_Obot(tc_fun(_1131100, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1131100), c_Big__Operators_Olinorder__class_OMin(_1131100, _1131102)), _1131102)))], (25478 ^ _777959) ^ [_1260996, _1260998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1260996)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1260996), _1260998)), _1260996) = _1260998)], (10234 ^ _777959) ^ [_957500, _957502, _957504, _957506] : [hBOOL(hAPP(hAPP(c_member(_957500), _957502), _957504)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957500, tc_HOL_Obool)), _957504), hAPP(hAPP(c_Set_Oinsert(_957500), _957502), _957506)) = hAPP(hAPP(c_Set_Oinsert(_957500), _957502), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957500, tc_HOL_Obool)), _957504), _957506)))], (23567 ^ _777959) ^ [_1226487, _1226489, _1226491] : [class_Rings_Oring__1__no__zero__divisors(_1226487), -(_1226489 = c_Groups_Ozero__class_Ozero(_1226487)), hAPP(hAPP(c_Power_Opower__class_Opower(_1226487), _1226489), _1226491) = c_Groups_Ozero__class_Ozero(_1226487)], (2594 ^ _777959) ^ [_816419, _816421, _816423, _816425, _816427, _816429, _816431, _816433, _816435, _816437] : [-(c_Product__Type_Oprod_Oprod__size(_816437, _816433, _816429, _816425, _816421) = c_Product__Type_Oprod_Oprod__size(_816435, _816431, _816427, _816423, _816419)), _816437 = _816435, _816433 = _816431, _816429 = _816427, _816425 = _816423, _816421 = _816419], (29982 ^ _777959) ^ [_1344793, _1344795, _1344797, _1344799, _1344801, _1344803] : [class_Divides_Osemiring__div(_1344793), c_Divides_Odiv__class_Omod(_1344793, _1344795, _1344797) = c_Divides_Odiv__class_Omod(_1344793, _1344799, _1344797), c_Divides_Odiv__class_Omod(_1344793, _1344801, _1344797) = c_Divides_Odiv__class_Omod(_1344793, _1344803, _1344797), -(c_Divides_Odiv__class_Omod(_1344793, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344793), _1344795), _1344801), _1344797) = c_Divides_Odiv__class_Omod(_1344793, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1344793), _1344799), _1344803), _1344797))], (36636 ^ _777959) ^ [_1472963, _1472965, _1472967, _1472969] : [_1472963 = _1472965, 36639 ^ _777959 : [(36642 ^ _777959) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1472967, _1472969), _1472963) = hAPP(c_Product__Type_Osnd(_1472967, _1472969), _1472965))], (36640 ^ _777959) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1472967, _1472969), _1472963) = hAPP(c_Product__Type_Ofst(_1472967, _1472969), _1472965))]]], (35832 ^ _777959) ^ [_1457665, _1457667, _1457669, _1457671, _1457673, _1457675] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1457665, _1457667, _1457669), _1457671), hAPP(hAPP(c_Product__Type_OPair(_1457665, _1457667), _1457673), _1457675)) = hAPP(hAPP(_1457671, _1457673), _1457675))], (5622 ^ _777959) ^ [_863871, _863873] : [_863873 = _863871, -(c_Orderings_Obot__class_Obot(_863873) = c_Orderings_Obot__class_Obot(_863871))], (46623 ^ _777959) ^ [_1709462, _1709464, _1709466] : [-(hAPP(c_List_Oset(_1709462), c_List_Oinsert(_1709462, _1709464, _1709466)) = hAPP(hAPP(c_Set_Oinsert(_1709462), _1709464), hAPP(c_List_Oset(_1709462), _1709466)))], (15248 ^ _777959) ^ [_1068435, _1068437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1068435)), hAPP(c_Nat_OSuc, _1068437))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1068435), _1068437)))], (21687 ^ _777959) ^ [_1189907, _1189909, _1189911] : [hBOOL(hAPP(_1189907, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1189909), _1189911))), 21690 ^ _777959 : [(21697 ^ _777959) ^ [_1190098] : [_1189909 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1189911), _1190098), -(hBOOL(hAPP(_1189907, _1190098)))], (21691 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1189909), _1189911)), -(hBOOL(hAPP(_1189907, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (22826 ^ _777959) ^ [_1213369, _1213371, _1213373, _1213375] : [class_Rings_Ocomm__semiring__1(_1213369), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213369), hAPP(hAPP(c_Power_Opower__class_Opower(_1213369), _1213371), _1213373)), hAPP(hAPP(c_Power_Opower__class_Opower(_1213369), _1213371), _1213375)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1213369), _1213371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1213373), _1213375)))], (30786 ^ _777959) ^ [_1359593, _1359595] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1359593), _1359595)), _1359595) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1359593), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1359593, _1359595)))], (11324 ^ _777959) ^ [_979551, _979553, _979555, _979557, _979559] : [class_Groups_Ocomm__monoid__add(_979551), hBOOL(hAPP(c_Finite__Set_Ofinite(_979553), _979555)), hBOOL(hAPP(c_Finite__Set_Ofinite(_979553), _979557)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979553, tc_HOL_Obool)), _979555), _979557) = c_Orderings_Obot__class_Obot(tc_fun(_979553, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_979553, _979551), _979559), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979553, tc_HOL_Obool)), _979555), _979557)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_979551), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_979553, _979551), _979559), _979555)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_979553, _979551), _979559), _979557)))], (48348 ^ _777959) ^ [_1750878, _1750880] : [-(c_Code__Numeral_Onat__of__aux(_1750878, _1750880) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1750878)), _1750880))], (10334 ^ _777959) ^ [_960002, _960004, _960006, _960008, _960010, _960012] : [c_Finite__Set_Ofun__left__comm__idem(_960002, _960004, _960006), hBOOL(hAPP(c_Finite__Set_Ofinite(_960002), _960008)), -(hAPP(hAPP(c_Finite__Set_Ofold(_960002, _960004, _960006), _960010), hAPP(hAPP(c_Set_Oinsert(_960002), _960012), _960008)) = hAPP(hAPP(_960006, _960012), hAPP(hAPP(c_Finite__Set_Ofold(_960002, _960004, _960006), _960010), _960008)))], (44330 ^ _777959) ^ [_1659448, _1659450] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1659448, _1659450))))], (25178 ^ _777959) ^ [_1255064, _1255066, _1255068, _1255070] : [class_Groups_Ocomm__monoid__add(_1255064), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1255066), _1255068)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1255064), _1255070), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1255066), _1255068)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1255064), hAPP(_1255070, _1255066)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1255064), _1255070), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1255066)), _1255068))))], (4712 ^ _777959) ^ [_849542, _849544, _849546, _849548, _849550, _849552, _849554, _849556, _849558, _849560, _849562, _849564, _849566, _849568] : [-(c_New__Random__Sequence_Oneg__decr__bind(_849568, _849564, _849560, _849556, _849552, _849548, _849544) = c_New__Random__Sequence_Oneg__decr__bind(_849566, _849562, _849558, _849554, _849550, _849546, _849542)), _849568 = _849566, _849564 = _849562, _849560 = _849558, _849556 = _849554, _849552 = _849550, _849548 = _849546, _849544 = _849542], (13115 ^ _777959) ^ [_1017191, _1017193, _1017195] : [class_Complete__Lattice_Ocomplete__lattice(_1017191), -(c_Complete__Lattice_OSup__class_OSup(_1017191, hAPP(hAPP(c_Set_Oinsert(_1017191), _1017193), _1017195)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1017191), _1017193), c_Complete__Lattice_OSup__class_OSup(_1017191, _1017195)))], (46868 ^ _777959) ^ [_1717753, _1717755] : [c_Wellfounded_Owf(_1717753, _1717755), -(c_Wellfounded_Owf(tc_List_Olist(_1717753), c_List_Olex(_1717753, _1717755)))], (7058 ^ _777959) ^ [_895585, _895587, _895589, _895591] : [hBOOL(hAPP(hAPP(c_member(_895585), _895591), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895585, tc_HOL_Obool)), _895587), _895589))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_895585, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_895585, tc_fun(_895585, tc_HOL_Obool), tc_HOL_Obool), c_member(_895585)), _895587)), hAPP(hAPP(c_COMBC(_895585, tc_fun(_895585, tc_HOL_Obool), tc_HOL_Obool), c_member(_895585)), _895589)), _895591)))], (22661 ^ _777959) ^ [_1210251, _1210253, _1210255, _1210257] : [class_Rings_Ocomm__semiring__1(_1210251), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1210251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210251), _1210253), _1210255)), _1210257) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1210251), hAPP(hAPP(c_Power_Opower__class_Opower(_1210251), _1210253), _1210257)), hAPP(hAPP(c_Power_Opower__class_Opower(_1210251), _1210255), _1210257)))], (40608 ^ _777959) ^ [_1566711, _1566713, _1566715, _1566717] : [class_Groups_Ocomm__monoid__add(_1566711), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1566711), _1566713), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1566715, _1566717))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1566711), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1566711), _1566713), c_List_Oupto(_1566715, _1566717))))], (38382 ^ _777959) ^ [_1513635, _1513637, _1513639, _1513641, _1513643] : [-(c_Fun_Oinj__on(_1513635, _1513637, _1513639, hAPP(hAPP(c_Set_Oinsert(_1513635), _1513641), _1513643))), c_Fun_Oinj__on(_1513635, _1513637, _1513639, _1513643), -(hBOOL(hAPP(hAPP(c_member(_1513637), hAPP(_1513639, _1513641)), hAPP(c_Set_Oimage(_1513635, _1513637, _1513639), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1513635, tc_HOL_Obool)), _1513643), hAPP(hAPP(c_Set_Oinsert(_1513635), _1513641), c_Orderings_Obot__class_Obot(tc_fun(_1513635, tc_HOL_Obool))))))))], (14740 ^ _777959) ^ [_1055020, _1055022, _1055024, _1055026, _1055028] : [-(hBOOL(hAPP(hAPP(c_member(_1055020), _1055022), c_SetInterval_Oord_OgreaterThanLessThan(_1055020, _1055024, _1055026, _1055028)))), hBOOL(hAPP(hAPP(_1055024, _1055026), _1055022)), hBOOL(hAPP(hAPP(_1055024, _1055022), _1055028))], (34397 ^ _777959) ^ [_1425515, _1425517] : [class_Int_Onumber__ring(_1425515), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1425515), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1425515), c_Groups_Oone__class_Oone(_1425515)), c_Groups_Oone__class_Oone(_1425515))), hAPP(c_Int_Onumber__class_Onumber__of(_1425515), _1425517)) = hAPP(c_Int_Onumber__class_Onumber__of(_1425515), c_Int_OBit0(_1425517)))], (50138 ^ _777959) ^ [_1794251] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), _1794251)), -(hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1794251))))], (35669 ^ _777959) ^ [_1454036, _1454038, _1454040, _1454042, _1454044, _1454046] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1454036, tc_fun(_1454038, tc_HOL_Obool))), _1454040), _1454042), _1454044), _1454046)), 35672 ^ _777959 : [(35675 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1454042, _1454044), _1454046)))], (35673 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(_1454040, _1454044), _1454046)))]]], (41637 ^ _777959) ^ [_1594613, _1594615, _1594617, _1594619, _1594621, _1594623] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594613), tc_List_Olist(_1594613))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594613), tc_List_Olist(_1594613)), hAPP(hAPP(c_List_Olist_OCons(_1594613), _1594615), _1594617)), hAPP(hAPP(c_List_Olist_OCons(_1594613), _1594619), _1594621))), c_List_Olistrel1(_1594613, _1594623)))), 41638 ^ _777959 : [(41645 ^ _777959) ^ [] : [_1594615 = _1594619, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1594613), tc_List_Olist(_1594613))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1594613), tc_List_Olist(_1594613)), _1594617), _1594621)), c_List_Olistrel1(_1594613, _1594623)))], (41639 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594613, _1594613)), hAPP(hAPP(c_Product__Type_OPair(_1594613, _1594613), _1594615), _1594619)), _1594623)), _1594617 = _1594621]]], (34071 ^ _777959) ^ [_1419739, _1419741] : [c_Int_OBit0(_1419739) = c_Int_OBit0(_1419741), -(_1419739 = _1419741)], (50476 ^ _777959) ^ [_1802016, _1802018, _1802020, _1802022, _1802024] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802018, _1802016)), hAPP(hAPP(c_Product__Type_OPair(_1802018, _1802016), _1802022), _1802024)), hAPP(c_Relation_Oconverse(_1802016, _1802018), _1802020))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1802016, _1802018, hAPP(hAPP(c_COMBC(_1802016, tc_fun(tc_prod(_1802016, _1802018), tc_HOL_Obool), tc_fun(_1802018, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1802018, tc_fun(tc_fun(tc_prod(_1802016, _1802018), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1802016, _1802018), tc_HOL_Obool), tc_fun(_1802018, tc_HOL_Obool)), _1802016), c_COMBC(_1802018, tc_fun(tc_prod(_1802016, _1802018), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1802018, tc_prod(_1802016, _1802018)), tc_fun(_1802018, tc_fun(tc_fun(tc_prod(_1802016, _1802018), tc_HOL_Obool), tc_HOL_Obool)), _1802016), hAPP(c_COMBB(tc_prod(_1802016, _1802018), tc_fun(tc_fun(tc_prod(_1802016, _1802018), tc_HOL_Obool), tc_HOL_Obool), _1802018), c_member(tc_prod(_1802016, _1802018)))), c_Product__Type_OPair(_1802016, _1802018)))), _1802020)), _1802022), _1802024)))], (43338 ^ _777959) ^ [_1638904, _1638906, _1638908, _1638910] : [-(hAPP(hAPP(c_List_Odrop(_1638904), _1638906), hAPP(hAPP(c_List_Olist_OCons(_1638904), _1638908), _1638910)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1638904), hAPP(hAPP(c_List_Olist_OCons(_1638904), _1638908), _1638910), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1638904), tc_List_Olist(_1638904)), c_List_Odrop(_1638904)), _1638910), _1638906))], (51294 ^ _777959) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (6567 ^ _777959) ^ [_884205, _884207, _884209, _884211, _884213] : [class_Orderings_Oord(_884205), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884207, _884205)), _884209), _884211)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_884205), hAPP(_884209, _884213)), hAPP(_884211, _884213))))], (16575 ^ _777959) ^ [_1095758, _1095760, _1095762] : [class_Groups_Olinordered__ab__group__add(_1095758), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1095758), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1095758), _1095760), _1095762)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1095758), hAPP(c_Groups_Ouminus__class_Ouminus(_1095758), _1095760)), hAPP(c_Groups_Ouminus__class_Ouminus(_1095758), _1095762)))], (33839 ^ _777959) ^ [_1415083, _1415085, _1415087, _1415089] : [-(c_Nat_Onat_Onat__case(_1415083, _1415085, _1415087, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1415089)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1415083), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1415089))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1415083, _1415083), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1415083, tc_fun(_1415083, _1415083)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1415083, tc_fun(_1415083, _1415083)), tc_Int_Oint), c_If(_1415083)), c_Nat__Numeral_Oneg)), _1415085)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1415083, tc_Int_Oint), _1415087), c_Int_Onat))))], (33323 ^ _777959) ^ [_1406534] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1406534), 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), _1406534)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1406534)))], (35301 ^ _777959) ^ [_1441587] : [-(c_Wellfounded_Ofinite__psubset(_1441587) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1441587, tc_HOL_Obool), tc_fun(_1441587, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1441587, tc_HOL_Obool), tc_fun(_1441587, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1441587, tc_HOL_Obool), tc_fun(tc_fun(_1441587, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1441587, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1441587, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1441587, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1441587, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1441587, tc_HOL_Obool)), c_COMBS(tc_fun(_1441587, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1441587, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1441587, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1441587, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1441587, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1441587, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1441587)))))], (39350 ^ _777959) ^ [_1536720, _1536722, _1536724, _1536726, _1536728, _1536730] : [c_Finite__Set_Ofolding(_1536720, _1536722, _1536724, _1536726), -(hAPP(c_Fun_Ocomp(_1536722, _1536722, _1536722, hAPP(_1536724, _1536728)), hAPP(_1536724, _1536730)) = hAPP(c_Fun_Ocomp(_1536722, _1536722, _1536722, hAPP(_1536724, _1536730)), hAPP(_1536724, _1536728)))], (9386 ^ _777959) ^ [_939207, _939209, _939211] : [class_Lattices_Olattice(_939207), hBOOL(hAPP(c_Finite__Set_Ofinite(_939207), _939209)), -(hBOOL(hAPP(hAPP(c_member(_939207), _939211), _939209))), -(_939209 = c_Orderings_Obot__class_Obot(tc_fun(_939207, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_939207, hAPP(hAPP(c_Set_Oinsert(_939207), _939211), _939209)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939207), _939211), c_Big__Operators_Olattice__class_OSup__fin(_939207, _939209)))], (37357 ^ _777959) ^ [_1491090, _1491092, _1491094] : [-(hAPP(c_Relation_OImage(_1491090, _1491090, c_Relation_OId__on(_1491090, _1491092)), _1491094) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1491090, tc_HOL_Obool)), _1491092), _1491094))], (15156 ^ _777959) ^ [_1066683, _1066685, _1066687, _1066689] : [class_Rings_Ocomm__semiring__1(_1066683), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066683), _1066685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066683), _1066687), _1066689)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1066683), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066683), _1066685), _1066687)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1066683), _1066685), _1066689)))], (49028 ^ _777959) ^ [_1768386, _1768388] : [-(hAPP(c_Relation_OField(_1768386), hAPP(c_Relation_Oconverse(_1768386, _1768386), _1768388)) = hAPP(c_Relation_OField(_1768386), _1768388))], (638 ^ _777959) ^ [_787758, _787760] : [-(c_Nitpick_Ounknown(_787758)), _787760 = _787758, c_Nitpick_Ounknown(_787760)], (19538 ^ _777959) ^ [_1151742] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151742) = _1151742)], (7876 ^ _777959) ^ [_911886, _911888, _911890, _911892] : [c_Com_Ocom_OSemi(_911886, _911888) = c_Com_Ocom_OWhile(_911890, _911892)], (35279 ^ _777959) ^ [_1441069, _1441071] : [-(hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint), _1441069), _1441071) = c_Smallcheck_Osmall_H(_1441069, hAPP(c_Code__Numeral_Oint__of, _1441071), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Code__Numeral_Oint__of, _1441071))))], (45540 ^ _777959) ^ [_1686050, _1686052, _1686054, _1686056, _1686058] : [c_List_Opartition(_1686050, _1686052, _1686054) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1686050), tc_List_Olist(_1686050)), _1686056), _1686058), 45543 ^ _777959 : [(45550 ^ _777959) ^ [_1686312] : [hBOOL(hAPP(hAPP(c_member(_1686050), _1686312), hAPP(c_List_Oset(_1686050), _1686058))), hBOOL(hAPP(_1686052, _1686312))], (45544 ^ _777959) ^ [_1686203] : [hBOOL(hAPP(hAPP(c_member(_1686050), _1686203), hAPP(c_List_Oset(_1686050), _1686056))), -(hBOOL(hAPP(_1686052, _1686203)))]]], (46597 ^ _777959) ^ [_1709038, _1709040, _1709042] : [hBOOL(hAPP(hAPP(c_member(_1709038), _1709040), hAPP(c_List_Oset(_1709038), _1709042))), -(c_List_Oinsert(_1709038, _1709040, _1709042) = _1709042)], (36892 ^ _777959) ^ [] : [-(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))], (20113 ^ _777959) ^ [_1161881, _1161883, _1161885] : [class_Rings_Olinordered__ring__strict(_1161881), 20116 ^ _777959 : [(20131 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), c_Groups_Ozero__class_Ozero(_1161881)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161881), _1161883), _1161885)))), 20132 ^ _777959 : [(20139 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), _1161883), c_Groups_Ozero__class_Ozero(_1161881))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), _1161885), c_Groups_Ozero__class_Ozero(_1161881)))], (20133 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), c_Groups_Ozero__class_Ozero(_1161881)), _1161883)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), c_Groups_Ozero__class_Ozero(_1161881)), _1161885))]]], (20117 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), c_Groups_Ozero__class_Ozero(_1161881)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1161881), _1161883), _1161885))), 20122 ^ _777959 : [(20125 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), c_Groups_Ozero__class_Ozero(_1161881)), _1161885)))], (20123 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), c_Groups_Ozero__class_Ozero(_1161881)), _1161883)))]], 20126 ^ _777959 : [(20129 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), _1161885), c_Groups_Ozero__class_Ozero(_1161881))))], (20127 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1161881), _1161883), c_Groups_Ozero__class_Ozero(_1161881))))]]]]], (28283 ^ _777959) ^ [_1311150, _1311152, _1311154] : [class_Orderings_Oorder(_1311150), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311150, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1311150, _1311152, _1311154)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1311150), _1311154)) = c_Orderings_Obot__class_Obot(tc_fun(_1311150, tc_HOL_Obool)))], (44863 ^ _777959) ^ [_1670336, _1670338, _1670340] : [_1670338 = _1670340, -(hAPP(c_List_Orev(_1670336), _1670338) = hAPP(c_List_Orev(_1670336), _1670340))], (13819 ^ _777959) ^ [_1033442, _1033444, _1033446] : [-(c_Map_Omap__add(_1033442, _1033444, _1033446, hAPP(c_COMBK(tc_Option_Ooption(_1033444), _1033442), c_Option_Ooption_ONone(_1033444))) = _1033446)], (39135 ^ _777959) ^ [_1531771, _1531773, _1531775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531771, _1531771), tc_HOL_Obool)), _1531773), _1531775)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531771, tc_HOL_Obool)), c_Wellfounded_Oacc(_1531771, _1531775)), c_Wellfounded_Oacc(_1531771, _1531773))))], (7548 ^ _777959) ^ [_904707, _904709, _904711, _904713, _904715] : [c_Finite__Set_Ofolding__one__idem(_904707, _904709, _904711), hBOOL(hAPP(c_Finite__Set_Ofinite(_904707), _904713)), -(_904715 = c_Orderings_Obot__class_Obot(tc_fun(_904707, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_904707, tc_HOL_Obool)), _904715), _904713)), -(hAPP(hAPP(_904709, hAPP(_904711, _904715)), hAPP(_904711, _904713)) = hAPP(_904711, _904713))], (13091 ^ _777959) ^ [_1016697, _1016699, _1016701, _1016703, _1016705] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1016697, tc_fun(_1016699, tc_HOL_Obool)), _1016701), hAPP(hAPP(c_COMBS(_1016697, tc_fun(_1016699, tc_HOL_Obool), tc_fun(_1016699, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1016699, tc_HOL_Obool), tc_fun(tc_fun(_1016699, tc_HOL_Obool), tc_fun(_1016699, tc_HOL_Obool)), _1016697), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016699, tc_HOL_Obool))), _1016703)), _1016705)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1016699, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1016699, tc_HOL_Obool), hAPP(c_Set_Oimage(_1016697, tc_fun(_1016699, tc_HOL_Obool), _1016703), _1016701))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1016699, tc_HOL_Obool), hAPP(c_Set_Oimage(_1016697, tc_fun(_1016699, tc_HOL_Obool), _1016705), _1016701))))], (43306 ^ _777959) ^ [_1638163, _1638165, _1638167] : [hAPP(hAPP(c_List_Odrop(_1638163), _1638165), _1638167) = c_List_Olist_ONil(_1638163), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1638163)), _1638167)), _1638165)))], (30649 ^ _777959) ^ [_1357269] : [class_Groups_Osgn__if(_1357269), -(c_Groups_Osgn__class_Osgn(_1357269, c_Groups_Ozero__class_Ozero(_1357269)) = c_Groups_Ozero__class_Ozero(_1357269))], (1790 ^ _777959) ^ [_803058, _803060] : [-(class_Groups_Ozero(_803058)), _803060 = _803058, class_Groups_Ozero(_803060)], (37428 ^ _777959) ^ [] : [-(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))], (45398 ^ _777959) ^ [_1682893, _1682895] : [-(c_List_OdropWhile(_1682893, _1682895, c_List_Olist_ONil(_1682893)) = c_List_Olist_ONil(_1682893))], (18418 ^ _777959) ^ [_1131544, _1131546, _1131548] : [class_Orderings_Olinorder(_1131544), hAPP(_1131546, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1131544), 18423 ^ [_1131544, _1131546, _1131548]), 18424 ^ [_1131544, _1131546, _1131548])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1131544), hAPP(_1131546, 18423 ^ [_1131544, _1131546, _1131548])), hAPP(_1131546, 18424 ^ [_1131544, _1131546, _1131548])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1131544), _1131548)), -(_1131548 = c_Orderings_Obot__class_Obot(tc_fun(_1131544, tc_HOL_Obool))), -(hAPP(_1131546, c_Big__Operators_Olattice_OSup__fin(_1131544, c_Orderings_Oord__class_Omax(_1131544), _1131548)) = c_Big__Operators_Olattice_OSup__fin(_1131544, c_Orderings_Oord__class_Omax(_1131544), hAPP(c_Set_Oimage(_1131544, _1131544, _1131546), _1131548)))], (22733 ^ _777959) ^ [_1211454] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1211454)) = 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), _1211454)))], (3430 ^ _777959) ^ [_829679, _829681, _829683, _829685] : [-(c_List_Olinorder__class_Osorted__list__of__set(_829685, _829681) = c_List_Olinorder__class_Osorted__list__of__set(_829683, _829679)), _829685 = _829683, _829681 = _829679], (27177 ^ _777959) ^ [_1292742] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1292742)) = _1292742)], (48938 ^ _777959) ^ [_1766072, _1766074] : [-(c_Transitive__Closure_Ortrancl(_1766072, hAPP(c_Relation_Oconverse(_1766072, _1766072), _1766074)) = hAPP(c_Relation_Oconverse(_1766072, _1766072), c_Transitive__Closure_Ortrancl(_1766072, _1766074)))], (32077 ^ _777959) ^ [_1383678, _1383680, _1383682] : [class_Int_Onumber(_1383678), class_Orderings_Oord(_1383678), 32084 ^ _777959 : [(32091 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383678), hAPP(c_Int_Onumber__class_Onumber__of(_1383678), _1383680)), hAPP(c_Int_Onumber__class_Onumber__of(_1383678), _1383682)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1383678), hAPP(c_Int_Onumber__class_Onumber__of(_1383678), _1383680)), hAPP(c_Int_Onumber__class_Onumber__of(_1383678), _1383682)) = hAPP(c_Int_Onumber__class_Onumber__of(_1383678), _1383682))], (32085 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383678), hAPP(c_Int_Onumber__class_Onumber__of(_1383678), _1383680)), hAPP(c_Int_Onumber__class_Onumber__of(_1383678), _1383682))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1383678), hAPP(c_Int_Onumber__class_Onumber__of(_1383678), _1383680)), hAPP(c_Int_Onumber__class_Onumber__of(_1383678), _1383682)) = hAPP(c_Int_Onumber__class_Onumber__of(_1383678), _1383680))]]], (37092 ^ _777959) ^ [] : [-(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)))], (34163 ^ _777959) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (39356 ^ _777959) ^ [_1536865, _1536867, _1536869, _1536871, _1536873, _1536875, _1536877, _1536879] : [c_Finite__Set_Ofolding(_1536865, _1536867, _1536869, _1536871), -(hAPP(c_Fun_Ocomp(_1536867, _1536867, _1536873, hAPP(_1536869, _1536875)), hAPP(c_Fun_Ocomp(_1536867, _1536867, _1536873, hAPP(_1536869, _1536877)), _1536879)) = hAPP(c_Fun_Ocomp(_1536867, _1536867, _1536873, hAPP(_1536869, _1536877)), hAPP(c_Fun_Ocomp(_1536867, _1536867, _1536873, hAPP(_1536869, _1536875)), _1536879)))], (4030 ^ _777959) ^ [_839013, _839015] : [_839015 = _839013, -(c_Code__Numeral_OSuc__code__numeral(_839015) = c_Code__Numeral_OSuc__code__numeral(_839013))], (18610 ^ _777959) ^ [_1135571, _1135573] : [class_Orderings_Olinorder(_1135571), hBOOL(hAPP(c_Finite__Set_Ofinite(_1135571), _1135573)), -(c_Big__Operators_Olattice_OInf__fin(_1135571, c_Orderings_Oord__class_Omin(_1135571), _1135573) = hAPP(c_Finite__Set_Ofold1(_1135571, c_Orderings_Oord__class_Omin(_1135571)), _1135573))], (36147 ^ _777959) ^ [_1463424, _1463426] : [36148 ^ _777959 : [(36151 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1463426), _1463424))], (36149 ^ _777959) ^ [] : [_1463424 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Divides_Odivmod__nat(_1463426, _1463424) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1463426))], (14251 ^ _777959) ^ [_1043372, _1043374, _1043376, _1043378] : [class_Rings_Ocomm__semiring__1(_1043372), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043372), _1043374), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043372), _1043376), _1043378)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043372), _1043376), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1043372), _1043374), _1043378)))], (358 ^ _777959) ^ [_783550, _783552, _783554, _783556, _783558, _783560, _783562, _783564] : [-(c_Finite__Set_Ofolding__idem(_783562, _783558, _783554, _783550)), c_Finite__Set_Ofolding__idem(_783564, _783560, _783556, _783552), _783564 = _783562, _783560 = _783558, _783556 = _783554, _783552 = _783550], (14942 ^ _777959) ^ [_1061731, _1061733, _1061735] : [class_Groups_Olinordered__ab__semigroup__add(_1061731), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061731), _1061733)), -(_1061733 = c_Orderings_Obot__class_Obot(tc_fun(_1061731, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1061731), _1061735), c_Big__Operators_Olinorder__class_OMax(_1061731, _1061733)) = c_Big__Operators_Olinorder__class_OMax(_1061731, hAPP(c_Set_OCollect(_1061731), hAPP(hAPP(c_COMBB(tc_fun(_1061731, tc_HOL_Obool), tc_HOL_Obool, _1061731), c_HOL_OEx(_1061731)), hAPP(hAPP(c_COMBC(_1061731, tc_fun(_1061731, tc_HOL_Obool), tc_fun(_1061731, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061731, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1061731, tc_HOL_Obool), tc_fun(_1061731, tc_HOL_Obool)), _1061731), c_COMBS(_1061731, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061731, tc_HOL_Obool), tc_fun(_1061731, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1061731), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1061731), c_fconj)), hAPP(hAPP(c_COMBC(_1061731, tc_fun(_1061731, _1061731), tc_fun(_1061731, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1061731, tc_HOL_Obool), tc_fun(tc_fun(_1061731, _1061731), tc_fun(_1061731, tc_HOL_Obool)), _1061731), c_COMBB(_1061731, tc_HOL_Obool, _1061731)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1061731), _1061735))))), hAPP(hAPP(c_COMBC(_1061731, tc_fun(_1061731, tc_HOL_Obool), tc_HOL_Obool), c_member(_1061731)), _1061733))))))], (2642 ^ _777959) ^ [_817191, _817193, _817195, _817197, _817199, _817201, _817203, _817205, _817207, _817209] : [-(c_Product__Type_Oprod_Oprod__rec(_817209, _817205, _817201, _817197, _817193) = c_Product__Type_Oprod_Oprod__rec(_817207, _817203, _817199, _817195, _817191)), _817209 = _817207, _817205 = _817203, _817201 = _817199, _817197 = _817195, _817193 = _817191], (5038 ^ _777959) ^ [_854875, _854877, _854879, _854881, _854883, _854885, _854887, _854889] : [-(c_Lazy__Sequence_Ohb__bind(_854889, _854885, _854881, _854877) = c_Lazy__Sequence_Ohb__bind(_854887, _854883, _854879, _854875)), _854889 = _854887, _854885 = _854883, _854881 = _854879, _854877 = _854875], (48164 ^ _777959) ^ [_1747541, _1747543, _1747545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1747541), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1747543), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1747543)), _1747545)))), -(hBOOL(hAPP(hAPP(c_member(_1747543), hAPP(c_Random_Opick(_1747543, _1747545), _1747541)), hAPP(c_List_Oset(_1747543), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1747543), _1747543), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1747543)), _1747545)))))], (50360 ^ _777959) ^ [_1799134, _1799136, _1799138] : [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), _1799134), _1799136))), -(hBOOL(hAPP(hAPP(_1799138, _1799134), _1799136))), 50367 ^ _777959 : [(50370 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 50365 ^ [_1799134, _1799136, _1799138]), 50366 ^ [_1799134, _1799136, _1799138]))), -(hBOOL(hAPP(hAPP(_1799138, 50365 ^ [_1799134, _1799136, _1799138]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 50366 ^ [_1799134, _1799136, _1799138]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (50376 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(_1799138, 50365 ^ [_1799134, _1799136, _1799138]), 50366 ^ [_1799134, _1799136, _1799138]))], (50368 ^ _777959) ^ [] : [-(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), 50365 ^ [_1799134, _1799136, _1799138]), 50366 ^ [_1799134, _1799136, _1799138]))))]]], (35349 ^ _777959) ^ [_1443686, _1443688, _1443690, _1443692, _1443694, _1443696] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1443686, tc_fun(_1443688, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1443686, tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_fun(_1443688, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1443688, tc_fun(tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_fun(_1443688, tc_HOL_Obool)), _1443686), c_COMBC(_1443688, tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1443688, tc_prod(_1443686, _1443688)), tc_fun(_1443688, tc_fun(tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_HOL_Obool)), _1443686), hAPP(c_COMBB(tc_prod(_1443686, _1443688), tc_fun(tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_HOL_Obool), _1443688), c_member(tc_prod(_1443686, _1443688)))), c_Product__Type_OPair(_1443686, _1443688)))), _1443690)), hAPP(hAPP(c_COMBC(_1443686, tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_fun(_1443688, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1443688, tc_fun(tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_fun(_1443688, tc_HOL_Obool)), _1443686), c_COMBC(_1443688, tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1443688, tc_prod(_1443686, _1443688)), tc_fun(_1443688, tc_fun(tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_HOL_Obool)), _1443686), hAPP(c_COMBB(tc_prod(_1443686, _1443688), tc_fun(tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool), tc_HOL_Obool), _1443688), c_member(tc_prod(_1443686, _1443688)))), c_Product__Type_OPair(_1443686, _1443688)))), _1443692)), _1443694), _1443696)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1443686, _1443688)), hAPP(hAPP(c_Product__Type_OPair(_1443686, _1443688), _1443694), _1443696)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1443686, _1443688), tc_HOL_Obool)), _1443690), _1443692))))], (38878 ^ _777959) ^ [_1524822, _1524824, _1524826, _1524828, _1524830] : [c_Fun_Oinj__on(_1524822, _1524824, _1524826, c_Orderings_Otop__class_Otop(tc_fun(_1524822, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524824, tc_HOL_Obool)), _1524828), hAPP(c_Set_Oimage(_1524822, _1524824, _1524826), _1524830))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1524822, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1524822, _1524824, _1524826), _1524828)), _1524830)))], (33267 ^ _777959) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41364 ^ _777959) ^ [_1588249, _1588251, _1588253, _1588255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1588249), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588251)), _1588253))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1588249), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1588251)), _1588255))), 41374 ^ _777959 : [(41377 ^ _777959) ^ [] : [hAPP(hAPP(c_List_Onth(_1588251), _1588253), 41373 ^ [_1588249, _1588251, _1588253, _1588255]) = hAPP(hAPP(c_List_Onth(_1588251), _1588255), 41373 ^ [_1588249, _1588251, _1588253, _1588255])], (41375 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 41373 ^ [_1588249, _1588251, _1588253, _1588255]), _1588249)))]], -(hAPP(hAPP(c_List_Otake(_1588251), _1588249), _1588253) = hAPP(hAPP(c_List_Otake(_1588251), _1588249), _1588255))], (45838 ^ _777959) ^ [_1692838, _1692840, _1692842] : [class_Enum_Oenum(_1692838), class_Enum_Oenum(_1692840), 45845 ^ _777959 : [(45852 ^ _777959) ^ [] : [c_Enum_Oex__n__lists(_1692838, hAPP(hAPP(c_COMBB(tc_fun(_1692840, _1692838), tc_HOL_Obool, tc_List_Olist(_1692838)), _1692842), hAPP(hAPP(c_COMBB(tc_fun(_1692840, tc_Option_Ooption(_1692838)), tc_fun(_1692840, _1692838), tc_List_Olist(_1692838)), c_Fun_Ocomp(tc_Option_Ooption(_1692838), _1692838, _1692840, c_Option_Othe(_1692838))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1692840, _1692838)), tc_fun(_1692840, tc_Option_Ooption(_1692838)), tc_List_Olist(_1692838)), c_Map_Omap__of(_1692840, _1692838)), hAPP(c_List_Ozip(_1692840, _1692838), c_Enum_Oenum__class_Oenum(_1692840))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692840)), c_Enum_Oenum__class_Oenum(_1692840))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1692840, _1692838)), _1692842)))], (45846 ^ _777959) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(_1692840, _1692838)), _1692842)), -(c_Enum_Oex__n__lists(_1692838, hAPP(hAPP(c_COMBB(tc_fun(_1692840, _1692838), tc_HOL_Obool, tc_List_Olist(_1692838)), _1692842), hAPP(hAPP(c_COMBB(tc_fun(_1692840, tc_Option_Ooption(_1692838)), tc_fun(_1692840, _1692838), tc_List_Olist(_1692838)), c_Fun_Ocomp(tc_Option_Ooption(_1692838), _1692838, _1692840, c_Option_Othe(_1692838))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_prod(_1692840, _1692838)), tc_fun(_1692840, tc_Option_Ooption(_1692838)), tc_List_Olist(_1692838)), c_Map_Omap__of(_1692840, _1692838)), hAPP(c_List_Ozip(_1692840, _1692838), c_Enum_Oenum__class_Oenum(_1692840))))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1692840)), c_Enum_Oenum__class_Oenum(_1692840))))]]], (34383 ^ _777959) ^ [_1425156, _1425158] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1425156)), _1425158) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1425156), _1425158))), _1425158))], (33265 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23431 ^ _777959) ^ [_1224117, _1224119, _1224121] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224117), _1224119)), _1224121) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1224119), _1224121)))], (42776 ^ _777959) ^ [_1625409, _1625411, _1625413, _1625415, _1625417, _1625419] : [hAPP(hAPP(c_List_Oappend(_1625409), _1625411), _1625413) = _1625415, _1625417 = hAPP(hAPP(c_List_Oappend(_1625409), _1625413), _1625419), -(hAPP(hAPP(c_List_Oappend(_1625409), _1625411), _1625417) = hAPP(hAPP(c_List_Oappend(_1625409), _1625415), _1625419))], (27790 ^ _777959) ^ [_1302960, _1302962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1302960), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1302960), _1302962)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1302960))), hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1302962))))], (36467 ^ _777959) ^ [_1469264, _1469266] : [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), _1469264), _1469266))), 36470 ^ _777959 : [(36477 ^ _777959) ^ [] : [-(_1469266 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1469264, _1469266) = c_Nitpick_Onat__gcd(_1469266, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1469264, _1469266)))], (36471 ^ _777959) ^ [] : [_1469266 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1469264, _1469266) = _1469264)]]], (45212 ^ _777959) ^ [_1679137, _1679139, _1679141, _1679143, _1679145] : [hBOOL(hAPP(hAPP(c_member(_1679137), _1679139), hAPP(c_List_Oset(_1679137), _1679141))), -(hBOOL(hAPP(_1679143, _1679139))), -(c_List_OtakeWhile(_1679137, _1679143, hAPP(hAPP(c_List_Oappend(_1679137), _1679141), _1679145)) = c_List_OtakeWhile(_1679137, _1679143, _1679141))], (14153 ^ _777959) ^ [_1041243, _1041245, _1041247] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1041243), _1041245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1041243, tc_HOL_Obool)), _1041247), _1041245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1041243), _1041247)), hAPP(c_Finite__Set_Ocard(_1041243), _1041245))))], (1560 ^ _777959) ^ [_800183, _800185] : [-(class_Groups_Ocomm__monoid__mult(_800183)), _800185 = _800183, class_Groups_Ocomm__monoid__mult(_800185)], (17107 ^ _777959) ^ [_1105158] : [class_Orderings_Olinorder(_1105158), -(c_Finite__Set_Ofun__left__comm__idem(_1105158, _1105158, c_Orderings_Oord__class_Omax(_1105158)))], (17337 ^ _777959) ^ [_1109495, _1109497, _1109499, _1109501] : [class_Orderings_Olinorder(_1109495), hBOOL(hAPP(c_Finite__Set_Ofinite(_1109495), _1109497)), hBOOL(hAPP(hAPP(c_member(_1109495), _1109499), _1109497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1109495), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1109495), _1109499), _1109501)), hAPP(hAPP(c_Finite__Set_Ofold(_1109495, _1109495, c_Orderings_Oord__class_Omax(_1109495)), _1109501), _1109497))))], (31863 ^ _777959) ^ [_1379745, _1379747] : [class_Int_Onumber__ring(_1379745), -(hAPP(c_Int_Oring__1__class_Oof__int(_1379745), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1379747)) = hAPP(c_Int_Onumber__class_Onumber__of(_1379745), _1379747))], (17209 ^ _777959) ^ [_1106982, _1106984, _1106986] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_1106982, tc_HOL_Obool), tc_HOL_Obool)), _1106984), _1106986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1106982, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1106982, tc_HOL_Obool), _1106986)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1106982, tc_HOL_Obool), _1106984))))], (17815 ^ _777959) ^ [_1118577, _1118579] : [class_Orderings_Olinorder(_1118577), hBOOL(hAPP(c_Finite__Set_Ofinite(_1118577), _1118579)), -(_1118579 = c_Orderings_Obot__class_Obot(tc_fun(_1118577, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1118577), c_Big__Operators_Olattice_OInf__fin(_1118577, c_Orderings_Oord__class_Omin(_1118577), _1118579)), c_Big__Operators_Olattice_OSup__fin(_1118577, c_Orderings_Oord__class_Omax(_1118577), _1118579))))], (20828 ^ _777959) ^ [_1174470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174470), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1174470 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (15490 ^ _777959) ^ [_1072391, _1072393] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1072391)), hAPP(c_Nat_OSuc, _1072393)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1072391), _1072393))], (15654 ^ _777959) ^ [_1075934, _1075936, _1075938] : [class_Rings_Ocomm__semiring__1(_1075934), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075934), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075934), _1075936), _1075938)), _1075938) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075934), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1075934), _1075936), c_Groups_Oone__class_Oone(_1075934))), _1075938))], (51426 ^ _777959) ^ [_1814626, _1814628] : [hBOOL(_1814626), -(hBOOL(hAPP(hAPP(c_fdisj, _1814628), _1814626)))], (43837 ^ _777959) ^ [_1649630, _1649632, _1649634] : [-(_1649630 = c_List_Olist_ONil(_1649632)), -(c_List_Olast(_1649632, hAPP(hAPP(c_List_Oappend(_1649632), _1649634), _1649630)) = c_List_Olast(_1649632, _1649630))], (49046 ^ _777959) ^ [_1768864, _1768866, _1768868, _1768870] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1768864, _1768864)), hAPP(hAPP(c_Product__Type_OPair(_1768864, _1768864), _1768866), _1768868)), c_Transitive__Closure_Otrancl(_1768864, hAPP(c_Relation_Oconverse(_1768864, _1768864), _1768870)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1768864, _1768864)), hAPP(hAPP(c_Product__Type_OPair(_1768864, _1768864), _1768866), _1768868)), hAPP(c_Relation_Oconverse(_1768864, _1768864), c_Transitive__Closure_Otrancl(_1768864, _1768870)))))], (20213 ^ _777959) ^ [_1163656, _1163658, _1163660, _1163662] : [class_Rings_Olinordered__semidom(_1163656), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163656), c_Groups_Ozero__class_Ozero(_1163656)), _1163658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163656), _1163660), _1163662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163656), _1163660), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163656), _1163658), _1163662))))], (914 ^ _777959) ^ [_791906, _791908, _791910, _791912, _791914, _791916] : [-(c_List_Olist__ex1(_791914, _791910, _791906)), c_List_Olist__ex1(_791916, _791912, _791908), _791916 = _791914, _791912 = _791910, _791908 = _791906], (48463 ^ _777959) ^ [_1753169, _1753171, _1753173, _1753175, _1753177] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1753169, _1753169)), hAPP(hAPP(c_Product__Type_OPair(_1753169, _1753169), _1753171), _1753173)), _1753175)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1753169, _1753169)), hAPP(hAPP(c_Product__Type_OPair(_1753169, _1753169), _1753173), _1753177)), c_Transitive__Closure_Otrancl(_1753169, _1753175))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1753169, _1753169)), hAPP(hAPP(c_Product__Type_OPair(_1753169, _1753169), _1753171), _1753177)), c_Transitive__Closure_Otrancl(_1753169, _1753175))))], (44140 ^ _777959) ^ [_1656287, _1656289, _1656291, _1656293, _1656295] : [class_Orderings_Olinorder(_1656287), c_List_Olinorder__class_Osorted(_1656287, hAPP(hAPP(c_List_Omap(_1656289, _1656287), _1656291), _1656293)), -(c_List_Olinorder__class_Osorted(_1656287, hAPP(hAPP(c_List_Omap(_1656289, _1656287), _1656291), hAPP(c_List_Ofilter(_1656289, _1656295), _1656293))))], (5400 ^ _777959) ^ [_860546, _860548, _860550, _860552] : [-(c_List_Oupt(_860552, _860548) = c_List_Oupt(_860550, _860546)), _860552 = _860550, _860548 = _860546], (40016 ^ _777959) ^ [_1552788, _1552790, _1552792, _1552794, _1552796] : [c_Fun_Oinj__on(_1552788, _1552790, _1552792, c_Orderings_Otop__class_Otop(tc_fun(_1552788, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1552788, _1552790), _1552792), hAPP(c_List_OremoveAll(_1552788, _1552794), _1552796)) = hAPP(c_List_OremoveAll(_1552790, hAPP(_1552792, _1552794)), hAPP(hAPP(c_List_Omap(_1552788, _1552790), _1552792), _1552796)))], (438 ^ _777959) ^ [_784794, _784796, _784798, _784800] : [-(c_Predicate_Oreflp(_784798, _784794)), c_Predicate_Oreflp(_784800, _784796), _784800 = _784798, _784796 = _784794], (27960 ^ _777959) ^ [_1305570, _1305572, _1305574] : [class_Rings_Olinordered__idom(_1305570), 27963 ^ _777959 : [(27970 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1305572), _1305574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305570), hAPP(c_Int_Oring__1__class_Oof__int(_1305570), _1305572)), hAPP(c_Int_Oring__1__class_Oof__int(_1305570), _1305574))))], (27964 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1305570), hAPP(c_Int_Oring__1__class_Oof__int(_1305570), _1305572)), hAPP(c_Int_Oring__1__class_Oof__int(_1305570), _1305574))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1305572), _1305574)))]]], (26172 ^ _777959) ^ [_1274182, _1274184, _1274186, _1274188] : [class_Fields_Olinordered__field__inverse__zero(_1274182), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274182), _1274184), _1274186)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274182), _1274188), c_Groups_Ozero__class_Ozero(_1274182))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1274182), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274182), _1274186), _1274188)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1274182), _1274184), _1274188))))], (36305 ^ _777959) ^ [_1466250, _1466252] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1466250, _1466252), c_Divides_Odivmod__nat(_1466250, _1466252))))], (42170 ^ _777959) ^ [_1608979, _1608981, _1608983, _1608985, _1608987, _1608989] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608979, _1608981)), hAPP(hAPP(c_Product__Type_OPair(_1608979, _1608981), _1608983), _1608985)), hAPP(hAPP(c_Product__Type_OSigma(_1608979, _1608981), _1608987), _1608989))), 42173 ^ _777959 : [(42176 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1608981), _1608985), hAPP(_1608989, _1608983))))], (42174 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1608979), _1608983), _1608987)))]]], (20197 ^ _777959) ^ [_1163373, _1163375] : [class_Groups_Olinordered__ab__group__add(_1163373), 20200 ^ _777959 : [(20207 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163373), c_Groups_Ozero__class_Ozero(_1163373)), _1163375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163373), c_Groups_Ozero__class_Ozero(_1163373)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163373), _1163375), _1163375))))], (20201 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163373), c_Groups_Ozero__class_Ozero(_1163373)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1163373), _1163375), _1163375))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1163373), c_Groups_Ozero__class_Ozero(_1163373)), _1163375)))]]], (43288 ^ _777959) ^ [_1637709, _1637711, _1637713, _1637715] : [-(hAPP(hAPP(c_List_Odrop(_1637709), hAPP(c_Nat_OSuc, _1637711)), hAPP(hAPP(c_List_Olist_OCons(_1637709), _1637713), _1637715)) = hAPP(hAPP(c_List_Odrop(_1637709), _1637711), _1637715))], (45706 ^ _777959) ^ [_1689966, _1689968] : [class_Orderings_Olinorder(_1689966), -(c_List_Olinorder__class_Osorted(_1689966, c_List_Olinorder__class_Osort__key(_1689966, _1689966, c_COMBI(_1689966), _1689968)))], (50023 ^ _777959) ^ [_1792347] : [class_Nat_Osize(_1792347), -(c_FunDef_Ois__measure(_1792347, c_Nat_Osize__class_Osize(_1792347)))], (44316 ^ _777959) ^ [_1659253, _1659255, _1659257] : [class_Orderings_Olinorder(_1659253), c_List_Olinorder__class_Osorted(_1659253, _1659255), -(c_List_Olinorder__class_Osorted(_1659253, c_List_Oremove1(_1659253, _1659257, _1659255)))], (36678 ^ _777959) ^ [_1473746, _1473748, _1473750] : [-(_1473746 = hAPP(hAPP(c_Product__Type_OPair(_1473748, _1473750), hAPP(c_Product__Type_Ofst(_1473748, _1473750), _1473746)), hAPP(c_Product__Type_Osnd(_1473748, _1473750), _1473746)))], (19204 ^ _777959) ^ [_1146850, _1146852] : [class_Groups_Ocomm__monoid__add(_1146850), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146850), _1146852), c_Groups_Ozero__class_Ozero(_1146850)) = _1146852)], (27814 ^ _777959) ^ [_1303454, _1303456] : [-(c_Int_Onat__aux(_1303454, _1303456) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1303454)), _1303456))], (13777 ^ _777959) ^ [_1032768, _1032770] : [class_Lattices_Obounded__lattice__top(_1032768), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1032768), c_Orderings_Otop__class_Otop(_1032768)), _1032770) = c_Orderings_Otop__class_Otop(_1032768))], (12497 ^ _777959) ^ [_1005126, _1005128, _1005130, _1005132] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1005126), _1005128)), 12503 ^ _777959 : [(12506 ^ _777959) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1005130), hAPP(_1005132, 12502 ^ [_1005126, _1005128, _1005130, _1005132])))], (12504 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1005126), 12502 ^ [_1005126, _1005128, _1005130, _1005132]), _1005128)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1005130), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1005126, tc_fun(_1005130, tc_HOL_Obool)), _1005128), _1005132))))], (23347 ^ _777959) ^ [_1222731] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1222731)), _1222731) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11794 ^ _777959) ^ [_991548, _991550, _991552, _991554, _991556] : [hBOOL(hAPP(hAPP(c_member(_991548), _991550), _991552)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991554, tc_HOL_Obool)), hAPP(_991556, _991550)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_991548, tc_fun(_991554, tc_HOL_Obool)), _991552), _991556))))], (33717 ^ _777959) ^ [_1412738, _1412740] : [class_Int_Onumber__ring(_1412738), class_Rings_Olinordered__idom(_1412738), 33724 ^ _777959 : [(33731 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1412740)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412738), c_Groups_Oone__class_Oone(_1412738)), hAPP(c_Int_Onumber__class_Onumber__of(_1412738), _1412740))))], (33725 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1412738), c_Groups_Oone__class_Oone(_1412738)), hAPP(c_Int_Onumber__class_Onumber__of(_1412738), _1412740))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1412740)))]]], (51264 ^ _777959) ^ [] : [-(class_HOL_Oequal(tc_Code__Evaluation_Oterm))], (50886 ^ _777959) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (38500 ^ _777959) ^ [_1516580] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1516580))], (6525 ^ _777959) ^ [_883359, _883361, _883363, _883365] : [class_Orderings_Oorder(_883359), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883359), _883361), _883363)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883359), _883365), _883361)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_883359), _883365), _883363)))], (524 ^ _777959) ^ [_786087, _786089] : [-(c_List_Onat__list(_786087)), _786089 = _786087, c_List_Onat__list(_786089)], (14622 ^ _777959) ^ [_1052676, _1052678, _1052680, _1052682, _1052684, _1052686] : [-(hBOOL(hAPP(hAPP(c_member(_1052676), _1052678), _1052680))), -(hAPP(c_Fun_Ooverride__on(_1052676, _1052682, _1052684, _1052686, _1052680), _1052678) = hAPP(_1052684, _1052678))], (17065 ^ _777959) ^ [_1104449] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1104449) = c_Orderings_Oord__class_Omax(_1104449)), class_Lattices_Osemilattice__sup(_1104449), class_Orderings_Olinorder(_1104449)], (8682 ^ _777959) ^ [_927822, _927824, _927826] : [class_Orderings_Opreorder(_927822), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927822), _927824), _927826)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_927822), _927826), _927824))], (48340 ^ _777959) ^ [_1750738, _1750740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1750738)), hAPP(c_Code__Numeral_Onat__of, _1750740))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1750738), _1750740)))], (2168 ^ _777959) ^ [_809832, _809834, _809836, _809838, _809840, _809842] : [-(c_Finite__Set_Ofold1Set(_809842, _809838, _809834) = c_Finite__Set_Ofold1Set(_809840, _809836, _809832)), _809842 = _809840, _809838 = _809836, _809834 = _809832], (7190 ^ _777959) ^ [_898369, _898371, _898373, _898375] : [hBOOL(hAPP(_898369, _898371)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898373, tc_HOL_Obool)), _898369), _898375)), -(hBOOL(hAPP(_898375, _898371)))], (1180 ^ _777959) ^ [_795433, _795435] : [-(class_Int_Oring__char__0(_795433)), _795435 = _795433, class_Int_Oring__char__0(_795435)], (3376 ^ _777959) ^ [_828846, _828848] : [_828848 = _828846, -(c_Power_Opower__class_Opower(_828848) = c_Power_Opower__class_Opower(_828846))], (7506 ^ _777959) ^ [_904039, _904041, _904043, _904045, _904047, _904049] : [-(c_Hoare__Mirabelle_Otriple_Otriple__case(_904039, _904041, _904043, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_904039), _904045), _904047), _904049)) = hAPP(hAPP(hAPP(_904043, _904045), _904047), _904049))], (27762 ^ _777959) ^ [_1302507] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1302507)), -(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, _1302507))))], (43053 ^ _777959) ^ [_1631647, _1631649, _1631651] : [-(hBOOL(hAPP(c_List_Odistinct(_1631647), hAPP(hAPP(c_List_Oappend(_1631647), _1631649), _1631651)))), hBOOL(hAPP(c_List_Odistinct(_1631647), _1631649)), hBOOL(hAPP(c_List_Odistinct(_1631647), _1631651)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1631647, tc_HOL_Obool)), hAPP(c_List_Oset(_1631647), _1631649)), hAPP(c_List_Oset(_1631647), _1631651)) = c_Orderings_Obot__class_Obot(tc_fun(_1631647, tc_HOL_Obool))], (51110 ^ _777959) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (50810 ^ _777959) ^ [_1808109, _1808111] : [class_Orderings_Oorder(_1808109), -(class_Orderings_Oorder(tc_fun(_1808111, _1808109)))], (11928 ^ _777959) ^ [_994514, _994516] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994514), _994516)), _994514) = _994516)], (32903 ^ _777959) ^ [_1399476] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1399476))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1399476)))))], (25246 ^ _777959) ^ [_1256298, _1256300, _1256302] : [hBOOL(hAPP(_1256298, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1256300), _1256302))), 25249 ^ _777959 : [(25274 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1256302), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 25277 ^ _777959 : [(25278 ^ _777959) ^ [_1256962] : [-(hBOOL(hAPP(_1256298, _1256962))), 25279 ^ _777959 : [(25280 ^ _777959) ^ [_1257036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1256302), _1257036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1257036), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1256300 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1256302), _1256962)), _1257036)]]]]], (25256 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256302)), 25259 ^ _777959 : [(25260 ^ _777959) ^ [_1256632] : [-(hBOOL(hAPP(_1256298, _1256632))), 25261 ^ _777959 : [(25262 ^ _777959) ^ [_1256703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256703)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1256703), _1256302)), _1256300 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1256302), _1256632)), _1256703)]]]]], (25250 ^ _777959) ^ [] : [_1256302 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1256298, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (6783 ^ _777959) ^ [_888247, _888249, _888251] : [hBOOL(hAPP(hAPP(c_member(_888247), _888249), _888251)), -(hAPP(hAPP(c_Set_Oinsert(_888247), _888249), _888251) = _888251)], (31570 ^ _777959) ^ [_1374088, _1374090, _1374092] : [hBOOL(hAPP(c_Com_OWT, c_Com_Ocom_OCond(_1374088, _1374090, _1374092))), 31573 ^ _777959 : [(31576 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1374092)))], (31574 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Com_OWT, _1374090)))]]], (5430 ^ _777959) ^ [_861001, _861003] : [_861003 = _861001, -(c_Groups_Ozero__class_Ozero(_861003) = c_Groups_Ozero__class_Ozero(_861001))], (9926 ^ _777959) ^ [_950421, _950423, _950425, _950427, _950429] : [class_Lattices_Osemilattice__inf(_950421), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950421), _950423), _950425)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950421), _950427), _950429)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_950421), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950421), _950423), _950427)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_950421), _950425), _950429))))], (28932 ^ _777959) ^ [_1323319, _1323321] : [class_Groups_Oordered__ab__group__add(_1323319), -(hAPP(c_Set_Oimage(_1323319, _1323319, c_Groups_Ouminus__class_Ouminus(_1323319)), hAPP(c_SetInterval_Oord__class_OatLeast(_1323319), _1323321)) = hAPP(c_SetInterval_Oord__class_OatMost(_1323319), hAPP(c_Groups_Ouminus__class_Ouminus(_1323319), _1323321)))], (50940 ^ _777959) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (38967 ^ _777959) ^ [_1527823, _1527825, _1527827, _1527829, _1527831] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1527823), tc_List_Olist(_1527825), tc_List_Olist(_1527827), hAPP(c_List_Omap(_1527823, _1527825), _1527829)), hAPP(c_List_Omap(_1527827, _1527823), _1527831)) = hAPP(c_List_Omap(_1527827, _1527825), hAPP(c_Fun_Ocomp(_1527823, _1527825, _1527827, _1527829), _1527831)))], (10124 ^ _777959) ^ [_954707, _954709, _954711, _954713] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954707, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954707, tc_HOL_Obool)), _954709), _954711)), _954713) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_954707, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954707, tc_HOL_Obool)), _954709), _954713)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_954707, tc_HOL_Obool)), _954711), _954713)))], (44783 ^ _777959) ^ [_1668713, _1668715, _1668717] : [hAPP(hAPP(c_List_Olist_OCons(_1668713), _1668715), c_List_Olist_ONil(_1668713)) = hAPP(c_List_Orev(_1668713), _1668717), -(_1668717 = hAPP(hAPP(c_List_Olist_OCons(_1668713), _1668715), c_List_Olist_ONil(_1668713)))], (5644 ^ _777959) ^ [_867002, _867004] : [hAPP(_867002, 5645 ^ [_867002, _867004]) = hAPP(_867004, 5645 ^ [_867002, _867004]), -(_867002 = _867004)], (15825 ^ _777959) ^ [_1078842] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1078842) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1078842)))], (35900 ^ _777959) ^ [_1459202, _1459204] : [35901 ^ _777959 : [(35904 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1459204), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (35902 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1459202), _1459204)))]], -(c_Divides_OnegDivAlg(_1459202, _1459204) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1459202), _1459204)))], (9878 ^ _777959) ^ [_949601, _949603, _949605] : [class_Lattices_Osemilattice__inf(_949601), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_949601), _949603), _949605)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_949601), _949603), _949605) = _949603)], (44809 ^ _777959) ^ [_1669301, _1669303, _1669305, _1669307] : [-(hAPP(c_List_Orev(_1669301), hAPP(hAPP(c_List_Omap(_1669303, _1669301), _1669305), _1669307)) = hAPP(hAPP(c_List_Omap(_1669303, _1669301), _1669305), hAPP(c_List_Orev(_1669303), _1669307)))], (33795 ^ _777959) ^ [_1414097, _1414099] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1414097, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1414099)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1414097, 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)))), _1414099)))], (48579 ^ _777959) ^ [_1756801, _1756803, _1756805, _1756807, _1756809] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1756801, _1756801)), hAPP(hAPP(c_Product__Type_OPair(_1756801, _1756801), _1756803), _1756805)), _1756807)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1756801, _1756801)), hAPP(hAPP(c_Product__Type_OPair(_1756801, _1756801), _1756805), _1756809)), c_Transitive__Closure_Ortrancl(_1756801, _1756807))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1756801, _1756801)), hAPP(hAPP(c_Product__Type_OPair(_1756801, _1756801), _1756803), _1756809)), c_Transitive__Closure_Otrancl(_1756801, _1756807))))], (4412 ^ _777959) ^ [_844746, _844748] : [_844748 = _844746, -(c_Nitpick_Odenom(_844748) = c_Nitpick_Odenom(_844746))], (40930 ^ _777959) ^ [_1575027, _1575029, _1575031] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575027, _1575027), tc_HOL_Obool)), _1575029), _1575031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1575027), tc_List_Olist(_1575027)), tc_HOL_Obool)), c_List_Olistrel(_1575027, _1575029)), c_List_Olistrel(_1575027, _1575031))))], (34869 ^ _777959) ^ [_1434202, _1434204] : [class_Rings_Osemiring__1(_1434202), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1434204)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1434202), 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)))), _1434204))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1434202), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1434202), hAPP(c_Int_Onat, _1434204))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1434202), hAPP(c_Int_Onat, _1434204))))], (14369 ^ _777959) ^ [_1046339, _1046341, _1046343, _1046345, _1046347, _1046349] : [class_Groups_Ocomm__monoid__add(_1046339), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046341), _1046343)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046341, _1046339), _1046345), _1046343) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046347, _1046339), hAPP(hAPP(c_COMBB(tc_fun(_1046341, tc_HOL_Obool), _1046339, _1046347), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1046341, _1046339), _1046345)), hAPP(hAPP(c_COMBB(tc_fun(_1046341, tc_HOL_Obool), tc_fun(_1046341, tc_HOL_Obool), _1046347), c_Set_OCollect(_1046341)), hAPP(hAPP(c_COMBB(tc_fun(_1046341, tc_HOL_Obool), tc_fun(_1046341, tc_HOL_Obool), _1046347), hAPP(c_COMBS(_1046341, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1046341), c_fconj), hAPP(hAPP(c_COMBC(_1046341, tc_fun(_1046341, tc_HOL_Obool), tc_HOL_Obool), c_member(_1046341)), _1046343)))), hAPP(c_COMBC(_1046341, _1046347, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1046347, tc_fun(_1046347, tc_HOL_Obool), _1046341), c_fequal), _1046349)))))), hAPP(c_Set_Oimage(_1046341, _1046347, _1046349), _1046343)))], (44346 ^ _777959) ^ [_1659702, _1659704, _1659706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1659702), _1659704)), _1659706)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1659704), c_List_Oupt(_1659702, _1659706)) = c_List_Oupt(_1659702, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1659702), _1659704)))], (42945 ^ _777959) ^ [_1629064, _1629066, _1629068] : [-(hAPP(hAPP(c_List_Oappend(_1629064), _1629066), _1629068) = c_List_Olist_ONil(_1629064)), _1629066 = c_List_Olist_ONil(_1629064), _1629068 = c_List_Olist_ONil(_1629064)], (2574 ^ _777959) ^ [_816121, _816123, _816125, _816127] : [-(c_Divides_OnegDivAlg(_816127, _816123) = c_Divides_OnegDivAlg(_816125, _816121)), _816127 = _816125, _816123 = _816121], (40146 ^ _777959) ^ [_1556293, _1556295, _1556297, _1556299] : [class_Orderings_Olinorder(_1556293), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1556293, _1556293, c_COMBI(_1556293)), _1556295), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1556293, _1556293, c_COMBI(_1556293)), _1556297), _1556299)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1556293, _1556293, c_COMBI(_1556293)), _1556297), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1556293, _1556293, c_COMBI(_1556293)), _1556295), _1556299)))], (30846 ^ _777959) ^ [_1360799, _1360801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1360799)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1360799), _1360801)), _1360799) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (49774 ^ _777959) ^ [_1787522, _1787524, _1787526, _1787528] : [c_List_Olist__all(_1787522, _1787524, hAPP(hAPP(c_List_Olist_OCons(_1787522), _1787526), _1787528)), 49777 ^ _777959 : [(49780 ^ _777959) ^ [] : [-(c_List_Olist__all(_1787522, _1787524, _1787528))], (49778 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1787524, _1787526)))]]], (5498 ^ _777959) ^ [_861979, _861981, _861983, _861985] : [-(tc_prod(_861985, _861981) = tc_prod(_861983, _861979)), _861985 = _861983, _861981 = _861979], (50782 ^ _777959) ^ [_1807743, _1807745] : [class_Lattices_Oboolean__algebra(_1807743), -(class_Lattices_Oboolean__algebra(tc_fun(_1807745, _1807743)))], (38156 ^ _777959) ^ [_1508915, _1508917, _1508919, _1508921, _1508923] : [c_Fun_Oinj__on(_1508915, _1508917, _1508919, c_Orderings_Otop__class_Otop(tc_fun(_1508915, tc_HOL_Obool))), 38159 ^ _777959 : [(38166 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1508915), _1508921), _1508923)), -(hBOOL(hAPP(hAPP(c_member(_1508917), hAPP(_1508919, _1508921)), hAPP(c_Set_Oimage(_1508915, _1508917, _1508919), _1508923))))], (38160 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1508917), hAPP(_1508919, _1508921)), hAPP(c_Set_Oimage(_1508915, _1508917, _1508919), _1508923))), -(hBOOL(hAPP(hAPP(c_member(_1508915), _1508921), _1508923)))]]], (4104 ^ _777959) ^ [_840098, _840100, _840102, _840104] : [-(c_Relation_ORange(_840104, _840100) = c_Relation_ORange(_840102, _840098)), _840104 = _840102, _840100 = _840098], (33131 ^ _777959) ^ [_1403595] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1403595))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1403595)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (48631 ^ _777959) ^ [_1758143, _1758145, _1758147, _1758149, _1758151] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1758143, _1758143)), hAPP(hAPP(c_Product__Type_OPair(_1758143, _1758143), _1758145), _1758147)), c_Transitive__Closure_Ortrancl(_1758143, _1758149))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1758143, _1758143)), hAPP(hAPP(c_Product__Type_OPair(_1758143, _1758143), _1758147), _1758151)), c_Transitive__Closure_Ortrancl(_1758143, _1758149))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1758143, _1758143)), hAPP(hAPP(c_Product__Type_OPair(_1758143, _1758143), _1758145), _1758151)), c_Transitive__Closure_Ortrancl(_1758143, _1758149))))], (51080 ^ _777959) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (12902 ^ _777959) ^ [_1012236, _1012238, _1012240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012236, tc_HOL_Obool)), _1012240), _1012238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1012236, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1012236, tc_HOL_Obool)), _1012238)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1012236, tc_HOL_Obool)), _1012240))))], (10426 ^ _777959) ^ [_962179, _962181, _962183, _962185, _962187] : [c_Finite__Set_Ofolding__one(_962179, _962181, _962183), hBOOL(hAPP(c_Finite__Set_Ofinite(_962179), _962185)), -(hBOOL(hAPP(hAPP(c_member(_962179), _962187), _962185))), -(hAPP(_962183, hAPP(hAPP(c_Set_Oinsert(_962179), _962187), _962185)) = hAPP(hAPP(c_Finite__Set_Ofold(_962179, _962179, _962181), _962187), _962185))], (1150 ^ _777959) ^ [_795058, _795060] : [-(class_Rings_Ocomm__ring__1(_795058)), _795060 = _795058, class_Rings_Ocomm__ring__1(_795060)], (14544 ^ _777959) ^ [_1051298, _1051300] : [class_Groups_Oone(_1051298), 14547 ^ _777959 : [(14554 ^ _777959) ^ [] : [_1051300 = c_Groups_Oone__class_Oone(_1051298), -(c_Groups_Oone__class_Oone(_1051298) = _1051300)], (14548 ^ _777959) ^ [] : [c_Groups_Oone__class_Oone(_1051298) = _1051300, -(_1051300 = c_Groups_Oone__class_Oone(_1051298))]]], (45314 ^ _777959) ^ [_1681103, _1681105] : [c_List_Oremdups(_1681103, _1681105) = _1681105, -(hBOOL(hAPP(c_List_Odistinct(_1681103), _1681105)))], (14281 ^ _777959) ^ [_1044165, _1044167, _1044169, _1044171] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1044165, tc_HOL_Obool)), c_Map_Odom(_1044165, _1044167, _1044169)), c_Map_Odom(_1044165, _1044167, _1044171)) = c_Orderings_Obot__class_Obot(tc_fun(_1044165, tc_HOL_Obool)), -(c_Map_Omap__add(_1044165, _1044167, _1044169, _1044171) = c_Map_Omap__add(_1044165, _1044167, _1044171, _1044169))], (37574 ^ _777959) ^ [_1495879, _1495881, _1495883, _1495885, _1495887] : [c_Equiv__Relations_Oequiv(_1495879, _1495881, _1495883), hBOOL(hAPP(hAPP(c_member(_1495879), _1495885), _1495881)), hBOOL(hAPP(hAPP(c_member(_1495879), _1495887), _1495881)), 37585 ^ _777959 : [(37592 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1495879, _1495879)), hAPP(hAPP(c_Product__Type_OPair(_1495879, _1495879), _1495885), _1495887)), _1495883)), -(hAPP(c_Relation_OImage(_1495879, _1495879, _1495883), hAPP(hAPP(c_Set_Oinsert(_1495879), _1495885), c_Orderings_Obot__class_Obot(tc_fun(_1495879, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1495879, _1495879, _1495883), hAPP(hAPP(c_Set_Oinsert(_1495879), _1495887), c_Orderings_Obot__class_Obot(tc_fun(_1495879, tc_HOL_Obool)))))], (37586 ^ _777959) ^ [] : [hAPP(c_Relation_OImage(_1495879, _1495879, _1495883), hAPP(hAPP(c_Set_Oinsert(_1495879), _1495885), c_Orderings_Obot__class_Obot(tc_fun(_1495879, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1495879, _1495879, _1495883), hAPP(hAPP(c_Set_Oinsert(_1495879), _1495887), c_Orderings_Obot__class_Obot(tc_fun(_1495879, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1495879, _1495879)), hAPP(hAPP(c_Product__Type_OPair(_1495879, _1495879), _1495885), _1495887)), _1495883)))]]], (20805 ^ _777959) ^ [_1174131, _1174133, _1174135, _1174137] : [class_Groups_Ocomm__monoid__add(_1174131), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1174133), _1174135))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1174133, _1174131), _1174137), _1174135) = c_Groups_Ozero__class_Ozero(_1174131))], (9624 ^ _777959) ^ [_944361, _944363, _944365, _944367] : [hBOOL(hAPP(hAPP(c_member(_944361), _944363), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_944361, tc_HOL_Obool)), _944365), _944367))), 9627 ^ _777959 : [(9630 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_944361), _944363), _944367)))], (9628 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_944361), _944363), _944365)))]]], (42214 ^ _777959) ^ [_1610081, _1610083, _1610085, _1610087, _1610089, _1610091] : [hBOOL(hAPP(hAPP(c_member(_1610081), _1610083), _1610085)), 42217 ^ _777959 : [(42224 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610087, tc_HOL_Obool)), _1610089), _1610091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1610087, _1610081), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1610087, _1610081), _1610089), hAPP(c_COMBK(tc_fun(_1610081, tc_HOL_Obool), _1610087), _1610085))), hAPP(hAPP(c_Product__Type_OSigma(_1610087, _1610081), _1610091), hAPP(c_COMBK(tc_fun(_1610081, tc_HOL_Obool), _1610087), _1610085)))))], (42218 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1610087, _1610081), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1610087, _1610081), _1610089), hAPP(c_COMBK(tc_fun(_1610081, tc_HOL_Obool), _1610087), _1610085))), hAPP(hAPP(c_Product__Type_OSigma(_1610087, _1610081), _1610091), hAPP(c_COMBK(tc_fun(_1610081, tc_HOL_Obool), _1610087), _1610085)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1610087, tc_HOL_Obool)), _1610089), _1610091)))]]], (28167 ^ _777959) ^ [_1309228, _1309230] : [class_Rings_Olinordered__idom(_1309228), 28170 ^ _777959 : [(28177 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309228), c_Groups_Ozero__class_Ozero(_1309228)), hAPP(c_Int_Oring__1__class_Oof__int(_1309228), _1309230))))], (28171 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309228), c_Groups_Ozero__class_Ozero(_1309228)), hAPP(c_Int_Oring__1__class_Oof__int(_1309228), _1309230))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1309230)))]]], (47419 ^ _777959) ^ [_1730959, _1730961, _1730963, _1730965] : [47420 ^ _777959 : [(47421 ^ _777959) ^ [_1731013] : [hBOOL(hAPP(hAPP(_1730963, _1730965), _1731013))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1730959, _1730961, _1730963), _1730965)))], (22521 ^ _777959) ^ [_1207210, _1207212, _1207214] : [class_Orderings_Olinorder(_1207210), 22524 ^ _777959 : [(22531 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207210), _1207212), _1207214)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1207210, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1207210), _1207212)), hAPP(c_SetInterval_Oord__class_OlessThan(_1207210), _1207214))))], (22525 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1207210, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_1207210), _1207212)), hAPP(c_SetInterval_Oord__class_OlessThan(_1207210), _1207214))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1207210), _1207212), _1207214)))]]], (42062 ^ _777959) ^ [_1606873, _1606875, _1606877] : [-(_1606873 = c_List_Olist_ONil(_1606875)), -(c_List_Obutlast(_1606875, hAPP(hAPP(c_List_Olist_OCons(_1606875), _1606877), _1606873)) = hAPP(hAPP(c_List_Olist_OCons(_1606875), _1606877), c_List_Obutlast(_1606875, _1606873)))], (6435 ^ _777959) ^ [_881880, _881882, _881884, _881886] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881880, tc_HOL_Obool)), _881882), _881884)), hBOOL(hAPP(hAPP(c_member(_881880), _881886), _881882)), -(hBOOL(hAPP(hAPP(c_member(_881880), _881886), _881884)))], (6923 ^ _777959) ^ [_891214, _891216, _891218, _891220, _891222] : [hBOOL(hAPP(hAPP(c_member(_891214), _891216), _891218)), -(hAPP(hAPP(c_Set_Oinsert(_891220), hAPP(_891222, _891216)), hAPP(c_Set_Oimage(_891214, _891220, _891222), _891218)) = hAPP(c_Set_Oimage(_891214, _891220, _891222), _891218))], (45584 ^ _777959) ^ [_1687485, _1687487] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1687485), tc_fun(_1687485, tc_HOL_Obool), c_List_Oset(_1687485)), hAPP(c_List_Oset(tc_List_Olist(_1687485)), c_Enum_Osublists(_1687485, _1687487))) = hAPP(c_Set_OPow(_1687485), hAPP(c_List_Oset(_1687485), _1687487)))], (25950 ^ _777959) ^ [_1269878, _1269880, _1269882, _1269884, _1269886] : [class_Orderings_Olinorder(_1269878), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1269878, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1269878, _1269880, _1269882)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1269878, _1269884, _1269886)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1269878, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1269878), _1269880), _1269884), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1269878), _1269882), _1269886)))], (51370 ^ _777959) ^ [_1813895, _1813897] : [hBOOL(hAPP(hAPP(c_fequal, _1813895), _1813897)), -(_1813895 = _1813897)], (27900 ^ _777959) ^ [_1304740, _1304742] : [c_Nat__Transfer_Onat__set(_1304740), c_Nat__Transfer_Onat__set(_1304742), 27907 ^ _777959 : [(27914 ^ _777959) ^ [] : [hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1304740) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1304742), -(_1304740 = _1304742)], (27908 ^ _777959) ^ [] : [_1304740 = _1304742, -(hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1304740) = hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1304742))]]], (47234 ^ _777959) ^ [_1725522, _1725524, _1725526] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1725522, _1725524)), _1725526)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1725524), hAPP(c_Relation_ORange(_1725522, _1725524), _1725526))))], (16251 ^ _777959) ^ [_1088458, _1088460, _1088462, _1088464, _1088466] : [c_Hoare__Mirabelle_Otriple__valid(_1088458, hAPP(c_Nat_OSuc, _1088460), hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1088458), _1088462), hAPP(c_Com_Ocom_OBODY, _1088464)), _1088466)), -(c_Hoare__Mirabelle_Otriple__valid(_1088458, _1088460, hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(_1088458), _1088462), hAPP(c_Option_Othe(tc_Com_Ocom), hAPP(c_Com_Obody, _1088464))), _1088466)))], (1590 ^ _777959) ^ [_800558, _800560] : [-(class_Rings_Ono__zero__divisors(_800558)), _800560 = _800558, class_Rings_Ono__zero__divisors(_800560)], (10250 ^ _777959) ^ [_957980, _957982, _957984] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957980, tc_HOL_Obool)), _957982), _957984) = c_Orderings_Obot__class_Obot(tc_fun(_957980, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_957980, tc_HOL_Obool)), _957982), _957984) = _957982)], (51336 ^ _777959) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (33965 ^ _777959) ^ [_1417851] : [class_Rings_Osemiring__1(_1417851), c_Int_Oiszero(_1417851, c_Groups_Oone__class_Oone(_1417851))], (28271 ^ _777959) ^ [_1310904, _1310906] : [class_Groups_Oordered__ab__group__add(_1310904), -(hAPP(c_Set_Oimage(_1310904, _1310904, c_Groups_Ouminus__class_Ouminus(_1310904)), hAPP(c_SetInterval_Oord__class_OlessThan(_1310904), _1310906)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1310904), hAPP(c_Groups_Ouminus__class_Ouminus(_1310904), _1310906)))], (1986 ^ _777959) ^ [_806785, _806787, _806789, _806791, _806793, _806795] : [-(c_SetInterval_Oord_OatLeast(_806795, _806791, _806787) = c_SetInterval_Oord_OatLeast(_806793, _806789, _806785)), _806795 = _806793, _806791 = _806789, _806787 = _806785], (50204 ^ _777959) ^ [_1795426, _1795428] : [hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint), c_Int_OBit1(_1795426)), c_Int_OBit0(_1795428)))], (17197 ^ _777959) ^ [_1106718, _1106720] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1106718, tc_HOL_Obool), _1106720) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_1106718, tc_HOL_Obool), tc_fun(_1106718, tc_HOL_Obool)), _1106720), c_COMBI(tc_fun(_1106718, tc_HOL_Obool))))], (27834 ^ _777959) ^ [] : [-(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))))], (27307 ^ _777959) ^ [_1294781, _1294783, _1294785] : [class_Orderings_Oorder(_1294781), 27310 ^ _777959 : [(27317 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294781), _1294783), _1294785))), -(c_Orderings_Obot__class_Obot(tc_fun(_1294781, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1294781, _1294783, _1294785))], (27311 ^ _777959) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1294781, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1294781, _1294783, _1294785), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1294781), _1294783), _1294785))]]], (13002 ^ _777959) ^ [_1014541, _1014543, _1014545] : [class_Groups_Oab__group__add(_1014541), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1014541), _1014543), _1014545) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1014541), _1014543), hAPP(c_Groups_Ouminus__class_Ouminus(_1014541), _1014545)))], (4266 ^ _777959) ^ [_842543, _842545, _842547, _842549] : [-(c_Complete__Lattice_OSup__class_OSup(_842549, _842545) = c_Complete__Lattice_OSup__class_OSup(_842547, _842543)), _842549 = _842547, _842545 = _842543], (2064 ^ _777959) ^ [_808050, _808052, _808054, _808056, _808058, _808060, _808062, _808064, _808066, _808068] : [-(c_SetInterval_Oord_OatLeastLessThan(_808068, _808064, _808060, _808056, _808052) = c_SetInterval_Oord_OatLeastLessThan(_808066, _808062, _808058, _808054, _808050)), _808068 = _808066, _808064 = _808062, _808060 = _808058, _808056 = _808054, _808052 = _808050], (42893 ^ _777959) ^ [_1628162, _1628164, _1628166] : [c_List_Olist_ONil(_1628162) = hAPP(hAPP(c_List_Oappend(_1628162), _1628164), _1628166), 42896 ^ _777959 : [(42899 ^ _777959) ^ [] : [-(_1628166 = c_List_Olist_ONil(_1628162))], (42897 ^ _777959) ^ [] : [-(_1628164 = c_List_Olist_ONil(_1628162))]]], (18321 ^ _777959) ^ [_1129372, _1129374, _1129376, _1129378, _1129380, _1129382, _1129384] : [c_Finite__Set_Ofun__left__comm(_1129372, _1129374, _1129376), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1129372, _1129374, _1129376, _1129378, _1129380), _1129382)), hBOOL(hAPP(hAPP(c_member(_1129372), _1129384), _1129380)), 18333 ^ _777959 : [(18336 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1129372, _1129374, _1129376, _1129378, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1129372, tc_HOL_Obool)), _1129380), hAPP(hAPP(c_Set_Oinsert(_1129372), _1129384), c_Orderings_Obot__class_Obot(tc_fun(_1129372, tc_HOL_Obool))))), 18332 ^ [_1129372, _1129374, _1129376, _1129378, _1129380, _1129382, _1129384])))], (18334 ^ _777959) ^ [] : [-(_1129382 = hAPP(hAPP(_1129376, _1129384), 18332 ^ [_1129372, _1129374, _1129376, _1129378, _1129380, _1129382, _1129384]))]]], (40140 ^ _777959) ^ [_1556190, _1556192, _1556194] : [hBOOL(hAPP(c_List_Odistinct(_1556190), _1556192)), -(hBOOL(hAPP(c_List_Odistinct(_1556190), c_List_Osublist(_1556190, _1556192, _1556194))))], (36696 ^ _777959) ^ [_1474273, _1474275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1474273), 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)), _1474275)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1474273), _1474275) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1474273, _1474275)))], (38368 ^ _777959) ^ [_1513217, _1513219, _1513221, _1513223] : [c_Fun_Oinj__on(_1513217, _1513219, _1513221, c_Orderings_Otop__class_Otop(tc_fun(_1513217, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1513219, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1513217, _1513219, _1513221), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1513217, tc_HOL_Obool)), _1513223))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1513219, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1513217, _1513219, _1513221), _1513223)))))], (42160 ^ _777959) ^ [_1608767, _1608769] : [-(c_List_Olist_Olist__size(_1608767, _1608769, c_List_Olist_ONil(_1608767)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7160 ^ _777959) ^ [_897654, _897656, _897658, _897660] : [class_Lattices_Olattice(_897654), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897654), _897656), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897654), _897658), _897660)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897654), _897658), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_897654), _897656), _897660)))], (42467 ^ _777959) ^ [_1616557, _1616559, _1616561, _1616563, _1616565] : [-(_1616557 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1616559, _1616561, _1616563), _1616557), _1616565) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1616561), _1616559), tc_prod(_1616561, _1616559), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1616561), _1616559), c_List_Olist_ONil(_1616561)), _1616565), hAPP(c_Product__Type_Oprod_Oprod__case(_1616561, _1616559, tc_prod(tc_List_Olist(_1616561), _1616559)), hAPP(hAPP(c_COMBC(_1616561, tc_fun(_1616559, tc_prod(tc_List_Olist(_1616561), _1616559)), tc_fun(_1616559, tc_prod(tc_List_Olist(_1616561), _1616559))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1616561), _1616559), tc_prod(tc_List_Olist(_1616561), _1616559)), tc_fun(tc_fun(_1616559, tc_prod(tc_List_Olist(_1616561), _1616559)), tc_fun(_1616559, tc_prod(tc_List_Olist(_1616561), _1616559))), _1616561), c_COMBB(tc_prod(tc_List_Olist(_1616561), _1616559), tc_prod(tc_List_Olist(_1616561), _1616559), _1616559)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1616561), tc_fun(_1616559, tc_prod(tc_List_Olist(_1616561), _1616559))), tc_fun(tc_prod(tc_List_Olist(_1616561), _1616559), tc_prod(tc_List_Olist(_1616561), _1616559)), _1616561), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1616561), _1616559, tc_prod(tc_List_Olist(_1616561), _1616559))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1616561), tc_List_Olist(_1616561)), tc_fun(tc_List_Olist(_1616561), tc_fun(_1616559, tc_prod(tc_List_Olist(_1616561), _1616559))), _1616561), hAPP(c_COMBB(tc_List_Olist(_1616561), tc_fun(_1616559, tc_prod(tc_List_Olist(_1616561), _1616559)), tc_List_Olist(_1616561)), c_Product__Type_OPair(tc_List_Olist(_1616561), _1616559))), c_List_Olist_OCons(_1616561))))), hAPP(c_Lazy__Sequence_Oanamorph(_1616559, _1616561, _1616563), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1616557), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))), hAPP(_1616563, _1616565)))], (16497 ^ _777959) ^ [_1093883, _1093885, _1093887, _1093889] : [class_Orderings_Olinorder(_1093883), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093883), _1093885), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093883), _1093887), _1093889)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1093883), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093883), _1093885), _1093887)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1093883), _1093885), _1093889)))], (15048 ^ _777959) ^ [_1064189] : [hAPP(c_Nat_OSuc, _1064189) = _1064189], (15785 ^ _777959) ^ [_1078228, _1078230] : [class_Groups_Olinordered__ab__group__add(_1078228), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078228), _1078230)), -(_1078230 = c_Orderings_Obot__class_Obot(tc_fun(_1078228, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1078228), c_Big__Operators_Olinorder__class_OMax(_1078228, _1078230)) = c_Big__Operators_Olinorder__class_OMin(_1078228, hAPP(c_Set_Oimage(_1078228, _1078228, c_Groups_Ouminus__class_Ouminus(_1078228)), _1078230)))], (27726 ^ _777959) ^ [_1301818, _1301820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1301818)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1301818)), _1301820) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1301818), _1301820)))], (50266 ^ _777959) ^ [_1796937, _1796939, _1796941, _1796943, _1796945] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1796937, _1796939, _1796941) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1796937, _1796943, _1796945)), _1796939 = _1796943, _1796941 = _1796945], (42577 ^ _777959) ^ [_1620396, _1620398, _1620400, _1620402] : [class_Groups_Ocomm__monoid__mult(_1620396), c_Fun_Oinj__on(_1620398, _1620396, _1620400, _1620402), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1620398, _1620396), _1620400), _1620402) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1620396, _1620396), c_Fun_Oid(_1620396)), hAPP(c_Set_Oimage(_1620398, _1620396, _1620400), _1620402)))], (12002 ^ _777959) ^ [_995843, _995845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _995843), _995845)), 12005 ^ _777959 : [(12008 ^ _777959) ^ [] : [_995843 = _995845], (12006 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _995843), _995845)))]]], (30008 ^ _777959) ^ [_1345346, _1345348, _1345350, _1345352] : [class_Divides_Osemiring__div(_1345346), -(c_Divides_Odiv__class_Omod(_1345346, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345346), _1345348), _1345350), _1345352) = c_Divides_Odiv__class_Omod(_1345346, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345346), c_Divides_Odiv__class_Omod(_1345346, _1345348, _1345352)), c_Divides_Odiv__class_Omod(_1345346, _1345350, _1345352)), _1345352))], (30253 ^ _777959) ^ [_1350164, _1350166] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1350164)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1350164), _1350166)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1350164, _1350166) = _1350164)], (4 ^ _777959) ^ [_778009, _778011] : [_778011 = _778009, -(_778009 = _778011)], (39830 ^ _777959) ^ [_1548015, _1548017, _1548019, _1548021, _1548023, _1548025, _1548027, _1548029] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1548015, _1548017), _1548019), _1548021), hAPP(hAPP(c_List_Ozip(_1548015, _1548017), _1548023), hAPP(hAPP(c_List_Omap(_1548025, _1548017), _1548027), _1548029))) = hAPP(hAPP(c_List_Omap(tc_prod(_1548015, _1548025), _1548019), hAPP(c_Product__Type_Oprod_Oprod__case(_1548015, _1548025, _1548019), hAPP(hAPP(c_COMBB(tc_fun(_1548025, tc_prod(_1548015, _1548017)), tc_fun(_1548025, _1548019), _1548015), hAPP(c_COMBB(tc_prod(_1548015, _1548017), _1548019, _1548025), _1548021)), hAPP(hAPP(c_COMBC(_1548015, tc_fun(_1548025, _1548017), tc_fun(_1548025, tc_prod(_1548015, _1548017))), hAPP(hAPP(c_COMBB(tc_fun(_1548017, tc_prod(_1548015, _1548017)), tc_fun(tc_fun(_1548025, _1548017), tc_fun(_1548025, tc_prod(_1548015, _1548017))), _1548015), c_COMBB(_1548017, tc_prod(_1548015, _1548017), _1548025)), c_Product__Type_OPair(_1548015, _1548017))), _1548027)))), hAPP(hAPP(c_List_Ozip(_1548015, _1548025), _1548023), _1548029)))], (28050 ^ _777959) ^ [_1307225] : [28052 ^ _777959 : [(28055 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 28051 ^ [_1307225]))], (28053 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 28051 ^ [_1307225]), _1307225)))]], -(c_Nat__Transfer_Onat__set(_1307225))], (41874 ^ _777959) ^ [_1602203, _1602205, _1602207] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1602203), tc_List_Olist(_1602203))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1602203), tc_List_Olist(_1602203)), _1602205), c_List_Olist_ONil(_1602203))), c_List_Olistrel(_1602203, _1602207))), -(_1602205 = c_List_Olist_ONil(_1602203))], (48543 ^ _777959) ^ [_1756012, _1756014] : [-(c_Transitive__Closure_Otrancl(_1756012, c_Transitive__Closure_Ortrancl(_1756012, _1756014)) = c_Transitive__Closure_Ortrancl(_1756012, _1756014))], (37333 ^ _777959) ^ [_1490530, _1490532, _1490534] : [_1490532 = c_Orderings_Obot__class_Obot(tc_fun(_1490530, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1490530), _1490532), _1490534) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1490530, tc_HOL_Obool), tc_HOL_Obool)))], (44981 ^ _777959) ^ [_1672837, _1672839, _1672841] : [-(hAPP(c_List_Orev(_1672837), hAPP(hAPP(c_List_Otake(_1672837), _1672839), _1672841)) = hAPP(hAPP(c_List_Odrop(_1672837), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1672837)), _1672841)), _1672839)), hAPP(c_List_Orev(_1672837), _1672841)))], (48667 ^ _777959) ^ [_1759093, _1759095, _1759097] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1759093, _1759093), tc_HOL_Obool)), _1759095), _1759097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1759093, _1759093), tc_HOL_Obool)), _1759097), c_Transitive__Closure_Ortrancl(_1759093, _1759095))), -(c_Transitive__Closure_Ortrancl(_1759093, _1759097) = c_Transitive__Closure_Ortrancl(_1759093, _1759095))], (33971 ^ _777959) ^ [_1417929, _1417931, _1417933] : [-(hAPP(c_Nat_Onat_Onat__rec(_1417929, _1417931, _1417933), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1417931)], (43767 ^ _777959) ^ [_1648501, _1648503, _1648505] : [43768 ^ _777959 : [(43769 ^ _777959) ^ [_1648590, _1648592] : [_1648503 = hAPP(hAPP(c_List_Olist_OCons(_1648501), _1648592), _1648590)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1648501), tc_List_Olist(_1648501))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1648501), tc_List_Olist(_1648501)), c_List_Olist_ONil(_1648501)), _1648503)), c_List_Olexord(_1648501, _1648505))))], (2282 ^ _777959) ^ [_811707, _811709] : [_811709 = _811707, -(c_Nat_Onat_Onat__size(_811709) = c_Nat_Onat_Onat__size(_811707))], (15450 ^ _777959) ^ [_1071741, _1071743] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1071741), _1071743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1071741)), hAPP(c_Nat_OSuc, _1071743))))], (29160 ^ _777959) ^ [_1327641, _1327643] : [c_Nat__Transfer_Ois__nat(_1327641), c_Nat__Transfer_Ois__nat(_1327643), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1327641, _1327643) = 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, _1327641), hAPP(c_Int_Onat, _1327643))))], (7862 ^ _777959) ^ [_911604, _911606, _911608, _911610] : [-(c_Com_Ocom_OSemi(_911604, _911606) = c_Com_Ocom_OSemi(_911608, _911610)), _911604 = _911608, _911606 = _911610], (43544 ^ _777959) ^ [_1643378, _1643380, _1643382, _1643384] : [-(hAPP(c_List_Orotate(_1643378, _1643380), hAPP(c_List_Orotate(_1643378, _1643382), _1643384)) = hAPP(c_List_Orotate(_1643378, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1643380), _1643382)), _1643384))], (45772 ^ _777959) ^ [_1691431, _1691433, _1691435] : [class_Enum_Oenum(_1691431), 45775 ^ _777959 : [(45785 ^ _777959) ^ [] : [-(c_Enum_Oex__n__lists(_1691431, _1691433, _1691435)), 45786 ^ _777959 : [(45787 ^ _777959) ^ [_1691687] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1691431)), _1691687), hAPP(c_List_Oset(tc_List_Olist(_1691431)), c_Enum_On__lists(_1691431, _1691435, c_Enum_Oenum__class_Oenum(_1691431))))), hBOOL(hAPP(_1691433, _1691687))]]], (45776 ^ _777959) ^ [] : [c_Enum_Oex__n__lists(_1691431, _1691433, _1691435), 45780 ^ _777959 : [(45783 ^ _777959) ^ [] : [-(hBOOL(hAPP(_1691433, 45779 ^ [_1691431, _1691433, _1691435])))], (45781 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1691431)), 45779 ^ [_1691431, _1691433, _1691435]), hAPP(c_List_Oset(tc_List_Olist(_1691431)), c_Enum_On__lists(_1691431, _1691435, c_Enum_Oenum__class_Oenum(_1691431))))))]]]]], (44961 ^ _777959) ^ [_1672525, _1672527, _1672529] : [-(hAPP(c_List_Orev(_1672525), hAPP(hAPP(c_List_Olist_OCons(_1672525), _1672527), _1672529)) = hAPP(hAPP(c_List_Oappend(_1672525), hAPP(c_List_Orev(_1672525), _1672529)), hAPP(hAPP(c_List_Olist_OCons(_1672525), _1672527), c_List_Olist_ONil(_1672525))))], (12770 ^ _777959) ^ [_1009658, _1009660, _1009662] : [class_Groups_Oordered__ab__group__add(_1009658), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009658), _1009660), _1009662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1009658), hAPP(c_Groups_Ouminus__class_Ouminus(_1009658), _1009662)), hAPP(c_Groups_Ouminus__class_Ouminus(_1009658), _1009660))))], (6679 ^ _777959) ^ [_886358, _886360, _886362, _886364] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886358, tc_HOL_Obool)), _886360), hAPP(hAPP(c_Set_Oinsert(_886358), _886362), _886364)) = hAPP(hAPP(c_Set_Oinsert(_886358), _886362), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_886358, tc_HOL_Obool)), _886360), _886364)))], (43450 ^ _777959) ^ [_1641909, _1641911, _1641913] : [-(hAPP(c_List_Ohd(_1641909), hAPP(hAPP(c_List_Olist_OCons(_1641909), _1641911), _1641913)) = _1641911)], (48513 ^ _777959) ^ [_1754715, _1754717, _1754719, _1754721] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1754715, tc_fun(_1754715, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1754715, tc_fun(tc_prod(_1754715, _1754715), tc_HOL_Obool), tc_fun(_1754715, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1754715, tc_fun(tc_fun(tc_prod(_1754715, _1754715), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1754715, _1754715), tc_HOL_Obool), tc_fun(_1754715, tc_HOL_Obool)), _1754715), c_COMBC(_1754715, tc_fun(tc_prod(_1754715, _1754715), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1754715, tc_prod(_1754715, _1754715)), tc_fun(_1754715, tc_fun(tc_fun(tc_prod(_1754715, _1754715), tc_HOL_Obool), tc_HOL_Obool)), _1754715), hAPP(c_COMBB(tc_prod(_1754715, _1754715), tc_fun(tc_fun(tc_prod(_1754715, _1754715), tc_HOL_Obool), tc_HOL_Obool), _1754715), c_member(tc_prod(_1754715, _1754715)))), c_Product__Type_OPair(_1754715, _1754715)))), _1754717)), c_fequal), _1754719), _1754721)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1754715, _1754715)), hAPP(hAPP(c_Product__Type_OPair(_1754715, _1754715), _1754719), _1754721)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1754715, _1754715), tc_HOL_Obool)), _1754717), c_Relation_OId(_1754715)))))], (49282 ^ _777959) ^ [_1774545, _1774547, _1774549] : [c_Relation_Osingle__valued(_1774545, _1774545, _1774547), -(c_Relation_Osingle__valued(_1774545, _1774545, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1774545, _1774545), tc_HOL_Obool), _1774549), _1774547)))], (896 ^ _777959) ^ [_791637, _791639, _791641, _791643, _791645, _791647] : [-(c_List_Olist__all(_791645, _791641, _791637)), c_List_Olist__all(_791647, _791643, _791639), _791647 = _791645, _791643 = _791641, _791639 = _791637], (49078 ^ _777959) ^ [_1769812, _1769814, _1769816] : [c_Relation_Orefl__on(_1769812, _1769814, _1769816), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1769812, _1769812), tc_HOL_Obool)), _1769816), hAPP(hAPP(c_Relation_Orel__comp(_1769812, _1769812, _1769812), hAPP(c_Relation_Oconverse(_1769812, _1769812), _1769816)), _1769816))))], (32837 ^ _777959) ^ [_1398160, _1398162, _1398164] : [class_Int_Onumber__ring(_1398160), 32840 ^ _777959 : [(32847 ^ _777959) ^ [] : [-(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), _1398162)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1398160), hAPP(c_Int_Onumber__class_Onumber__of(_1398160), _1398164)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1398162))) = c_Groups_Oone__class_Oone(_1398160))], (32841 ^ _777959) ^ [] : [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), _1398162))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1398160), hAPP(c_Int_Onumber__class_Onumber__of(_1398160), _1398164)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1398162))) = hAPP(hAPP(c_HOL_OLet(_1398160, _1398160), hAPP(hAPP(c_Power_Opower__class_Opower(_1398160), hAPP(c_Int_Onumber__class_Onumber__of(_1398160), _1398164)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1398162))), hAPP(hAPP(c_COMBS(_1398160, _1398160, _1398160), hAPP(hAPP(c_COMBB(_1398160, tc_fun(_1398160, _1398160), _1398160), c_Groups_Otimes__class_Otimes(_1398160)), hAPP(c_Groups_Otimes__class_Otimes(_1398160), hAPP(c_Int_Onumber__class_Onumber__of(_1398160), _1398164)))), c_COMBI(_1398160))))]]], (35155 ^ _777959) ^ [_1439215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1439215)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1439215), c_Int_OMin)))], (16125 ^ _777959) ^ [_1085329, _1085331, _1085333, _1085335, _1085337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1085329), _1085331)), 16128 ^ _777959 : [(16135 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1085335), 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), _1085331), _1085329)), _1085333)), _1085337))), -(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), _1085329), _1085333)), _1085335)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1085331), _1085333)), _1085337))))], (16129 ^ _777959) ^ [] : [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), _1085329), _1085333)), _1085335)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1085331), _1085333)), _1085337))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1085335), 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), _1085331), _1085329)), _1085333)), _1085337))))]]], (8822 ^ _777959) ^ [_930186, _930188, _930190] : [class_Orderings_Olinorder(_930186), 8825 ^ _777959 : [(8832 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930186), _930190), _930188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930186), _930188), _930190))], (8826 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_930186), _930188), _930190))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_930186), _930190), _930188)))]]], (17567 ^ _777959) ^ [_1113601, _1113603, _1113605] : [class_Orderings_Olinorder(_1113601), hBOOL(hAPP(c_Finite__Set_Ofinite(_1113601), _1113603)), -(hBOOL(hAPP(hAPP(c_member(_1113601), _1113605), _1113603))), -(_1113603 = c_Orderings_Obot__class_Obot(tc_fun(_1113601, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1113601, hAPP(hAPP(c_Set_Oinsert(_1113601), _1113605), _1113603)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1113601), _1113605), c_Big__Operators_Olinorder__class_OMin(_1113601, _1113603)))], (42609 ^ _777959) ^ [_1621204, _1621206, _1621208] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1621204, _1621204), tc_HOL_Obool)), _1621206), hAPP(hAPP(c_Product__Type_OSigma(_1621204, _1621204), _1621208), hAPP(c_COMBK(tc_fun(_1621204, tc_HOL_Obool), _1621204), _1621208)))), 42615 ^ _777959 : [(42618 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621204, _1621204)), hAPP(hAPP(c_Product__Type_OPair(_1621204, _1621204), 42614 ^ [_1621204, _1621206, _1621208]), 42614 ^ [_1621204, _1621206, _1621208])), _1621206))], (42616 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621204), 42614 ^ [_1621204, _1621206, _1621208]), _1621208)))]], -(c_Relation_Orefl__on(_1621204, _1621208, _1621206))], (25106 ^ _777959) ^ [_1253587, _1253589, _1253591, _1253593] : [class_Divides_Osemiring__div(_1253587), -(_1253589 = c_Groups_Ozero__class_Ozero(_1253587)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1253587), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253587), _1253591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253587), _1253593), _1253589))), _1253589) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253587), _1253593), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1253587), _1253591), _1253589)))], (33645 ^ _777959) ^ [_1411557, _1411559] : [class_Int_Onumber__ring(_1411557), -(hAPP(c_Int_Onumber__class_Onumber__of(_1411557), c_Int_Osucc(_1411559)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411557), c_Groups_Oone__class_Oone(_1411557)), hAPP(c_Int_Onumber__class_Onumber__of(_1411557), _1411559)))], (11812 ^ _777959) ^ [_992039, _992041, _992043, _992045, _992047] : [-(_992039 = c_Orderings_Obot__class_Obot(tc_fun(_992041, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_992043), _992045), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992041, tc_fun(_992043, tc_HOL_Obool)), _992039), _992047)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_992041, tc_fun(_992043, tc_HOL_Obool)), _992039), hAPP(hAPP(c_COMBB(tc_fun(_992043, tc_HOL_Obool), tc_fun(_992043, tc_HOL_Obool), _992041), hAPP(c_Set_Oinsert(_992043), _992045)), _992047)))], (46617 ^ _777959) ^ [_1709351, _1709353, _1709355] : [hBOOL(hAPP(hAPP(c_member(_1709351), _1709353), hAPP(c_List_Oset(_1709351), _1709355))), -(c_List_Oinsert(_1709351, _1709353, _1709355) = _1709355)], (41797 ^ _777959) ^ [_1600297, _1600299, _1600301] : [c_Relation_Orefl__on(_1600297, _1600299, _1600301), -(c_Relation_Orefl__on(tc_List_Olist(_1600297), c_List_Olists(_1600297, _1600299), c_List_Olistrel(_1600297, _1600301)))], (13337 ^ _777959) ^ [_1021922, _1021924, _1021926, _1021928, _1021930, _1021932, _1021934, _1021936] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1021922, tc_fun(_1021924, tc_fun(_1021926, tc_HOL_Obool))), _1021928), _1021930), _1021932), _1021934)), hBOOL(hAPP(hAPP(c_member(_1021922), _1021936), _1021928)), -(hBOOL(hAPP(hAPP(hAPP(_1021930, _1021936), _1021932), _1021934)))], (32459 ^ _777959) ^ [_1390848, _1390850, _1390852, _1390854] : [class_Fields_Olinordered__field__inverse__zero(_1390848), class_Int_Onumber(_1390848), 32466 ^ _777959 : [(32467 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1390848), _1390850), _1390852)), hAPP(c_Int_Onumber__class_Onumber__of(_1390848), _1390854))), 32470 ^ _777959 : [(32477 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), c_Groups_Ozero__class_Ozero(_1390848)), _1390852))), 32480 ^ _777959 : [(32487 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), _1390852), c_Groups_Ozero__class_Ozero(_1390848)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), c_Groups_Ozero__class_Ozero(_1390848)), hAPP(c_Int_Onumber__class_Onumber__of(_1390848), _1390854))))], (32481 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), _1390852), c_Groups_Ozero__class_Ozero(_1390848))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390848), hAPP(c_Int_Onumber__class_Onumber__of(_1390848), _1390854)), _1390852)), _1390850)))]]], (32471 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), c_Groups_Ozero__class_Ozero(_1390848)), _1390852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), _1390850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390848), hAPP(c_Int_Onumber__class_Onumber__of(_1390848), _1390854)), _1390852))))]]], (32493 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1390848), _1390850), _1390852)), hAPP(c_Int_Onumber__class_Onumber__of(_1390848), _1390854)))), 32496 ^ _777959 : [(32499 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), _1390850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390848), hAPP(c_Int_Onumber__class_Onumber__of(_1390848), _1390854)), _1390852)))], (32497 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), c_Groups_Ozero__class_Ozero(_1390848)), _1390852)))]], 32500 ^ _777959 : [(32503 ^ _777959) ^ [] : [32504 ^ _777959 : [(32507 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1390848), hAPP(c_Int_Onumber__class_Onumber__of(_1390848), _1390854)), _1390852)), _1390850))], (32505 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), _1390852), c_Groups_Ozero__class_Ozero(_1390848))))]], 32508 ^ _777959 : [(32511 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), c_Groups_Ozero__class_Ozero(_1390848)), hAPP(c_Int_Onumber__class_Onumber__of(_1390848), _1390854)))], (32509 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), _1390852), c_Groups_Ozero__class_Ozero(_1390848)))]]], (32501 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1390848), c_Groups_Ozero__class_Ozero(_1390848)), _1390852))]]]]], (9158 ^ _777959) ^ [_935131, _935133, _935135, _935137] : [class_Lattices_Osemilattice__sup(_935131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935131), _935133), _935135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_935131), _935133), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_935131), _935135), _935137))))], (28598 ^ _777959) ^ [_1316614, _1316616, _1316618] : [class_Groups_Oordered__ab__group__add(_1316614), -(hAPP(c_Set_Oimage(_1316614, _1316614, c_Groups_Ouminus__class_Ouminus(_1316614)), c_SetInterval_Oord__class_OatLeastAtMost(_1316614, _1316616, _1316618)) = c_SetInterval_Oord__class_OatLeastAtMost(_1316614, hAPP(c_Groups_Ouminus__class_Ouminus(_1316614), _1316618), hAPP(c_Groups_Ouminus__class_Ouminus(_1316614), _1316616)))], (41938 ^ _777959) ^ [_1603984, _1603986, _1603988, _1603990] : [-(c_Map_Omap__upds(_1603984, _1603986, _1603988, c_List_Olist_ONil(_1603984), _1603990) = _1603988)], (24868 ^ _777959) ^ [_1249546, _1249548, _1249550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1249546), _1249548)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1249550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1249546), _1249550)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1249548), _1249550))))], (50002 ^ _777959) ^ [_1791977, _1791979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 50003 ^ [_1791977, _1791979]), hAPP(_1791977, 50003 ^ [_1791977, _1791979]))), -(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)), _1791977)), _1791979)))))], (35605 ^ _777959) ^ [_1452814, _1452816, _1452818, _1452820, _1452822] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1452814, _1452816), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1452818), _1452820))), -(_1452816 = 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), _1452822), _1452814), _1452816), 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), _1452822), _1452818)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1452822), _1452820)), _1452816))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1452822), _1452820), _1452816)))))], (33641 ^ _777959) ^ [] : [-(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)))))], (39753 ^ _777959) ^ [_1546320, _1546322, _1546324, _1546326, _1546328, _1546330, _1546332, _1546334] : [class_Groups_Ocomm__monoid__mult(_1546320), c_Fun_Oinj__on(_1546322, _1546324, _1546326, _1546328), _1546330 = hAPP(c_Set_Oimage(_1546322, _1546324, _1546326), _1546328), 39767 ^ _777959 : [(39770 ^ _777959) ^ [] : [hAPP(_1546332, 39766 ^ [_1546320, _1546322, _1546324, _1546326, _1546328, _1546330, _1546332, _1546334]) = hAPP(hAPP(c_Fun_Ocomp(_1546324, _1546320, _1546322, _1546334), _1546326), 39766 ^ [_1546320, _1546322, _1546324, _1546326, _1546328, _1546330, _1546332, _1546334])], (39768 ^ _777959) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1546322), 39766 ^ [_1546320, _1546322, _1546324, _1546326, _1546328, _1546330, _1546332, _1546334]), _1546328)))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1546324, _1546320), _1546334), _1546330) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1546322, _1546320), _1546332), _1546328))], (16515 ^ _777959) ^ [_1094344, _1094346, _1094348, _1094350] : [class_Orderings_Olinorder(_1094344), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094344), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094344), _1094346), _1094348)), _1094350) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094344), _1094346), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1094344), _1094348), _1094350)))], (35095 ^ _777959) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (36868 ^ _777959) ^ [_1477569, _1477571] : [_1477569 = _1477571, -(c_Code__Numeral_OSuc__code__numeral(_1477569) = c_Code__Numeral_OSuc__code__numeral(_1477571))], (47552 ^ _777959) ^ [_1733548, _1733550] : [c_Nitpick_Owf_H(_1733548, _1733550), 47555 ^ _777959 : [(47558 ^ _777959) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1733548, _1733548)), _1733550))), -(c_Nitpick_Ounknown(tc_HOL_Obool))], (47556 ^ _777959) ^ [] : [-(c_Wellfounded_Oacyclic(_1733548, _1733550))]]], (28061 ^ _777959) ^ [_1307398, _1307400, _1307402] : [class_Orderings_Oord(_1307398), 28064 ^ _777959 : [(28071 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307398), _1307402), _1307400)), -(hBOOL(hAPP(hAPP(c_member(_1307398), _1307400), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1307398), _1307402))))], (28065 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1307398), _1307400), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1307398), _1307402))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1307398), _1307402), _1307400)))]]], (49094 ^ _777959) ^ [_1770130, _1770132] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1770130, _1770130)), _1770132)), c_Wellfounded_Oacyclic(_1770130, _1770132), -(c_Wellfounded_Owf(_1770130, hAPP(c_Relation_Oconverse(_1770130, _1770130), _1770132)))], (39806 ^ _777959) ^ [_1547390, _1547392, _1547394, _1547396] : [-(_1547390 = _1547392), 39809 ^ _777959 : [(39816 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1547394), _1547390), hAPP(c_List_Oset(_1547394), _1547396))), -(hBOOL(hAPP(hAPP(c_member(_1547394), _1547390), hAPP(c_List_Oset(_1547394), c_List_Oremove1(_1547394, _1547392, _1547396)))))], (39810 ^ _777959) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1547394), _1547390), hAPP(c_List_Oset(_1547394), c_List_Oremove1(_1547394, _1547392, _1547396)))), -(hBOOL(hAPP(hAPP(c_member(_1547394), _1547390), hAPP(c_List_Oset(_1547394), _1547396))))]]], (11596 ^ _777959) ^ [_985553, _985555, _985557, _985559, _985561, _985563] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985553, tc_fun(_985555, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985557, tc_fun(_985553, tc_HOL_Obool)), _985559), _985561)), _985563) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985557, tc_fun(_985555, tc_HOL_Obool)), _985559), hAPP(hAPP(c_COMBC(_985557, tc_fun(_985553, tc_fun(_985555, tc_HOL_Obool)), tc_fun(_985555, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_985553, tc_HOL_Obool), tc_fun(tc_fun(_985553, tc_fun(_985555, tc_HOL_Obool)), tc_fun(_985555, tc_HOL_Obool)), _985557), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_985553, tc_fun(_985555, tc_HOL_Obool))), _985561)), _985563)))], (11936 ^ _777959) ^ [_994704, _994706, _994708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _994704), _994706)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994708), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _994706), _994704)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _994708), _994704)), _994706))], (14269 ^ _777959) ^ [_1043819, _1043821, _1043823, _1043825, _1043827] : [-(c_Map_Odom(_1043819, _1043821, hAPP(hAPP(c_COMBS(_1043819, tc_Option_Ooption(_1043821), tc_Option_Ooption(_1043821)), hAPP(hAPP(c_COMBS(_1043819, tc_Option_Ooption(_1043821), tc_fun(tc_Option_Ooption(_1043821), tc_Option_Ooption(_1043821))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_Option_Ooption(_1043821), tc_fun(tc_Option_Ooption(_1043821), tc_Option_Ooption(_1043821))), _1043819), c_If(tc_Option_Ooption(_1043821))), _1043823)), _1043825)), _1043827)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1043819, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1043819, tc_HOL_Obool)), c_Map_Odom(_1043819, _1043821, _1043825)), hAPP(c_Set_OCollect(_1043819), _1043823))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1043819, tc_HOL_Obool)), c_Map_Odom(_1043819, _1043821, _1043827)), hAPP(c_Set_OCollect(_1043819), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1043819), c_fNot), _1043823)))))]], input).
% 45.35/44.01  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, v_pn))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))],start(51474 ^ 0)).
% 45.35/44.01  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)), hAPP(c_Hoare__Mirabelle_OMGT, hAPP(c_Com_Ocom_OBODY, v_pn))), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate), tc_HOL_Obool))))), c_Hoare__Mirabelle_Ostate__not__singleton, c_Com_OWT__bodies, hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, v_pn)))],extension(5655 ^ 1,bind([[_867194], [hAPP(c_Com_Ocom_OBODY, v_pn)]]))).
% 45.35/44.01  ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Ostate__not__singleton)],extension(51464 ^ 2)).
% 45.35/44.01  ncf('1.1.2',plain,[-(c_Com_OWT__bodies)],extension(51466 ^ 2)).
% 45.35/44.01  ncf('1.1.3',plain,[-(hBOOL(hAPP(c_Com_OWT, hAPP(c_Com_Ocom_OBODY, v_pn)))), 5716 : hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y)],extension(5714 ^ 2,bind([[_868142, _868190], [v_pn, v_y]]))).
% 45.35/44.01  ncf('1.1.3.1',plain,[-(hAPP(c_Com_Obody, v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom), v_y))],extension(51470 ^ 5)).
% 45.35/44.01  %-----------------------------------------------------
% 45.35/44.01  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------